Random sampling does not exclude spatial dependence: The importance of neutral models for ecological hypothesis testing

Lájer (2007) notes that, to investigate phytosociological and ecological relationships, many authors apply traditional inferential tests to sets of relevés obtained by non-random methods. Unfortunately, this procedure does not provide reliable support for hypothesis testing because non-random sampling violates the assumptions of independence required by many parametric inferential tests. Instead, a random sampling scheme is recommended. Nonetheless, random sampling will not eliminate spatial autocorrelation. For instance, a classical law of geography holds that everything in a piece of (biotic) space is interrelated, but near objects are more related than distant ones. Because most ecological processes that shape community structure and species coexistence are spatially explicit, spatial autocorrelation is a vital part of almost all ecological data. This means that, independently from the underlying sampling design, ecological data are generally spatially autocorrelated, violating the assumption of independence that is generally required by traditional inferential tests. To overcome this drawback, randomization tests may be used. Such tests evaluate statistical significance based on empirical distributions generated from the sample and do not necessarily require data independence. However, as concerns hypothesis testing, randomization tests are not the universal remedy for ecologists, because the choice of inadequate null models can have significant effects on the ecological hypotheses tested. In this paper, I emphasize the need of developing null models for which the statistical assumptions match the underlying biological mechanisms.     

The net result: evaluating species richness extrapolation techniques for littoral pond invertebrates

1. Total species richness for an assemblage or site is a valuable measure in conservation monitoring and assessment, but protocols for sampling and species richness determination in wetland habitats such as ponds, bogs or mires remain largely unrefined. 2. Techniques for estimation of total richness of an assemblage based upon replicated sampling offer the opportunity to derive useful estimates of total richness based upon small numbers of samples, and limit sampling‐derived disturbance which can be particularly problematic in small aquatic habitats. 3. We quantified the performance of eight of the most commonly encountered estimators of species richness for a variety of littoral zone macrofauna from ponds, comparing estimated richness to maximum richness derived from sampling. 4. Estimates using non‐parametric techniques based on species incidence provided the most accurate and precise estimates. The estimators Chao 2 and incidence‐based coverage estimator (ICE) from this category were reliable and consistent slight over‐estimators; the abundance‐based estimator Chao1 also performed well. 5. Species inventory based on relatively small numbers of samples might be significantly improved by use of non‐parametric estimators for quantification of species richness. 6. Use of non‐parametric estimators of species richness can assist biodiversity inventory by preventing erroneous rankings of habitat richness based upon observed species numbers from limited sampling.     

Structure of fish assemblages along spatial gradients in a deep subtropical reservoir (Itaipu Reservoir,Brazil-Paraguay border)

Synopsis We assessed the structure of the fish assemblages in the Itaipu Reservoir (Paraná River, Brazil-Paraguay) along a longitudinal or river-dam gradient (composed of riverine, transitional and lacustrine zones) and transversal or upstream–downstream gradients of the tributaries (composed of lotic and lentic stretches of tributaries and reservoir shores). We sampled stations distributed along the environmental gradients quarterly during two years. We caught mostly piscivorous, detritivorous and insectivorous fishes. The structure of the whole fish assemblage both at the regional spatial scale and at the zones of each gradient was significantly non-random according to null models and ordination analysis. When the assemblage was broken into groups, the piscivores and detritivores as well as the predators and prey showed significant non-random structure whereas the insectivores, omnivores, herbivores, benthophages and mud-eaters showed random structure. The first groups are those that had more species and the last mentioned are those with fewer species. The tributaries varied more in composition among themselves than the reservoir shores, showing a high heterogeneity in the transversal gradient. The most widespread species was the introduced piscivore Plagioscion squamosissimus. The loricariids were most abundant in the lotic and lentic stretches of the tributaries. We also observed temporal variability in species composition, mainly in the reservoir shores possibly due to the influence of the upstream floodplain on the migratory fish that periodically use the reservoir as feeding habitat. In the tributaries, the temporal changes were less predictable. A combination of habitat preferences and interactions among species, especially predator–prey relations, might be responsible for the observed structure patterns.     

