Ecological models: higher complexity in, higher feasibility out

Creating simple predictive models in ecology, conservation and environmental policy based on Bayesian belief networks

Predictive models are often complex to produce and interpret, yet can offer valuable insights for management, conservation and policy-making. Here we introduce a new modelling tool (the R package 'BBNet'), which is simple to use, and requires little mathematical or computer programming background. By using straightforward concepts to describe interactions between model components, predictive models can be effectively constructed using basic spreadsheet tools and loaded into the R package. These models can be analysed, visualised, and sensitivity tested to assess how information flows through the system's components and provide predictions for future outcomes of the systems. This paper provides a theoretical background to the models, which are modified Bayesian belief networks (BBNs), and an overview of how the package can be used. The models are not fully quantitative, but outcomes between different modelled scenarios can be considered ordinally (i.e. ranked from 'best' to 'worse'). Parameterisation of models can also be through data, literature, expert opinion, questionnaires and/or surveys of opinion, which are expressed as a simple 'weak' to 'very strong' or 1-4 integer value for interactions between model components. While we have focussed on the use of the models in environmental and ecological problems (including with links to management and social outcomes), their application does not need to be restricted to these disciplines, and use in financial systems, molecular biology, political sciences and many other disciplines are possible.

The development of ecological systems along paths of least resistance

A long-standing question in biology is whether there are common principles that characterize the development of ecological systems (the appearance of a group of taxa), regardless of organismal diversity and environmental context.1,2,3,4,5,6,7,8,9,10,11 Classic ecological theory holds that these systems develop following a sequenced, orderly process that generally proceeds from fast-growing to slow-growing taxa and depends on life-history trade-offs.2,12,13 However, it is also possible that this developmental order is simply the path with the least environmental resistance for survival of the component species and hence favored by probability alone. Here, we use theory and data to show that the order from fast- to slow-growing taxa is the most likely developmental path for diverse systems when local taxon interactions self-organize in light of environmental resistance. First, we demonstrate theoretically that a sequenced development is more likely than a simultaneous one, at least until the number of iterations becomes so large as to be ecologically implausible. We then show that greater diversity of taxa and life histories improves the likelihood of a sequenced order from fast- to slow-growing taxa. Using data from bacterial and metazoan systems,14,15,16,17,18,19 we present empirical evidence that the developmental order of ecological systems moves along the paths of least environmental resistance. The capacity of simple principles to explain the trend in the developmental order of diverse ecological systems paves the way to an enhanced understanding of collective features of life.

Stability of Ecological Systems: A Theoretical Review

The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on the theoretical frameworks for analyzing the stability of ecological systems. Notably, we survey various stability notions, including linear stability, sign stability, diagonal stability, D-stability, total stability, sector stability, and structural stability. For each of these stability notions, we examine necessary or sufficient conditions for achieving such stability and demonstrate the intricate interplay of these conditions on the network structures of ecological systems. We further discuss the stability of ecological systems with higher-order interactions.

Multitrophic Higher-Order Interactions Modulate Species Persistence

AbstractEcologists increasingly recognize that interactions between two species can be affected by the density of a third species. How these higher-order interactions (HOIs) affect species persistence remains poorly understood. To explore the effect of HOIs stemming from multiple trophic layers on a plant community composition, we experimentally built a mesocosm with three plants and three pollinator species arranged in a fully nested and modified network structure. We estimated pairwise interactions among plants and between plants and pollinators, as well as HOIs initiated by a plant or a pollinator affecting plant species pairs. Using a structuralist approach, we evaluated the consequences of the statistically supported HOIs on the persistence probability of each of the three competing plant species and their combinations. HOIs substantially redistribute the strength and sign of pairwise interactions between plant species, promoting the opportunities for multispecies communities to persist compared with a non-HOI scenario. However, the physical elimination of a plant-pollinator link in the modified network structure promotes changes in per capita pairwise interactions and HOIs, resulting in a single-species community. Our study provides empirical evidence of the joint importance of HOIs and network structure in determining species persistence within diverse communities.

Trophic tug-of-war: Coexistence mechanisms within and across trophic levels

Ecological communities encompass rich diversity across multiple trophic levels. While modern coexistence theory has been widely applied to understand community assembly, its traditional formalism only allows assembly within a single trophic level. Here, using an expanded definition of niche and fitness differences applicable to multitrophic communities, we study how diversity within and across trophic levels affects species coexistence. If each trophic level is analysed separately, both lower- and higher trophic levels are governed by the same coexistence mechanisms. In contrast, if the multitrophic community is analysed as a whole, different trophic levels are governed by different coexistence mechanisms: coexistence at lower trophic levels is predominantly limited by fitness differences, whereas coexistence at higher trophic levels is predominantly limited by niche differences. This dichotomy in coexistence mechanisms is supported by theoretical derivations, simulations of phenomenological and trait-based models, and a case study of a primeval forest ecosystem. Our work provides a general and testable prediction of coexistence mechanism operating in multitrophic communities.

