Abstract

Anderson, M.J. 2008. Animal-sediment relationships revisited: characterising species’ distributions along an environmental gradient using canonical analysis and quantile regression splines. Journal of Experimental Marine Biology and Ecology. in press.

Benthic soft-sediment organisms generally show strong relationships with the grain-size characteristics of the sediments they inhabit. These relationships, when characterised from field data, tend to be asymmetrical, non-linear and heteroscedastic, due to the existence of multiple other potentially important and interacting factors, some of which are inevitably unmeasured. For multivariate data, canonical analysis of principal coordinates (CAP) can be used to isolate particular gradients of interest, despite the presence of other potentially important factors. For univariate abundance data, models focusing on upper quantiles of species' distributions can ameliorate the problem of heterogeneity induced by other variables. Here, a multivariate model of the relationship between benthic inter-tidal estuarine soft-sediment assemblages (sampled over a period of 3 years from 70 sites across the Auckland region) and the percentage of mud in the sediments was generated using CAP. To characterise changes in assemblage structure, quantile regression splines (of the 0.95 quantile) were used to model each of the twenty most abundant individual taxa along the gradient in percentage mud. This approach provided an effective instrumental quantitative predictive model of species' turnover, while allowing for the asymmetric, non-linear animal-sediment relationships and heterogeneous scatter observed in species' abundances along the mud gradient.

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Abstract

Lear, G., Anderson, M.J., Smith, J.P., Boxen, K. and Lewis, G.D. 2008. Spatial and temporal heterogeneity of the bacterial communities in stream epilithic biofilms. FEMS Microbiology Ecology 65: 463-473.

The spatial and temporal variability in bacterial communities within freshwater systems is poorly understood. The bacterial composition of stream epilithic biofilms across a range of different spatial and temporal scales both within and between streams and across the profile of individual stream rocks was characterized using a community DNA-fingerprinting technique (Automated Ribosomal Intergenic Spacer Analysis ARISA). The differences in bacterial community structure between two different streams were found to be greater than the spatial variability within each stream site, and were larger than the weekly temporal variation measured over a 10-week study period. Greater variations in bacterial community profiles were detected on different faces of individual stream rocks than between whole rocks sampled within a 9-m stream section. Stream temperature was found to be the most important determinant of bacterial community variability using distance-based redundancy analysis (dbRDA) of ARISA data, which may have broad implications for riparian zone management and ecological change as a consequence of global warming. The combination of ARISA with multivariate statistical methods and ordination, such as multidimensional scaling (MDS), permutational MANOVA and RDA, provided rapid and effective methods for quantifying and visualizing variation in bacterial community structure, and to identify potential drivers of ecological change.

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Abstract

Cullen, L.E., Adams, M.A., Anderson, M.J. and Grierson, P.F. 2008. Analyses of d13C and d18O in tree rings of Callitris columellaris provide evidence of a change in stomatal control of photosynthesis in response to regional changes in climate. Tree Physiology 28: 1525-1533.

We examined relationships between stable isotopes of carbon (δ13C) and oxygen (δ18O) in tree rings of Callitris columellaris F. Muell in the semi-arid Pilbara region of north-western Australia. To test the hypothesis that stomatal control of photosynthesis decreases during drier periods, we developed δ13C and δ18O chronologies spanning 1919–1999, and used a permutation regression approach to relate a 21-year running correlation between δ13C and δ18O to rainfall and temperature at Marble Bar and our study site. The relationship between δ13C and δ18O switched from being always negative before 1955 to being consistently positive after 1976, suggesting an increase in stomatal control of photosynthesis in recent decades. Changes in the δ13C–δ18O relationship reflected changes in rainfall, which has increased in the region by 30% since 1976. The correlation between δ13C and δ18O was positively related to the 21-year running mean of normalized rainfall anomalies at both the study site (P = 0.045, Adj. r2 = 0.47) and Marble Bar (P = 0.046, Adj. r2 = 0.48). In addition, the δ13C–δ18O correlation was negatively related (P = 0.047, Adj. r2 = 0.61) to temperatures at Marble Bar. Our interpretation of the role of changes in climate affecting the relationship between tree-ring δ13C and δ18O is supported by evidence from the isotope composition of foliage samples: foliar δ13C and δ18O were negatively correlated with log stomatal conductance (δ13C, r = –0.41; δ18O, r = –0.42), whereas the correlation between foliar δ13C and δ18O was positive (r = 0.63, P = 0.027) after the summer wet period. Our data indicate that stomatal control of photosynthesis in Callitris adjusts to region-wide changes in climate and that, in a warmer and drier world, trees might adapt by increasing non-stomatal control of photosynthesis.

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Abstract

Watson, D.L., Harvey, E.S., Kendrick, G.A., Nardi, K. and Anderson, M.J. 2007. Protection from fishing alters the species composition of fish assemblages in a temperate-tropical transition zone. Marine Biology 152: 1197-1206.

Closure of areas to fishing is expected to result in an increase in the abundance of targeted species; however, changes to populations of species not targeted by fishermen will depend upon their role in the ecosystem and their relationship with targeted species. The effects of protection on targeted and non-targeted reef fish species at the Houtman Abrolhos Islands, Western Australia were studied using baited remote underwater stereo–video cameras. Video images were collected from shallow (8–12 m) and deep (22–26 m) reef sites inside a Marine Protected Area (MPA) at each of three island groups and from three replicate fished locations at each of these groups that span a temperate-tropical transition area. The MPAs were established in 1994 and vary in size from 13.72 km2 at the Pelsaert group in the south to 22.29 km2 at the Easter group to 27.44 km2 at the Wallabi group in the north. The relative abundances of 137 fish species from 42 families were recorded. Large differences in fish assemblage structure existed between MPA and fished locations, and also between shallow and deep regions. Targeted fish species Plectropomus leopardus, Lethrinus miniatus, Lethrinus nebulosus, Pagrus auratus and Glaucosoma hebraicum were more abundant inside MPAs than in areas open to fishing. Their abundance inside MPAs was between 1.13 and 8 times greater than their abundance at fished locations. For non-targeted fish species many were more abundant in areas open to fishing, e.g. Coris auricularis, Thalassoma lutescens, Thalassoma lunare, Dascyllus trimaculatus, however others were conversely more abundant inside MPAs, e.g. Gymnothorax spp, Kyphosus sydneyanus, Scarus microhinos, Chromis westaustralis, Chaetodon spp. This study demonstrates that the removal of abundant targeted species from an ecosystem by fishing can indirectly impact non-fished species and alter the trophic structure of fish assemblages.

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Abstract

McGill, B., Etienne, R., Gray, J., Alonso, D., Anderson, M., Benecha, H., Dornelas, M., Enquist, B., Green, J., He, F., Hurlbert, A., Magurran, A., Marquet, P., Maurer, B., Ostling, A., Soykan, C., Ugland, K., White, E. 2007. Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. Ecology Letters 10: 995-1015.

Species abundance distributions (SADs) follow one of ecology’s oldest and most universal laws – every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science.

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Abstract

Atalah, J., Otto, S., Anderson, M.J., Costello, M.J., Lenz, M. and Wahl, M. 2007. Temporal variance of disturbance did not affect diversity and structure of a marine fouling community in north-eastern New Zealand. Marine Biology 153: 199-211.

Natural heterogeneity in ecological parameters, like population abundance, is more widely recognized and investigated than variability in the processes that control these parameters. Experimental ecologists have focused mainly on the mean intensity of predictor variables and have largely ignored the potential to manipulate variances in processes, which can be considered explicitly in experimental designs to explore variation in causal mechanisms. In the present study, the effect of the temporal variance of disturbance on the diversity of marine assemblages was tested in a field experiment replicated at two sites on the northeast coast of New Zealand. Fouling communities grown on artificial settlement substrata experienced disturbance regimes that differed in their inherent levels of temporal variability and timing of disturbance events, while disturbance intensity was identical across all levels. Additionally, undisturbed assemblages were used as controls. After 150 days of experimental duration, the assemblages were then compared with regard to their species richness, abundance and structure. The disturbance effectively reduced the average total cover of the assemblages, but no consistent effect of variability in the disturbance regime on the assemblages was detected. The results of this study were corroborated by the outcomes from simultaneous replicate experiments carried out in each of eight different biogeographical regions around the world.

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Abstract

Wheldon, M.C., Anderson, M.J. and Johnson, B.W. 2007. Identifying treatment effects in multi-channel measurements in electroencephalographic studies: multivariate permutation tests and multiple comparisons. Australian & New Zealand Journal of Statistics 49: 397-413.

A versatile procedure is described comprising an application of statistical techniques to the analysis of the large, multi-dimensional data arrays produced by electroencephalographic (EEG) measurements of human brain function. Previous analytical methods have been unable to identify objectively the precise times at which statistically significant experimental effects occur, owing to the large number of variables (electrodes) and small number of subjects, or have been restricted to two-treatment experimental designs. Many time-points are sampled in each experimental trial, making adjustment for multiple comparisons mandatory. Given the typically large number of comparisons and the clear dependence structure among time-points, simple Bonferroni-type adjustments are far too conservative. A three-step approach is proposed: (i) summing univariate statistics across variables; (ii) using permutation tests for treatment effects at each time-point; and (iii) adjusting for multiple comparisons using permutation distributions to control family-wise error across the whole set of time-points. Our approach provides an exact test of the individual hypotheses while asymptotically controlling family-wise error in the strong sense, and can provide tests of interaction and main effects in factorial designs. An application to two experimental data sets from EEG studies is described, but the approach has application to the analysis of spatio-temporal multivariate data gathered in many other contexts.