A test for deviation from island-model population structure

The neutral island model forms the basis for several estimation models that relate patterns of genetic structure to microevolutionary processes. Estimates of gene flow are often based on this model and may be biased when the model's assumptions are violated. An appropriate test for violations is to compare FST scores for individual loci to a null distribution based on the average FST taken over multiple loci. A parametric bootstrap method is described here based on Wright's beta-distribution to generate null distributions of FST for each locus. These null distributions account for error introduced by sampling populations, individuals and loci, and also biological sources of error, including variable alleles/locus and inbreeding. Confidence limits can be obtained directly from these distributions. Significant deviations from the island model may be the result of selection, deviations from the island model's migration pattern, nonequilibrium conditions, or other deviations from island-model assumptions. Only strong biases are likely to be detected because of the inherently large sampling variation of FST. Nevertheless, a coefficient, Nb, describing bias in the spread of the beta-distribution in units comparable to the gene flow parameter, Nm, can be obtained for each locus. In samples from populations of the butterfly Coenonympha tullia, the loci Idh-1, Mdh-1, Pgi and Pgm showed significantly lower FST than expected.     

Diet analysis in piscivorous birds: What can the addition of molecular tools offer?

In trophic studies on piscivorous birds, it is vital to know which kind of dietary sample provides the information of interest and how the prey can be identified reliably and efficiently. Often, noninvasively obtained dietary samples such as regurgitated pellets, feces, and regurgitated fish samples are the preferred source of information. Fish prey has usually been identified via morphological analysis of undigested hard parts, but molecular approaches are being increasingly used for this purpose. What remains unknown, however, is which dietary sample type is best suited for molecular diet analysis and how the molecular results compare to those obtained by morphological analysis. Pellets, feces, and regurgitated fish samples of Great Cormorants (Phalacrocorax carbo sinensis) were examined for prey using both morphological hard part analysis and molecular prey identification. The sample types and methods were compared regarding number of species detected (overall and per sample) as well as the prey species composition and its variability among individual samples. Via molecular analysis, significantly higher numbers of prey species were detected in pellets, feces, and fish samples. Of the three sample types, pellets contained the most comprehensive trophic information and could be obtained with the lowest sampling effort. Contrastingly, dietary information obtained from feces was least informative and most variable. For all sample types, the molecular approach outperformed morphological hard part identification regarding the detectable prey spectrum and prey species composition. We recommend the use of pellets in combination with molecular prey identification to study the diet of piscivorous birds.     

Optimizing performance of nonparametric species richness estimators under constrained sampling

Understanding the functional relationship between the sample size and the performance of species richness estimators is necessary to optimize limited sampling resources against estimation error. Nonparametric estimators such as Chao and Jackknife demonstrate strong performances, but consensus is lacking as to which estimator performs better under constrained sampling. We explore a method to improve the estimators under such scenario. The method we propose involves randomly splitting species‐abundance data from a single sample into two equally sized samples, and using an appropriate incidence‐based estimator to estimate richness. To test this method, we assume a lognormal species‐abundance distribution (SAD) with varying coefficients of variation (CV), generate samples using MCMC simulations, and use the expected mean‐squared error as the performance criterion of the estimators. We test this method for Chao, Jackknife, ICE, and ACE estimators. Between abundance‐based estimators with the single sample, and incidence‐based estimators with the split‐in‐two samples, Chao2 performed the best when CV < 0.65, and incidence‐based Jackknife performed the best when CV > 0.65, given that the ratio of sample size to observed species richness is greater than a critical value given by a power function of CV with respect to abundance of the sampled population. The proposed method increases the performance of the estimators substantially and is more effective when more rare species are in an assemblage. We also show that the splitting method works qualitatively similarly well when the SADs are log series, geometric series, and negative binomial. We demonstrate an application of the proposed method by estimating richness of zooplankton communities in samples of ballast water. The proposed splitting method is an alternative to sampling a large number of individuals to increase the accuracy of richness estimations; therefore, it is appropriate for a wide range of resource‐limited sampling scenarios in ecology.     

