Assessing mutualistic metacommunity capacity by integrating spatial and interaction networks

We develop a spatially realistic model of mutualistic metacommunities that exploits the joint structure of spatial and interaction networks. Assuming that all species have the same colonisation and extinction parameters, this model exhibits a sharp transition between stable non-null equilibrium states and a global extinction state. This behaviour allows defining a threshold on colonisation/extinction parameters for the long-term metacommunity persistence. This threshold, the 'metacommunity capacity', extends the metapopulation capacity concept and can be calculated from the spatial and interaction networks without needing to simulate the whole dynamics. In several applications we illustrate how the joint structure of the spatial and the interaction networks affects metacommunity capacity. It results that a weakly modular spatial network and a power-law degree distribution of the interaction network provide the most favourable configuration for the long-term persistence of a mutualistic metacommunity. Our model that encodes several explicit ecological assumptions should pave the way for a larger exploration of spatially realistic metacommunity models involving multiple interaction types.

Flexible foraging behaviour increases predator vulnerability to climate change

Higher temperatures are expected to reduce species coexistence by increasing energetic demands. However, flexible foraging behaviour could balance this effect by allowing predators to target specific prey species to maximize their energy intake, according to principles of optimal foraging theory. Here we test these assumptions using a large dataset comprising 2,487 stomach contents from six fish species with different feeding strategies, sampled across environments with varying prey availability over 12 years in Kiel Bay (Baltic Sea). Our results show that foraging shifts from trait- to density-dependent prey selectivity in warmer and more productive environments. This behavioural change leads to lower consumption efficiency at higher temperature as fish select more abundant but less energetically rewarding prey, thereby undermining species persistence and biodiversity. By integrating this behaviour into dynamic food web models, our study reveals that flexible foraging leads to lower species coexistence and biodiversity in communities under global warming.

A metagenomic alpha-diversity index for microbial functional biodiversity

Alpha-diversity indices are an essential tool for describing and comparing biodiversity. Microbial ecologists apply indices originally intended for, or adopted by, macroecology to address questions relating to taxonomy (conserved marker) and function (metagenome-based data). In this Perspective piece, I begin by discussing the nature and mathematical quirks important for interpreting routinely employed alpha-diversity indices. Secondly, I propose a metagenomic alpha-diversity index (MD) that measures the (dis)similarity of protein-encoding genes within a community. MD has defined limits, whereby a community comprised mostly of similar, poorly diverse protein-encoding genes pulls the index to the lower limit, while a community rich in divergent homologs and unique genes drives it toward the upper limit. With data acquired from an in silico and three in situ metagenome studies, I derive MD and typical alpha-diversity indices applied to taxonomic (ribosomal rRNA) and functional (all protein-encoding) genes, and discuss their relationships with each other. Not all alpha-diversity indices detect biological trends, and taxonomic does not necessarily follow functional biodiversity. Throughout, I explain that protein Richness and MD provide complementary and easily interpreted information, while probability-based indices do not. Finally, considerations regarding the unique nature of microbial metagenomic data and its relevance for describing functional biodiversity are discussed.

Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.

Heteroclinic cycling and extinction in May-Leonard models with demographic stochasticity

May and Leonard (SIAM J Appl Math 29:243-253, 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.

Let's Train More Theoretical Ecologists - Here Is Why

A tangled web of vicious circles, driven by cultural issues, has prevented ecology from growing strong theoretical roots. Now this hinders development of effective conservation policies. To overcome these barriers in view of urgent societal needs, we propose a global network of postgraduate theoretical training programs.

Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time

Population structure can be modeled by evolutionary graphs, which can have a substantial influence on the fate of mutants. Individuals are located on the nodes of these graphs, competing to take over the graph via the links. Applications for this framework range from the ecology of river systems and cancer initiation in colonic crypts to biotechnological search for optimal mutations. In all these applications, both the probability of fixation and the associated time are of interest. We study this problem for all undirected and unweighted graphs up to a certain size. We devise a genetic algorithm to find graphs with high or low fixation probability and short or long fixation time and study their structure searching for common themes. Our work unravels structural properties that maximize or minimize fixation probability and time, which allows us to contribute to a first map of the universe of evolutionary graphs.

Unifying relationships between complexity and stability in mutualistic ecological communities

Conserving ecosystem function and associated services requires deep understanding of the underlying basis of system stability. While the study of ecological dynamics is a mature and diverse field, the lack of a general model that predicts a broad range of theoretical and empirical observations has allowed unresolved contradictions to persist. Here we provide a general model of mutualistic ecological interactions between two groups and show for the first time how the conditions for bi-stability, the nature of critical transitions, and identifiable leading indicators in time-series can be derived from the basic parameters describing the underlying ecological interactions. Strong mutualism and nonlinearity in handling-time are found to be necessary conditions for the occurrence of critical transitions. We use the model to resolve open questions concerning the effects of heterogeneity in inter-species interactions on both resilience and abundance, and discuss these in terms of potential trade-offs in real systems. This framework provides a basis for rich investigations of ecological system dynamics, and may be generalizable across many ecological contexts.

Differentiating and defusing theoretical Ecology's criticisms: A rejoinder to Sagoff's reply to Donhauser (2016)

In a (2016) paper in this journal, I defuse allegations that theoretical ecological research is problematic because it relies on teleological metaphysical assumptions. Mark Sagoff offers a formal reply. In it, he concedes that I succeeded in establishing that ecologists abandoned robust teleological views long ago and that they use teleological characterizations as metaphors that aid in developing mechanistic explanations of ecological phenomena. Yet, he contends that I did not give enduring criticisms of theoretical ecology a fair shake in my paper. He says this is because enduring criticisms center on concerns about the nature of ecological networks and forces, the instrumentality of ecological laws and theoretical models, and the relation between theoretical and empirical methods in ecology that that paper does not broach. Below I set apart the distinct criticisms Sagoff presents in his commentary and respond to each in turn.

Partial differential equation techniques for analysing animal movement: A comparison of different methods

Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement.

Theoretical ecology as etiological from the start

The world's leading environmental advisory institutions look to ecological theory and research as an objective guide for policy and resource management decision-making. In addition to the theoretical and broadly philosophical merits of doing so, it is therefore practically significant to clear up confusions about ecology's conceptual foundations and to clarify the basic workings of inferential methods used in the science. Through discussion of key moments in the genesis of the theoretical branch of ecology, this essay elucidates a general heuristic role of teleological metaphors in ecological research and defuses certain enduring confusions about work in ecology.

Multiple dimensions of biodiversity and ecosystem processes: Exploring the joint influence of intraspecific, specific and interspecific diversity

The positive influence of biodiversity on ecosystem processes was the focus of intense debate in ecology throughout the recent decades, becoming accepted and treated as a new paradigm in contemporary ecology. However, the available literature in this research field extensively explores species richness as an unidimensional measure for biodiversity. The present study explores how different components of biological diversity (number of genotypes, species, and functional groups) can influence an ecosystem process (biomass fixation). A mathematical model was employed and the simulation results showed that species richness per se does not affect the ecosystem productivity. Genotypic richness affected positively the ecosystem, but only if the genotypes are functionally complementary. The functional groups richness always affected positively the simulated ecosystem process. When together, richness at the different components of biological diversity showed stronger effect on ecosystem, and the scenarios with high species, genotypes and functional groups richness were the most productive ones. The results also allowed to observe that the ecosystems which are diverse in terms of functional groups and genotypes can be less susceptible to species loss. Finally, it is argued that a multiple dimension approach to biodiversity is relevant to advance the current knowledge on the relation between biodiversity and ecosystem functioning.