Null model analysis of species nestedness patterns

Nestedness is a common biogeographic pattern in which small communities form proper subsets of large communities. However, the detection of nestedness in binary presence-absence matrices will be affected by both the metric used to quantify nestedness and the reference null distribution. In this study, we assessed the statistical performance of eight nestedness metrics and six null model algorithms. The metrics and algorithms were tested against a benchmark set of 200 random matrices and 200 nested matrices that were created by passive sampling. Many algorithms that have been used in nestedness studies are vulnerable to type I errors (falsely rejecting a true null hypothesis). The best-performing algorithm maintains fixed row and fixed column totals, but it is conservative and may not always detect nestedness when it is present. Among the eight indices, the popular matrix temperature metric did not have good statistical properties. Instead, the Brualdi and Sanderson discrepancy index and Cutler's index of unexpected presences performed best. When used with the fixed-fixed algorithm, these indices provide a conservative test for nestedness. Although previous studies have revealed a high frequency of nestedness, a reanalysis of 288 empirical matrices suggests that the true frequency of nested matrices is between 10% and 40%.     

Random binary matrices in biogeographical ecology—Instituting a good neighbor policy

Binary matrices originating from presence/absence data on species (rows) distributed over sites (columns) have been a subject of much controversy in ecological biogeography. Under the null hypothesis that every matrix is equally likely, the distributions of some test statistics measuring co-occurrences between species are sought, conditional on the row and column totals being fixed at the values observed for some particular matrix. Many ad hoc methods have been proposed in the literature, but at least some of them do not provide uniform random samples of matrices. In particular, some swap algorithms have not accounted for the number of neighbors each matrix has in the universe of matrices with a set of fixed row and column sums. We provide a Monte-Carlo method using random walks on graphs that gives correct estimates for the distributions of statistics. We exemplify its use with one statistic.     

Testing sexual segregation and aggregation: old ways are best

The study of sexual segregation has received increasing attention over the last two decades. Several hypotheses have been proposed to explain the existence of sexual segregation, such as the "predation risk hypothesis," the "forage selection hypothesis," and the "activity budget hypothesis." Testing which hypothesis drives sexual segregation is hampered, however, by the lack of consensus regarding a formal measurement of sexual segregation. By using a derivation of the well-known chi-square (here called the sexual segregation and aggregation statistic [SSAS]) instead of existent segregation coefficients, we offer a reliable way to test for temporal variation in the occurrence of sexual segregation and aggregation, even in cases where a large proportion of animals are observed alone. A randomization procedure provides a test for the null hypothesis of independence of the distributions of males and females among the groups. The usefulness of SSAS in the study of sexual segregation is demonstrated with three case studies on ungulate populations belonging to species with contrasting life histories and annual grouping patterns (isard, red deer, and roe deer). The existent segregation coefficients were unreliable since, for a given value, sexual segregation could or could not occur. Similarly, the existent segregation coefficients performed badly when males and females aggregated. The new SSAS was not prone to such limitations and allowed clear conclusions regarding whether males and females segregate, aggregate, or simply mix at random applicable to all species.     

Nearest neighbor methods for testing reflexivity

Nearest neighbor (NN) methods are widely employed for drawing inferences about spatial point patterns of two or more classes. We introduce a method for testing reflexivity in the NN structure (i.e., NN reflexivity) based on a contingency table which will be called reflexivity contingency table (RCT) henceforth. The RCT is based on the NN relationships among the data points and was used for testing niche specificity in literature, but we demonstrate that it is actually more appropriate for testing the NN reflexivity pattern. We derive the asymptotic distribution of the entries of the RCT under random labeling and introduce tests of reflexivity based on these entries. We also consider Pielou’s approach on RCT and show that it is not appropriate for completely mapped spatial data. We determine the appropriate null hypotheses and the underlying conditions/assumptions required for all tests considered. We investigate the finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two real-life ecological data sets.     

