Metacommunity dynamics and the spurious detection of species associations in co-occurrence analyses: patch disturbance matters

Many methods attempt to detect species associations from co-occurrence patterns. Such associations are then typically used to infer inter-specific interactions. However, correlation is not equivalent to interaction. Habitat heterogeneity and out-of-equilibrium colonization histories are acknowledged to cause species associations even when inter-specific interactions are absent. Here we show how classical metacommunity dynamics, within a homogeneous habitat at equilibrium, can also lead to statistical associations. This occurs even when species do not interact. All that is required is patch disturbance (i.e. simultaneous extinction of several species in a patch) a common phenomenon in a wide range of real systems. We compare direct tests of pairwise independence, matrix permutation approaches and joint species distribution modelling. We use mathematical analysis and example simulations to show that patch disturbance leads all these methods to produce characteristic signatures of spurious association from "null" co-occurrence matrices. Including patch age (i.e. the time since the last patch disturbance event) as a covariate is necessary to resolve this artefact. However, this would require data that very often are not available in practice for these types of analyses. We contend that patch disturbance is a key (but hitherto overlooked) factor which must be accounted for when analysing species co-occurrence.

Approximation theorems for spaces of localities

The classical Artin–Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations exist, for example for finitely many (Krull) valuations, where one usually requires that these are independent, i.e. induce different topologies on the field. Ribenboim proved a generalization for finitely many valuations where the condition of independence is relaxed for a natural compatibility condition, and Ershov proved a statement about simultaneously approximating finitely many different elements with respect to finitely many possibly infinite sets of pairwise independent valuations. We prove approximation theorems for infinite sets of valuations and orderings without requiring pairwise independence.

Dependence and dependence structures: estimation and visualization using the unifying concept of distance multivariance

Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise overview and use it as the basis for several new results and concepts: in particular, we show that distance multivariance unifies (and extends) distance covariance and the Hilbert-Schmidt independence criterion HSIC, moreover also the classical linear dependence measures: covariance, Pearson’s correlation and the RV coefficient appear as limiting cases. Based on distance multivariance several new measures are defined: a multicorrelation which satisfies a natural set of multivariate dependence measure axioms and m-multivariance which is a dependence measure yielding tests for pairwise independence and independence of higher order. These tests are computationally feasible and under very mild moment conditions they are consistent against all alternatives. Moreover, a general visualization scheme for higher order dependencies is proposed, including consistent estimators (based on distance multivariance) for the dependence structure.Many illustrative examples are provided. All functions for the use of distance multivariance in applications are published in the R-package multivariance.

Learning Disentangled Representation with Pairwise Independence

Unsupervised disentangled representation learning is one of the foundational methods to learn interpretable factors in the data. Existing learning methods are based on the assumption that disentangled factors are mutually independent and incorporate this assumption with the evidence lower bound. However, our experiment reveals that factors in real-world data tend to be pairwise independent. Accordingly, we propose a new method based on a pairwise independence assumption to learn the disentangled representation. The evidence lower bound implicitly encourages mutual independence of latent codes so it is too strong for our assumption. Therefore, we introduce another lower bound in our method. Extensive experiments show that our proposed method gives competitive performances as compared with other state-of-the-art methods.