相关论文: Using mathematical modeling to ask meaningful biol…
Replicator equations (RE) are among the basic tools in mathematical theory of selection and evolution. The method of Hidden keystone variables (HKV) for reducing a wide class of RE of high or even infinite dimensionality to low-dimensional…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
Ecological systems can often be characterised by changes among a finite set of underlying states pertaining to individuals, populations, communities, or entire ecosystems through time. Owing to the inherent difficulty of empirical field…
Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behavior, especially given the inherent heterogeneity and…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
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…
1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics,…
The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…
Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years,…
How do mammalian cells that share the same genome exist in notably distinct phenotypes, exhibiting differences in morphology, gene expression patterns, and epigenetic chromatin statuses? Furthermore how do cells of different phenotypes…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…