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A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…
Phenotypic plasticity is a key factor in driving the evolution of species in the predator-prey interaction. The natural environment is replete with phenotypic plasticity, which is the source of inducible defences against predators,…
Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction…
We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates…
In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment…
We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success…
A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in…
All living things exhibit adaptations that enable them to survive and reproduce in the natural environment that they inhabit. From a biological standpoint, it has long been understood that adaptation comes from natural selection, whereby…
We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical…
A class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure is introduced in a context of quantitative genetic applications. The methods introduced can be used in many applications in…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
We propose a type-dependent branching model with mutation and competition for modeling phylogenies of a virus population. The competition kernel depends for any two virus particles on the particles' types, the total mass of the population…
Logit dynamics are evolution equations that describe transitions to equilibria of actions among many players. We formulate a pair-wise logit dynamic in a continuous action space with a generalized exponential function, which we call a…
This paper concerns applications of genetic algorithms and genetic programming to tasks for which it is difficult to find a representation that does not map to a highly complex and discontinuous fitness landscape. In such cases the standard…
In this paper, we are concerned with a two-species competitive model with diffusive terms on a periodically evolving domain and study the impact of the spatial periodic evolution on the dynamics of the model. The Lagrangian transformation…
Using as a narrative theme the example of Darwin's finches, a microscopic agent-based model is introduces to study sympatric speciation as a result of competition for resources in the same ecological niche. Varying competition among…
Molecular ecology uses molecular genetic data to answer traditional ecological questions in biogeography and biodiversity among others. Several ecological principles, such as the niche hypothesis and the competitive exclusions, are based on…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and…
The dynamics of city's spatial structures are determined by the coupling of functional components (such as restaurants and shops) and human beings within the city. Yet, there still lacks mechanism models to quantify the spatial distribution…