Presence-absence Matrices Research Articles

Binary matrices and checkerboard distributions of birds in the Bismarck Archipelago

Aim We examine a presence–absence matrix of the avifauna of the Bismarck Archipelago, for which the concept of competitively driven community assembly rules was formulated, to determine whether data support widespread competitive determination of geographical distributions. Location Bismarck Archipelago. Methods We obtained occurrences of 154 land and freshwater bird species on 31 islands. We calculated the observed number of checkerboards for all species pairs, for congeneric species pairs and for pairs of species within guilds, and employed randomization techniques to detect unusual co-occurrence patterns. Results Compared with random expectations, there are excesses of checkerboard pairs within both genera and defined guilds, but a detailed examination shows that competition is a cogent possible explanation in few instances. For many checkerboard pairs, species are not widely interspersed but are regionally allopatric, which probably reflects historical biogeography and dispersal limitation. Most congeneric and intraguild checkerboards include a species classified as a supertramp; when supertramps are omitted, there are 11 congeneric checkerboards and four intraguild but heterogeneric checkerboards. Main conclusions In isolation, presence–absence matrices provide limited insight into the role of competition in structuring bird communities of the Bismarcks. A major problem is disentangling historical geography and colonization history of the archipelago from the present-day ecology of the species. Examination of observed checkerboards from a geographically explicit perspective and with knowledge of colonization routes suggests that many checkerboards are likely to result, at least in part, from historical biogeography and supertramps. Although species may be forced into supertramp status by competition, other factors (e.g. habitat preference) may be causal, and biogeographical distributions alone cannot distinguish between causes.

Testing multiple assembly rule models in avian communities on islands of an inundated lake, Zhejiang Province, China

Aim A fundamental question in community ecology is whether general assembly rules determine the structure of natural communities. Although many types of assembly rules have been described, including Diamond';s assembly rules, constant body-size ratios, favoured states, and nestedness, few studies have tested multiple assembly rule models simultaneously. Therefore, little is known about the relative importance of potential underlying factors such as interspecific competition, inter-guild competition, selective extinction and habitat nestedness in structuring community composition. Here, we test the above four assembly rule models and examine the causal basis for the observed patterns using bird data collected on islands of an inundated lake. Location Thousand Island Lake, China. Methods We collected data on presence-absence matrices, body size and functional groups for bird assemblages on 42 islands from 2007 to 2009. To test the above four assembly rule models, we used null model analyses to compare observed species co-occurrence patterns, body-size distributions and functional group distributions with randomly generated assemblages. To ensure that the results were not biased by the inclusion of species with extremely different ecologies, we conducted separate analyses for the entire assemblage and for various subset matrices classified according to foraging guilds. Results The bird assemblages did not support predictions by several competitively structured assembly rule models, including Diamond';s assembly rules, constant body-size ratios, and favoured states. In contrast, bird assemblages were highly significantly nested and were apparently shaped by extinction processes mediated through area effects and habitat nestedness. The nestedness of bird assemblages was not a result of passive sampling or selective colonization. These results were very consistent, regardless of whether the entire assemblage or the subset matrices were analysed. Main conclusions Our results suggest that bird assemblages were shaped by extinction processes mediated through area effects and habitat nestedness, rather than by interspecific or inter-guild competition. From a conservation point of view, our results indicate that we should protect both the largest islands with the most species-rich communities and habitat-rich islands in order to maximize the number of species preserved.

Snail herbivory decreases cyanobacterial abundance and lichen diversity along cracks of limestone pavements