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Abstract

Oppenheimer, S., Astheimer, L., Anderson, M.J. and Buttemer, B. 2007. Morphometric measures as a moderate predictor of gender in the White-browed Babbler Pomatostomus superciliosus gilgandra. Corella 31: 15-18.

White-browed Babblers have monomorphic plumage but exhibit size and weight dimorphism. Males are heavier, have longer tarsi, wings, and culmens than females. Two hundred and eighty-three White-browed Babblers from the central western region of NSW were sexed using laparotomy, and discriminant function analysis was used to determine the extent to which morphometric data could be used to identify gender. Cross-validation using a jackknife procedure indicated that 81 percent of males and 84 percent of females were correctly identified using the resultant discriminant function. Culmen length contributed most to the classification of gender, followed by wing length and tarsus length. The discriminant function is presented as a potentially useful, non-invasive, and inexpensive tool for gender identification in White-browed Babblers.

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Abstract

Atalah, J., Anderson, M.J. and Costello, M.C. 2007. Temporal variability and intensity of grazing: a mesocosm experiment. Marine Ecology Progress Series 341: 15-24.

Grazing has long been recognized as a structuring force for plant assemblages. Most of this knowledge comes from experiments where grazers have been excluded or their densities manipulated. However, the intensity of grazing can vary, in space and time. Recently, an increasing number of studies have stressed the importance of the variance around the mean of ecological processes, but the potential effects of temporal variability in grazing in marine systems have not yet been explored. Here, we examined the separate effects of intensity and temporal variability of gastropod grazing on algal assemblages in a mesocosm experiment. In replicated experiments, algal assemblages grown on artificial substrata were subject to grazing regimes with mean intensity and temporal variance as crossed factors. In the first experiment, the more variable regimes led to greater reductions in algal cover, regardless of the level of grazing intensity. In the second experiment, variability elicited a similar effect, but this effect was larger for the low- than for the high-intensity treatments. These results indicate that temporally variable grazing regimes may lead to greater effects on algal assemblages than those anticipated from changes in the mean intensity of grazing alone. Thus, we suggest that temporal variability is a potentially important aspect of grazing processes that should be examined and incorporated into predictive models.

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Abstract

Ford, R.B., Anderson, M.J. and Kelly, S. 2007. Subtle and negligible effects of rainfall on estuarine infauna: evidence from three years of event-driven sampling. Marine Ecology Progress Series 340: 17-27.

Events of heavy rainfall can impact benthic fauna in estuaries. The occurrence of heavy rainfall is predicted to increase in many places due to climatic warming. It is therefore important to know the likely impact of events of heavy rainfall, both now and in the future, particularly as the discharge of some contaminants, such as sediments from large-scale urban developments, is correlated with such events. We tested for evidence of any impacts of rainfall on the structure of assemblages over a period of 3 years, using event-driven sampling of macrofaunal soft-sediment communities across 5 estuaries in the Auckland region. Changes in assemblage structure that was correlated with gradients in rainfall were detected at only 2 of the 50 sites sampled. These site-specific impacts were only detected in one estuary and did not coincide with the largest amount of rainfall measured in the region over that period. Impacts were characterised by a short-term increase in the number of taxa, which probably resulted from deposition of fauna transported with bedload eroded from upstream sites due to increased flow rates. This contrasts with results from previous studies, which reported catastrophic decreases in biodiversity or abundance with storm events. Our work provides a realistic baseline against which potential future impacts of rainfall associated with land development can be tested. We suggest long-term monitoring studies that incorporate measurements of relevant physical variables, including rainfall, are needed in order to more effectively assess significant changes in naturally temporally variable communities.

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Abstract

Terlizzi, A., Anderson, M.J., Fraschetti, S. and Benedetti-Cecchi, L. 2007. Scales of spatial variation in Mediterranean subtidal sessile assemblages at different depths. Marine Ecology Progress Series 332: 25-39.

Analyses of spatial patterns of distribution of populations and assemblages along environmental gradients are common in marine ecology. How these patterns vary at different spatial scales has seldom been examined, despite the fact that patterns in nature are intrinsically scale-dependent. This study quantified variability in subtidal assemblages at a hierarchy of spatial scales along a depth gradient, using several univariate and multivariate techniques. Despite variation in the sizes of depth effects in time and space, there were large, significant and generally characterisable differences in the structure of assemblages at different depths. The sizes of multivariate and univariate components of variation at different spatial scales were compared at each of 3 different depths (5, 15 and 25 m), using a bias-corrected bootstrapping approach. The sizes of variance components at different spatial scales varied with depth and choice of transformation. In all cases, the largest component of variation was at the smallest scale (tens of centimeters). A pattern of decreasing residual variance with depth was seen for untransformed data, while a pattern of increasing residual variance with depth was seen for presence/absence data. In contrast, variation among locations (separated by >1 km) and among sites (separated by hundreds of metres) was largest at intermediate depths (~15 m), regardless of the transformation used. The multivariate procedures used here offer several advantages over previously used techniques, providing suitable quantitative methods for analysing, at multiple scales, the patchy and complex nature of rocky subtidal assemblages.

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Abstract

Langlois, T.J., Anderson, M.J. and Babcock, R.C. 2006. Inconsistent effects of reefs on different size classes of macrofauna in adjacent sand habitats. Journal of Experimental Marine Biology and Ecology 334: 269-282.

In soft-sediment communities near reefs, a variety of patterns have been described with distance from the reef edge. Various studies have observed contrasting patterns and one study has reported different patterns for different size classes of macrofauna. This study in northeastern New Zealand obtained samples from 24 randomly allocated sites across three locations in a large-scale mensurative sampling design. At each location, there was a manipulation of reef-associated predator populations provided by established marine reserves. A concurrent study using the same sites found large macrofauna (>4 mm) to vary with distance from the reef and relative to predator density. The present study sampled small-bodied infauna (<4 mm and >0.5 mm), which was also predicted to change with distance from the reef and predator density. In contrast to patterns found for larger fauna and to previous studies of small macrofauna, no consistent patterns were found for small-bodied infauna. These results suggest that models of community structure need to consider different size classes of macrofauna separately and that multiple sampling methods will assist their investigation. The ‘haloes’ in small-bodied macrofauna around reefs may not be as widespread or consistent as previous studies have suggested, particularly in mobile sediments on open coasts.

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Abstract

Anderson, M.J., Ellingsen, K.E., McArdle, B.H. 2006. Multivariate dispersion as a measure of beta diversity. Ecology Letters 9: 683-693.

Beta diversity can be defined as the variability in species composition among sampling units for a given area. We propose that it can be measured as the average dissimilarity from individual observation units to their group centroid in multivariate space, using an appropriate dissimilarity measure. Differences in beta diversity among different areas or groups of samples can be tested using this approach. The choice of transformation and dissimilarity measure has important consequences for interpreting results. For kelp holdfast assemblages from New Zealand, variation in species composition was greater in smaller holdfasts, while variation in relative abundances was greater in larger holdasts. Variation in community structure of Norwegian continental shelf macrobenthic fauna increased with increases in environmental heterogeneity, regardless of the measure used. We propose a new dissimilarity measure which allows the relative weight placed on changes in composition vs. abundance to be specified explicitly.

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Abstract

Langlois, T.J., Anderson, M.J., Brock, M. and Murman, G. 2006. Importance of rock lobster size-structure for trophic interactions: choice of soft-sediment bivalve prey. Marine Biology 149: 447-454.

Ecologists are becoming increasingly interested in how variation in predator demographics influences prey communities. In northeastern New Zealand, the contrasting populations of previously exploited predators in highly protected marine reserves and fished areas have been used to investigate the effects of predation in soft-sediment habitats. However, these experiments have been unable to separate the role of predator size from that of density. This study provides evidence to support the model that foraging by different sizes of the rock lobster Jasus edwardsii affects soft-sediment bivalve populations in different ways. Feeding trials were conducted to investigate whether rock lobsters of different sizes vary in their choice of taxa and size of their bivalve prey. Trials with two morphologically similar species, Dosinia subrosea and Dosinia anus, indicated that lobsters of all sizes choose D. subrosea more frequently than the heavier shelled D. anus. Further results indicated that both large (>130 mm carapace length (CL)) and small (<100 mm CL) lobsters are capable of preying on a wide size range of D. subrosea (20–60 mm). However, small lobsters more frequently chose smaller shells (<30 mm) and large lobsters more frequently chose larger shells (>40 mm). Patterns in the abundance and size class distributions of these two bivalve species at protected and fished sites supported the feeding choices observed in the laboratory. These results suggest that populations of rock lobsters with large individuals inside reserves are capable of controlling the demography of bivalve populations in adjacent soft-sediment systems.

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Abstract

Terlizzi, A., Scuderi, D., Fraschetti, S. and Anderson, M.J. 2005. Quantifying effects of pollution on biodiversity: a case study of highly diverse molluscan assemblages in the Mediterranean. Marine Biology 148: 293-305.

