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Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with "specialist" individuals that are adapted to the environment; this maximum moves…
Everyone can see that over the last 150 years, theoretical ecology has become considerably more mathematical. But what is the nature of this phenomenon? Are mathematics applied, as in the use of statistical tests, for example, or are they…
Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
Standard micro-economics concentrate on the description of markets but is seldom interested in production. Several economists discussed the concept of a firm, as opposed to an open labour market where entrepreneurs would recrute workers on…
Recent studies of in vitro evolution of DNA via protein binding indicate that the evolution behavior is qualitatively different in different parameter regimes. I here present a general theory that is valid for a wide range of parameters,…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
Competition between individuals drives the evolution of whole species. Although the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species may not be optimally fit. Here, using…
Kinetic exchange models have been successful in explaining the shape of the income/wealth distribution in the economies. However, such models usually make some ad-hoc assumptions when it comes to determining the savings factor. Here, we…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
The concept of fitness is introduced, and a simple derivation of the Fundamental Theorem of Natural Selection (which states that the average fitness of a population increases if its variance is nonzero) is given. After a short discussion of…
Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and…
The origin of economic crises is a key problem for economics. We present a model of long-run competitive markets to show that the multiplicity of behaviors in an economic system, over a long time scale, emerge as statistical regularities…
Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an…
We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the…
A major problem in evolutionary biology is how species learn and adapt under the constraint of environmental conditions and competition of other species. Models of cyclic dominance provide simplified settings in which such questions can be…
We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We…
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,…
The accurate prediction of biological features from genomic data is paramount for precision medicine and sustainable agriculture. For decades, neural network models have been widely popular in fields like computer vision, astrophysics and…