Variability in Population Abundance and the Classification of Extinction Risk

Abstract: Classifying species according to their risk of extinction is a common practice and underpins much conservation activity. The reliability of such classifications rests on the accuracy of threat categorizations, but very little is known about the magnitude and types of errors that might be expected. The process of risk classification involves combining information from many sources, and understanding the quality of each source is critical to evaluating the overall status of the species. One common criterion used to classify extinction risk is a decline in abundance. Because abundance is a direct measure of conservation status, counts of individuals are generally the preferred method of evaluating whether populations are declining. Using the thresholds from criterion A of the International Union for Conservation of Nature (IUCN) Red List (critically endangered, decline in abundance of >80% over 10 years or 3 generations; endangered, decline in abundance of 50–80%; vulnerable, decline in abundance of 30–50%; least concern or near threatened, decline in abundance of 0–30%), we assessed 3 methods used to detect declines solely from estimates of abundance: use of just 2 estimates of abundance; use of linear regression on a time series of abundance; and use of state‐space models on a time series of abundance. We generated simulation data from empirical estimates of the typical variability in abundance and assessed the 3 methods for classification errors. The estimates of the proportion of falsely detected declines for linear regression and the state‐space models were low (maximum 3–14%), but 33–75% of small declines (30–50% over 15 years) were not detected. Ignoring uncertainty in estimates of abundance (with just 2 estimates of abundance) allowed more power to detect small declines (95%), but there was a high percentage (50%) of false detections. For all 3 methods, the proportion of declines estimated to be >80% was higher than the true proportion. Use of abundance data to detect species at risk of extinction may either fail to detect initial declines in abundance or have a high error rate.     

Declines in migrant shorebird populations from a winter‐quarter perspective

Many long‐distance migrating shorebird (i.e., sandpipers, plovers, flamingos, oystercatchers) populations are declining. Although regular shorebird monitoring programs exist worldwide, most estimates of shorebird population trends and sizes are poor or nonexistent. We built a state‐space model to estimate shorebird population trends. Compared with more commonly used methods of trend estimation, state‐space models are more mechanistic, allow for the separation of observation and state process, and can easily accommodate multivariate time series and nonlinear trends. We fitted the model to count data collected from 1990 to 2013 on 18 common shorebirds at the 2 largest coastal wetlands in southern Africa, Sandwich Harbour (a relatively pristine bay) and Walvis Bay (an international harbor), Namibia. Four of the 12 long‐distance migrant species declined since 1990: Ruddy Turnstone (Arenaria interpres), Little Stint (Calidris minuta), Common Ringed Plover (Charadrius hiaticula), and Red Knot (Calidris canutus). Populations of resident species and short‐distance migrants increased or were stable. Similar patterns at a key South African wetland suggest that shorebird populations migrating to southern Africa are declining in line with the global decline, but local conditions in southern Africa's largest wetlands are not contributing to these declines. State‐space models provide estimates of population levels and trends and could be used widely to improve the current state of water bird estimates.     

Predicting abundance of desert riparian birds: validation and calibration of the Effective Area Model.

Reliable prediction of the effects of landscape change on species abundance is critical to land managers who must make frequent, rapid decisions with long-term consequences. However, due to inherent temporal and spatial variability in ecological systems, previous attempts to predict species abundance in novel locations and/or time frames have been largely unsuccessful. The Effective Area Model (EAM) uses change in habitat composition and geometry coupled with response of animals to habitat edges to predict change in species abundance at a landscape scale. Our research goals were to validate EAM abundance predictions in new locations and to develop a calibration framework that enables absolute abundance predictions in novel regions or time frames. For model validation, we compared the EAM to a null model excluding edge effects in terms of accurate prediction of species abundance. The EAM outperformed the null model for 83.3% of species (N=12) for which it was possible to discern a difference when considering 50 validation sites. Likewise, the EAM outperformed the null model when considering subsets of validation sites categorized on the basis of four variables (isolation, presence of water, region, and focal habitat). Additionally, we explored a framework for producing calibrated models to decrease prediction error given inherent temporal and spatial variability in abundance. We calibrated the EAM to new locations using linear regression between observed and predicted abundance with and without additional habitat covariates. We found that model adjustments for unexplained variability in time and space, as well as variability that can be explained by incorporating additional covariates, improved EAM predictions. Calibrated EAM abundance estimates with additional site-level variables explained a significant amount of variability (P < 0.05) in observed abundance for 17 of 20 species, with R2 values >25% for 12 species, >48% for six species, and >60% for four species when considering all predictive models. The calibration framework described in this paper can be used to predict absolute abundance in sites different from those in which data were collected if the target population of sites to which one would like to statistically infer is sampled in a probabilistic way.     