Structured sampling designs are important in the assessment of environmental impacts of variable ecological systems. Recent developments have provided a useful framework extending existing univariate techniques into a multivariate context. Measures of taxonomic relatedness have also been introduced which complement existing measures of diversity of assemblages. In this study, the potential effects of sewage discharge on spatial patterns of highly diverse molluscan assemblages in a Mediterranean rocky subtidal habitat were investigated. Nine 20cm x 20cm quadrats were taken from each of 3 sites (80-100 m apart) within a putatively impacted location near a sewage outfall (I) and at each of two control locations (Cs) by destructive sampling by SCUBA divers at a depth of 3-4 m. A total of 5507 specimens of 151 species were collected. The average and the variance in total abundance of molluscs were greater, on average, at I than at Cs. Higher abundances at the sewage outfall were largely driven by greater numbers of juvenile molluscs. The Shannon diversity of molluscs (H') was significantly lower at I, but no difference among locations was detected for the total number of species (S). In addition, the taxonomic distinctness (∆*) of molluscs was greater at Cs, although it was more variable at I. Multivariate analyses showed that there was a significant difference in the structure of assemblages at I compared with Cs. The location near the outfall was characterized by greater abundances of several species, including especially the gastropods Pusillina philippi, Bittium latreilli and B. reticulatum. There was also greater variability in the structure of assemblages among sites and among quadrats at control locations compared to those near the outfall. Using a suite of univariate and multivariate measures, including diversity indices, detailed information on taxonomic structure and analyses of variability at different spatial scales, provided useful insights into the effects of sewage impacts on these diverse assemblages. These results also highlighted the importance of analysing measures of variance as well as mean in considering effects of stress in natural communities.

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Abstract

Watson, D.L., Harvey, E.S., Anderson, M.J. and Kendrick, G.A. 2005. A comparison of temperate reef fish assemblages recorded by three underwater stereo-video techniques. Marine Biology 148: 415-425.

Three underwater stereo-video techniques were used to sample the relative densities and species richness of temperate reef fish assemblages at three reef locations and two habitats (high and low-relief reef) within Hamelin Bay, south-western Australia. The three techniques compared were diver-operated stereo-video strip transects, baited remote stereo-video and unbaited remote stereo-video. While unbaited remote stereo-video and diver operated stereo-video transects recorded greater species richness at high compared to low-relief reefs, baited remote stereo-video recorded similar species richness at the two habitat types. The diver operated stereo-video system was manoeuvred through caves and under overhangs recording small, cryptic, cave-dwelling species that were not recorded by either remote video technique (Trachinops noarlungae, Trachinops brauni, Chromis klunzingeri, Trachichthys australis). Both remote video techniques recorded greater species richness and relative density of the most common species of Labridae, Ophthalmolepsis lineolatus. Baited remote video recorded the rarer, large predatory fish species (e.g. Seriola hippos, Glaucosoma hebraicum, Heterodontus portusjacksoni). None of the techniques sampled small cryptic fish families such as Gobiidae or Blenniidae. A combination of survey techniques is recommended for comprehensive fishery-independent studies that aim to sample broad components of fish assemblages.

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Abstract

Anderson, M.J. 2006. Distance-based tests for homogeniety of multivariate dispersions. Biometrics 62: 245-253

The traditional likelihood-based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero-inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non-Euclidean dissimilarity would be more appropriate. Distance-based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene’s test, with P-values obtained either using the traditional F-distribution or using permutation of either least-squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Niño. Monte Carlo simulations from the real data sets show that the distance-based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.

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Abstract

Anderson, M.J., Millar, R.B., Blom, W.M. and Diebel, C.E. 2005. Nonlinear multivariate models of successional change in community structure using the von Bertalanffy curve. Oecologia 146: 279-286.

Von Bertalanffy curves were used to describe the nonlinear relationship between assemblages inhabiting holdfasts of the kelp, Ecklonia radiata, and the volume of the holdfast. This was done using nonlinear canonical analyses of principal coordinates (NCAP). The volume of the holdfast is a proxy for the age of the plant and, thus, the canonical axis is a proxy for succession in the marine invertebrate community inhabiting the holdfast. Analyses were done at several different taxonomic resolutions on the basis of various dissimilarity measures. Assemblages in relatively large holdfasts demonstrated ongoing variation in community structure with increasing volume when the dissimilarity used was independent of sample size. Smaller holdfasts had proportionately greater abundances of ophiuroids and encrusting organisms (bryozoans, sponges, ascidians) while larger holdfasts were characterized by proportionately greater abundances of crustaceans, polychaetes and molluscs. Such linear and nonlinear multivariate models may be applied to analyse system-level responses to the growth of many habitat-forming organisms, such as sponges, coral reefs, coralline algal turf, or forest canopies.

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Abstract
Langlois, T.J., Anderson, M.J. and Babcock, R.C. 2006.
Marine reserves demonstrate trophic interactions across habitats. Oecologia 147: 134-142.

Several infaunal bivalve taxa show patterns of decreased biomass in areas with higher densities of adjacent reef-associated predators (the snapper, Pagrus auratus and rock lobster, Jasus edwardsii). A caging experiment was used to test the hypothesis that patterns observed were caused by predation, using plots seeded with a known initial density of the bivalve Dosinia subrosea to estimate survivorship. The caging experiment was replicated at several sites inside and outside two highly protected marine reserves: predators are significantly more abundant inside these reserves. Survivorship in fully caged, partially caged and open plots were then compared at sites having either low (non reserve) or high (reserve) predator density. The highest rates of survivorship of the bivalve were found in caged plots inside reserves and in all treatments outside reserves. However, inside reserves, open and partially caged treatments exhibited low survivorship. It was possible to specifically attribute much of this mortality to predation by large rock lobsters, due to distinctive marks on the valves of dead D. subrosea. This suggests that predation by large rock lobster could indeed account for the distributional patterns previously documented for certain bivalve populations. Our results illustrate that protection afforded by marine reserves is necessary to investigate how depletion through fishing pressure can change the role of upper-level predators and trophic processes between habitats.

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Abstract
Anderson, M.J., Diebel, C.E., Blom, W.M and Landers, T.J. 2005.
Consistency and variation in kelp holdfast assemblages: spatial patterns of biodiversity for the major phyla at different taxonomic resolutions. Journal of Experimental Marine Biology and Ecology 320: 35-56.

The focus of this study was to measure natural spatial variability in the biodiversity of fauna inhabiting kelp holdfasts in northeastern New Zealand at several spatial scales: from meters up to hundreds of kilometers. We wished to test the hypothesis that multivariate variation and biodiversity would vary significantly at different spatial scales in different ways for the major phyla in the holdfast community (Arthropoda, Annelida, Mollusca and Bryozoa). Biodiversity was considered in terms of richness, total abundance, structural composition (as measured by the Bray-Curtis dissimilarity measure) and taxonomic breadth for each major phylum and for the assemblage as a whole. We also examined the effect of taxonomic resolution on multivariate patterns. Species richness and total abundance increased with increases in holdfast volume. Multivariate variation was greatest at the smallest spatial scale for all phyla, but different phyla showed different patterns of multivariate variation at different spatial scales. Variations among locations at the largest spatial scale were primarily due to differences in the composition and richness of bryozoans and molluscs. Location effects became less and less distinct with decreases in taxonomic resolution. There were very few significant differences in richness or abundance for holdfasts of a given volume, taxonomic breadth did not vary significantly across locations, nor did the proportional abundances of phyla. These consistencies across large spatial scales in the absence of environmental impacts and results from other studies suggest that holdfast communities in New Zealand systems would provide a useful model assemblage against which future impacts may be detected as changes in proportions of component phyla. In addition, high variability detected at small and large scales at the species level, especially for bryozoans and molluscs, suggest that these communities may also provide unique opportunities for studying and understanding sources and functions of marine biodiversity.

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Abstract
Anderson, M.J., Connell, S.D., Gillanders, B.M., Diebel, C.E., Blom, W.M., Landers, T.J. and Saunders, J.E. 2005.
Relationships between taxonomic resolution and spatial scales of multivariate variation in kelp holdfast assemblages. Journal of Animal Ecology 74: 636-646.

Summary

1.  We investigated the effects of changes in taxonomic resolution on analyses of patterns of multivariate variation at different spatial scales for the highly diverse fauna inhabiting holdfasts of the kelp Ecklonia radiata.
2.  Multivariate analyses were done using several transformations to examine differences in spatial patterns of variation from meters up to hundreds of kilometers for composition versus relative abundance in assemblages.
3.  The greatest variability in assemblages occurred at the smallest spatial scale, from plant to plant, pointing to the existence of important small-scale processes. The proportional amount of variation at the smallest spatial scale decreased with decreasing taxonomic resolution (i.e., from species through to phyla). For composition, the next-greatest source of variation was at the largest spatial scale (hundreds of kilometers), while for relative abundance, the next-greatest source of variation was at the level of sites (hundreds of meters to kilometers).
4.  For abundance data, location-level variation became less important and site-level variation became more important with decreasing taxonomic resolution, while for compositional data, the opposite pattern occurred. This suggests that variation in the presence of species or taxa at a particular location along the coast is driven by large-scale processes, while variation in relative abundances within locations is driven by medium-scale processes.
5.  The lack of significant variation in the proportional abundances of phyla at large spatial scales suggests that some consistency of pattern may emerge at larger scales (spatial and/or taxonomic), even in the presence of high small-scale variability. These findings strengthen the idea that substantial local variation need not preclude the existence of broad-scale organization in ecological patterns and biodiversity.