Partitioning species diversity across landscapes and regions: a hierarchical analysis of alpha, beta, and gamma diversity

Species diversity may be additively partitioned within and among samples (alpha and beta diversity) from hierarchically scaled studies to assess the proportion of the total diversity (gamma) found in different habitats, landscapes, or regions. We developed a statistical approach for testing null hypotheses that observed partitions of species richness or diversity indices differed from those expected by chance, and we illustrate these tests using data from a hierarchical study of forest-canopy beetles. Two null hypotheses were implemented using individual- and sample-based randomization tests to generate null distributions for alpha and beta components of diversity at multiple sampling scales. The two tests differed in their null distributions and power to detect statistically significant diversity components. Individual-based randomization was more powerful at all hierarchical levels and was sensitive to departures between observed and null partitions due to intraspecific aggregation of individuals. Sample-based randomization had less power but still may be useful for determining whether different habitats show a higher degree of differentiation in species diversity compared with random samples from the landscape. Null hypothesis tests provide a basis for inferences on partitions of species richness or diversity indices at multiple sampling levels, thereby increasing our understanding of how alpha and beta diversity change across spatial scales.     

Human Islet Morphology Revisited: Human and Rodent Islets Are Not So Different After All

There has been great interest in understanding how human islets differ from rodent islets. Three major issues about human islet morphology have remained controversial over recent decades: 1) the proportion of the islet made up of β-cells; 2) whether islet cell types have a non-random mantle-core pattern, as seen in rodents, or are randomly scattered throughout the islet; 3) the relation of the different cell types to the blood vessels within the islet, which has implications for intraislet function. We re-examined these issues on immunostained sections of non-diabetic adult human pancreas. The composition of the islets can vary by the analysis method (number vs volume) and by the sampling of islets by size. The majority of adult human islets have clear, non-random clustering of β-cells and blood vessels that penetrate into the β-cell cores. We conclude that although there is far more variability in islet composition both within each human pancreas and among different human pancreas than in rodent pancreas, the islet architecture is not so different between the species. The intrapancreatic variability raises important questions about how islets evolve and function throughout life and how this might relate to the pathogenesis of diabetes.     

Estimating Detection Probabilities from Sign of Collared Peccary

ABSTRACT Determining presence or absence of collared peccaries (Pecari tajacu) from surveys of sign (tracks and feces) requires information on whether animals in sample units are detected. We estimated detection probabilities of collared peccary from sign surveys using occupancy models. Because it was unlikely that residence status of collared peccary in sampling units remained the same over a survey season, which is a primary assumption of occupancy models, we first determined the time interval for which to pool data. We then examined the influence of rainfall and peccary abundance on detection probabilities. We placed 90 sign stations (25-m-diam circular plots) throughout Chaparral Wildlife Management Area, south Texas, USA. We surveyed plots weekly for the presence or non-presence of collared peccary during 2 11-week sampling seasons in spring and fall 2003. We examined sign data weekly and we pooled the data in intervals from 2 weeks to 5 weeks. Estimates of detection probabilities increased from 1 week to 3 weeks of pooled data and leveled off thereafter. We needed a 3-week time interval to meet the assumption of unchanging residence status. Using sign data pooled in 3-week increments, detection probabilities were influenced by areas that differed in peccary abundance, but they were not influenced by rainfall. Estimates of detection probabilities ranged from 0.43 to 0.77 for 3-week time intervals. Sign surveys and occupancy modeling of data can be used to measure spatial patterns of collared peccary in south Texas as long as multiple 3-week time intervals are sampled.     

Effects of habitat characteristics and interspecific interactions on co-occurrence patterns of saproxylic beetles breeding in tree boles after forest fire: null model analyses

It is often suggested that habitat attributes and interspecific interactions can cause non-random species co-occurrence patterns, but quantifying their contributions can be difficult. Null models that systematically exclude and include habitat effects can give information on the contribution of these factors to community assembly. In the boreal forest, saproxylic beetles are known to be attracted to recently burned forests where they breed in dead and dying trees. We examined whether species co-occurrences of saproxylic beetles that develop in, and emerge from, boles of recently burned trees show non-random patterns. We also estimated the extent to which both the post-fire habitat attributes and interspecific interactions among beetles contribute to such patterns. We sampled tree boles encompassing key attributes (tree species, tree size/dbh and burn severity) that are thought to characterize species–habitat associations of saproxylic beetles, a proposition that we tested using indicator species analysis. Two null models with no habitat constraints (“unconstrained”) indicated that a total of 29.4% of the species pairs tested had significant co-occurrence patterns. Habitat-constrained null models indicated that most of the detected species aggregations (72%) and segregations (59%) can be explained by shared and distinct species–habitat relationships, respectively. The assembly pattern was also driven by interspecific interactions, of which some were modulated by habitat; for example, predator and prey species tended to co-occur in large-sized trees (a proxy of available bark/wood food resource primarily for the prey). In addition, some species segregation suggesting antagonistic, competitive, or prey–predator interactions were evident after accounting for the species’ affinities for the same tree species. Overall, our results suggest that an intimate link between habitat and interspecific interactions can have important roles for community assembly of saproxylic assemblages even following disturbance by fire. We also show that a systematic application of null models can offer insight into the mechanisms behind the assembly of ecological communities.     