Role of competition and predation in determining habitat occupancy of Cerithiidae (Gastropoda: Prosobranchia) on the rocky,intertidal, Red Sea coasts of Sinai

Six cerithiid snail species occur on rocky intertidal flats along the Sinai coasts of the Red Sea: Clypeomorus moniliferum, Cerithium caeruleum, C. scabridum, C. columna, Clypeomorus tuberculatum and Cerithium echinatum. The present study, conducted at 22 stations covering almost the whole length of Sinai, covered the 4 yr period from October 1972 to August 1976, and describes the habitat occupancy of 5 of these species (C. echinatum is excluded for lack of data). Several of these species (sometimes all) often occur together, and in such cases are distincly segregated by habitat. However all species considerably overlap in their distribution along the axes of four major interrelated abiotic gradients, thus excluding the possibility that habitat segregation is determined by larval settlement preferences. Other distributional patterns observed at some sites, such as lack of overlap or contact between belts of the various species and the relative abundance of food available to all species, make postlarval competitive interactions unlikely. The existence and the degree of proximity of a coral reef with its associated predatory fishes, influence the cerithiids' distributional patterns. Differences between the cerithiid species in their vulnerability to fish predation, associated with differences between sites in the abundance and the accessibility of predatory fishes, and in the availability of refuges for each cerithiid species, can satisfactorily explain the observed distributional patterns including co-occurrence with habitat segregation. It is proposed that habitat segregation is caused by predation on young stages by generalist fishes which may totally eliminate a certain species at a given site; the same site may provide refuges for recruits of another species, allowing these to survive to an advanced age. In general, the flat's structural complexity is associated with its diversity of refuges from predation, and hence with the number of co-existing species. This mechanism for co-existence and habitat segregation in tropical Cerithiidae may also be instrumental in maintaining the high species diversity of other tropical benthic communities.Paper No. 12 in the series Colonization of the Eastern Mediterrancan by Red Sea species immigrating through the Suez Canal     

Reducing over-reporting of deterministic co-occurrence patterns in biotic communities

Null models of species co-occurrence are widely used to infer the existence of various ecological processes. Here we investigate the susceptibility of the most commonly used of these models (the C-score in conjunction with the sequential swap algorithm) to type 1 and type 2 errors. To do this we use simulated datasets with a range of numbers of sites, species and coefficients of variation (CV) in species abundance. We find that this model is particularly susceptible to type 1 errors when applied to large matrices and those with low CV in species abundance. As expected, type 2 error rates decrease with increasing numbers of sites and species, although they increase with increasing CV in species abundance. Despite this, power remains acceptable over a wide range of parameter combinations. The susceptibility of this analytical method to type 1 errors indicates that many previous studies may have incorrectly reported the existence of deterministic patterns of species co-occurrence. We demonstrate that in order to overcome the problem of high type 1 error rates, the number of swaps used to generate null distributions for smaller matrices needs to be increased to over 50,000 swaps (well beyond the 5000 commonly used in published analyses and the 30,000 suggested by Lehsten and Harmand, 2006). We also show that this approach reduces type 1 error rates in real datasets. However, even using this solution, larger datasets still suffer from high type 1 error rates. Such datasets therefore require the use of very large numbers of swaps, which calls for improvements in the most commonly used software. In general, users of this powerful analytical method must be aware that they need surprisingly large numbers of swaps to obtain unbiased estimates of structuring in biotic communities.     

Spatial variance in abundance and occupancy of corals across broad geographic scales

Species assemblages vary in structure due to a wide variety of processes operating at ecological and much broader biogeographical scales. Cross-scale studies of assemblage structure are necessary to fully understand this variability. Here, we evaluate the abundance and occupancy patterns of hierarchically sampled coral assemblages in three habitats (reef flat, crest, and slope) and five regions (Indonesia, Papua New Guinea, the Solomon Islands, American Samoa, and the Society Islands) across the west-central Pacific Ocean. Specifically, we compare two alternative models that unify spatial variance and occupancy via the negative binomial distribution. The first assumes a power-law scaling between the mean and variance of abundance; the second assumes a quadratic variance-mean relationship and a constant abundance-invariant aggregation parameter. Surprisingly, the well-established power-law model performs worse than the model assuming abundance-invariant aggregation, for both variance-mean and occupancy-abundance relationships. We also find strong evidence for regional and habitat variation in these relationships and in the levels of aggregation estimated by the abundance-invariant aggregation model. Among habitats, corals on reef flats exhibited lower occupancy and higher levels of aggregation compared to reef crests and slopes. Among regions, low occupancy and high aggregation were most pronounced across all habitats in American Samoa. These patterns may be related to habitat and regional differences in disturbance and recovery processes. Our results suggest that the spatial scaling of abundance and occupancy is sensitive to processes operating among these habitats and at regional scales. However, the consistency of these relationships across species within assemblages suggests that a theoretical unification of spatial variance and occupancy patterns is indeed possible.     