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Abstract
Millar, R.B., Anderson, M.J. and Zunun, G. 2005.
Fitting nonlinear environmental gradients to community data: a general distance-based approach. Ecology 86: 2245-2251.

A distance-based method is provided for the analysis and modeling of multivariate community data in response to a nonlinear gradient. Any reasonable dissimilarity measure can be used, and the method provides a natural extension from canonical analysis of principal coordinates (CAP) to nonlinear canonical analysis through the use of a link function, much like the extension of linear models to generalized linear models. The form of the nonlinear link function needs to be specified and will depend on the particular ecological system and the nature of the gradient. For example, an exponential decay curve could be used to model community structure after an environmental impact as a nonlinear function of time. This curve is used in our first example, where community structure is modeled as a nonlinear function of habitat size. Our second example uses a logistic curve to model change in community structure through a region of habitat transition from grassland to woodland. Computationally, this methodology uses a standard nonlinear optimization procedure to find the values of the parameters that maximize the correlation of the principal coordinates (obtained from an appropriately chosen distance measure) with the chosen form of nonlinear gradient. A simple randomization procedure is used to test the significance of the fitted nonlinear gradient over and above the fit of the linear gradient, and bootstrap confidence intervals for parameters are readily obtained. Any reasonable form of nonlinear gradient can be used, and it can be modeled as a nonlinear function of multiple environmental variables, making this a very flexible and versatile procedure for modeling multivariate ecological systems.

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Abstract
Langlois, T.J., Anderson, M.J. and Babcock, R.C. 2005.
Reef-associated predators influence adjacent soft-sediment communities. Ecology 86: 1508-1519.

Marine reserves provide a large-scale manipulation of predator densities, which provides a means to investigate the potential effects of predation. The effects of reef-associated predators were examined in northeastern New Zealand by comparing soft-sediment assemblages at sites having different densities of large predators. Large rock lobsters (Jasus edwardsii) were 3.8 times more abundant and large snapper (Pagrus auratus) 12 times more abundant, on average, at reserve sites compared with non-reserve sites. The overall structure of infaunal communities differed between areas with high predator densities (reserve) and those with lower densities (fished). Sites with consistently higher densities of snapper and lobster were found to have lower biomass of two bivalve species and the greatest decreases were found near the reef edge (2-5 m). For several fauna a strong gradient in their density with distance from the reef was observed at both reserve and non-reserve sites. The hermit crab Pagurus novizelandiae occurred more frequently near the reef edge, whilst the heart urchin Echinocardium cordatum and bivalve Dosinia subrosea occurred more frequently further away from the reef. The results suggest that certain species in this assemblage are affected differently by a combination of physical and biological forces. We concluded that, where reef predators are removed by fishing pressure, a resultant indirect effect is an increase in prey species in adjacent soft-sediment assemblages.

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Abstract
Millar, R.B. and Anderson, M.J. 2004.
Remedies for pseudoreplication. Fisheries Research 70: 397-407

Pseudoreplication is the failure of a statistical analysis to properly incorporate the true structure of randomness present in the data. It has been well documented and studied in the ecological literature but has received little attention in the fisheries literature. Avoiding pseudoreplication in analyses of fisheries data can be difficult due to the complexity of the statistical procedures required. However, recent developments in statistical methodology are decreasing the extent to which pseudoreplication has to be tolerated. Seven examples are given here, beginning with simple design-based remedies and progressing to more challenging examples including the model-based remedies of mixed-effects modelling, generalized linear mixed models, state-space models, and geostatistics.

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Abstract
Hewitt, J.E., Anderson, M.J. and Thrush, S.F. 2005.
Assessing and monitoring ecological community health in marine systems. Ecological Applications 15: 942-953.

The increased potential for long-term degradative change associated with large-scale diffuse impacts highlights the need to develop methods for assessing the ecological significance of any observed changes.  The approach used in this study defines relative “health” based on the range of communities present in locations not considered affected by anthropogenically-derived inputs.  Such a definition should serve to identify both acute effects and broader-scale degradation.  Three multivariate constrained-ordination techniques were used to assess changes in communities occurring along an anthropogenic disturbance gradient of storm-water pollution in two different habitats.  All three techniques detected changes, even with data sets that were not specifically designed for the purpose.  Comparison with five diversity indices suggested that the multivariate approach was more successful.  Moreover, the information could easily be examined for changes in individual species, or for changes in function, trophic status or biomass/size structure.  The approach allows for monitoring changes over time in community composition to determine whether sites are improving or degrading.  While this study occurred in one region only, the approach itself is not confined to this area and should be able to be utilised in other marine (or freshwater or terrestrial) systems where commensurable regional-scale multivariate databases exist.

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Abstract
Terlizzi, A., Benedetti-Cecchi, L., Bevilacqua, S., Fraschetti, S., Guidetti, P. and Anderson, M.J. 2005. Multivariate and univariate asymmetrical analyses in environmental impact assessment: a case study of Mediterranean subtidal sessile assemblages. Marine Ecology Progress Series 289: 27-42.

Characterizing the potential effects of human activities on natural systems is a central problem in applied ecology. This requires the development of analytical procedures able to separate human perturbation from natural spatio-temporal variability displayed by most populations. Beyond-BACI experimental designs provide a framework to address these issues but, to date, their use is limited to the analysis of human impacts on the abundance of single species or other univariate measures. Here, we describe in detail an asymmetrical design that included 1 impact location (I) and a set of 3 controls (Cs), sampled at a hierarchy of spatial scales 4 times over a period of 15 mo. We focused on shallow subtidal assemblages of sessile organisms exposed to sewage discharge along a stretch of coast in southern Italy. The purpose of this paper is to illustrate (1) the comparison of variance components for the assessment of impacts and (2) the use of recently developed multivariate methods (distance-based premutational MANOVA) in the analysis of multivariate species data in response to a complex asymmetrical design. Results indicated that temporal changes in the whole assemblage at I were distinct from those occurring at Cs, and that the nature of this difference (although not its size) was fairly consistent through time. A suite of taxa was identified as important in characterizing the differences found between I and Cs. Some algae (e.g. Colpomenia sinuosa, Gelidium sp. and Pterocladiella sp.), in particular, occurred uniquely at I. Univariate analyses indicated significant Time × I-v-Cs interactions for several taxa, and significantly smaller spatial variation at the scale of quadrats at I compared to Cs. In contrast, the small-scale spatial variation in the number of taxa was significantly greater at I than at Cs. The findings of this study have important implications for future multivariate and univariate analyses in environmental impact assessment.

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Abstract

Geffen, E., Anderson, M.J. and Wayne, R.K. 2004.
Climate and habitat barriers to dispersal in the highly mobile gray wolf. Molecular Ecology 13: 2481-2490.

 

We reanalyzed published data to evaluate whether climate and habitat are barriers to dispersal in one of the most mobile and widely distributed mammals, the gray wolf (Canis lupus). Distance-based redundancy analysis (dbRDA) was used to examine the amount of variation in genetic distances that could be explained by an array of environmental factors, including geographic distance. Patterns in genetic variation were also examined using MDS plots among populations and relationships between genetic structure and individual environmental variables were further explored using the BIOENV procedure. We found that, contrary to a previous report, a pattern of isolation with distance is evident on a continental scale in the North American wolf population. This pattern is apparently related to climate and habitat. Specifically, vegetation types appear to play a role in the genetic dissimilarities among populations. When we controlled for the effect of spatial variation, climate was still associated with genetic distance. Further, partitioning of geographic distances into latitudinal and longitudinal axes revealed that the east-west gradient had the strongest relationship with genetic distance. We suggest two possible mechanisms by which environmental conditions may influence the dispersal decisions made by wolves.


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Abstract

Anderson, M.J. and Thompson, A.A. 2004. Multivariate control charts for ecological and environmental monitoring. Ecological Applications 14: 1921-1935.

Ecological and environmental monitoring has become increasingly important, with increasing threats from human disturbances. Monitoring usually involves sampling from several sites of a similar habitat at regular (or irregular) intervals through time. The purpose of monitoring is to determine where and when an impact may have occurred or, once detected, may still be occurring. Sequential statistical methods, including control charts, as developed for industrial applications, offer some promise in this regard. These provide a way of identifying when a system (e.g., in a factory) is going “out of control,” so as to trigger an alarm to stop the system and employ appropriate remedial measures. Such techniques clearly would be useful in the context of environmental monitoring. Traditional control charts, however, cannot be used for many ecological applications because they do not handle multivariate data and individual counts of species abundances do not generally fulfill the necessary statistical assumptions. A distance-based multivariate control chart method is described here, with some examples of its use in monitoring coral reef fish assemblages of the Great Barrier Reef, Australia. The method is flexible, as it can be based on any dissimilarity measure of choice, and useful as it does not require any specific assumptions regarding distributions of variables. Bootstrapping techniques are used to provide control-chart limits for an appropriate multivariate distance-based criterion through time. The method is designed to identify impacts at individual sites as quickly as possible, thus triggering an “alarm bell” in the context of ecological monitoring. It can also be applied at several spatial scales in hierarchical designs.