The value of patches of intertidal seagrass to prawns depends on their proximity to mangroves

Penaeid prawns were sampled with a small seine net to test whether catches of postlarvae and juveniles in seagrass were affected by the distance of the seagrass (mainly Zostera capricorni) from mangroves and the density of the seagrass in a subtropical marine embayment. Sampling was replicated on the western and eastern sides of Moreton Bay, Queensland, Australia. Information on catches was combined with broad-scale spatial information on the distribution of habitats to estimate the contribution of four different categories of habitat (proximal dense seagrass, distal dense seagrass, proximal sparse seagrass, distal sparse seagrass) to the overall population of small prawns in these regions of Moreton Bay. The abundance of Penaeus plebejus and Metapenaeus bennettae was significantly and consistently greater in dense seagrass proximal to mangroves than in other types of habitat. Additionally, sparse seagrass close to mangroves supported more of these species than dense seagrass farther away, indicating that the role of spatial arrangement of habitats was more important than the effects of structural complexity alone. In contrast, the abundance of P. esculentus tended to be greatest in sparse seagrass distal from mangroves compared with the other habitats. The scaling up of the results from different seagrass types suggests that proximal seagrass beds on both sides of Moreton Bay provide by far the greatest contribution of juvenile M. bennettae and P. plebejus to the overall populations in the Bay.Communicated by M.S. Johnson, Crawley     

Effects of uncertainty and variability on population declines and IUCN Red List classifications

The International Union for Conservation of Nature (IUCN) Red List Categories and Criteria is a quantitative framework for classifying species according to extinction risk. Population models may be used to estimate extinction risk or population declines. Uncertainty and variability arise in threat classifications through measurement and process error in empirical data and uncertainty in the models used to estimate extinction risk and population declines. Furthermore, species traits are known to affect extinction risk. We investigated the effects of measurement and process error, model type, population growth rate, and age at first reproduction on the reliability of risk classifications based on projected population declines on IUCN Red List classifications. We used an age‐structured population model to simulate true population trajectories with different growth rates, reproductive ages and levels of variation, and subjected them to measurement error. We evaluated the ability of scalar and matrix models parameterized with these simulated time series to accurately capture the IUCN Red List classification generated with true population declines. Under all levels of measurement error tested and low process error, classifications were reasonably accurate; scalar and matrix models yielded roughly the same rate of misclassifications, but the distribution of errors differed; matrix models led to greater overestimation of extinction risk than underestimations; process error tended to contribute to misclassifications to a greater extent than measurement error; and more misclassifications occurred for fast, rather than slow, life histories. These results indicate that classifications of highly threatened taxa (i.e., taxa with low growth rates) under criterion A are more likely to be reliable than for less threatened taxa when assessed with population models. Greater scrutiny needs to be placed on data used to parameterize population models for species with high growth rates, particularly when available evidence indicates a potential transition to higher risk categories.     

Roles of Patch Characteristics,Drought Frequency,and Restoration in Long‐Term Trends of a Widespread Amphibian

Despite the high profile of amphibian declines and the increasing threat of drought and fragmentation to aquatic ecosystems, few studies have examined long‐term rates of change for a single species across a large geographic area. We analyzed growth in annual egg‐mass counts of the Columbia spotted frog (Rana luteiventris) across the northwestern United States, an area encompassing 3 genetic clades. On the basis of data collected by multiple partners from 98 water bodies between 1991 and 2011, we used state‐space and linear‐regression models to measure effects of patch characteristics, frequency of summer drought, and wetland restoration on population growth. Abundance increased in the 2 clades with greatest decline history, but declined where populations are considered most secure. Population growth was negatively associated with temporary hydroperiods and landscape modification (measured by the human footprint index), but was similar in modified and natural water bodies. The effect of drought was mediated by the size of the water body: populations in large water bodies maintained positive growth despite drought, whereas drought magnified declines in small water bodies. Rapid growth in restored wetlands in areas of historical population declines provided strong evidence of successful management. Our results highlight the importance of maintaining large areas of habitat and underscore the greater vulnerability of small areas of habitat to environmental stochasticity. Similar long‐term growth rates in modified and natural water bodies and rapid, positive responses to restoration suggest pond construction and other forms of management can effectively increase population growth. These tools are likely to become increasingly important to mitigate effects of increased drought expected from global climate change. Papeles de las Características del Fragmento, Frecuencia de Sequía y Restauración en las Tendencias a Largo Plazo de un Anfibio Ampliamente Distribuido     