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 memory of spatial patterns: changes in local abundance and aggregation in a tropical forest

The current spatial pattern of a population is the result of previous individual birth, death, and dispersal events. We present a simple model followed by a comparative analysis for a species-rich plant community to show how the current spatial aggregation of a population may hold information about recent population dynamics. Previous research has shown how locally restricted seed dispersal often leads to stronger aggregation in less abundant populations than it does in more abundant populations. In contrast, little is known about how changes in the local abundance of a species may affect the spatial distribution of individuals. If the level of aggregation within a species depends to some extent on the abundance of the species, then changes in abundance should lead to subsequent changes in aggregation. However, an overall change of spatial pattern relies on many individual birth and death events, and a surplus of deaths or births may have short-term effects on aggregation that are opposite to the long-term change predicted by the change in abundance. The change in aggregation may therefore lag behind the change in abundance, and consequently, the current aggregation may hold information about recent population dynamics. Using an individual-based simulation model with local dispersal and density-dependent competition, we show that, on average, recently growing populations should be more aggregated than shrinking populations of the same current local abundance. We tested this hypothesis using spatial data on individuals from a long-term tropical rain forest plot, and find support for this relationship in canopy trees, but not in understory and shrub species. On this basis we argue that current spatial aggregation is an important characteristic that contains information on recent changes in local abundance, and may be applied to taxonomic groups where dispersal is limited and within-species aggregation is observed.     

Species, functional groups, and thresholds in ecological resilience

The cross-scale resilience model states that ecological resilience is generated in part from the distribution of functions within and across scales in a system. Resilience is a measure of a system's ability to remain organized around a particular set of mutually reinforcing processes and structures, known as a regime. We define scale as the geographic extent over which a process operates and the frequency with which a process occurs. Species can be categorized into functional groups that are a link between ecosystem processes and structures and ecological resilience. We applied the cross-scale resilience model to avian species in a grassland ecosystem. A species' morphology is shaped in part by its interaction with ecological structure and pattern, so animal body mass reflects the spatial and temporal distribution of resources. We used the log-transformed rank-ordered body masses of breeding birds associated with grasslands to identify aggregations and discontinuities in the distribution of those body masses. We assessed cross-scale resilience on the basis of 3 metrics: overall number of functional groups, number of functional groups within an aggregation, and the redundancy of functional groups across aggregations. We assessed how the loss of threatened species would affect cross-scale resilience by removing threatened species from the data set and recalculating values of the 3 metrics. We also determined whether more function was retained than expected after the loss of threatened species by comparing observed loss with simulated random loss in a Monte Carlo process. The observed distribution of function compared with the random simulated loss of function indicated that more functionality in the observed data set was retained than expected. On the basis of our results, we believe an ecosystem with a full complement of species can sustain considerable species losses without affecting the distribution of functions within and across aggregations, although ecological resilience is reduced. We propose that the mechanisms responsible for shaping discontinuous distributions of body mass and the nonrandom distribution of functions may also shape species losses such that local extinctions will be nonrandom with respect to the retention and distribution of functions and that the distribution of function within and across aggregations will be conserved despite extinctions.     

Effects of Patch Size and Type of Coffee Matrix on Ithomiine Butterfly Diversity and Dispersal in Cloud-Forest Fragments

Abstract: Determining the permeability of different types of landscape matrices to animal movement is essential for conserving populations in fragmented landscapes. We evaluated the effects of habitat patch size and matrix type on diversity, isolation, and dispersal of ithomiine butterflies in forest fragments surrounded by coffee agroecosystems in the Colombian Andes. Because ithomiines prefer a shaded understory, we expected the highest diversity and abundance in large fragments surrounded by shade coffee and the lowest in small fragments surrounded by sun coffee. We also thought shade coffee would favor butterfly dispersal and immigration into forest patches. We marked 9675 butterflies of 39 species in 12 forest patches over a year. Microclimate conditions were more similar to the forest interior in the shade‐coffee matrix than in the sun‐coffee matrix, but patch size and matrix type did not affect species richness and abundance in forest fragments. Furthermore, age structure and temporal recruitment patterns of the butterfly community were similar in all fragments, independent of patch size or matrix type. There were no differences in the numbers of butterflies flying in the matrices at two distances from the forest patch, but their behavior differed. Flight in the sun‐coffee matrix was rapid and directional, whereas butterflies in shade‐coffee matrix flew slowly. Seven out of 130 recaptured butterflies immigrated into patches in the shade‐coffee matrix, and one immigrated into a patch surrounded by sun coffee. Although the shade‐coffee matrix facilitated movement in the landscape, sun‐coffee matrix was not impermeable to butterflies. Ithomiines exhibited behavioral plasticity in habitat use and high mobility. These traits favor their persistence in heterogeneous landscapes, opening opportunities for their conservation. Understanding the dynamics and resource requirements of different organisms in rural landscapes is critical for identifying management options that address both animals’ and farmers’ needs.     