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Abstract

McArdle, B.H. and Anderson, M.J. 2004. Variance heterogeneity, transformations and models of species abundance: a cautionary tale. Canadian Journal of Fisheries and Aquatic Sciences 61: 1294-1302.

Ecological systems have intrinsic heterogeneity. Counts of abundances of species often show heterogeneity of variances among observational groups or populations. This is most often dealt with by using a transformation of the data, followed by a traditional statistical analysis that requires homogeneity. Such an approach is extremely useful when the mean-variance relationship is consistent across the data set. In some situations, however, the mean-variance relationship does not stay constant: e.g., the degree of spatial aggregation of organisms can change in space and time. In these cases, transforming the data to “fix” the problem of heterogeneity can result in apparently grossly inflated type I error. The use of a transformation alters the model under test and also has an important effect on the spatial scale of the hypothesis. The use of non-parametric alternatives, such as permutation or bootstrap tests, does not solve this problem. Explicit models of these kinds of distributional changes, where they occur, are necessary.

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Abstract

Anderson, M.J. and Millar, R.B. 2004. Spatial variation and effects of habitat on temperate reef fish assemblages in north eastern New Zealand. Journal of Experimental Marine Biology and Ecology 305(2): 191-221.

Reef-associated fishes can respond to changes in habitat structure and the nature of their response can change with different spatial scales of observation. A structured hierarchical mensurative sampling design was used to sample temperate reef fish assemblages in north-eastern New Zealand at several spatial scales over two years. The three spatial scales examined were tens of meters (transects), hundreds to thousands of meters (sites) and hundreds of kilometers (locations). We tested the hypothesis that fish assemblages differed between kelp forest habitat (relatively dense stands of the kelp, Ecklonia radiata (C. Agardh) J. Agardh, median depth = 13.5 m) and barrens habitat (rocky reef dominated by turfing and encrusting red algae and the grazing urchin, Evechinus chloroticus (Valenciennes), median depth = 6.7 m). Recently developed multivariate techniques were used to test for and quantify multivariate variation at different spatial scales. There were significant effects of habitat on the spatial distribution of fish assemblages, characterised by greater abundances or frequencies of Parika scaber, Chromis dispilus, Trachurus novaezelandiae, Nemadactylus douglasii, Bodianus unimaculatus, Odax pullus and Pseudolabrus miles in kelp forest habitat, and greater abundances or frequencies of Notolabrus celidotus, Notolabrus fucicola, Girella tricuspidata, Coris sandageri, Chironemus marmoratus, Parma alboscapularis, Scorpis violaceus and Kyphosus sydneyanus in barrens habitat. Some of the more common species, including Upeneichthys lineatus, Scorpis lineolatus and Cheilodactylus spectabilis showed no strong consistent effects of these two differing habitats on their distributions. There was, however, a significant habitat x locations interaction: effects of habitat did not occur at all locations. Variability was highest at the scale of individual transects and variability from site to site and from location to location was comparable. Spatial variation was large compared to inter-annual variation, which was minimal, and spatial patterns were consistent in the two years examined. Further experiments, including manipulations, are required to understand what mechanisms and processes might be driving these patterns. This study, coupled with results from previous studies, suggests that there may be a dynamic inter-play between effects of habitat on fish and effects of fish on biogenic habitat, such as kelp forests.

 

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Abstract

Anderson, M.J., Ford, R.B., Feary, D.A. and Honeywill, C. 2004. Quantitative measures of sedimentation in an estuarine system and its relationship with intertidal soft-sediment infauna. Marine Ecology Progress Series 272: 33-48.

Increased sedimentation from changes in land use in coastal areas is a potentially important impact of human urbanisation. The potential impact of sedimentation on benthic infauna was quantitatively investigated in Okura estuary, which is at the northern fringes of urban development in Auckland, New Zealand. A structured mensurative sampling programme, measuring benthic infauna and various environmental variables, is described. Seventy percent of the variance in macrofaunal assemblages from 15 sites throughout the Okura estuary on 6 sampling occasions was explained by the environmental variables. Proportions of ambient sediment grain sizes, depositional categories from previous models, the amount and characteristics of trapped sediments, organic content, changes in bed height and distance from the mouth of the estuary were all useful in explaining variation in macrofaunal assemblages. Levels of sedimentation recorded in this study were sub-catastrophic (< 3 cm of deposition per day), corresponding to natural fluctuations in sedimentation. Bivalves generally had a negative relationship with sedimentation, while certain burrowing crabs and polychaetes were more abundant in high depositional environments. The total amount and the grain size characteristics of trapped sediments explained a significant proportion of the variation in soft-sediment assemblages, over and above the variation explained by ambient sediment variables. Thus, sedimentation appears to be an important structuring force in these intertidal estuarine macrobenthic assemblages.

 

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Abstract

Willis, T.J. and Anderson, M.J. 2003. Structure of cryptic reef fish assemblages: relationships with habitat characteristics and predator density. Marine Ecology Progress Series 257: 209-221.

Cryptic fish assemblages on temperate rocky reefs in New Zealand are among the most speciose in the world, yet very little is known regarding ecological processes that may affect their density and diversity. The potential effects of reef structural complexity, kelp density, and the increased density of predatory fish on assemblages of small, cryptic reef fishes were examined in northeastern New Zealand. Sampling was conducted in replicated areas inside and outside of a marine reserve, where differential densities of predatory fishes were known to occur. There was a strong positive correlation between substratum complexity and the density and diversity of cryptic fish assemblages. While the more common fish species occurred in both kelp (Ecklonia radiata) forest habitat and rocky reefs grazed by urchins, the composition of less abundant species differed between these two habitats. Assemblages in kelp forests were more variable than those in urchin barrens. The sites inside the marine reserve contained, on average, lower densities of cryptic fishes than sites outside the reserve, which might be explained by effects of predators. The effect of the marine reserve appeared to be strongest in the kelp forest habitat, with relatively little difference seen between reserve and non-reserve assemblages in unvegetated habitats. If these observed patterns are found to be consistent at other reserves and at other times, they imply that removal of predators by fishing may have large-scale positive effects on assemblages of small cryptic reef fishes.

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Abstract

Millar, R.B. and Anderson, M.J. 2003. The kinetics of monospermic and polyspermic fertilization in free-spawning marine invertebrates. Journal of Theoretical Biology 224: 79-85.

The equation of Vogel et al. (1982) is widely used in fertilization studies of free-spawning marine invertebrates to predict the percentage of viable eggs that will be fertilized at any specified levels of gamete concentration and contact time. Here, the random collision model that underlies the Vogel et al. equation is extended to distinguish between monospermic and polyspermic fertilization, and separate equations for the percentages of monospermic and polyspermic fertilization are obtained. These equations provide an explanation for empirical observations which have shown a decreased percentage of successful egg development at high sperm concentrations. Comparison is made with an earlier heuristic attempt (Styan, 1998) to predict the rate of polyspermic fertilization, and it is found that this earlier method can underestimate the percentage of polyspermic fertilization by up to 10 percent. Moreover, the approach used here retains the flexibility to model changes in sperm concentration due to dispersal mechanisms, and is able to model different mechanisms for the block to polyspermy.

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Abstract

Anderson, M.J. and Willis, T.J. 2003. Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology. Ecology 84: 511-525.

A flexible method is needed for constrained ordination on the basis of any distance or dissimilarity measure, which will display a cloud of multivariate points by reference to a specific a priori hypothesis. We suggest the use of principal coordinate analysis (PCO, metric MDS) followed by either a canonical discriminant analysis (CDA, when the hypothesis concerns groups) or a canonical correlation analysis (CCorA, when the hypothesis concerns relationships with environmental or other variables) to provide a flexible and meaningful constrained ordination of ecological species abundance data. Called “CAP” for “Canonical Analysis of Principal coordinates,” this method will allow a constrained ordination to be done on the basis of any distance or dissimilarity measure. We describe CAP in detail, including how it can uncover patterns that are masked in an unconstrained MDS ordination. Canonical tests using permutations are also given and we show how the method can be used (1) to place a new observation into the canonical space using only inter-point dissimilarities, (2) to classify observations and obtain misclassification or residual errors, and (3) to correlate the original variables with patterns on canonical plots. Misclassification error or residual error is used to obtain a non-arbitrary decision concerning the appropriate dimensionality of the response data cloud (number of PCO axes) for the ensuing canonical analysis. We suggest that a CAP ordination and an unconstrained ordination, such as MDS, together will provide important information for meaningful multivariate analyses of ecological data by reference to explicit a priori hypotheses.

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Abstract

Anderson, M.J. 2001. Permutation tests for univariate or multivariate analysis of variance and regression. Canadian Journal of Fisheries and Aquatic Sciences 58: 629-636.

