Stability indicatrices of nonnegative matrices and some of their applications in problems of biology and epidemiology

The method of constructing a stability indicatrix of a nonnegative matrix having the form of a polynomial of its coefficients is presented. The algorithm of construction and conditions of its applicability are specified. The applicability of the algorithm is illustrated on examples of constructing the stability indicatrix for a series of functions widely used in simulation of the dynamics of discrete biological communities, for solving evolutionary optimality problems arising in biological problems of evolutionary selection, for identification of the conditions of the pandemic in a distributed host population.

Evolutionary optimality in stochastic search problems

‘Optimal’ behaviour in a biological system is not simply that which maximizes a mean, or temporally and spatially averaged, fitness function. Rather, population dynamics and demographic and environmental stochasticity are fundamental evolutionary ingredients. Here, we revisit the problem of optimal foraging, where some recent studies claim that organisms should forage according to Lévy walks. We show that, in an ecological scenario dominated by uncertainty and high mortality, Lévy walks can indeed be evolutionarily favourable. However, this conclusion is dependent on the definition of efficiency and the details of the simulations. We analyse measures of efficiency that incorporate population-level characteristics, such as variance, superdiffusivity and heavy tails, and compare the results with those generated by simple maximizing of the average encounter rate. These results have implications on stochastic search problems in general, and also on computational models of evolutionary optima.

Computational Exploration of the Biological Basis of Black-Scholes Expected Utility Function

It has often been argued that there exists an underlying biological basis of utility functions. Taking this line of argument a step further in this paper, we have aimed to computationally demonstrate the biological basis of the Black-Scholes functional form as applied to classical option pricing and hedging theory. The evolutionary optimality of the classical Black-Scholes function has been computationally established by means of a haploid genetic algorithm model. The objective was to minimize the dynamic hedging error for a portfolio of assets that is built to replicate the payoff from a European multi-asset option. The functional form that is seen to evolve over successive generations which best attains this optimization objective is the classical Black-Scholes function extended to a multiasset scenario.Computational Exploration of the Biological Basis of Black-Scholes Expected Utility Function