Unravelling changing interspecific interactions across environmental gradients using Markov random fields

Abstract

Inferring interactions between co-occurring species is key to identify processes governing community assembly. Incorporating interspecific interactions in predictive models is common in ecology, yet most methods do not adequately account for indirect interactions (where an interaction between two species is masked by their shared interactions with a third) and assume interactions do not vary along environmental gradients. Markov random fields (MRF) overcome these limitations by estimating interspecific interactions, while controlling for indirect interactions, from multispecies occurrence data. We illustrate the utility of MRFs for ecologists interested in interspecific interactions, and demonstrate how covariates can be included (a set of models known as Conditional Random Fields, CRF) to infer how interactions vary along environmental gradients. We apply CRFs to two data sets of presence-absence data. The first illustrates how blood parasite (Haemoproteus, Plasmodium, and nematode microfilaria spp.) co-infection probabilities covary with relative abundance of their avian hosts. The second shows that co-occurrences between mosquito larvae and predatory insects vary along water temperature gradients. Other applications are discussed, including the potential to identify replacement or shifting impacts of highly connected species along climate or land-use gradients. We provide tools for building CRFs and plotting/interpreting results as an R package.

Microbial associations and spatial proximity predict North American moose (Alces alces) gastrointestinal community composition

“…Here, we have demonstrated that graphical network models can untangle how interspecific interactions can shape gut microbial communities in moose. Additionally, we show that MRF and CRF models can robustly construct co-occurrence networks (Clark et al, 2018b) and, coupled with taxonomic and functional information, find high-resolution insights into interspecific associations. Graphical network models, as with other correlation-based approaches, do have limitations.…”

“…In contrast, the roles that interspecific associations play in governing the assembly of microbial systems (microbial interspecific associations) are less understood (Ganz et al, 2017;Herren & McMahon, 2018;Zelezniak et al, 2015), particularly for within-host microbial communities. Even when microbial interspecific associations are quantified in communities, the relative importance of microbe dispersal (Evans, Martiny, & Allison, 2017;Zhou & Ning, 2017) and host characteristics in shaping microbial communities is rarely assessed (Clark, Wells, & Lindberg, 2018b). The quantification of interspecific associations of gut microbes is rare in wildlife populations but, given the significant ecological insights derived from studies of human gut microbial communities (e.g.…”

The failure of success: cyclic recurrences of a globally invasive pest

“…Let t 1 represent the first year of detection in a cell; we estimated the recurrent probability (RP) after x years from a reference year t as the conditional probability RP ( x , t ) = Prob(DY ( t 1 , t + x ) = T + 1|DY ( t 1 , t ) = T ), where RP (1, t ) represents the transmission rate for the recurrence immediately after year t and T represents the number of detection years (Clark et al. ). The RP was computed for 166 infested cells based on their time series (58‐yr) from 1960 to 2017.…”

“…represents the transmission rate for the recurrence immediately after year t and T represents the number of detection years (Clark et al 2018). The RP was computed for 166 infested cells based on their time series (58-yr) from 1960 to 2017.…”

A pathway for multivariate analysis of ecological communities using copulas

“…Associations can also be generated indirectly through species responding in similar (or opposing) ways to environmental gradients or habitats (Dunstan, Foster, & Darnell, 2011;Warton et al, 2015). Furthermore, relationships among species vary in time and space under changing biotic or abiotic conditions (Clark, Wells, & Lindberg, 2018); for example, species may only compete when resources are limiting (Perry, Mitchell, Zutter, Glover, & Gjerstad, 1994), in certain parts of their range (Pacala & Roughgarden, 1985), or in the absence of predation (Chase et al, 2002).…”