The most appropriate strategy to be used to create a permutation distribution for tests of individual terms in complex experimental designs is currently unclear. There are often many possibilities, including restricted permutation or permutation of some form of residuals. This paper provides a summary of recent empirical and theoretical results concerning available methods and gives recommendations for their use in univariate and multivariate applications. The focus of the paper is on complex designs in analysis of variance and multiple regression (i.e., linear models). The assumption of exchangeability required for a permutation test is assured by random allocation of treatments to units in experimental work. For observational data, exchangeability is tantamount to the assumption of independent and identically distributed errors under a null hypothesis. For partial regression, the method of permutation of residuals under a reduced model has been shown to provide the best test. For analysis of variance, one must first identify exchangeable units by considering expected mean squares. Then, one may generally produce either (i) an exact test by restricting permutations or (ii) an approximate test by permuting permuting raw data or some form of residuals. The latter can provide a more powerful test in many situations.

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Abstract

Anderson, M. J. and Robinson, J. 2003. Generalized discriminant analysis based on distances. Australian & New Zealand Journal of Statistics 45: 301-318.

This paper describes a method of generalized discriminant analysis based on a dissimilarity matrix to test for differences in a priori groups of multivariate observations. Use of classical multidimensional scaling produces a low-dimensional representation of the data for which Euclidean distances approximate the original dissimilarities. The resulting scores are then analysed using discriminant analysis, giving tests based on the canonical correlations. The asymptotic distributions of these statistics under permutations of the observations are shown to be invariant to changes in the distributions of the original variables, unlike the distributions of the multi-response permutation test statistics which have been considered by other workers for testing differences among groups. This canonical method is applied to multivariate fish assemblage data, with Monte Carlo simulations to make power comparisons and to compare theoretical results and empirical distributions. The paper proposes classification based on distances. Error rates are estimated using cross-validation.

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Abstract

Anderson, M.J. and ter Braak, C.J.F. 2003. Permutation tests for multi-factorial analysis of variance. Journal of Statistical Computation and Simulation 73: 85-113.

Several permutation strategies are often possible for tests of individual terms in analysis-of-variance (ANOVA) designs. These include restricted permutations, permutation of whole groups of units, permutation of some form of residuals or some combination of these. It is unclear, especially for complex designs involving random factors, mixed models or nested hierarchies, just which permutation strategy should be used for any particular test. The purpose of this paper is two-fold: (i) we provide a guideline for constructing an exact permutation strategy, where possible, for any individual term in any ANOVA design; and (ii) we provide results of Monte Carlo simulations to compare the level accuracy and power of different permutation strategies in two-way ANOVA, including random and mixed models, nested hierarchies and tests of interaction terms. Simulation results showed that permutation of residuals under a reduced model generally had greater power than the exact test or alternative approximate permutation methods (such as permutation of raw data). In several cases, restricted permutations, in particular, suffered more than other procedures, in terms of loss of power, challenging the conventional wisdom of using this approach. Our simulations also demonstrated that the choice of correct exchangeable units under the null hypothesis, in accordance with the guideline we provide, is essential for any permutation test, whether it be an exact test or an approximate test. For reference, we also provide appropriate permutation strategies for individual terms in any two-way or three-way ANOVA for the exact test (where possible) and for the approximate test using permutation of residuals.

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Abstract

Anderson, M.J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology 26: 32-46.

Hypothesis-testing methods for multivariate data are needed to make rigorous probability statements about effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps more intuitive formulation for ANOVA (based on sums of squared distances) to complement the description provided by McArdle and Anderson (in press) for the analysis of any linear model. It is an improvement on previous non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack of formal assumptions of other non-parametric methods. The test-statistic is a multivariate analogue to Fisher’s F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.

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Abstract

Anderson, M. J. and Clements, A. 2000. Resolving environmental disputes: a statistical method for choosing among competing cluster models. Ecological Applications 10: 1341-1355.

The protection of whole assemblages of species requires that such assemblages be identified in some nonarbitrary, quantitative manner. Clustering methods can be used to identify groups or clusters of observations (i.e. sites, transects, quadrats, etc.) on the basis of multivariate assemblage data, where each species is a variable. There are many kinds of cluster analyses, all potentially providing different outcomes, that is, different clusters of the multivariate observations. The wide choice of clustering methods and the necessarily subjective choice of which method and measure of similarity to use for a particular data set is problematic. It can lead (and has led) to disputes about the way multivariate observations should be grouped, causing conflicts in making environmental decisions. We present a statistical test for choosing among competing cluster models and demonstrate its use with a case in point. The method provides an objective way to discriminate among competing models in order to determine the model that best fits the available data. Provided each party in a dispute identifies and articulates the cluster model it supports, the method can give a nonarbitrary judgment concerning the best model. This method provides an important tool for the resolution of environmental disputes concerning the presence of a particular community at a particular place and time, which may be impacted by a proposed development.

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Abstract

Anderson, M. J. and Robinson, J. 2001. Permutation tests for linear models. Australian and New Zealand Journal of Statistics 43: 75-88.

Several approximate permutation tests have been proposed for tests of partial regression coefficients in a linear model based on sample partial correlations. This paper begins with an explanation and notation for an exact test. It then compares the distributions of the test statistics under the various permutation methods proposed, and shows that the partial correlations under permutation are asymptotically jointly normal with means 0 and variances 1. The method of Freedman & Lane (1983) is found to have asymptotic correlation 1 with the exact test, and the other methods have smaller correlations with this test. Under local alternatives the critical values of all the approximate permutation tests converge to the same constant, so they all have the same asymptotic power. Simulations demonstrate these theoretical results.

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Abstract

McArdle, B.H. and Anderson, M.J. 2001. Fitting multivariate models to community data: comment on distance-based redundancy analysis. Ecology 82: 290-297.

Nonparametric multivariate analysis of ecological data using permutation tests has two main challenges: (1) to partition the variability in the data according to a complex design or model, as is often required in ecological experiments and (2) to base the analysis on a multivariate distance measure (such as the semimetric Bray-Curtis measure) that is reasonable for ecological data sets. Previous nonparametric methods have succeeded in one or other of these areas, but not in both. A recent contribution to Ecological Monographs by Legendre and Anderson, called distance-based redundancy analysis (db-RDA), does achieve both. It does this by calculating principal coordinates and subsequently correcting for negative eigenvalues, if they are present, by adding a constant to squared distances. We show here that such a correction is not necessary. Partitioning can be achieved directly from the distance matrix itself, with no corrections and no eigenanalysis, even if the distance measure used is semimetric. An ecological example is given to show the differences in these statistical methods. Empirical simulations, based on parameters estimated from real ecological species abundance data, showed that db-RDA done on multi-factorial designs (using the correction) does not have type 1 error consistent with the significance level chosen for the analysis (i.e. does not provide an exact test), whereas the direct method described and advocated here does.

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Abstract

Anderson, M. J. 1999. Distinguishing direct from indirect effects of grazers in intertidal estuarine assemblages. Journal of Experimental Marine Biology and Ecology 234: 199-218.

Previous work demonstrated that gastropod grazers (Bembicium auratum and Austrocochlea porcata) are important in structuring ecological succession in an intertidal estuarine assemblage in New South Wales, Australia.  This paper describes work designed to test the hypothesis that the effects of grazers on the intertidal assemblages are primarily indirect, due to their removal of algae.  The experiment done to distinguish direct from indirect effects included independent and replicated removals of grazers or algae in a crossed design, along with controls for potential artifacts associated with removals.  In addition to specific tests on individual species, a new non-parametric multivariate randomization test (distance-based redundancy analysis, db-RDA) was used to test the hypothesis that simultaneous effects of grazers on the whole assemblage of species were indirect.  Results showed that the grazers had indirect positive effects on oysters (Saccostrea commercialis) and indirect negative effects on some species of barnacles (Balanus variegatus and B. amphitrite).  Other species of barnacles (Hexaminius sp. and Elminius covertus) were not affected, either by algae or grazers.  Multivariate analyses showed that the effects of grazers on the entire assemblage of species were indeed indirect, through their removal of algae.  This study highlights the importance of considering the implications of indirect effects of herbivores on the ecology of whole communities, in addition to their impacts on single-species populations.

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Abstract

Anderson, M. J. and Connell, S. D. 1999. Predation by fish on intertidal oysters. Marine Ecology Progress Series 187: 203-211.

Experiments in many parts of the world have indicated that sessile intertidal organisms are affected by fish predation. Farming of oysters (Saccostrea commercialis (Iredale & Roughley) and Crassostrea gigas (Thunberg)) in New South Wales depends on their natural recruitment and growth on intertidal structures in estuaries. We investigated the effects of predation by fish on numbers of oysters recruiting to experimental panels of three different sizes.  We tested effects of excluding fish of different sizes using different sizes of mesh (12.5 mm and 50 mm). Numbers of oysters were significantly reduced on panels open to predatory fish. Numbers of oysters per unit area and subsequent predation on them did not vary, however, across three different sizes of panels, indicating that predation was not dependent on patch size. Mortality on panels open to predation averaged 40.0% (± 4.3% s.e.).  Fish also significantly altered the sizes of oysters.  The effect of predation was almost entirely attributable to toadfish (Tetractenos spp.).   Previous knowledge of the life-history of oysters and succession in these intertidal assemblages suggests that effects of predation may not, however, have important long-term consequences on natural populations.

