Permanence via invasion graphs: incorporating community assembly into modern coexistence theory

Structural stability of invasion graphs for Lotka-Volterra systems

In this paper, we study in detail the structure of the global attractor for the Lotka-Volterra system with a Volterra-Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.

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.

Combining intransitive and higher-order effects in a coupled oscillator framework: A case study of an ant community

A growing body of literature recognizes that pairwise species interactions are not necessarily an appropriate metaphorical molecule of community ecology. Two examples are intransitive competition and nonlinear higher-order effects. While these two processes have been discussed extensively, the explicit analysis of how the two of them behave when simultaneously part of the same dynamic system has not yet been explored theoretically. A concrete situation exists on coffee farms in Puerto Rico in which three ant species form an intransitive competitive triplet, and that triplet is strongly influenced, nonlinearly, by a fly parasitoid that modifies the competitive ability of one of the species. Using this arrangement as a template, we explore the dynamical consequences with a simple ordinary differential equation (ODE) model. Results are complicated and include alternative periodic and chaotic attractors. The qualitative structures of those complications, however, may be approximately retrieved from the basic natural history of the system.

On the limits to invasion prediction using coexistence outcomes

The dynamics of ecological communities in nature are typically characterized by probabilistic processes involving invasion dynamics. Because of technical challenges, however, the majority of theoretical and experimental studies have focused on coexistence dynamics. Therefore, it has become central to understand the extent to which coexistence outcomes can be used to predict analogous invasion outcomes relevant to systems in nature. Here, we study the limits to this predictability under a geometric and probabilistic Lotka-Volterra framework. We show that while individual survival probability in coexistence dynamics can be fairly closely translated into invader colonization probability in invasion dynamics, the translation is less precise between community persistence and community augmentation, and worse between exclusion probability and replacement probability. These results provide a guiding and testable theoretical framework regarding the translatability of outcomes between coexistence and invasion outcomes when communities are represented by Lotka-Volterra dynamics under environmental uncertainty.

Building modern coexistence theory from the ground up: The role of community assembly

Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates-the average, per-capita growth rate of a rare species-to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a 'mutual invasibility' condition designed for two-species communities but poorly defined for species-rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. We propose a clear framework for expanding MCT to species-rich communities and for understanding invasion resistance as well as coexistence, especially for communities that could not be analysed with MCT so far. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence.

Eco-evolutionary maintenance of diversity in fluctuating environments

Growing evidence suggests that temporally fluctuating environments are important in maintaining variation both within and between species. To date, however, studies of genetic variation within a population have been largely conducted by evolutionary biologists (particularly population geneticists), while population and community ecologists have concentrated more on diversity at the species level. Despite considerable conceptual overlap, the commonalities and differences of these two alternative paradigms have yet to come under close scrutiny. Here, we review theoretical and empirical studies in population genetics and community ecology focusing on the 'temporal storage effect' and synthesise theories of diversity maintenance across different levels of biological organisation. Drawing on Chesson's coexistence theory, we explain how temporally fluctuating environments promote the maintenance of genetic variation and species diversity. We propose a further synthesis of the two disciplines by comparing models employing traditional frequency-dependent dynamics and those adopting density-dependent dynamics. We then address how temporal fluctuations promote genetic and species diversity simultaneously via rapid evolution and eco-evolutionary dynamics. Comparing and synthesising ecological and evolutionary approaches will accelerate our understanding of diversity maintenance in nature.

Mechanistic Models of Trophic Interactions: Opportunities for Species Richness and Challenges for Modern Coexistence Theory

AbstractMany potential mechanisms promote species coexistence, but we know little about their relative importance. To compare multiple mechanisms, we modeled a two-trophic planktonic food web based on mechanistic species interactions and empirically measured species traits. We simulated thousands of possible communities under realistic and altered interaction strengths to assess the relative importance of three potential drivers of phytoplankton and zooplankton species richness: resource-mediated coexistence mechanisms, predator-prey interactions, and trait trade-offs. Next, we computed niche and fitness differences of competing zooplankton to obtain a deeper understanding of how these mechanisms determine species richness. We found that predator-prey interactions were the most important driver of phytoplankton and zooplankton species richness and that large zooplankton fitness differences were associated with low species richness, but zooplankton niche differences were not associated with species richness. However, for many communities we could not apply modern coexistence theory to compute niche and fitness differences of zooplankton because of conceptual issues with the invasion growth rates arising from trophic interactions. We therefore need to expand modern coexistence theory to fully investigate multitrophic-level communities.

Navigation between initial and desired community states using shortcuts

Ecological management problems often involve navigating from an initial to a desired community state. We ask whether navigation without brute-force additions and deletions of species is possible via: adding/deleting a small number of individuals of a species, changing the environment, and waiting. Navigation can yield direct paths (single sequence of actions) or shortcut paths (multiple sequences of actions with lower cost than a direct path). We ask (1) when is non-brute-force navigation possible?; (2) do shortcuts exist and what are their properties?; and (3) what heuristics predict shortcut existence? Using a state diagram framework applied to several empirical datasets, we show that (1) non-brute-force navigation is only possible between some state pairs, (2) shortcuts exist between many state pairs; and (3) changes in abundance and richness are the strongest predictors of shortcut existence, independent of dataset and algorithm choices. State diagrams thus unveil hidden strategies for manipulating species coexistence and efficiently navigating between states.