Populations of strongyloid nematode infective stages in sheep pastures: Comparison between direct pasture sampling and tracer lambs as estimators of larval abundance

Waller P.J., Dobson R.J., Donald A.D. and Thomas R.J. 1981. Populations of strongyloid nematode infective stages in sheep pastures : comparison between direct pasture sampling and tracer lambs as estimators of larval abundance. International Journal for Parasitology11: 359–367. Over a 2-year period, numbers of infective larvae in samples of pasture herbage, and numbers of worms in previously worm-free “tracer” lambs allowed 4 weeks grazing, were compared as estimators of the abundance of infective larvae on pastures.Transformation of sample estimates of infective larval numbers per 100 g herbage dry matter (DM) and of worm numbers in tracer sheep, according to the expression y = log₁₀ (x+25), was effective in stabilizing variances. Estimates of error variance for each technique did not differ significantly among the genera Haemonchus, Ostertagia or Trichostrongylus and the pooled estimate for the tracer sheep method was 4 times greater than that for pasture sampling. From these results, more tracer sheep than pasture samples would be required to achieve the same level of precision with the two techniques. Using conventional statistical methods, the effects of numbers of pasture samples or tracer sheep on the size of the difference between two means which can be detected as significant and on the width of the confidence interval about a single mean, are illustrated. These can be used as a guide in the choice of sample sizes. Error variances for Nematodirus spp. were significantly less than for the other genera by pasture sampling, and greater by the tracer sheep technique. Possible reasons for this are discussed, but it is concluded that pasture sampling is likely to be much the more precise method for estimating Nematodirus spp. infective larval availability.Changes with time in infective larval abundance, for Haemonchus, Trichostrongylus and Nematodirus spp. which were present in moderate to low numbers, followed similar trends by both techniques. However, for Ostertagia spp. larvae, which were much more abundant, peak levels were defined more sharply and occurred earlier by pasture sampling than by the tracer method. It is suggested that worm counts from tracer sheep, especially those grazing for 4 weeks rather than shorter periods, may systematically underestimate the infective larval population on pasture at high levels of abundance owing to density-dependent worm loss.     

Scaling Occupancy Estimates up to Abundance for Wolves

Management of wildlife populations often requires reliable estimates of population size or distribution. Estimating abundance can be logistically difficult, and occupancy models have been used as a less expensive proxy for abundance estimation. Another alternative is to use independent estimates of home-range size and mean group size to directly scale occupancy estimates up to abundance. We used simulations to explore when scaling occupancy up to abundance is reliable, and as an example we applied an occupancy approach to estimate abundance of wolves (Canis lupus) from roadside snow-tracking surveys in northern Wisconsin, USA, in 2016 and 2018. Estimates of wolf abundance were plausible and compared favorably with independent estimates produced by territory mapping, and snow-tracking data requirements were lower than for territory mapping. Simulation results suggested that reasonable abundance estimates could be obtained under some conditions but also that severe positive bias could result under other conditions, especially when populations were small and dispersed, home range size was small, and areal sampling units were large. Positive bias in abundance estimates occurs because of closure assumption violations when tracks from a single wolf or pack are detected in >1 sample unit, and the sum of the sample unit areas where tracks were detected exceed the sum of the home range areas. Bias was minimized when sampling units were small relative to home range size or when sampling units were route segments that approximate point sample units, and when home ranges were highly aggregated. We conclude that, although caution is warranted when scaling occupancy estimates up to abundance, scaled occupancy models can provide feasible and reliable estimates of abundance, assuming home range size and mean group size are accurately known or estimated, sampling units are appropriately chosen, and covariates that aggregate home ranges can be used to accurately predict occupancy probability. © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.     