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Abstract

Anderson, M. J. and Legendre, P. 1999. An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. Journal of Statistical Computation and Simulation 62: 271-303.

This study compared empirical type I error and power of different permutation techniques for the test of significance of a single partial regression coefficient in a multiple regression model, using simulations.  The methods compared were permutation of raw data values, two alternative methods proposed for permutation of residuals under the reduced model, and permutation of residuals under the full model.  The normal-theory t-test was also included in simulations.  We investigated effects of 1) the sample size, 2) the degree of collinearity between the predictor variables, 3) the size of the covariable’s parameter, 4) the distribution of the added random error and 5) the presence of an outlier in the covariable on these methods.  We found that two methods that had been identified as equivalent formulations of permutation under the reduced model were actually quite different.  One of these methods resulted in consistently inflated type 1 error. In addition, when the covariable contained an extreme outlier, permutation of raw data resulted in unstable (often inflated) type 1 error.  There were no significant differences in power among the three permutation methods (raw data permutation, reduced-model permutation and full-model permutation), but all had greater power than the normal-theory t-test when errors were non-normal.  The reduced model permutation method had the most consistent and reliable results of the methods investigated here for the test of a partial regression coefficient.  However, reasonably extreme situations needed to be simulated in order to distinguish methods from the normal-theory t-test and from one another.  Permutation of raw data, permutation under the reduced model, and permutation under the full model are generally asymptotically equivalent.

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Abstract

Connell, S. D. and Anderson, M. J. 1999. Predation by fish on assemblages of intertidal epibiota: effects of predator size and patch size. Journal of Experimental Marine Biology and Ecology 241: 15-29.

We tested the hypothesis that effects of predation by fish on epibiota are independent of the size of fish and the area foraged.  We used cages with different sizes of mesh to exclude fish of different sizes.  Sizes of mesh were chosen following observations that there were small (<200 mm TL) and large (>200mm TL) predatory fish at the study site.  Predation by fish was intense on oysters and directly or indirectly reduced the density of the gastropod, Bembicium auratum.  The cover of algae was positively affected by predation, possibly because predation on oysters created more space for algae.  Predation by small fish (toadfish) was intense, but the effects of large fish were negligible.  Predation was, however, independent of the sizes of experimental panels (i.e. area foraged) over the range examined (5 x 5, 10 x 10, 20 x 20 cm).  Our results highlight the importance of doing experiments to test hypotheses derived from known aspects of the biology of the predators and prey being studied.

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Abstract

Legendre, P. and Anderson, M. J. 1999. Distance-based redundancy analysis: testing multi-species responses in multi-factorial ecological experiments. Ecological Monographs 69: 1-24.

We present a new multivariate technique for testing the significance of individual terms in a multi-factorial analysis-of-variance model for multi-species response variables. The technique will allow researchers to base analyses on measures of association (distance measures) which are ecologically relevant. In addition, unlike other distance-based hypothesis-testing techniques, this method allows tests of significance of interaction terms in a linear model. The technique uses the existing method of redundancy analysis (RDA), but allows the analysis to be based on Bray-Curtis or other ecologically meaningful measures through the use of principal coordinate analysis (PCoA). Steps in the procedure include: 1) calculating a matrix of distances among replicates using a distance measure of choice (e.g. Bray-Curtis); 2) determining the principal coordinates (including a correction for negative eigenvalues, if necessary), which preserve these distances; 3) creating a matrix of dummy variables corresponding to the design of the experiment (i.e. individual terms in a linear model); 4) analyzing the relationship between the principal coordinates (species data) and the dummy variables (model) using RDA; 5) implementing a test by permutation for particular statistics corresponding to the particular terms in the model. This method has certain advantages not shared by other multivariate testing procedures. We demonstrate the use of this technique with experimental ecological data from intertidal assemblages, and show how the presence of significant multivariate interactions can be interpreted. It is our view that distance-based RDA will be extremely useful to ecologists measuring multi-species responses to structured multi-factorial experimental designs.

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Abstract

Anderson, M. J. 1998. Effects of patch size on colonization in estuaries: revisiting the species-area relationship. Oecologia 118: 87-98.

The effects of patch size on the colonisation and succession of intertidal invertebrates and algae were investigated in an estuary near Sydney in New South Wales, Australia.  The specific aim was to test explicitly for the presence of a species-area relationship, and to test whether this could be explained by the random placement hypothesis (i.e. that the number of species per unit area was the same on patches of different sizes).  In addition, I tested the extent to which differences in numbers of species reflected differences in the composition of assemblages. Wooden panels of three different sizes (10 cm x 10 cm, 20 cm x 20 cm, and 40 cm x 40 cm) were placed in the field on intertidal oyster leases in each of two different experimental trials: spring (October 1994) and summer (January 1995).  Independent replicate measures of the number of colonising species on panels were obtained after different periods of time, up to 25 months.  I also obtained measures of abundance of individual species and composition of assemblages on panels of different sizes.  This allowed specific tests of the hypothesis that the size of the patch being colonised is important in structuring these assemblages. The strength of the species-area relationship increased through time on panels submersed in October, but the opposite trend occurred for panels submersed in January.  There was a significant interaction between factors of patch size and time of submersion for multivariate measures of differences in composition among replicates.  The random placement hypothesis was supported in certain situations, but not in others.  When the random placement hypothesis was rejected, it was for different reasons on panels submersed in the two different trials.  Panels initiated in October tended to have proportionally greater numbers of species per unit area on larger panels, while the panels initiated in January tended to have greater numbers of species per unit area on smaller panels.  There was an identifiable relationship between differences in numbers of species and differences in species composition for panels submersed in October.  This was not true, however, for panels submersed in January, where the species-area relationship did not hold after longer periods. The succession of organisms through time was, overall, more important in structuring the assemblages than was the size of the patch being colonised.  The species-area relationship should not necessarily be regarded as a truism; in this system, the species-area relationship did not always hold.  The initial timing of experiments with respect to recruitment and succession influenced results.

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Abstract

Anderson, M. J. and Gribble, N. A. 1998. Partitioning the variation among spatial, temporal and environmental components in a multivariate data set. Australian Journal of Ecology 23: 158-167.

We propose a method of partitioning the variation in a multivariate set of data according to 1) environmental variables, 2) variables describing the spatial structure in the data, and 3) temporal variables.  This method is an extension of an existing method for partialling out the spatial component of environmental variation, using canonical analysis.  Our proposed method extends this approach by including temporal variables in the analysis.  Thus, the partitioning of variation for a data matrix of species’ abundances or biomass can include, by our methodology, the following components: 1) pure environmental, 2) pure spatial, 3) pure temporal, 4) pure spatial component of environmental, 5) pure temporal component of environmental, 6) pure combined spatial/temporal component, 7) combined spatial/temporal component of environmental and 8) unexplained.  In addition, permutation testing accompanying the analyses allowed tests of significance for the relationship between the different components and the species data.  We illustrate the method with a set of survey data of penaeid species (prawns) obtained on the far northern Great Barrier Reef of Australia.   This extension is a useful tool for multivariate analysis of ecological data from surveys, where space, time and environment commonly overlap and are important influences on observed variation.

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Abstract

Iliadou, K. and Anderson, M. J. 1998. Interspecific comparative analysis using morphometrics of pharyngeal bones vs. body measurements of the genus Scardinius (Pisces: Cyprinidae) in Greece. Journal of Natural History 32: 923-941.

Morphometric data have long been used in the classification of different fish species.  This paper presents the first morphometric study of the pharyngeal bones and teeth of three species of freshwater fish of the genus Scardinius from Greece.  Two of the species are endemic to Greece (S. graecus and S. acarnanicus) and one is widely distributed in Europe as well (S. erythrophthalmus).  Morphometric data were collected from individual fish with regard to pharyngeal bone and teeth measurements and external body measurements. Discriminant function analysis was used, showing that the pharyngeal bone measurements could be used to successfully discriminate different species with identical tooth type and tooth formulae within the same genus.  The results of separate discriminant function analyses on 1) pharyngeal bones and their teeth vs. 2) external body measurements are discussed.

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Abstract

Anderson, M. J. and Underwood, A. J. 1997. Effects of gastropod grazers on recruitment and succession of an estuarine assemblage: a univariate and multivariate approach. Oecologia 109: 442-453.

Grazers have been shown to affect assemblages of species in many habitats.  This was a study of the effects of the gastropod grazers, Austrocochlea porcata and Bembicium auratum, on intertidal estuarine assemblages in a sheltered bay in New South Wales, Australia.  We examined effects of gastropods on individual species and on the assemblage as a whole.  The multivariate response was compared with data on succession in these assemblages to estimate potential effects of grazers on succession.  The experiment was repeated several times to determine the generality of grazers' effects in the light of possible variation in the timing or intensity of recruitment. There were different responses of individual species to the presence of grazers.  Grazers reduced abundances of ephemeral algal species, bryozoans, copepods, insect larvae and Balanus sp. barnacles.  They had a positive effect on oysters and spirorbids and no effect on the barnacles Elminius covertus and Hexaminius sp.  These effects were consistent through time. Multivariate analyses confirmed that grazers caused significant changes to whole assemblages and that these effects were far-reaching and not caused only by changes to algal species.  The removal of grazers appeared neither to speed up nor to slow down succession, but rather caused a completely different assemblage to develop.  Apparent important mechanisms affecting composition of animal species when grazers were removed included accumulation of sediments and detritus and pre-emption of space by algae.

