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There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibrium-like behavior in localized or nonlocalized domains within non-equilibrium…
Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most…
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
The dynamics of many microbial ecosystems are driven by cross-feeding interactions, in which metabolites excreted by some species are metabolised further by others. The population dynamics of such ecosystems are governed by…
We present a complete analysis of the Schelling dynamical system [Haw2018] of two connected neighbourhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable…
We consider a population of agents that are heterogeneous with respect to (i) their strategy when interacting $n_{g}$ times with other agents in an iterated prisoners dilemma game, (ii) their spatial location on $K$ different islands. After…
Mutualistic interactions, which are beneficial for both interacting species, are recurrently present in ecosystems. Observations of natural systems showed that, if we draw mutualistic relationships as binary links between species, the…
Microorganisms live in environments that inevitably fluctuate between mild and harsh conditions. As harsh conditions may cause extinctions, the rate at which fluctuations occur can shape microbial communities and their diversity, but we…
Dynamics of species' abundances in ecological communities are often described using models that only account for a few species. It is not clear when and why this would be possible, as most species form part of diverse ecological…
Ecosystems are commonly organized into trophic levels -- organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic…
Ecological systems have a high level of complexity combined with stability and rich biodiversity. Recently, the analysis of their properties and evolution has been pushed forward on a basis of concept of mutualistic networks that provides a…
Bacterial chemotaxis systems are as diverse as the environments that bacteria inhabit, but how much environmental variation can cells tolerate with a single system? Diversification of a single chemotaxis system could serve as an…
Marine ecosystem models are an important tool to assess the role of the ocean biota in climate change and to identify relevant biogeochemical processes by validating the model outputs against observational data. For the assessment of the…
An ongoing debate in ecology concerns the impacts of ecological drift and selection on community assembly. Here, we show that there is a sharp phase transition in diverse ecological communities between a selection dominated regime (the…
Ecosystems are governed by dynamic processes such as competition for resources, reproduction and dispersal. These shape their biodiversity and how the system responds to change. Current approaches to modelling ecosystems, especially plants,…
We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are…
In abstract terms, ecosystem ecology is about determining when two ecosystems, superficially different, are alike in some deeper way. An external observer can choose any ecosystem property as being important. In contrast, two ecosystems are…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…