Herbivores are known to decrease plant species diversity in ecosystems with low productivity. Limestone pavements are low-productive habitats harboring specialized communities of cyanobacteria, and endo- and epilithic lichens exposed to extreme temperature and humidity fluctuations. Pavements of the Great Alvar (O¨ land, Sweden) are covered by free-living cyanobacteria giving the rock surface a dark color. Based on cyanobacterial abundance along the edges, two types of cracks intersecting the pavements have been described: Type one with abundant cyanobacteria and type two without cyanobacteria resulting in light-colored edges. Erosion and different lengths of inundation by melt water have been suggested to cause the conspicuous differences in community composition and hence color between cracks. We hypothesized that this pattern results from the grazing activity of the cyanobacteria- and lichen-feeding snail Chondrina clienta, which reduces cyanobacterial cover along light-colored cracks and facilitates endolithic lichens. Three dark and three light-colored cracks were investigated at each of three localities. Crack characteristics (i.e., aspect, width, depth and erosion) and snail density were assessed at the crack level. Cyanobacterial cover and lichen diversity were recorded in 1-cm sections, sampled every 5 cm along eight 160-cm-long transects per crack. Model selection was applied to estimate effects of snail density and distance from crack edges on cyanobacterial abundance and lichen diversity. Crack characteristics explained no differences in cyanobacterial cover or lichen diversity. However, cyanobacterial cover decreased towards the edges of cracks with high snail densities. A transplant experiment supported the correlational evidence. The abundant cyanobacterial cover on pieces of stone placed close to cracks with high snail densities was completely grazed within 19 months. By contrast, cyanobacteria recolonized initially completely grazed pieces of stone when fixed near cracks without snails. Abundance and diversity of endolithic lichens increased along cracks with high compared to low snail densities but decreased in epilithic lichens and lichens with cyanobacterial symbionts. However, the presence of the gastropod herbivore decreased overall lichen diversity. Comparing presence-absence matrices with null models revealed that species co-occurred less frequently than expected. Taken together, we provide evidence that herbivory indirectly released endolithic lichens from competition for light by reducing cyanobacterial cover. (Less)

Spatial patterns of biological diversity in a neotropical lowland savanna of northeastern Bolivia

Understanding large-scale patterns of beta- and alpha diversity is essential for ecoregional conservation planning. Using the 110,000 km 2 shallow basin of the Beni savannas of northeastern Bolivia, we examined the spatial patterns of biological diversity of four taxonomic groups (bats, palms, reptiles, and amphibians). Since the Beni savannas are shaped by cycles of drought and flood, and farming, which, together with topography, create a mosaic of sub-ecoregions from Amazonian forests to aquatic vegetation, we hypothesize that this landscape heterogeneity results in a high turnover in species com- position across sub-ecoregions. We compiled species lists for each taxon and modeled the potential distribution of each species using the algorithm MaxEnt. For those species whose modeled potential distribution produced incongruous results, we built presence-absence maps. Using the potential distribution maps, we estimated the lists of species for each sub- ecoregion. In order to establish present similarities in species composition between sub- ecoregions, we constructed dendrograms using cluster analysis of presence-absence matrices. The sub-ecoregions associated with the Moxos (southern part of the Beni savannas) were richer than the sub-ecoregions composing the Beni Cerrado (northern part of the Beni savannas). Centers of species richness were detected in the savanna-type sub- ecoregions (bats and reptiles) or associated with the Varzea forests (palms and amphibi- ans). A south-north gradient in the pattern of distribution of four taxonomic groups was also recorded. The results suggest that the patterns of biological diversity partially respond to the mosaic arrangement of the landscape. Future exercises on conservation planning will

Nestedness of small mammal assemblages and role of indicator species in isolated marshland habitats

The concept of nestedness has important role in community ecology of fragmented habitats that measures the order in presence-absence matrices of species in different communities, and the vulnerability of species to habitat change can be quantified. We have been examining the composition of small mammal assemblages of Kis-Balaton Landscape Protection Area since 1999 within the framework of Hungarian Biodiversity Monitoring System Programme. Our basic question was how much the species turnover processes and the water-level increase following bountiful precipitation as a natural disturbance predominate in directing the composition of small mammal assemblages and in the nestedness pattern in human disturbed habitat patches. Our investigation was based on nestedness analysis and the IndVal method. The results of nestedness analysis showed that the small mammal assemblages of the isolated Kis-Balaton marshland habitat patches are ordered contrary to the random pattern and showed nested pattern. The endangered habitat-specialist root vole appeared as an asymmetrical indicator species regarding its optimal habitat patch, and we evaluated it as an idiosyncratic species in the nestedness analysis. These results proved admittedly that the root vole – as a habitat specialist species – is very sensitive to habitat fragmentation and human disturbance, so the pattern of its presence influences considerably the nestedness of small mammal assemblages of the examined marshlands.

