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Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of food-web structure are reproducible across diverse habitats, yet little is known about the driving force behind this…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We incorporate the generic hierarchical architecture of foodwebs into a "{\it unified}" model that describes both "micro" and "macro" evolutions within a single theoretical framework. This model describes the "micro" -evolution in detail by…
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation…
Mutualistic interactions benefit both partners, promoting coexistence and genetic diversity. Spatial structure can promote cooperation, but spatial expansions may also make it hard for mutualistic partners to stay together, since genetic…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
In classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories have emphasized that developmental variability and…
Dispersal is a well recognized driver of ecological and evolutionary dynamics, and simultaneously an evolving trait. Dispersal evolution has traditionally been studied in single-species metapopulations so that it remains unclear how…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
The role of species interactions in controlling the interplay between the stability of an ecosystem and its biodiversity is still not well understood. The ability of ecological communities to recover after a small perturbation of the…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…
Ecology and evolution are inseparable. Motivated by some recent experiments, we have developed models of evolutionary ecology from the perspective of dynamic networks. In these models, in addition to the intra-node dynamics, which…