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Interspecific interactions can influence species' activity and movement patterns. In particular, species may avoid or attract each other through reactive responses in space and/or time. However, data and methods to study such reactive interactions have remained scarce and were generally limited to two interacting species. At this time, the deployment of camera traps opens new opportunities but adapted statistical techniques are still required to analyze interaction patterns with such data. We present the multivariate Hawkes process (MHP) and show how it can be used to analyze interactions between several species using camera trap data. Hawkes processes use flexible pairwise interaction functions, allowing us to consider asymmetries and variations over time when depicting reactive temporal interactions. After describing the theoretical foundations of the MHP, we outline how its framework can be used to study interspecific interactions with camera trap data. We design a simulation study to evaluate the performance of the MHP and of another existing method to infer interactions from camera trap‐like data. We also use the MHP to infer reactive interactions from real camera trap data for five species from South African savannas (impala Aepyceros melampus, greater kudu Tragelaphus strepsiceros, lion Panthera leo, blue wildebeest Connochaetes taurinus and Burchell's zebra Equus quagga burchelli). The simulation study shows that the MHP can be used as a tool to benchmark other methods of interspecific interaction inference and that this model can reliably infer interactions when enough data are considered. The analysis of real data highlights evidence of predator avoidance by prey and herbivore–herbivore attraction. Lastly, we present the advantages and limits of the MHP and discuss how it can be improved to infer attraction/avoidance patterns more reliably. As camera traps are increasingly used, the multivariate Hawkes process provides a promising framework to decipher the complexity of interactions structuring ecological communities. [ABSTRACT FROM AUTHOR]

The fourth‐corner analysis aims to quantify and test for relationships between species traits and site‐specific environmental variables, mediated by site‐specific species abundances. Since there is no common unit of observation, the significance of the relationships is tested using a double permutation procedure (site based and species based). This method implies that all species and sites are independent of each other. However, this fundamental hypothesis might be flawed because of phylogenetic relatedness between species and spatial autocorrelation in the environmental data. Here, using a simulation‐based experiment, we demonstrate how the presence of spatial and phylogenetic autocorrelations can, in some circumstances, lead to inflated type I error rates, suggesting that significant associations can be misidentified. As an alternative, we propose a new randomization approach designed to avoid this issue, based on Moran's spectral randomization. In this approach, standard permutations are replaced by constrained randomizations so that the distribution of the statistic under the null hypothesis is built with additional constraints to preserve the phylogenetic and spatial structures of the observed data. The inclusion of this new randomization approach provides total control over type I error rates and should be used in real studies where spatial and phylogenetic autocorrelations often occur. [ABSTRACT FROM AUTHOR]

Correspondence analysis with linear external constraints on both the rows and the columns has been mentioned in the ecological literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by defining the method as maximizing the fourth-corner correlation between linear combinations, by providing novel algorithms, which demonstrate relationships with related methods, and by making a detailed study of possible biplots and associated approximations. The method is illustrated using ecological data on the abundances of species in sites and where the species are characterized by traits and sites by environmental variables. The trait data and environment data form the external constraints and the question is which traits and environmental variables are associated, how these associations drive species abundances and how they can be displayed in biplots. With microbiome data becoming widely available, these and related multivariate methods deserve more study as they might be routinely used in the future. [ABSTRACT FROM AUTHOR]

The development of neutral community theory has shown that the assumption of species neutrality, although implausible on the level of individual species, can lead to reasonable predictions on the community level. While Hubbell's neutral model and several of its variants have been analysed in quite some detail, the comparison of theoretical predictions with empirical abundance data is often hindered by technical problems. Only for a few models the exact solution of the stationary abundance distribution is known and sufficiently simple to be applied to data. For other models, approximate solutions have been proposed, but their accuracy is questionable., Here, we argue that many of these technical problems can be overcome by replacing the assumption of constant community size (the zero-sum constraint) by the assumption of independent species abundances., We present a general sampling formula for community abundance data under this assumption. We show that for the few models for which an exact solution with zero-sum constraint is known, our independent species approach leads to very similar parameter estimates as the zero-sum models, for six frequently studied tropical forest community samples., We show that our general sampling formula can be easily confronted to a much wider range of datasets (very large datasets, relative abundance data, presence-absence data, and sets of multiple samples) for a large class of models, including non-neutral ones. We provide an R package, called SADISA (Species Abundance Distributions under the Independent Species Assumption), to facilitate the use of the sampling formula. [ABSTRACT FROM AUTHOR]