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Abstract

Anderson, M. J. 1996. A chemical cue induces settlement of Sydney rock oysters, Saccostrea commercialis, in the laboratory and in the field. Biological Bulletin 190: 350-358.

The physical and chemical nature of a substratum's surface, including the presence of dissolved compounds or a bacterial film, may induce the settlement of invertebrate larvae.  Based on previous observations of 1) enhanced recruitment of Sydney rock oysters (Saccostrea commercialis) on concrete surfaces and 2) high alkalinity at the surface of concrete due to the leaching of calcium hydroxide (Ca(OH)2) from the cement, experiments were designed to test the hypothesis that a surface containing Ca(OH)2 enhances settlement of oysters.  The effect of a biofilm on settlement of Sydney rock oysters was also tested.  There were slight differences in results obtained from the field experiment compared with results obtained in the laboratory.  In both the laboratory and the field, Ca(OH)2 had a positive effect on settlement.  Also, in both experiments there was no significant effect of a biofilm on settlement on concrete substrata and a positive effect of a biofilm on substrata made with sand only or on sandstone.  For the substrata made with Ca(OH)2 and sand, however, the effect of a biofilm was positive in the field and negative in the lab.  Although the results from the lab and field experiments were similar, the discrepancy was crucial in accepting/rejecting one of the hypotheses under test.  The results of the study demonstrated that 1) the effects of a biofilm on settlement vary with the substratum and 2) these oysters can respond to a chemical cue (Ca(OH)2) in the field.  The ecological implications of the ability of larvae actively to select a habitat in response to chemical cues are discussed.

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Abstract

Anderson, M. J. 1996. Indirect effects of grazing gastropods on recruitment of Sydney Rock oysters. pp. 339-347.  In: Floyd, R. B., Sheppard, A. W. and De Barro, P. J. (eds.). Frontiers of Population Ecology. CSIRO Publishing, Melbourne, Victoria.

Populations do not exist in isolation but usually interact with populations of other species in an assemblage.  Indirect effects can occur if the presence or activity of a third species changes the effect that one species has on another.  In temperate marine habitats, experimental work has shown the importance of the direct effects of gastropod grazers on algal assemblages and concomitant indirect effects of grazing on recruitment of other invertebrate animals, including oysters, barnacles and mussels.  Oyster farmers in New South Wales, Australia depend on natural recruitment of Sydney Rock oysters, Saccostrea commercialis, but the ecology of populations of this species on commercial oyster leases, including potential indirect effects of other species, has not been studied.  In this study, grazing marine gastropod snails (Austrocochlea constricta and Bembicium auratum) were experimentally excluded from concrete panels attached to commercial oyster leases to determine their effect on recruitment of Sydney Rock oysters.  The presence of grazers significantly increased recruitment of oysters in experiments initiated in the early spring (October 1993).  The growth of algae inhibited oyster recruitment by pre-empting available space; therefore grazers indirectly increased oyster settlement by removing this algae.  This effect did not occur in experiments initiated in summer (January 1994), because algae did not grow sufficiently to pre-empt much of the space before oysters recruited in February/March 1994.  These results showed that grazers can have important indirect effects on populations of oysters and that their influence depends on the timing of initiation of experiments with respect to the settlement of oysters.

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Abstract

Anderson, M. J. 1995. Variations in biofilms colonizing artificial surfaces: seasonal effects and effects of grazers. Journal of the Marine Biological Association, U.K. 75: 705-714.

The colonisation of microscopic organisms, commonly called a biofilm, was examined on fibreglass panels situated intertidally at Quibray Bay of Botany Bay in New South Wales, Australia.  Panels were examined by incident light microscopy, measuring percentage cover, and by a computer image analysis technique, measuring optical density.  Optical density was positively correlated with and was therefore a reliable estimate of total percentage cover of the biofilm.  Optical density has not been used before in this application and, although some drawbacks are discussed, it is a much more efficient sampling method than microscopic examination of panels. Variations in the percentage cover and composition of the biofilm colonising surfaces were assessed with regard to: i) different seasons and periods of exposure and ii) the presence of grazing gastropods.  The greatest cover of the biofilm occurred on panels in summer and spring.  Diatoms and bacteria dominated the assemblage in summer, the alga Enteromorpha sp. in spring and the protozoan Vorticella sp. dominated panels for one month in winter.  Also, the presence of grazers significantly decreased total microscopic cover (as measured by optical density).  These results demonstrated complex variations in the percentage cover and composition of microscopic assemblages which should be taken into account when considering the effects of a biofilm on macroscopic patterns and processes.

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Abstract

Anderson, M. J. and Underwood, A. J. 1994. Effects of substratum on the recruitment and development of an intertidal estuarine fouling assemblage. Journal of Experimental Marine Biology and Ecology 184: 217-236.

The effect of four substrata (concrete, plywood, fibreglass and aluminium) on the recruitment of species and development of an intertidal estuarine fouling assemblage was examined in Quibray Bay of Botany Bay, New South Wales, Australia.  Many species, including the oyster Saccostrea commercialis (Iredale & Roughley) and the barnacles Hexaminius sp., Balanus amphitrite Darwin and B. variegatus Darwin, recruited in greater numbers on concrete or plywood surfaces than on fibreglass or aluminium.  As a result, patterns of change in the number of species through time were dependent on the substratum.  Multivariate analyses indicated that assemblages on different substrata were significantly different after one or two months of submersion, but became more similar after longer periods (up to 4-5 months).  The reasons for this gradual conformity varied depending on the season of submersion and the composition of the species settling in a particular season. The results of this study indicated that the nature of the substratum can affect both initial colonisation of particular species and the development of the assemblage over time.  Because the effect of substratum varies with the period of submersion, comparisons of various studies on fouling assemblages using different natural and artificial substrata and for varying lengths of time are likely to be very difficult.

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Abstract

Byrne, M. and Anderson, M.J. 1994. Hybridization of sympatric Patiriella species (Echinodermata: Asteroidea) in New South Wales. Evolution 48: 564-576.

Three species of the asteroid genus Patiriella occur sympatrically in New South Wales and the possibility for hybridization among them was examined through a series of cross-fertilization experiments. Patiriella calcar and P. gunnii are morphologically distinct as adults but indistinguishable as larvae. Patiriella exigua is morphologically distinct in both its adult and larval morphologies. The gametes of P. calcar and P. gunnii were reciprocally compatible: laboratory crosses between these species produced viable hybrid juveniles. In crosses between female P. calcar and male P. gunnii, most of the juveniles metamorphosed with an arm number intermediate between that of the parents, whereas crosses between female P. gunnii and male P. calcar produced juveniles with an arm number more similar to the maternal phenotype. Heterospecific crosses with P. exigua resulted in low fertilization rates, and viable hybrids were not produced. This species appears capable of sef-fertilization. Because hybrids between P. calcar and P. gunnii were viable, neither gametic incompatibility nor hybrid inviability appears to ensure reproductive isolation between these species. Ecological or habitat segregation and temporal separation in breeding may isolate these species in the field. The results demonstrate that if gamete surface recognition molecules are involved in fertilization of P. calcar and P. gunnii, then they are not strongly species specific, at least at the sperm concentrations used in this study. Reproductive isolation between these species has evolved despite their gametic compatibility. In contrast, P. exigua is isolated from its congeners because of gametic incompatibility and several features characteristic of its reproduction and development. The implications of these findings for reproductive isolation and speciation of Patiriella and for the evolution and reproductive isolation in free-spawning marine organisms are discussed.

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Abstract

Underwood, A. J. and Anderson, M. J. 1994. Seasonal and temporal aspects of recruitment and succession in an intertidal estuarine fouling assemblage. Journal of the Marine Biological Association, U.K. 74: 563-584.

The recruitment and succession of fouling organisms was examined on four substrata (concrete, plywood, fibreglass and aluminium) in Quibray Bay of Botany Bay in New South Wales, Australia. Eighteen 10x10 cm panels of each substratum were submersed in each of four seasons: January (summer), March (autumn), May (winter) and October (spring) 1992. Six of each substratum were retrieved after 1 month, 2 months and 4-5 months. Thus in this study, as a methodological improvement over many other studies of succession, samples were taken independently with regard to time. Seasonal recruitment was important in determining the pattern of succession and the composition of the assemblage. Sydney Rock oysters, Saccostrea commercialis (Iredale & Roughly), recruited in large numbers on panels submersed in January and, by their rapid growth, dominated the available space after 4-5 months. The greatest recruitment of the barnacle Hexaminius sp. and the greatest percentage cover of algae (six species) occurred on panels submersed from October to March. While panels submersed in January for a period of 4-5 months resulted in a single outcome, an oyster-dominated assemblage, panels submersed in October for the same period of time resulted in a set of alternative outcomes depending on the relative abundance of barnacles and algae. The results of this study suggested that models and mechanisms of succession in the marine environment should be based on the traits of individual species (including seasonal recruitment, growth and the ability to resist invasion) with respect to the limiting resource(s) in the system, which for many sessile marine species is the available space.

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