Distribution of shallow-water epibenthic macrofauna in Moreton Bay,Queensland, Australia

The distribution of epibenthic penaeid prawn postlarvae has previously been shown to relate to the degree of marine influences in the flora, sediment and water conditions in littoral and infralittoral habitats in Moreton Bay. The postlarvae are part of a complex faunal assemblage of approximately 400 mobile epibenthic species. Samples of the assemblage from stations situated throughout Moreton Bay were analysed by multivariable methods, to detect whether the environmental influences volated to the distribution of penaeid prawns, were related to the fauna as a whole. This was found to be so. The fauna occurred in two groups in areas of either less marine or more marine influences. Animals in the first group were less diverse, with distributions unrelated to depth or presence of seagrasses, but related to the level of marine influences between geographical areas sampled. Animals in the second group were closely related to depth and presence of seagrasses, but no overall differences were attributable to marine influeces apart from those attributable to depth. Temporal changes in species composition were smaller than spatial changes, and changes in relative abundance were, in both groups, related to differences between (i) summer and winter, and (ii) spring and the rest of the year.     

Predictive vegetation modeling for conservation: impact of error propagation from digital elevation data.

The effect of digital elevation model (DEM) error on environmental variables, and subsequently on predictive habitat models, has not been explored. Based on an error analysis of a DEM, multiple error realizations of the DEM were created and used to develop both direct and indirect environmental variables for input to predictive habitat models. The study explores the effects of DEM error and the resultant uncertainty of results on typical steps in the modeling procedure for prediction of vegetation species presence/absence. Results indicate that all of these steps and results, including the statistical significance of environmental variables, shapes of species response curves in generalized additive models (GAMs), stepwise model selection, coefficients and standard errors for generalized linear models (GLMs), prediction accuracy (Cohen's kappa and AUC), and spatial extent of predictions, were greatly affected by this type of error. Error in the DEM can affect the reliability of interpretations of model results and level of accuracy in predictions, as well as the spatial extent of the predictions. We suggest that the sensitivity of DEM-derived environmental variables to error in the DEM should be considered before including them in the modeling processes.     

Use of Community‐Composition Data to Predict the Fecundity and Abundance of Species

Abstract: Species distribution models are critical tools for the prediction of invasive species spread and conservation of biodiversity. The majority of species distribution models have been built with environmental data. Community ecology theory suggests that species co‐occurrence data could also be used to predict current and potential distributions of species. Species assemblages are the products of biotic and environmental constraints on the distribution of individual species and as a result may contain valuable information for niche modeling. We compared the predictive ability of distribution models of annual grassland plants derived from either environmental or community‐composition data. Composition‐based models were built with the presence or absence of species at a site as predictors of site quality, whereas environment‐based models were built with soil chemistry, moisture content, above‐ground biomass, and solar radiation as predictors. The reproductive output of experimentally seeded individuals of 4 species and the abundance of 100 species were used to evaluate the resulting models. Community‐composition data were the best predictors of both the site‐specific reproductive output of sown individuals and the site‐specific abundance of existing populations. Successful community‐based models were robust to omission of data on the occurrence of rare species, which suggests that even very basic survey data on the occurrence of common species may be adequate for generating such models. Our results highlight the need for increased public availability of ecological survey data to facilitate community‐based modeling at scales relevant to conservation.     

Geographic Range Fragmentation and Abundance in Neotropical Migratory Birds

Populations of neotropical migrant landbirds have experienced significant declines in recent years. We investigated potential consequences of these declines by examining the relationship between abundance and fragmentation of geographic ranges of species on the North American breeding grounds. We estimated areograpbic fragmentation using the box dimension of a species' geographic range and demographic fragmentation using the fractal dimension of the semivariance function calculated from samples of population abundance across species' geographic ranges. We found a negative relationship between average abundance and demographic fragmentation for neotropical migrants, but not for residents. We also showed that demographic fragmentation and areographic fragmentation are inversely related for residents, but not for neotropical migrants. These results imply that neotropical migrants may be more sensitive to extinction than are residents.     

