Evolutionary Substitution and Replacement in N-Species Lotka-Volterra Systems

The successful invasion of a multi-species resident system by mutants has received a great deal of attention in theoretical ecology but less is known about what happens after the successful invasion. Here, in the framework of Lotka-Volterra (LV) systems, we consider the general question where there is one resident phenotype in each species and the evolutionary outcome after invasion remains one phenotype in each species but these include all the mutant phenotypes. In the first case, called evolutionary substitution, a mutant appears in only one species, the resident phenotype in this species dies out and the mutant coexists with the original phenotypes of the other species. In the second case, called evolutionary replacement, a mutant appears in each species, all resident phenotypes die out and the evolutionary outcome is coexistence among all the mutant phenotypes. For general LV systems, we show that dominance of the resident phenotype by the mutant (i.e. the mutant is always more fit) in each species where the mutant appears leads to evolutionary substitution/replacement. However, it is shown by example that, when dominance is weakened to only assuming the average fitness of the mutants is greater than the average for the resident phenotype, the residents may not die out. We also show evolutionary substitution occurs in two-species competitive LV systems when the initial invasion of the resident system (respectively, of the new coexistence system) is successful (respectively, unsuccessful). Moreover, if sequential evolutionary substitution occurs for either order that the two mutant phenotypes appear (called historically independent replacement), then it is shown evolutionar

On the suitability of Illius and Gordon\'s model for simulating the intake and digestibility of roughage diets by ruminants

predicting the digestibility and intake of tropical roughages by ruminants. Data from seven suitable empirical studies (i.e. studies that reported all requisite data needed to run the model) in which tropical roughages were fed to ruminants were used. These seven studies had 235 intake and 70 digestibility measurements on goats, sheep and cattle. The coefficient of variation (cv) of the observed digestibility was 13.8%. A linear least square regression relationship between the observed (Y) and predicted (X) digestibility accounted for barely 37% of the variation for the entire data set [Y = 0.24(s.e. = 0.056) + 0.61(SE = 0.100) X] and for 53% of the variation when 5% of the observations were treated as outliers: [Y = 0.17 (SE = 0.047) + 0.72 (SE = 0.084) X]. For both equations the intercept and the slope were different from zero and unity, respectively. Although, a plot of residual digestibility showed no distinct pattern, this model should be used with extreme caution because of its inherent noise. The observed intake had a higher cv of 18.3%. Regression relationships between the observed and predicted intakes accounted for barely 15% of the variation for the entire data set: [Y = 30.1(SE = 7.39) + 0.71(SE = 0.111) X] and for 20% of the variation when 5% of the extreme values were treated as outliers: [Y = 28.7(SE = 6.73) + 0.75(SE = 0.101) X]. A residual plot showed that the model systematically underestimated the intake of roughages which elicited high intakes. The discussion was structured to identify, justify and propose pathways for enhancing the model. Keywords: Ruminant, roughage intake, digestibility, modelSouth African Journal of Animal Science Vol. 37 (4) 2007: pp. 275-28

Resolving an issue arising from translocation strategy for saving the black rhino

In response to the In response to alarming a decline in black rhino decline in black rhino populations conservationists developed a plan to grow the South African population to 2000 in the shortest time possible. This was to be achieved by possible. This was to be achieved by removing animals from the high-density population in the Umfolozii-Hluhluwe Game Reserve. These animals would be translocated to new reserves with more abundant resources. This reduction in intra-specific competition would result in faster growth rates. The magnitude of proposed removals, however, did not take into consideration some important perspectives of the managers of the source population. In this paper we attempt to provide insight into the trade-offs between the needs and perspective of source managers and those of the propoents of maximun translocation

Multi-species evolutionary dynamics

Dynamical attainability of an evolutionarily stable strategy (ESS) through the process of mutations and natural selection has mostly been addressed through the use of the continuously stable strategy (CSS) concept for species evolutionary games in which strategies are drawn from a continuum, and by the adaptive trait dynamics method. We address the issue of dynamical attainability of an ESS in coevolving species through the use of the concept of an ESNIS. It is shown that the definition of an ESNIS coalition for coevolving species is not in general equivalent to other definitions for CSS given in the literature. We show under some additional conditions that, in a dynamic system which involves the strategies of a dimorphic ESNIS coalition and at most two strategies that are not members of ESNIS coalition, the ESNIS coalition will emerge as the winner. In addition an ESNIS will be approached because of the invasion structure of strategies in its neighborhood. This proves that under the above conditions an ESNIS has a better chance of being attained than a strategy coalition which is a CSS. The theory developed is applied to a class of coevolutionary game models with Lotka-Volterra type interactions and we show that for such models, an ESS coalition will be dynamically attainable through mutations and natural selection if the ESS coalition is also an ESNIS coalition

Frequency‐dependent two‐sex models: a new approach to sex ratio evolution with multiple maternal conditions

Mothers that experience different individual or environmental conditions may produce different proportions of male to female offspring. The Trivers-Willard hypothesis, for instance, suggests that mothers with different qualities (size, health, etc.) will use different sex ratios if maternal quality differentially affects sex-specific reproductive success. Condition-dependent, or facultative, sex ratio strategies like these allow multiple sex ratios to coexist within a population. They also create complex population structure due to the presence of multiple maternal conditions. As a result, modeling facultative sex ratio evolution requires not only sex ratio strategies with multiple components, but also two-sex population models with explicit stage structure. To this end, we combine nonlinear, frequency-dependent matrix models and multidimensional adaptive dynamics to create a new framework for studying sex ratio evolution. We illustrate the applications of this framework with two case studies where the sex ratios depend one of two possible maternal conditions (age or quality). In these cases, we identify evolutionarily singular sex ratio strategies, find instances where one maternal condition produces exclusively male or female offspring, and show that sex ratio biases depend on the relative reproductive value ratios for each sex