Joseph Apaloo

Exponentiated modified Weibull extension distribution

A new modified Weibull extension distribution is proposed by Xie et al. [20]. Recently, El-Gohary et al. [9] proposed a new distribution referred to as the generalized Gompertz distribution. In this paper, we propose a new model of a life time distribution that mainly generalizes these two distributions. We refer to this new distribution as the exponentiated modified Weibull extension distribution. This distribution generalizes, in addition to the above two mentioned distributions, the exponentiated Weibull distribution, the generalized exponential and the generalized Rayleigh distributions. Parameter estimation of the four parameters of this distribution is studied. Two real data sets are analyzed using the new distribution, which show that the exponentiated modified Weibull extension distribution can be used quite effectively in fitting and analyzing real lifetime data.

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.

Ecological Species Coevolution

The concepts of evolutionary stable strategies (ESS) and neighborhood invader strategies (NIS) are used to examine the dynamics of coevolving species. When an ESS as well as its near neighbors are ecologically stable and phenotypic space is unconstrained, the strong NIS concept shows that each member of the ESS coalition can always be repelled by some coalition strategies that are sufficiently close to the ESS. Thus an ESS for coevolving species may not be attained by selection unless phenotypic constraints are imposed.

Single species evolutionary dynamics

Not long after the introduction of evolutionary stable strategy (ESS) concept, it was noticed that dynamic selection did not always lead to the establishment of the ESS. The concept of continuously stable strategy (CSS) was thereafter developed. It was generally accepted that dynamic selection leads to the establishment of an ESS if it is a CSS. Examination of an evolutionary stability concept which is called neighborhood invader strategy (NIS) shows that it may be impossible for an ESS to be established through dynamic selection even if it is a CSS and no polymorphisms occur. We will examine the NIS concept and its implications for two evolutionary game models: root-shoot allocation in plant competition and Lotka–Volterra competition. In the root-shoot model we show that an ESS will be attained through dynamic selection if it is a NIS. Similarly for the Lotka–Volterra model, we show that an ESS will be attained through dynamic selection even if protected dimorphisms occur during the evolutionary process if it is an NIS.

Investigating strategies for minimising damage caused by the sugarcane pest Eldana saccharina

Abstract The control of Eldana saccharina Walker (Lepidoptera: Pyralidae) in sugarcane of KwaZulu-Natal, South Africa has proved problematical. Among various methods of control available are early harvesting and the use of insecticides. A precise and detailed simulation model is developed to investigate the effectiveness of such methods of control and in particular the optimal timing of such applications. The model is cohort-based and includes the effect of temperature on the physiological development of individuals in each life-stage of the insect. Further, the model gives a sugarcane damage index which indicates levels of damage on any given day of the simulation. Relationships are obtained involving the damage index, timing of harvest and duration of insecticide effectiveness under selected temperature patterns.

Evolutionary matrix games and optimization theory.

An evolutionarily stable strategy (ESS) is only required to be capable of resisting invasion by rare mutant strategies. In contrast, an absolute invader strategy (AIS) is a rare mutant strategy that can invade any established strategy. We show that the predictions of the outcome of evolution made by optimization models are compatible with those made by the classical expected payoff comparisons in matrix games. We also show that if a matrix game has an AIS that AIS is unique and is also an ESS. But an ESS need not be an AIS. In pure-strategy submodels, an AIS need not be unique. An AIS of a matrix game has global asymptotic stability property in the game dynamics which involve only pure strategies including the AIS.

FREQUENCY INDEPENDENT EVOLUTIONARY MODELS

Using general classes of evolutionary models in which fitnesses are frequency independent and density dependent, we show that a phenotype is an ESS if and only if it is a NIS. This result is seen to hold in single species and multi species evolutionary models with and without structure. Frequency independent and density dependent evolutionary models are thus more likely to attain an ESS.