The spatial structuring of populations or communities is an important driver of their functioning and their influence on ecosystems. Identifying the (in)stability of the spatial structure of populations is a first step towards understanding the underlying causes of these structures. Here we studied the relative importance of spatial vs. interannual variability in explaining the patterns of abundance of a large herbivore community (8 species) at waterholes in Hwange National Park (Zimbabwe). We analyzed census data collected over 13 years using multivariate methods. Our results showed that variability in the census data was mostly explained by the spatial structure of the community, as some waterholes had consistently greater herbivore abundance than others. Some temporal variability probably linked to Park-scale migration dependent on annual rainfall was noticeable, however. Once this was accounted for, little temporal variability remained to be explained, suggesting that other factors affecting herbivore abundance over time had a negligible effect at the scale of the study. The extent of spatial and temporal variability in census data was also measured for each species. This study could help in projecting the consequences of surface water management, and more generally presents a methodological framework to simultaneously address the relative importance of spatial vs. temporal effects in driving the distribution of organisms across landscapes. [ABSTRACT FROM AUTHOR]

Functional ecology aims at determining the relationships between species traits and environmental variables in order to better understand biological processes in ecosystems. From a methodological point of view, this biological objective calls for a method linking three data matrix tables: a table L with abundance or presence-absence values for species at a series of sites, a table R with variables describing the environmental conditions of the sites, and a table Q containing traits (e.g., morphological or behavioral attributes) of the species. Ten years ago, the fourth-corner method was proposed to measure and test the relationships between species traits and environmental variables using tables R, L, and Q simultaneously. In practice, this method is rarely used. The major reasons for this lack of interest are the restriction of the original method and program to presence-absence data in L and to the analysis of a single trait and a single environmental variable at a time. Moreover, ecologists often have problems in choosing a permutation model among the four originally proposed. In this paper, we revisit the fourth-corner method and propose improvements to the original approach. First, we present an extension to measure the link between species traits and environmental variables when the ecological community is described by abundance data. A new multivariate fourth-corner statistic is also proposed. Then, using numerical simulations, we discuss and evaluate the existing testing procedures. A new two-step testing procedure is presented. We hope that these elements will help ecologists use the best possible methodology to analyze this type of ecological problem. [ABSTRACT FROM AUTHOR]

Abstract: Spatial structures of ecological communities may originate either from the dependence of community structure on environmental variables or/and from community-based processes. In order to assess the importance of these two sources, spatial relationships must be explicitly introduced into statistical models. Recently, a new approach called principal coordinates of neighbour matrices (PCNM) has been proposed to create spatial predictors that can be easily incorporated into regression or canonical analysis models, providing a flexible tool especially when contrasted to the family of autoregressive models and trend surface analysis, which are of common use in ecological and geographical analysis. In this paper, we explore the theory of the PCNM approach and demonstrate how it is linked to spatial autocorrelation structure functions. The method basically consists of diagonalizing a spatial weighting matrix, then extracting the eigenvectors that maximize the Moran''s index of autocorrelation. These eigenvectors can then be used directly as explanatory variables in regression or canonical models. We propose improvements and extensions of the original method, and illustrate them with examples that will help ecologists choose the variant that will better suit their needs. [Copyright &y& Elsevier]

The fourth-corner problem entails estimation and statistical testing of the relationship between species traits and environmental variables from the analysis of three data tables. In a 2008 paper, S. Dray and P. Legendre proposed and evaluated five permutation methods for statistical significance testing, including a new two-step testing procedure. However, none of these attained the correct type I error in all cases of interest. We solve this problem by showing that a small modification of their two-step procedure controls the type 1 error in all cases. The modification consists of adjusting the significance level from √&agr; to &agr; or, equivalently, of reporting the maximum of the individual P values as the final one. The test is also applicable to the three-table ordination method RLQ. [ABSTRACT FROM AUTHOR]

Separating environmental effects from those of interspecific interactions on species distributions has always been a central objective of community ecology. Despite years of effort in analysing patterns of species co-occurrences and the developments of sophisticated tools, we are still unable to address this major objective. A key reason is that the wealth of ecological knowledge is not sufficiently harnessed in current statistical models, notably the knowledge on interspecific interactions. Here, we develop ELGRIN, a statistical model that simultaneously combines knowledge on interspecific interactions (i.e , the metanetwork), environmental data and species occurrences to tease apart their relative effects on species distributions. Instead of focusing on single effects of pairwise species interactions, which have little sense in complex communities, ELGRIN contrasts the overall effect of species interactions to that of the environment. Using various simulated and empirical data, we demonstrate the suitability of ELGRIN to address the objectives for various types of interspecific interactions like mutualism, competition and trophic interactions. We then apply the model on vertebrate trophic networks in the European Alps to map the effect of biotic interactions on species distributions. We find that altitude, species richness and connectance significantly impact the overall effect of biotic interactions. Data on ecological networks are everyday increasing and we believe the time is ripe to mobilise these data to better understand biodiversity patterns. ELGRIN provides this opportunity to unravel how interspecific interactions actually influence species distributions. [ABSTRACT FROM AUTHOR]