A straightforward computational approach for measuring nestedness using quantitative matrices

Nestedness has been one of the most reported patterns of species distribution in metacommunities as well as of species interactions in bipartite networks. We propose here a straightforward approach for quantifying nestedness using quantitative instead of presence–absence data. We named our estimator WNODF because it is a simple modification of the nestedness index called NODF. We also introduce the NODF-Program that calculates the above described nestedness metrics as well as metrics for idiosyncratic species and sites. Statistical inference is done through a null model approach, in which the user can choose among five null models commonly used for presence–absence matrices as well as three randomization algorithms for matrices that contain quantitative data. The program performs multiple analyses using many matrices. Finally, the NODF-Program provides four sorting options that, together with the null algorithms, cover a range of possibilities to test hypotheses on the possible mechanisms producing nested patterns. By using a set of model matrices, we showed that WNODF differentiates nested matrices with distinct structures and correctly identifies matrices with no nested pattern as having zero degree of nestedness.

Use of Habitats as Surrogates of Biodiversity for Efficient Coral Reef Conservation Planning in Pacific Ocean Islands

Marine protected areas (MPAs) have been highlighted as a means toward effective conservation of coral reefs. New strategies are required to more effectively select MPA locations and increase the pace of their implementation. Many criteria exist to design MPA networks, but generally, it is recommended that networks conserve a diversity of species selected for, among other attributes, their representativeness, rarity, or endemicity. Because knowledge of species' spatial distribution remains scarce, efficient surrogates are urgently needed. We used five different levels of habitat maps and six spatial scales of analysis to identify under which circumstances habitat data used to design MPA networks for Wallis Island provided better representation of species than random choice alone. Protected-area site selections were derived from a rarity-complementarity algorithm. Habitat surrogacy was tested for commercial fish species, all fish species, commercially harvested invertebrates, corals, and algae species. Efficiency of habitat surrogacy varied by species group, type of habitat map, and spatial scale of analysis. Maps with the highest habitat thematic complexity provided better surrogates than simpler maps and were more robust to changes in spatial scales. Surrogates were most efficient for commercial fishes, corals, and algae but not for commercial invertebrates. Conversely, other measurements of species-habitat associations, such as richness congruence and composition similarities provided weak results. We provide, in part, a habitat-mapping methodology for designation of MPAs for Pacific Ocean islands that are characterized by habitat zonations similar to Wallis. Given the increasing availability and affordability of space-borne imagery to map habitats, our approach could appreciably facilitate and improve current approaches to coral reef conservation and enhance MPA implementation.

Calculating minimum discrepancy to assess the nestedness of species assemblages

Nestedness is a pattern whereby species-poor assemblages are composed of subsets of the species occurring in richer assemblages. One of the most commonly used measures of the degree of nestedness for presence-absence matrices is the ‘discrepancy’ metric. A hitherto neglected property of that metric is that it may take several values for a given site-by-species matrix in the presence of ties in the marginal totals. This complicates the quantification of nestedness for the observed presence-absence matrix, as well as the assessment of statistical significance, which is typically achieved through Monte Carlo simulations. A solution to the problem is to calculate the minimum discrepancy using a modified algorithm involving permutations of columns with tied totals.

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.

“Active” Passive Sampling in Two Species of Lepomis from Par Pond, South Carolina, United States: a Case Study of Infracommunity Nestedness

The influence of ontological diet shifts on infracommunity nestedness was examined by comparing the infracommunity structure of Lepomis gulosus and Lepomis macrochirus at 2 localities in Par Pond, South Carolina, United States. Fill-constrained, occurrence-constrained, and abundance-constrained null models were used to evaluate the degree of nestedness. The presence-absence matrices from all 4 component communities had significantly fewer discrepancies than those produced by the fill-constrained model, and none had significantly fewer discrepancies than those produced by the occurrence-constrained model. Only the presence-absence matrix for the infracommunities of L. gulosus from the Cold Dam locality had significantly fewer discrepancies than those produced by the abundance-constrained null model. The nestedness of the 4 samples could not be distinguished from that expected under a hypothesis of passive sampling. A positive correlation between host size and total parasite abundance indicates the passive mechanism has a deterministic basis. Thus, even in the absence of habitat or diet shifts, nestedness can arise in infracommunities of freshwater fishes when older, larger fish have sampled more individuals from an uneven distribution of infective stages.