The empirical Bayes approach as a tool to identify non-random species associations

A statistical challenge in community ecology is to identify segregated and aggregated pairs of species from a binary presence–absence matrix, which often contains hundreds or thousands of such potential pairs. A similar challenge is found in genomics and proteomics, where the expression of thousands of genes in microarrays must be statistically analyzed. Here we adapt the empirical Bayes method to identify statistically significant species pairs in a binary presence–absence matrix. We evaluated the performance of a simple confidence interval, a sequential Bonferroni test, and two tests based on the mean and the confidence interval of an empirical Bayes method. Observed patterns were compared to patterns generated from null model randomizations that preserved matrix row and column totals. We evaluated these four methods with random matrices and also with random matrices that had been seeded with an additional segregated or aggregated species pair. The Bayes methods and Bonferroni corrections reduced the frequency of false-positive tests (type I error) in random matrices, but did not always correctly identify the non-random pair in a seeded matrix (type II error). All of the methods were vulnerable to identifying spurious secondary associations in the seeded matrices. When applied to a set of 272 published presence–absence matrices, even the most conservative tests indicated a fourfold increase in the frequency of perfectly segregated “checkerboard” species pairs compared to the null expectation, and a greater predominance of segregated versus aggregated species pairs. The tests did not reveal a large number of significant species pairs in the Vanuatu bird matrix, but in the much smaller Galapagos bird matrix they correctly identified a concentration of segregated species pairs in the genus Geospiza. The Bayesian methods provide for increased selectivity in identifying non-random species pairs, but the analyses will be most powerful if investigators can use a priori biological criteria to identify potential sets of interacting species.     

Macrobenthos of a tidal impoundment at the Mai Po Marshes Nature Reserve,Hong Kong

The composition and spatial distribution patterns of the macrobenthic faunal assemblages of an 8-ha tidal impoundment operated as a traditional shrimp pond at the Mai Po Marshes Nature Reserve, Hong Kong, were studied in relation to temporal changes in local environmental conditions. Species richness, abundance and biomass of macrobenthos across 5 different sub-habitats (seaward, middle, and landward parts of open water unvegetated areas, and Phragmites- and Kandelia-dominated, vegetated areas) within the pond were examined bimonthly between January 1997 and January 1998. Grab samples were collected randomly within the sub-habitats. Key physical environmental parameters of the sampling sites were also measured. A total of 46 species of macrobenthos was recorded: 11 polychaetes, 11 molluscs, 13 crustaceans and 11 insects. Mean species density in the five sub-habitats ranged from 0 to 3907 indm^–2, with mean biomass ranging from 0 to 96.9 gm^–2. The macrobenthos showed spatial and temporal differences among the sub-habitats and across sampling times. Species abundances of Polychaeta, Mollusca and Crustacea were significantly higher in the three open water areas than in the two vegetated (Phragmites- and Kandelia-dominated) areas, with an inverse pattern for Insecta. There were no clear temporal patterns although abundance and biomass generally increased in the cooler months. Results of a canonical correspondence analysis suggest that macrobenthic species richness, abundance and biomass in the open areas were positively correlated with salinity, while water depth, dissolved oxygen and sediment organic matter content had little relationship with the macrobenthic assemblage parameters. Ordination by multi-dimensional scaling suggests that different habitats supported distinct macrobenthic assemblages. The macrobenthic assemblage in the tidal pond was less species rich but denser than those in the neighboring tidal mangrove and mudflat, suggesting that conversion of these areas into extensively managed tidal aquaculture ponds results in reduced species richness in tropical mangrove habitats.     

Stabilizing effects of spatial heterogeneity in predator-prey systems

A general predator is assumed to divide its hunting time between two sub-habitats with different prey species, spending a larger fraction (φ) of search time in an area as the relative prey abundance there increases. This always causes switching in the model, and changes a functional response from one that imposes a risk on the average prey that decreases with prey density in the direction of one that imposes an increasing risk. I discuss the conditions for a response that is density dependent, and those predatory attributes that make such a response more likely. Transit time between subhabitats always increases the density dependent effect, and is necessary for “system stability” in a Lotka-Volterra model with two prey species. Experiments have confirmed the model's basic assumption. General predators do not fit easily into classical predator-prey models of simple “closed” communities, and then the degree of density dependence of the functional response becomes a useful measure of a predator's short-term stabilizing effect on a prey species. The model demonstrates how spatial heterogeneity can be stabilizing.     