Analysis of the small-scale spatial patterns of free-living marine nematodes from tidal flats in the East Frisian Wadden Sea

Serial samples with a multiple corer were taken in order to understand the small-scale aggregation patterns in the nematode community. A total of 77 species was found in the sample. Fifteen dominant nematode species were examined by means of a dispersion analysis. Only one species (Metachromadora scotlandica) may be considered randomly distributed. A variogram analysis gave no proof of aggregation in that species, but all the other (aggregated) species displayed different spatial patterns: (1) a maximum/aggregation at the sample's margin, (2) two maxima/aggregations in the centre of the sample, (3) aggregation of individuals distributed at random over the entire sample (Metalinhomoeus typicus) and (4) aggregation of individuals distributed at random only in the centre of the sample (Paralinhomoeus ilenensis). These results allow the prognosis that distribution patterns are repetitive in five species (Microlaimus conothelis, M. marinus, Odontophora rectangula, Oncholaimellus calvadosicus, Viscosia rustica). Finally, by means of MDS-ordination (based on cosine similarity) two nematode associations were distinguished: one group represented by diatom-feeders (sensu lato), the other one comprised of DOM-users (sensu lato). Received: 13 May 1998 / Accepted: 15 January 1999     

On the use of nearest neighbor contingency tables for testing spatial segregation

For two or more classes (or types) of points, nearest neighbor contingency tables (NNCTs) are constructed using nearest neighbor (NN) frequencies and are used in testing spatial segregation of the classes. Pielou’s test of independence, Dixon’s cell-specific, class-specific, and overall tests are the tests based on NNCTs (i.e., they are NNCT-tests). These tests are designed and intended for use under the null pattern of random labeling (RL) of completely mapped data. However, it has been shown that Pielou’s test is not appropriate for testing segregation against the RL pattern while Dixon’s tests are. In this article, we compare Pielou’s and Dixon’s NNCT-tests; introduce the one-sided versions of Pielou’s test; extend the use of NNCT-tests for testing complete spatial randomness (CSR) of points from two or more classes (which is called CSR independence, henceforth). We assess the finite sample performance of the tests by an extensive Monte Carlo simulation study and demonstrate that Dixon’s tests are also appropriate for testing CSR independence; but Pielou’s test and the corresponding one-sided versions are liberal for testing CSR independence or RL. Furthermore, we show that Pielou’s tests are only appropriate when the NNCT is based on a random sample of (base, NN) pairs. We also prove the consistency of the tests under their appropriate null hypotheses. Moreover, we investigate the edge (or boundary) effects on the NNCT-tests and compare the buffer zone and toroidal edge correction methods for these tests. We illustrate the tests on a real life and an artificial data set.     

A new technique for ordering asymmetrical three-dimensional data sets in ecology

The aim of this paper is to tackle the problem that arises from asymmetrical data cubes formed by two crossed factors fixed by the experimenter (factor A and factor B, e.g., sites and dates) and a factor which is not controlled for (the species). The entries of this cube are densities in species. We approach this kind of data by the comparison of patterns, that is to say by analyzing first the effect of factor B on the species-factor A pattern, and second the effect of factor A on the species-factor B pattern. The analysis of patterns instead of individual responses requires a correspondence analysis. We use a method we call Foucart's correspondence analysis to coordinate the correspondence analyses of several independent matrices of species x factor A (respectively B) type, corresponding to each modality of factor B (respectively A). Such coordination makes it possible to evaluate the effect of factor B (respectively A) on the species-factor A (respectively B) pattern. The results obtained by such a procedure are much more insightful than those resulting from a classical single correspondence analysis applied to the global matrix that is obtained by simply unrolling the data cube, juxtaposing for example the individual species x factor A matrices through modalities of factor B. This is because a single global correspondence analysis combines three effects of factors in a way that cannot be determined from factorial maps (factor A, factor B, and factor A x factor B interaction) whereas the applications of Foucart's correspondence analysis clearly discriminate two different issues. Using two data sets, we illustrate that this technique proves to be particularly powerful in the analyses of ecological convergence which include several distinct data sets and in the analyses of spatiotemporal variations of species distributions.     