Assemblage-structuring force of species interactions varies spatially and temporally: Co-occurrence analysis of canopy arthropod distributions

Abstract *Background/Question/Methods* Understanding how interactions amongst species contribute to their distribution is central to community ecology. However, it is not understood how these processes may change under different environmental conditions. In this study, we present evidence that suggests interactions amongst canopy arthropods contribute to assemblage structure, depending on both the sampling time and location. We sampled canopy arthropod species abundances on individual trees in three adjacent, monospecific stands of Populus fremontii (Fremont cottonwood), which differ in planting year (2000, 2002, 2005). We then conducted null-model based co-occurrence analysis using the freely available software EcoSim (Kesey-Bear and Acquired Intelligence, Inc.) to test for patterns suggestive of interactions influencing assemblage structure. Environmental heterogeneity amongst trees is low within stands; therefore environmental gradients are most likely not contributing to co-occurrence patterns. Also, all stands were planted recently and closely enough such that evolutionary processes (e.g. allopatric speciation) have not occurred. For the analyses of each stand at each sampling date we used a fixed-row, equiprobable-column matrix permutation algorithm in order to simulate presence-absence matrices in which species co-occurrences are effectively random with respect to species interactions. We chose to use the C-score index of co-occurence because of its robustness to Type I Errors when used with this simulation algorithm. P-values and standardized effect sizes (SES) were based on 5000 simulated matrixes. *Results/Conclusions* We found significant variation in SES values across both sampling dates and stands; and three main patterns emerged. 1) The SES values in the youngest stand (2005) were all near zero and none were statistically significant. This could be the result of unresolved species interactions, meaning that species interactions have not had sufficient time to produce consistent distributional patterns. 2) The SES values were primarily negative, indicating a dominating force of facilitative interactions. 3) The 2000 and 2002 stands varied in the size and significance of their SES values with the oldest (2000) stand switching from positive to negative as the season progressed, suggesting a switch from competitive to facilitative interactions driving structure. These results suggest that species interactions are indeed important in structuring canopy arthropod communities, but that the efficacy of these forces can vary across both space and time.

Nested structure of plankton communities from Chilean freshwaters

1. Nestedness has been recognized as a characteristic pattern of community organization. In a nested metacommunity, species-poor sites are proper subsets of relatively richer sites, implying that the conservation of many poor habitats can be ineffective. 2. Here we compiled the last 30 years of published limnological research on Chilean lakes, in order to determine whether or not species distribution of freshwater plankton communities exhibit a nested structure, and which habitat features best explain the observed biogeographic order. 3. We built presence–absence matrices for diatoms, green algae, blue-green algae, cladocerans, copepods, rotifers, as well as for the grouped phytoplankton and zooplankton. For each matrix, we calculated their degree of nestedness and tested whether or not they differ from matrices assembled according to two alternative null models. From nestedness results, we identified a minimal set of lakes that contain 75% of the regional species pool. After that, we evaluated whether nestedness is maintained when the community structure is organized according to latitude, altitude, area and isolation of lakes. 4. Our analyses reveal that total phytoplankton, total zooplankton, as well as diatom, cladoceran, copepod, and rotifer assemblages of Chilean lakes are not randomly assembled but highly nested. Conversely, green and blue-green algae did not show a clear nested structure. A few sites (3–5) ranked by nestedness for each taxonomic group, covered 75% of the species pool. Finally, we found that surface area and isolation of lakes were the two variables more likely to affect nestedness.

Null model analyses of presence–absence matrices need a definition of independence

AbstractTests for species interactions that involve the comparison of a statistic calculated from observed matrix of species presences and absences with the distribution of the same statistic generated from a null model have been used by ecologists for about 30 years. We argue that the validity of these tests requires a specific definition of independence. In particular, we note that an assumption that is often made is that all presence–absence matrices with the same row and column totals are equally likely if there is no interaction. However, we show using a simple model for species presences and absences without any species interactions that, in general, this assumption should be made with caution. Our model incorporates a definition of independence, allowing the computation of probabilities of different patterns in the null matrices. Other definitions of independence are possible; one of them is outlined using a new generalized linear model approach for carrying out tests applicable to different null models with or without the assumption of keeping row and column totals fixed.

