Ecological fitting describes a situation where species interact despite no shared evolutionary history. It is both a null model for adaptation and an important process in its own right, for example, the establishment of a non-native species is ecological fitting, and it is a major mechanism in the formation of Novel Ecosystems. In this paper we introduce and analyse a model of ecological fitting. We demonstrate both analytically and through simulation that the main factors determining invasion success are the invaded ecosystem's population and diversity, which set the size of the barrier for invaders. We also study the situation where many evolutionarily unrelated species simultaneously colonise an empty area. We show that a successful equilibrium is likely to be established, but the diversity tends to be very much less than the number of species in the starting pool and discuss the implications of this.

We introduce a new interacting particle system intended to model an example of ecological succession involving two species: the bracken and the european beech. The objective is to exhibit phase transitions by proving that there exist three possible evolutions of the system to distinct ecological balances. More precisely, the whole population may die out, the european beech may conquer the bracken, and coexistence of both species may occur.

Ecology studies the interactions between individuals, species and the environment. The ability to predict the dynamics of ecological systems would support the design and monitoring of control strategies and would help to address pressing global environmental issues. It is also important to plan for efficient use of natural resources and maintenance of critical ecosystem services. The mathematical modelling of ecological systems often includes nontrivial specifications of processes that influence the birth, death, development and movement of individuals in the environment, that take into account both biotic and abiotic interactions. To assist in the specification of such models, we introduce MELA, a process algebra for Modelling in Ecology with Location Attributes. Process algebras allow the modeller to describe concurrent systems in a high-level language. A key feature of concurrent systems is that they are composed of agents that can progress simultaneously but also interact - a good match to ecological systems. MELA aims to provide ecologists with a straightforward yet flexible tool for modelling ecological systems, with particular emphasis on the description of space and the environment. Here we present four example MELA models, illustrating the different spatial arrangements which can be accommodated and demonstrating the use of MELA in epidemiological and predator-prey scenarios.

May (1974,1976) opened the debate on whether biological populations might exhibit nonlinear dynamics and chaos. However, it has in general been difficult to verify nonlinear dynamics in biological populations. There are many reports concerning problems with this issue and some of them can be traced back to Hassell, Lawton, and May (1976) and Morris (1990) Our objective is not a discussion of the presence of nonlinear dynamics in biological populations. Instead, we analyze whether ecological census data can be used for validating nonlinearities at all. We choose our models and our situation so that as much as possible can be done rigorously with by hand computations. We consider a clearly nonlinear chemostat based model that is isolated. Some noise must be considered, and we choose a minimal approach: Only noise originating from the fact that ecological populations remain finite is considered, cf. Bailey (1964). Not only the interacting populations but also collected data sets tend to remain finite. Collection of long data sets might be associated with huge costs in ecology. Examples of exceptionally long and carefully studied ecological time series are those collected by Nicholson (1954) and Utida (1957). These data sets contain a few hundred data points, and we use this as a guideline for when an ecological time series should be considered exceptionally long in this chapter.

New observations are opening the possibility of characterising habitable environments in exoplanetary systems, with the recent example of the candidate hycean world K2-18 b. This motivates an exploration of the possible ecological conditions on such planets to better interpret biosignatures as well as understand the nature of potential life. On Earth, the Lotka-Volterra equations have been used to model numerous coupled populations within ecosystems, from interactions between large vertebrates, to systems with multiple microbial species. In this work, we apply the Lotka-Volterra equations to the ecology of habitable exoplanets for the first time, focusing on hycean worlds. We simulate scenarios in a vertical water column with between 1-5 bacterial species that thrive in anoxic environments on Earth, i.e. similar to predicted hycean conditions. We find that a wide range of ecological diversity is possible for microbial populations under hycean conditions. We demonstrate that dominating phototrophic bacteria at the top of a water column out-compete deeper dwelling phototrophic bacteria, analogous to bacterial blooms on Earth. Incorporating microbial viruses (bacteriophages) within our models can cause ecosystem collapse depending on the time of their introduction, and such phage inclusion can be beneficial to ecological diversity. Finally, our work shows that bacterial populations inhabiting tidally locked exoplanets may be more stable due to constant illumination of the ocean, but can have lower peak population densities in such cases when compared to seasonal scenarios. Our work provides an initial step towards understanding the possible ecological diversity on habitable worlds beyond Earth.

Modeling social-ecological systems is difficult due to the complexity of ecosystems and of individual and collective human behavior. Key components of the social-ecological system are often over-simplified or omitted. Generalized modeling is a dynamical systems approach that can overcome some of these challenges. It can rigorously analyze qualitative system dynamics such as regime shifts despite incomplete knowledge of the model's constituent processes. Here, we review generalized modeling and use a recent study on the Baltic Sea cod fishery's boom and collapse to demonstrate its application to modeling the dynamics of empirical social-ecological systems. These empirical applications demand new methods of analysis suited to larger, more complicated generalized models. Generalized modeling is a promising tool for rapidly developing mathematically rigorous, process-based understanding of a social-ecological system's dynamics despite limited knowledge of the system.

A fundamental problem in community ecology is to understand how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we present a simple, analytically tractable, presence-absence (PA) model for community assembly and use it to ask how ecological traits such as the strength of competition, the amount of diversity, and demographic and environmental stochasticity affect species composition in a community. In the PA model, species are treated as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent work on large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special ("critical") point corresponding to Hubbell's neutral theory of biodiversity. These results suggest that the concepts of ecological "phases" and phase diagrams can provide a powerful framework for thinking about community ecology and that the PA model captures the essential ecological dynamics of community assembly.

A three species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painleve analysis while chaotic behaviour is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model, in a paper by Rai ([1995] ``Modelling ecological systems'', Int. J. Bifurcation and Chaos 5, 537-543).

The value of Earth observation foundation models for high-impact ecological applications remains insufficiently characterized. This study is one of the first to systematically evaluate the performance, limitations and practical considerations across three common ecological use cases: forest functional trait estimation, land use and land cover mapping and peatland detection. We fine-tune two pretrained models (Prithvi-EO-2.0 and TerraMind) and benchmark them against a ResNet-101 baseline using datasets collected from open sources. Across all tasks, Prithvi-EO-2.0 and TerraMind consistently outperform the ResNet baseline, demonstrating improved generalization and transfer across ecological domains. TerraMind marginally exceeds Prithvi-EO-2.0 in unimodal settings and shows substantial gains when additional modalities are incorporated. However, performance is sensitive to divergence between downstream inputs and pretraining modalities, underscoring the need for careful dataset alignment. Results also indicate that higher-resolution inputs and more accurate pixel-level labels remain critical for capturing fine-scale ecological dynamics.

Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow and extinctions are permanent, with ecological dynamics reaching a stable fixed point between introductions of invaders or mutants. When new strains are slowly added to the community, the ecosystem converges, after an initial evolutionary transient, to a diverse eco-evolutionary steady state. In this "Red Queen" phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting any smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to "general fitness" differences in the intrinsic growth rates of strains. Via a dynamical mean field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particular limit of model parameters. Scaling arguments enable a more general understanding of the steady state and evolutionary transients toward it. This work therefore establishes simple models of continual evolution in an ecological context without host-pathogen arms races, and points to the generality of Red Queen evolution. However, we also find other eco-evolutionary phases in simple models: For generalized Lotka-Volterra models with weakly asymmetric interactions an "oligarch" phase emerges in which the evolutionary dynamics continually slow down and a substantial fraction of the community's abundance condenses into a handful of slowly turning-over strains.