Related papers: A statistical interpretation of biologically inspi…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
On infinitesimally short time interval various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann (1986)). This is one of the cornerstones for…
If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Essential to each other, growth and exploration are jointly observed in populations, be it alive such as animals and cells or inanimate such as goods and money. But their ability to move, crucial to cope with uncertainty and optimize…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
In this work, a proposal for the estimation of the populations using logistic curve fitting is presented. This type of curve is used to study population growth, in this case population of people infected with the Covid-19 virus; and it can…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which an individual produce their…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…