Effects of white‐nose syndrome on regional population patterns of 3 hibernating bat species

Hibernating bats have undergone severe recent declines across the eastern United States, but the cause of these regional‐scale declines has not been systematically evaluated. We assessed the influence of white‐nose syndrome (an emerging bat disease caused by the fungus Pseudogymnoascus destructans, formerly Geomyces destructans) on large‐scale, long‐term population patterns in the little brown myotis (Myotis lucifugus), the northern myotis (Myotis septentrionalis), and the tricolored bat (Perimyotis subflavus). We modeled population trajectories for each species on the basis of an extensive data set of winter hibernacula counts of more than 1 million individual bats from a 4‐state region over 13 years and with data on locations of hibernacula and first detections of white‐nose syndrome at each hibernaculum. We used generalized additive mixed models to determine population change relative to expectations, that is, how population trajectories differed with a colony's infection status, how trajectories differed with distance from the point of introduction of white‐nose syndrome, and whether declines were concordant with first local observation of the disease. Population trajectories in all species met at least one of the 3 expectations, but none met all 3. Our results suggest, therefore, that white‐nose syndrome has affected regional populations differently than was previously understood and has not been the sole cause of declines. Specifically, our results suggest that in some areas and species, threats other than white‐nose syndrome are also contributing to population declines, declines linked to white‐nose syndrome have spread across large geographic areas with unexpected speed, and the disease or other threats led to declines in bat populations for years prior to disease detection. Effective conservation will require further research to mitigate impacts of white‐nose syndrome, renewed attention to other threats to bats, and improved surveillance efforts to ensure early detection of white‐nose syndrome.     

Spatial statistics for modeling of abundance and distribution of wildlife species in the Masai Mara ecosystem, Kenya

This study illustrates the use of modern statistical procedures for better wildlife management by addressing three key issues: determination of abundance, modeling of animal distributions and variability of diversity in space and time. Prior information in Markov Chain Monte Carlo (MCMC) methods is used to improve estimates of abundance. Measures of autocorrelation are included when modeling distributions of animal counts, and a diversity index to indicate species abundance and richness for large herbivores is developed. Data from the Masai Mara ecosystem in Kenya are used to develop and demonstrate these procedures. The new abundance estimates are up to 35% more accurate than those obtained by existing methods. Significant temporal changes in spatial patterns are found from a space-time analysis of elephant counts over a 20-year period, with strong interactions over 5 km and 6 months space and time separations, respectively. The new diversity index is sensitive to both high abundance and species richness and is also able to capture year to year variation. It indicates an overall marginal decrease in diversity for large herbivores in the Mara ecosystem. The space-time analyses and diversity index can easily be computed thereby providing tools for rapid decision making.     

Measuring the impact of the pet trade on Indonesian birds

The trade in wild animals involves one‐third of the world's bird species and thousands of other vertebrate species. Although a few species are imperiled as a result of the wildlife trade, the lack of field studies makes it difficult to gauge how serious a threat it is to biodiversity. We used data on changes in bird abundances across space and time and information from trapper interviews to evaluate the effects of trapping wild birds for the pet trade in Sumatra, Indonesia. To analyze changes in bird abundance over time, we used data gathered over 14 years of repeated bird surveys in a 900‐ha forest in southern Sumatra. In northern Sumatra, we surveyed birds along a gradient of trapping accessibility, from the edge of roads to 5 km into the forest interior. We interviewed 49 bird trappers in northern Sumatra to learn which species they targeted and how far they went into the forest to trap. We used prices from Sumatran bird markets as a proxy for demand and, therefore, trapping pressure. Market price was a significant predictor of species declines over time in southern Sumatra (e.g., given a market price increase of approximately $50, the log change in abundance per year decreased by 0.06 on average). This result indicates a link between the market‐based pet trade and community‐wide species declines. In northern Sumatra, price and change in abundance were not related to remoteness (distance from the nearest road). However, based on our field surveys, high‐value species were rare or absent across this region. The median maximum distance trappers went into the forest each day was 5.0 km. This suggests that trapping has depleted bird populations across our remoteness gradient. We found that less than half of Sumatra's remaining forests are >5 km from a major road. Our results suggest that trapping for the pet trade threatens birds in Sumatra. Given the popularity of pet birds across Southeast Asia, additional studies are urgently needed to determine the extent and magnitude of the threat posed by the pet trade.     

Compositional analysis of overdispersed counts using generalized estimating equations

Multivariate abundance data are commonly collected in ecology, and used to explore questions of “community composition”—how relative abundance of different taxa changes with environmental conditions. In this paper, we propose a log-linear marginal modeling approach for analyzing such compositional count data, via generalized estimating equations. This method exploits the multiplicative nature of log-linear models for counts, by reparameterizing models that describe marginal effects on mean abundance. This allows partitioning into “main effects” and compositional effects, which is appealing for interpretation. We apply the proposed approach to reanalyze compositional counts of benthic invertebrates from Delaware Bay, and data of invertebrate communities inhabiting Acacia plants in eastern Australia. In both cases we resort to a resampling approach to make inferences about regression parameters, because the number of clusters was not large compared to cluster size.     

