Effect of variable surrounding on species creation

We constructed a model of speciation from evolution in an ecosystem consisting of a limited amount of energy recources. The species possesses genetic information, which is inherited according to the rules of the Penna model of genetic evolution. The increase in the number of the individuals of each species depends on the quality of their genotypes and the available energy resources. The decrease in number of the individuals results from genetic death or maximum-age reaching by the individual. The amount of energy resources is represented by a solution of the differential logistic equation, where the growth rate of the amount of the energy resources has been modified to include the number of individuals from all species in the ecosystem under consideration. The fluctuating surrounding is modelled with the help of the function V(x, t) = 1/4 x4 + 1/2 b(t)x2, where x represents phenotype and the coefficient b(t) shows the cos(omega t) time dependence. The closer the value x of an individual to the minimum of V(x, t), the better adapted its genotype to the surrounding. We observed that the life span of the organisms strongly depends on the value of the frequency omega. It becomes shorter the more frequent the changes of the surrounding. However, there is a tendency for the species that have a higher value of the reproduction age aR to win the competition with the other species. Another observation is that small evolutionary changes of the inherited genetic information lead to spontaneous bursts of the evolutionary activity when many new species may appear in a short period.     

A mathematical derivation of size spectra in fish populations

Taking into account a predator/prey size ratio in a size-structured population model leads to a partial derivative equation of which we study the properties. By expliciting the structure of the attractor of this equation, it is shown that a simple mechanism, size-based opportunistic predation, can explain the stability in the shape of size spectra observed in various marine ecosystems.     

Dispersal and fighting in male pollinating fig wasps

For more than two decades, it has been the dogma that the males of pollinating fig wasps do not fight and that they only mate in their native fig. Their extreme degree of local mating leads to highly female biased sex ratios that should eliminate the benefits of fighting and dispersal by males. Furthermore, males sharing a fig are often brothers, and fighting may be barred by kin selection. Therefore, theory supported the presumed absence of fighting and dispersal in pollinating fig wasp males. However, we report here that in pollinating fig wasps, fighting between brothers evolved at least four and possibly six time, and dispersal by males at least twice. This finding supports the idea that competition between relatives can cancel the ameliorating effects of relatedness. The explanation to this evolutionary puzzle, as well as the consequences of male dispersal and fighting, opens the doors to exciting new research.     

Contribution to the logistic theory of growth: temporal structure and growth potential

The analysis of a structured population according to three (juvenile, mature and senescent) cellular states is carried out within the framework of Delattre's transformation systems theory. Growth in number, with the dissymmetry of cell divisions, is determined by an autocatalysis process under the constraint of the availability of a source. Two models are presented: their dynamics results in a growth of the exponential type or of the sigmoidal type, respectively. In the sigmoidal case, the logistic equation (Richards-Nelder's function with adjunction of a lower asymptote Y not equal to 0) fits satisfactorily the simulated data of the total cell number Y. The growth potential is defined as the instantaneous capacity of autocatalysis, which is expressed in relation to the present 'mitotic resources' (source + non-senescing mature cells). The acceleration variations d2Y/dt2 are in close agreement with the growth potential gradient. The analysis is then generalized to other population structuring. As a result, the logistic equation can be interpreted in terms of a formal model of growth of a structured population submitted to autocatalysis and competition.     

An agent-based model of sleeping sickness: simulation trials of a forest focus in southern Cameroon

An agent-based model (AMB) used to simulate the spread of Human African Trypanosomiasis is presented together with the results of simulations of a focus of the disease. This model is a completely spatialized approach taking into account a series of often overlooked parameters such as human behaviour (activity-related movements), the density and mobility of the disease vectors--tsetse flies (Glossina spp.)--and the influence of other tsetse feeding hosts (livestock and wild animal populations). The agents that represent humans and tsetse flies move in a spatially structured environment managed by specialized location agents. Existing compartmental mathematical models governed by differential equations fail to incorporate the spatial dimension of the disease transmission. Furthermore, on a small scale, transmission is unrealistically represented by entities less than one. This ABM was tested with data from one village of the Bipindi sleeping sickness focus (southern Cameroon) and with obtained realistic simulations of stable transmission involving an animal reservoir. In varying different spatial configurations, we observe that the stability of spread is linked to the spatial complexity (number of heterogeneous locations). The prevalence is very sensitive to the human densities and to the number of tsetse flies initially infected in a given location. A relatively low and durable prevalence is obtained with shortening the phase I. In addition, we discuss some upgrading possibilities, in particular the linkage to a Geographical Information System (GIS). The agent-based approach offers new ways to understanding the spread of the disease and a tool to evaluate risk and test control strategies.     

A hierarchical matrix model to assess the impact of habitat fragmentation on population dynamics: an elasticity analysis

To better understand the role of habitat quality and boundaries on population dynamics at the landscape scale, we develop a model combining a spatially implicit approach, a spatial population Leslie-type model and an implicit model of habitat fragmentation. An original approach of elasticity permits to identify which types of element and boundary influence the most population viability according to the wood fragmentation degree. The studied species is a corridor forest insect sensitive to fragmentation (Abax parallelepipedus, Coleoptera, Carabidae). We show that a single large patch of wood is better than several small patches for the population viability.