Related papers: Global dynamics of a size-structured forest model
Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three…
We study a parabolic Lotka-Volterra type equation that describes the evolution of a population structured by a phenotypic trait, under the effects of mutations and competition for resources modelled by a nonlocal feedback. The limit of…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Models at various levels of resolution are commonly used, both for forest management and in ecological research. They all have comparative advantages and disadvantages, making desirable a better understanding of the relationships between…
The rapid increase of population and settlement structures in the Global South during recent decades motivates the development of suitable models to describe their formation and evolution. Such settlement formation has been previously…
Savannas are characterized by a discontinuous tree layer superimposed on a continuous layer of grass. Identifying the mechanisms that facilitate this tree-grass coexistence has remained a persistent challenge in ecology and is known as the…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…
We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their…
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
We consider $k$-dimensional discrete-time systems of the form $x_{n+1}=F(x_n,\ldots,x_{n-k+1})$ in which the map $F$ is continuous and monotonic in each one of its arguments. We define a partial order on $\mathbb{R}^{2k}_+$, compatible with…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
In this paper, a general tree algorithm processing a random flow of arrivals is analyzed. Capetanakis--Tsybakov--Mikhailov's protocol in the context of communication networks with random access is an example of such an algorithm. In…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be…
Cells maintain a stable size as they grow and divide. Inspired by the available experimental data, most proposed models for size homeostasis assume size control mechanisms that act on a timescale of one generation. Such mechanisms lead to…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected…
We consider a class of endomorphisms that contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. Our goal is to study a class of endomorphisms that preserve a foliation that is almost…
Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently,…