Local and Landscape Correlates of Primate Distribution and Persistence in the Remnant Lowland Rainforests of the Upper Brahmaputra Valley,Northeastern India

Habitat fragmentation affects species distribution and abundance, and drives extinctions. Escalated tropical deforestation and fragmentation have confined many species populations to habitat remnants. How worthwhile is it to invest scarce resources in conserving habitat remnants within densely settled production landscapes? Are these fragments fated to lose species anyway? If not, do other ecological, anthropogenic, and species‐related factors mitigate the effect of fragmentation and offer conservation opportunities? We evaluated, using generalized linear models in an information‐theoretic framework, the effect of local‐ and landscape‐scale factors on the richness, abundance, distribution, and local extinction of 6 primate species in 42 lowland tropical rainforest fragments of the Upper Brahmaputra Valley, northeastern India. On average, the forest fragments lost at least one species in the last 30 years but retained half their original species complement. Species richness declined as proportion of habitat lost increased but was not significantly affected by fragment size and isolation. The occurrence of western hoolock gibbon (Hoolock hoolock) and capped langur (Trachypithecus pileatus) in fragments was inversely related to their isolation and loss of habitat, respectively. Fragment area determined stump‐tailed (Macaca arctoides) and northern pig‐tailed macaque occurrence (Macaca leonina). Assamese macaque (Macaca assamensis) distribution was affected negatively by illegal tree felling, and rhesus macaque (Macaca mulatta) abundance increased as habitat heterogeneity increased. Primate extinction in a fragment was primarily governed by the extent of divergence in its food tree species richness from that in contiguous forests. We suggest the conservation value of these fragments is high because collectively they retained the entire original species pool and individually retained half of it, even a century after fragmentation. Given the extensive habitat and species loss, however, these fragments urgently require protection and active ecological restoration to sustain this rich primate assemblage. Correlaciones Locales y de Paisaje de la Distribución y Persistencia de Primates en los Bosques Lluviosos Remanentes en el Valle del Alto Brahmaputra, Noreste de India     

Range-wide effects of breeding- and nonbreeding-season climate on the abundance of a Neotropical migrant songbird

Geographic variation in the population dynamics of a species can result from regional variability in climate and how it affects reproduction and survival. Identifying such effects for migratory birds requires the integration of population models with knowledge of migratory connectivity between breeding and nonbreeding areas. We used Bayesian hierarchical models with 26 years of Breeding Bird Survey data (1982-2007) to investigate the impacts of breeding- and nonbreeding-season climate on abundance of American Redstarts (Setophaga ruticilla) across the species range. We focused on 15 populations defined by Bird Conservation Regions, and we included variation across routes and observers as well as temporal trends and climate effects. American Redstart populations that breed in eastern North America showed increased abundance following winters with higher plant productivity in the Caribbean where they are expected to overwinter. In contrast, western breeding populations showed little response to conditions in their expected wintering areas in west Mexico, perhaps reflecting lower migratory connectivity or differential effects of winter rainfall on individuals across the species range. Unlike the case with winter climate, we found few effects of temperature prior to arrival in spring (March-April) or during the nesting period (May-June) on abundance the following year. Eight populations showed significant changes in abundance, with the steepest declines in the Atlantic Northern Forest (-3.4%/yr) and the greatest increases in the Prairie Hardwood Transition (4%/yr). This study emphasizes how the effects of climate on populations of migratory birds are context dependent and can vary depending on geographic location and the period of the annual cycle. Such knowledge is essential for predicting regional variation in how populations of a species might vary in their response to climate change.     

A critique of statistical aspects of ecological studies in spatial epidemiology

In this article, the mathematical assumptions of a number of commonly used ecological regression models are made explicit, critically assessed, and related to ecological bias. In particular, the role and interpretation of random effects models are examined. The modeling of spatial variability is considered and related to an underlying continuous spatial field. The examination of such a field with respect to the modeling of risk in relation to a point source highlights an inconsistency in commonly used approaches. A theme of the paper is to examine how plausible individual-level models relate to those used in practice at the aggregate level. The individual-level models acknowledge confounding, within-area variability in exposures and confounders, measurement error and data anomalies and so we can examine how the area-level versions consider these aspects. We briefly discuss designs that efficiently sample individual data and would appear to be useful in environmental settings.     