A trait-based test for habitat filtering: convex hull volume

Community assembly theory suggests that two processes affect the distribution of trait values within communities: competition and habitat filtering. Within a local community, competition leads to ecological differentiation of coexisting species, while habitat filtering reduces the spread of trait values, reflecting shared ecological tolerances. Many statistical tests for the effects of competition exist in the literature, but measures of habitat filtering are less well-developed. Here, we present convex hull volume, a construct from computational geometry, which provides an n-dimensional measure of the volume of trait space occupied by species in a community. Combined with ecological null models, this measure offers a useful test for habitat filtering. We use convex hull volume and a null model to analyze California woody-plant trait and community data. Our results show that observed plant communities occupy less trait space than expected from random assembly, a result consistent with habitat filtering.     

High intervality explained by phylogenetic constraints in host-parasite webs

The finding of invariant structures in species interaction webs is of central importance for ecology, with the greatest challenge remaining the elucidation of the processes governing these universal web patterns. Here we quantify the degree of intervality of seven fish-metazoan and 33 mammal-flea webs, i.e., the number of irreducible gaps in parasite diets along the host spectrum, and then challenge the idea that some invariant structures may emerge in host-parasite webs. Using a null model of random links between parasite and host species we find that empirical host-parasite webs exhibit a strong bias toward contiguity of parasite diet, i.e., toward intervality. Going one step further, we demonstrate that a null model with phylogenetic constraints on host-parasite links produced webs very similar to empirical ones, particularly when phylogenetic constraints occur at the family level, that is, when two hosts from the same family are more likely to be infected than two random hosts. In addition, we propose a new standardized measure of intervality which describes a novel "facet" of natural networks as it is independent of connectance or web size. We suggest using this measure as a surrogate of web maturity or saturation as phylogenetic constraints can drive webs toward intervality.     

Simultaneous-count models to estimate abundance from counts of unmarked individuals with imperfect detection

We developed a method to estimate population abundance from simultaneous counts of unmarked individuals over multiple sites. We considered that at each sampling occasion, individuals in a population could be detected at 1 of the survey sites or remain undetected and used either multinomial or binomial simultaneous-count models to estimate abundance, the latter being equivalent to an N-mixture model with one site. We tested model performance with simulations over a range of detection probabilities, population sizes, growth rates, number of years, sampling occasions, and sites. We then applied our method to 3 critically endangered vulture species in Cambodia to demonstrate the real-world applicability of the model and to provide the first abundance estimates for these species in Cambodia. Our new approach works best when existing methods are expected to perform poorly (i.e., few sites and large variation in abundance among sites) and if individuals may move among sites between sampling occasions. The approach performed better when there were >8 sampling occasions and net probability of detection was high (>0.5). We believe our approach will be useful in particular for simultaneous surveys at aggregation sites, such as roosts. The method complements existing approaches for estimating abundance of unmarked individuals and is the first method designed specifically for simultaneous counts.     

Setting conservation priorities for migratory networks under uncertainty

Conserving migratory species requires protecting connected habitat along the pathways they travel. Despite recent improvements in tracking animal movements, migratory connectivity remains poorly resolved at a population level for the vast majority of species, thus conservation prioritization is hampered. To address this data limitation, we developed a novel approach to spatial prioritization based on a model of potential connectivity derived from empirical data on species abundance and distance traveled between sites during migration. We applied the approach to migratory shorebirds of the East Asian‐Australasian Flyway. Conservation strategies that prioritized sites based on connectivity and abundance metrics together maintained larger populations of birds than strategies that prioritized sites based only on abundance metrics. The conservation value of a site therefore depended on both its capacity to support migratory animals and its position within the migratory pathway; the loss of crucial sites led to partial or total population collapse. We suggest that conservation approaches that prioritize sites supporting large populations of migrants should, where possible, also include data on the spatial arrangement of sites.