Bat assemblages on Neotropical land‐bridge islands: nested subsets and null model analyses of species co‐occurrence patterns

ABSTRACTA fundamental goal of ecology is to understand whether ecological communities are structured according to general assembly rules or are essentially dictated by random processes. In the context of fragmentation, understanding assembly patterns and their mechanistic basis also has important implications for conservation. Using distribution data of 20 bat species collected on 11 islands in Gatún Lake, Panama, we tested for non‐randomness in presence–absence matrices with respect to nestedness and negative species co‐occurrence. We examined the causal basis for the observed patterns and conducted separate analyses for the entire assemblage and for various species submatrices reflecting differences in species’ trophic position and mobility. Furthermore, we explored the influence of weighting factors (area, isolation, abundance) on co‐occurrence analyses. Unweighted analyses revealed a significant negative co‐occurrence pattern for the entire assemblage and for phytophagous bats alone. Weighting analyses by isolation retained a pattern of species segregation for the whole assemblage but nullified the non‐random structure for phytophagous bats and suggested negative associations for animalivores and species with low mobility. Area‐ and abundance‐weighted analyses always indicated random structuring. Bat distributions followed a nested subset structure across islands, regardless of whether all species or different submatrices were analysed. Nestedness was in all cases unrelated to island area but weakly correlated with island isolation for incidence matrices of all species, phytophagous bats, and mobile species. Overall, evidence for negative interspecific interactions indicative of competitive effects was weak, corroborating previous studies based on ecomorphological analyses. Our findings indicate that bat assemblages on our study islands are most strongly shaped by isolation effects and species’ differential movement and colonization ability. From a conservation viewpoint this suggests that even in systems with high fragment–matrix contrast, a purely area‐based approach may be inadequate, and structural and functional connectivity among patches are important to consider in reserve planning.

Do climatically similar regions contain similar alien floras? A comparison between the mediterranean areas of central Chile and California

AbstractAim Taxonomic comparisons of alien floras across climatically similar regions have been proposed as a powerful approach for increasing our understanding of plant invasions across scales. However, detailed comparisons between the alien biotas of climatically similar regions are scarce. This study aims to compare the taxonomic patterns of alien species richness in mediterranean‐type climate areas of central Chile and California, in order to better understand how climatically similar regions converge or diverge in terms of their alien flora.Location Central Chile and California, United States.Methods We compared the alien floras of the state of California in the United States and central Chile, considering within‐region variation and taxonomic composition up to the species level. To test for within‐region variation, administrative units and counties were grouped within seven latitudinal bands for each region. We tested for differences in the relative contributions of the various origins of the naturalized species to each region. We used a family naturalization index to establish which families had relatively higher numbers of naturalized species in each region. We evaluated the similarity, using cluster analyses with Jaccard’s similarity index, of alien taxa between regions and latitudinal bands using presence–absence matrices at the species, genus and family levels. We used principal components analysis to determine the presence of a compositional gradient including all latitudinal bands.Results We recorded 1212 alien plant species in California and 593 in central Chile, of which 491 are shared between the two regions. These figures include 25 species that are native to California and 37 that are native to Chile. A comparison between the alien floras of central Chile and California reveals three major trends: (1) higher naturalized species diversity for California than for Chile, at all taxonomic levels; (2) differences in the proportion of species according to origin, with America, Africa, Asia and Australia providing a larger number of species in California than in Chile; (3) segregation between regions in terms of taxonomic composition of their alien flora, and a rather weak differentiation within regions; and (4) a trend towards higher similarity between the alien floras of latitudinal bands associated with higher levels of human disturbances.Main conclusions The alien floras of central Chile and California are significantly different, but this difference diminishes in highly disturbed areas. Thus, the current high levels of species movement caused by globalization, together with increasing levels of anthropogenic disturbances, should reduce the differentiation of the alien floras in these regions, increasing overall biotic homogenization.

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%.

Toward ecologically explicit null models of nestedness

A community is "nested" when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.