Defining ecologically relevant scales for spatial protection with long‐term data on an endangered seabird and local prey availability

Human activities are important drivers of marine ecosystem functioning. However, separating the synergistic effects of fishing and environmental variability on the prey base of nontarget predators is difficult, often because prey availability estimates on appropriate scales are lacking. Understanding how prey abundance at different spatial scales links to population change can help integrate the needs of nontarget predators into fisheries management by defining ecologically relevant areas for spatial protection. We investigated the local population response (number of breeders) of the Bank Cormorant (Phalacrocorax neglectus), a range‐restricted endangered seabird, to the availability of its prey, the heavily fished west coast rock lobster (Jasus lalandii). Using Bayesian state‐space modeled cormorant counts at 3 colonies, 22 years of fisheries‐independent data on local lobster abundance, and generalized additive modeling, we determined the spatial scale pertinent to these relationships in areas with different lobster availability. Cormorant numbers responded positively to lobster availability in the regions with intermediate and high abundance but not where regime shifts and fishing pressure had depleted lobster stocks. The relationships were strongest when lobsters 20–30 km offshore of the colony were considered, a distance greater than the Bank Cormorant's foraging range when breeding, and may have been influenced by prey availability for nonbreeding birds, prey switching, or prey ecology. Our results highlight the importance of considering the scale of ecological relationships in marine spatial planning and suggest that designing spatial protection around focal species can benefit marine predators across their full life cycle. We propose the precautionary implementation of small‐scale marine protected areas, followed by robust assessment and adaptive‐management, to confirm population‐level benefits for the cormorants, their prey, and the wider ecosystem, without negative impacts on local fisheries.     

Neglected biological patterns in the residuals

One of the fundamental assumptions underlying linear regression models is that the errors have a constant variance (i.e., homoscedastic). When this assumption is violated, standard errors from a regression can be biased and inconsistent, meaning that the associated p values and 95% confidence intervals cannot be trusted. The assumption of homoscedasticity is made for statistical reasons rather than biological reasons; in most real datasets, some form of heteroscedasticity is likely to exist. However, a survey of the behavioural ecology literature showed that only about 5% of articles explicitly mentioned heteroscedasticity, leaving 95% of articles in which heteroscedasticity was apparently absent. These results strongly indicate that the prevalence of heteroscedasticity is widely under-reported within behavioural ecology. The aim of this article is to raise awareness of heteroscedasticity amongst behavioural ecologists. Using topical examples from fields in behavioural ecology such as sexual dimorphism and animal personality, we highlight the biological importance of considering heteroscedasticity. We also emphasize that researchers should pay closer attention to the variance in their data and consider what factors could cause heteroscedasticity. In addition, we introduce some simple methods of dealing with heteroscedasticity. The two methods we focus on are: (1) incorporating variance functions within a generalised least squares (GLS) framework to model the functional form of heteroscedasticity and; (2) heteroscedasticity-consistent standard error (HCSE) estimators, which can be used when the functional form of heteroscedasticity is unknown. Using case studies, we show how both methods can influence the output from linear regression models. Finally, we hope that more researchers will consider heteroscedasticity as an important source of additional information about the particular biological process being studied, rather than an impediment to statistical analysis.     

Statistical modeling of seasonal and environmental influences on the population dynamics of an estuarine fish community

A statistical modeling study was performed on the population fluctuations of the 15 commonest fish species frequenting the tidal Scheldt estuary in Belgium. These included marine juvenile and seasonal visitors, estuarine residents and diadromous fish species that were recorded on the filter screens of a power plant cooling-water intake between September 1991 and April 2001. The species population abundance was regressed against a candidate set of 6 environmental variables and 13 instrumental variables, accounting for seasonality and long-term trends present in the data. Population abundances of the different species were, in general, best described by seasonal variables. Seasonal components contributed, on average, up to 63.8% of the variance explained by the models. Ten species were found to show a slightly negative, though significant, trend over the period of the survey. Most models also included at least one environmental variable, and 25.4% of the explained variance could be attributed to environmental fluctuations. Of all physico-chemical variables, dissolved oxygen was the most important predictor of fish abundance, suggesting that the estuary suffered from poor water quality during the survey. Temperature, salinity, freshwater flow, suspended solids and chlorophyll a concentrations were minor determinants of fish abundance.Communicated by O. Kinne, Oldendorf/Luhe