Gene-culture coevolution under selection.

The joint evolutionary dynamics of phenotypes and genotypes are usually couched in terms of genetic variance contributions to changes in the phenotypic mean. Here, we study the evolution of a dichotomous phenotype whose transmission is controlled by one multi-allelic locus. The phenotype is under selection, which may be genotype-dependent. We answer classical population genetic questions about the phenogenotypic evolution, including the conditions for phenotypic and genotypic polymorphism, in terms of selection coefficients and rates of phenotypic transmission.

Evolution of reduced mutation under frequency-dependent selection.

Most models for the evolution of mutation under frequency-dependent selection involve some form of host-parasite interaction. These generally involve cyclic dynamics under which mutation may increase. Here we show that the reduction principle for the evolution of mutation, which is generally true for frequency-independent selection, also holds under frequency-dependent selection on haploids and diploids that does not involve cyclic dynamics.

Two state model for a constant disease hazard in paratuberculosis (and other bovine diseases).

Many diseases are characterized by a long and varying sub-clinical period. Two main mechanisms can explain such periods: a slow progress toward disease or a sudden transition from a healthy state to a disease state induced by internal or external events. We here survey epidemiological features of the amount of bacteria shed during Mycobacterium Avium Paratuberculosis (MAP) infection to test which of these two models, slow progression or sudden transition (or a combination of the two), better explains the transition from intermittent and low shedding to high shedding. Often, but not always, high shedding is associated with the occurrence of clinical signs. In the case of MAP, the clinical signs include diarrhea, low milk production, poor fertility and eventually emaciation and death. We propose a generic model containing bacterial growth, immune control and fluctuations. This proposed generic model can represent the two hypothesized types of transitions in different parameter regimes. The results show that the sudden transition model provides a simpler explanation of the data, but also suffers from some limitations. We discuss the different immunological mechanism that can explain and support the sudden transition model and the interpretation of each term in the studied model. These conclusions are applicable to a wide variety of diseases, and MAP serves as a good test case based on the large scale measurements of single cow longitudinal profiles in this disease.

Commensal pathogens as a source of a coexistence mechanism.

Most known organisms carry commensal viruses or bacteria. These parasites are often treated as an inevitable nuisance. We here show that they may be essential for the survival of the host species, and may actually be the force driving speciation. Viruses that do not hurt their natural host but are deadly for other species have been argued to facilitate invasion. We show using a generic SIR model that the opposite may be the general case. Such viruses may be the force sustaining multiple distinct populations through spatial segregation, in the absence of physical barriers. This segregation protects the hosts against invasion by neighboring, possibly more fit, populations. The virus induced segregation can eventually lead to allopatric speciation, with no animal dispersal, geographical changes or human activities. We further propose a speculative mechanism, where the introduction of a new virus to a population with a heterogeneous response (based for example on the MHC polymorphism) may lead to the segregation of distinct sub-populations reacting to different strains of the virus. The existence of such a mechanism will require further experimental validation.

Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns.

Cooperative interactions, their stability and evolution, provide an interesting context in which to study the interface between cellular and population levels of organization. Here we study a public goods model relevant to microorganism populations actively extracting a growth resource from their environment. Cells can display one of two phenotypes - a productive phenotype that extracts the resources at a cost, and a non-productive phenotype that only consumes the same resource. Both proliferate and are free to move by diffusion; growth rate and diffusion coefficient depend only weakly phenotype. We analyze the continuous differential equation model as well as simulate stochastically the full dynamics. We find that the two sub-populations, which cannot coexist in a well-mixed environment, develop spatio-temporal patterns that enable long-term coexistence in the shared environment. These patterns are purely fluctuation-driven, as the corresponding continuous spatial system does not display Turing instability. The average stability of coexistence patterns derives from a dynamic mechanism in which the producing sub-population equilibrates with the environmental resource and holds it close to an extinction transition of the other sub-population, causing it to constantly hover around this transition. Thus the ecological interactions support a mechanism reminiscent of self-organized criticality; power-law distributions and long-range correlations are found. The results are discussed in the context of general pattern formation and critical behavior in ecology as well as in an experimental context.

Diffusion rate determines balance between extinction and proliferation in birth-death processes.

We here study spatially extended catalyst induced growth processes. This type of process exists in multiple domains of biology, ranging from ecology (nutrients and growth), through immunology (antigens and lymphocytes) to molecular biology (signaling molecules initiating signaling cascades). Such systems often exhibit an extinction-proliferation transition, where varying some parameters can lead to either extinction or survival of the reactants. When the stochasticity of the reactions, the presence of discrete reactants and their spatial distribution is incorporated into the analysis, a non-uniform reactant distribution emerges, even when all parameters are uniform in space. Using a combination of Monte Carlo simulation and percolation theory based estimations; the asymptotic behavior of such systems is studied. In all studied cases, it turns out that the overall survival of the reactant population in the long run is based on the size and shape of the reactant aggregates, their distribution in space and the reactant diffusion rate. We here show that for a large class of models, the reactant density is maximal at intermediate diffusion rates and low or zero at either very high or very low diffusion rates. We give multiple examples of such system and provide a generic explanation for this behavior. The set of models presented here provides a new insight on the population dynamics in chemical, biological and ecological systems.

Balance between absorbing and positive fixed points in resource consumption models.

The effect of resource usage on economic growth has been studied in multiple models. However, the generic effect of improving resource usage efficacy through improved technical skills has not been studied in detail. We here analyze a model incorporating resource usage by capital and the parallel production of technical skill in order to study the effect of improving the efficacy of resources usage with advanced technologies. We show that a practically inevitable result of such a model is that improving the resource usage efficacy leads to a lower steady-state level of resources. A surprising conclusion from ordinary differential equations realization of the model is an extreme sensitivity to parameters, where a small parameter change can lead to an irreversible state through a hysteresis mechanism between a scenario of a collapse of the economy and a scenario of sustainable economy. This sensitivity is lost when spatial stochastic simulations are performed. In the stochastic regime the two scenarios coexist, with different fractions of the lattice residing in each state. Changing parameters smoothly changes the fraction of lattice sites in each state. The transition between the collapsed economy and the sustainable one is not symmetrical. Escape from the collapsed situation can only occur through diffusion from neighboring sustained lattice sites. On the other hand, the collapse can occur even in the absence of diffusion. This difference leads to diffusion dependent capital growth, where an optimal capital is obtained for middiffusion values. Such a transition may actually be generic phenomena in ecological and economic systems.