The generation of diversity in systems of patches and ranked dominance

AbstractAim Mac Nally and Lake proposed a statistic (η) for determining whether the diversity in archipelagos is better generated by several small patches (SS‐dominance) or by a few large patches (SL‐dominance). The η statistic improves the study of the generation of diversity in systems of patches, but the dependence of η on a particular species–area relationship may reduce its effectiveness. In this paper we show that η may be affected by the criterion used to distinguish between large and small patches. We propose alternative measures (ranked m‐dominance indices) for the detection of SS/SL dominance, which separate the effects of each class of patch size on the generation of diversity.Location We use previously published species lists from three archipelagos: lizard species on 25 islands in the Gulf of California; non‐introduced species of reptiles of the Canary Islands (order Squamata); and finch species from 19 islands of the West Indies. We also use one artificial data set.Methods Presence–absence data and the rank order of patch areas are used to define the m‐dominance indices, interpreted as measures of preferential size of patches occupied by m species. A Monte Carlo procedure is implemented for testing the significance of the observed indices. Row and column totals in the simulated presence–absence matrices are kept fixed in order to maintain differences in species richness among sites and differences in occurrence frequencies among species, but the allocation of each occurrence to a specific ranked area is randomized. The analyses are exemplified with the three published data sets taken from the literature, and a hypothetical patch system neither SS‐ nor SL‐dominated.Results The new m‐dominance indices identified correctly the hypothetical patch system, while η was positive, suggesting an incorrect SL‐dominant result. For the lizard data set, the standardized ranked m‐dominance was significantly large for small m, confirming an SL‐dominated system. Islands of varying size in the Canary archipelago hosted restricted reptile species, but matrix sparseness seems to have caused the non‐significant results for the m‐dominance indices in this case. The overall pattern of the West Indies system shows that medium‐large islands are dominant, but most Monte Carlo analyses were not significant, also possibly as a result of matrix sparseness.Main conclusions The m‐dominance indices have the virtue of summarizing composition–area relationships, and including Monte Carlo procedures for testing whether patch size and the type of species distribution (species restricted to m patches, m = 1,…,s) are random or not. When m is as low as 1 or 2, the m‐dominance indices may typify the role of restricted species on the generation of diversity in the system of patches. The procedure developed here can be generalized to include other ordinal properties of patches, such as isolation or habitat heterogeneity.

A new algorithm to calculate the nestedness temperature of presence–absence matrices

AbstractAim The nestedness temperature of presence–absence matrices is currently calculated with the nestedness temperature calculator (NTC). In the algorithm implemented by the NTC: (1) the line of perfect order is not uniquely defined, (2) rows and columns are reordered in such a way that the packed matrix is not the one with the lowest temperature, and (3) the null model used to determine the probabilities of finding random matrices with the same or lower temperature is not adequate for most applications. We develop a new algorithm, BINMATNEST (binary matrix nestedness temperature calculator), that overcomes these difficulties.Methods BINMATNEST implements a line of perfect order that is uniquely defined, uses genetic algorithms to determine the reordering of rows and columns that leads to minimum matrix temperature, and provides three alternative null models to calculate the statistical significance of matrix temperature.Results The NTC performs poorly when the input matrix has checkerboard patterns. The more efficient packing of BINMATNEST translates into matrix temperatures that are lower than those computed with the NTC. The null model implemented in the NTC is associated with a large frequency of type I error, while the other null models implemented in BINMATNEST (null models 2 and 3) are conservative. Overall, null model 3 provides the best performance. The nestedness temperature of a matrix is affected by its size and fill, but the probability that such a temperature is obtained by chance is not. BINMATNEST reorders the input matrix in such a way that, if fragment size/isolation plays a role in determining community structure, there will be a significant rank correlation between the size/isolation of the fragments and the way that they are ordered in the packed matrix.Main conclusions The nestedness temperature of presence–absence matrices should not be calculated with the NTC. The algorithm implemented by BINMATNEST is more robust, allowing for across‐study comparisons of the extent to which the nestedness of communities departs from randomness. The sequence in which BINMATNEST reorders habitat fragments provides information about the causal role of immigration and extinction in shaping the community under study.

Estrutura de assembléias de Muscidae (Diptera) no Paraná: uma análise por modelos nulos

Community structure is often thought to be determined by interspecific competition. Critics of this idea state that we must first demonstrate structure with null models to test whether structure indeed exists. Here, we use 179 predatory and saprophagic species of flies in the family Muscidae (Diptera) that were captured in Malaise traps in six locations in Parana State during one year of study. To test community structure, we generated five presence-absence (1-0) matrices: two by trophic guilds, two by habitat, and one general matrix (taxonomic). Two indices of co-occurrence (C) and covariance (V) of species were calculated in the matrices developed through 5,000 Monte Carlo randomizations. Randomizations followed two different assumptions: 1) fixed number of species per location, and 2) constant proportions of species at all locations. Comparisons with null-model communities showed that taxonomic species assemblage had a false structure, while species assemblages had true structure. Although the ecological assemblages are consistent with the theory of interspecific competition as a cause of community structure, it remains possible that other causes of structure may also be important.