TEMPORAL VARIATION IN ALLELE FREQUENCIES: TESTING THE RIGHT HYPOTHESIS

Although standard statistical tests (such as contingency chi-square or G tests) are not well suited to the analysis of temporal changes in allele frequencies, they continue to be used routinely in this context. Because the null hypothesis stipulated by the test is violated if samples are temporally spaced, the true probability of a significant test statistic will not equal the nominal α level, and conclusions drawn on the basis of such tests can be misleading. A generalized method, applicable to a wide variety of organisms and sampling schemes, is developed here to estimate the probability of a significant test statistic if the only forces acting on allele frequencies are stochastic ones (i.e., sampling error and genetic drift). Results from analyses and simulations indicate that the rate at which this probability increases with time is determined primarily by the ratio of sample size to effective population size. Because this ratio differs considerably among species, the seriousness of the error in using the standard test will also differ. Bias is particularly strong in cases in which a high percentage of the total population can be sampled (for example, endangered species). The model used here is also applicable to the analysis of parent-offspring data and to comparisons of replicate samples from the same generation. A generalized test of the hypothesis that observed changes in allele frequency can be satisfactorily explained by drift follows directly from the model, and simulation results indicate that the true α level of this adjusted test is close to the nominal one under most conditions.     

Should fatty acid signature proportions sum to 1 for diet estimation?

Knowledge of predator diets, including how diets might change through time or differ among predators, provides essential insights into their ecology. Diet estimation therefore remains an active area of research within quantitative ecology. Quantitative fatty acid signature analysis (QFASA) is an increasingly common method of diet estimation. QFASA is based on a data library of prey signatures, which are vectors of proportions summarizing the fatty acid composition of lipids, and diet is estimated as the mixture of prey signatures that most closely approximates a predator’s signature. Diets are typically estimated using proportions from a subset of all fatty acids that are known to be solely or largely influenced by diet. Given the subset of fatty acids selected, the current practice is to scale their proportions to sum to 1.0. However, scaling signature proportions has the potential to distort the structural relationships within a prey library and between predators and prey. To investigate that possibility, we compared the practice of scaling proportions with two alternatives and found that the traditional scaling can meaningfully bias diet estimators under some conditions. Two aspects of the prey types that contributed to a predator’s diet influenced the magnitude of the bias: the degree to which the sums of unscaled proportions differed among prey types and the identifiability of prey types within the prey library. We caution investigators against the routine scaling of signature proportions in QFASA.     

Effect of variation in forest harvest intensity on winter occupancy of Barred Owls and Eastern Screech‐Owls in deciduous forests of the east‐central United States

Responses of resident owls to changes in forest structure associated with forest management in the Central Hardwood Forest Region of the United States have not been widely studied. We estimated the winter occupancy of Barred Owls (Strix varia) and Eastern Screech‐Owls (Megascops asio) in forests with varying levels of timber harvest in southern Indiana. Surveys were conducted from 2009 to 2013 in two state forests undergoing active harvesting, a national forest unit with little recent harvesting, and a forested state park with no harvesting since about 1940. We hypothesized that 1) Barred Owl occupancy would vary inversely with harvesting intensity because they prefer mature forest, 2) Eastern Screech‐Owl occupancy would be greatest in the actively managed forests given their affinity for edge habitat, and 3) Eastern Screech‐Owls would avoid Barred Owl sampling areas and, thus, Barred Owl predation. Barred Owl occupancy was lowest in the non‐harvested state park relative to other areas, and Eastern Screech‐Owls were less likely to co‐occur in Barred Owl sampling areas. We found no evidence that forest management was inversely related to Barred Owl occupancy or that active edge creation associated with forest management increased the magnitude of Eastern Screech‐Owl occupancy. Reduced rates of Barred Owl occupancy in the state park may have resulted from high levels of recreational activity, whereas increased rates of Eastern Screech‐Owl occupancy in the park may have resulted from ample hunting opportunities in an environment with fewer Barred Owl predators. Recreational activity, prey availability, and interspecific antagonism likely have greater influences than timber harvesting on winter site occupancy of these owls in our study areas.