Related papers: Stochastic eco-evolutionary model of a prey-predat…
The far-reaching consequences of ecological interactions in the dynamics of biological communities remain an intriguing subject. For decades, competition has been a cornerstone in ecological processes, but mounting evidence shows that…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Long-term evolutionary processes can strongly influence common-pool resource conservation by generating new traits or behaviours that modify the feedback between population strategies and the resource state. Here we develop an…
Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph $G=(V,E)$. The evolution is driven by a linear birth rate, a density dependent logistic death rate an the possibility of mutations along the…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
We introduce the Webworld model, which links together the ecological modelling of food web structure with the evolutionary modelling of speciation and extinction events. The model describes dynamics of ecological communities on an…
Species sharing a prey or a predator species may go extinct due to exploitative or apparent competition. We examine whether evolution of the shared species acts as a coexistence mechanism and to what extent the answer depends on the genetic…
Predator prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely…
This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a…
In complex ecosystems such as microbial communities, there is constant ecological and evolutionary feedback between the residing species and the environment occurring on concurrent timescales. Species respond and adapt to their surroundings…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…