Related papers: A host-pathogen coevolution model. Part I: Run str…
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under…
Coevolution is expected to follow two alternative dynamics, often called trench warfare and arms races in plant-pathogen systems. Trench warfare situations are stable cycles of allele frequencies at the coevolving loci of both host and…
Coevolutionary arms races form between interacting populations that constitute each other's environment and respond to mutual changes. This inherently far-from-equilibrium process finds striking manifestations in the adaptive immune system,…
We introduce a generalized version of the frog model to describe the invasion of a parasite population in a spatially structured immobile host population with host immunity on the integer line. Parasites move according to simple symmetric…
We consider a periodic reaction diffusion system which, because of competition between $u$ and $v$, does not enjoy the comparison principle. It also takes into account mutations, allowing $u$ to switch to $v$ and vice versa. Such a system…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and…
The complexity of interactions between networks and territories has been widely acknowledged empirically, in particular through the existence of circular causal relations in their co-development, that can be understood as a co-evolution.…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
We investigate a time-dependent spatial vector-host epidemic model with non-coincident domains for the vector and host populations. The host population resides in small non-overlapping sub-regions, while the vector population resides…
We investigate the dynamics of a simple epidemiological model for the invasion by a pathogen strain of a population where another strain circulates. We assume that reinfection by the same strain is possible but occurs at a reduced rate due…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this…
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 study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for…
This paper proposes a framework to ensure the existence of dynamical system trajectories in the state space of labeled, weighted, and attributed graphs. The evolution of such a system exhibits hybrid behavior: discrete jumps affecting the…
We model the immune surveillance of a pathogen which passes through $n$ immunologically distinct stages. The biological parameters of this system induce a partial order on the stages, and this, in turn, determines which stages will be…