Time delays modulate the stability of complex ecosystems

What drives the stability, or instability, of complex ecosystems? This question sits at the heart of community ecology and has motivated a large body of theoretical work exploring how community properties shape ecosystem dynamics. However, the overwhelming majority of current theory assumes that species interactions are instantaneous, meaning that changes in the abundance of one species will lead to immediate changes in the abundances of its partners. In practice, time delays in how species respond to one another are widespread across ecological contexts, yet the impact of these delays on ecosystems remains unclear. Here we derive a new body of theory to comprehensively study the impact of time delays on ecological stability. We find that time delays are important for ecosystem stability. Large delays are typically destabilizing but, surprisingly, short delays can substantially increase community stability. Moreover, in stark contrast to delay-free systems, delays dictate that communities with more abundant species can be less stable than ones with less abundant species. Finally, we show that delays fundamentally shift how species interactions impact ecosystem stability, with communities of mixed interaction types becoming the most stable class of ecosystem. Our work demonstrates that time delays can be critical for the stability of complex ecosystems.

Coexistence in diverse communities with higher-order interactions

A central assumption in most ecological models is that the interactions in a community operate only between pairs of species. However, two species may interactively affect the growth of a focal species. Although interactions among three or more species, called higher-order interactions, have the potential to modify our theoretical understanding of coexistence, ecologists lack clear expectations for how these interactions shape community structure. Here we analytically predict and numerically confirm how the variability and strength of higher-order interactions affect species coexistence. We found that as higher-order interaction strengths became more variable across species, fewer species could coexist, echoing the behavior of pairwise models. If interspecific higher-order interactions became too harmful relative to self-regulation, coexistence in diverse communities was destabilized, but coexistence was also lost when these interactions were too weak and mutualistic higher-order effects became prevalent. This behavior depended on the functional form of the interactions as the destabilizing effects of the mutualistic higher-order interactions were ameliorated when their strength saturated with species' densities. Last, we showed that more species-rich communities structured by higher-order interactions lose species more readily than their species-poor counterparts, generalizing classic results for community stability. Our work provides needed theoretical expectations for how higher-order interactions impact species coexistence in diverse communities.

Understanding the impact of third-party species on pairwise coexistence

The persistence of virtually every single species depends on both the presence of other species and the specific environmental conditions in a given location. Because in natural settings many of these conditions are unknown, research has been centered on finding the fraction of possible conditions (probability) leading to species coexistence. The focus has been on the persistence probability of an entire multispecies community (formed of either two or more species). However, the methodological and philosophical question has always been whether we can observe the entire community and, if not, what the conditions are under which an observed subset of the community can persist as part of a larger multispecies system. Here, we derive long-term (using analytical calculations) and short-term (using simulations and experimental data) system-level indicators of the effect of third-party species on the coexistence probability of a pair (or subset) of species under unknown environmental conditions. We demonstrate that the fraction of conditions incompatible with the possible coexistence of a pair of species tends to become vanishingly small within systems of increasing numbers of species. Yet, the probability of pairwise coexistence in isolation remains approximately the expected probability of pairwise coexistence in more diverse assemblages. In addition, we found that when third-party species tend to reduce (resp. increase) the coexistence probability of a pair, they tend to exhibit slower (resp. faster) rates of competitive exclusion. Long-term and short-term effects of the remaining third-party species on all possible specific pairs in a system are not equally distributed, but these differences can be mapped and anticipated under environmental uncertainty.

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

Understanding the emergence of contingent and deterministic exclusion in multispecies communities

Competitive exclusion can be classified as deterministic or as historically contingent. While competitive exclusion is common in nature, it has remained unclear when multispecies communities formed by more than two species should be dominated by deterministic or contingent exclusion. Here, we take a fully parameterised model of an empirical competitive system between invasive annual and native perennial plant species to explain both the emergence and sources of competitive exclusion in multispecies communities. Using a structural approach to understand the range of parameters promoting deterministic and contingent exclusions, we then find heuristic theoretical support for the following three general conclusions. First, we find that the life-history of perennial species increases the probability of observing contingent exclusion by increasing their effective intrinsic growth rates. Second, we find that the probability of observing contingent exclusion increases with weaker intraspecific competition, and not with the level of hierarchical competition. Third, we find a shift from contingent exclusion to deterministic exclusion with increasing numbers of competing species. Our work provides a heuristic framework to increase our understanding about the predictability of species persistence within multispecies communities.

Generalizing game-changing species across microbial communities

Microbes form multispecies communities that play essential roles in our environment and health. Not surprisingly, there is an increasing need for understanding if certain invader species will modify a given microbial community, producing either a desired or undesired change in the observed collection of resident species. However, the complex interactions that species can establish between each other and the diverse external factors underlying their dynamics have made constructing such understanding context-specific. Here we integrate tractable theoretical systems with tractable experimental systems to find general conditions under which non-resident species can change the collection of resident communities-game-changing species. We show that non-resident colonizers are more likely to be game-changers than transients, whereas game-changers are more likely to suppress than to promote resident species. Importantly, we find general heuristic rules for game-changers under controlled environments by integrating mutual invasibility theory with in vitro experimental systems, and general heuristic rules under changing environments by integrating structuralist theory with in vivo experimental systems. Despite the strong context-dependency of microbial communities, our work shows that under an appropriate integration of tractable theoretical and experimental systems, it is possible to unveil regularities that can then be potentially extended to understand the behavior of complex natural communities.