The costs and benefits of dispersal in small populations

Dispersal has three major effects on adaptation. First, the gene flow mixes alleles adapted to different environments, potentially hindering (swamping) adaptation. Second, it inflates genetic variance: this aids adaptation to spatially (and temporally) varying environments but if selection is hard, it lowers the mean fitness of the population. Third, neighbourhood size, which determines how weak genetic drift is, increases with dispersal -- when genetic drift is strong, increase of neighbourhood size with dispersal aids adaptation. In this note I focus on the role of dispersal in environments which change smoothly across space, and when local populations are quite small such that genetic drift has a significant effect. Using individual-based simulations, I show that in small populations, even leptokurtic dispersal benefits adaptation, by reducing the power of genetic drift. This has implications for management of small marginal populations: increased gene flow appears beneficial as long as adaptations involves a quantitative, rather than a discrete, trait. However, heavily leptokurtic dispersal will swamp continuous adaptation along steep environmental gradients so that only patches of locally adapted subpopulations remain.

Two-dimensional adaptive dynamics of evolutionary public goods games: finite-size effects on fixation probability and branching time

Public goods games (PGGs) describe situations in which individuals contribute to a good at a private cost, but others can free-ride by receiving a share of the public benefit at no cost. The game occurs within local neighbourhoods, which are subsets of the whole population. Free-riding and maximal production are two extremes of a continuous spectrum of traits. We study the adaptive dynamics of production and neighbourhood size. We allow the public good production and the neighbourhood size to coevolve and observe evolutionary branching. We explain how an initially monomorphic population undergoes evolutionary branching in two dimensions to become a dimorphic population characterized by extremes of the spectrum of trait values. We find that population size plays a crucial role in determining the final state of the population. Small populations may not branch or may be subject to extinction of a subpopulation after branching. In small populations, stochastic effects become important and we calculate the probability of subpopulation extinction. Our work elucidates the evolutionary origins of heterogeneity in local PGGs among individuals of two traits (production and neighbourhood size), and the effects of stochasticity in two-dimensional trait space, where novel effects emerge.

Simple Hyper-Heuristics Control the Neighbourhood Size of Randomised Local Search Optimally for LeadingOnes

Selection hyper-heuristics (HHs) are randomised search methodologies which choose and execute heuristics during the optimisation process from a set of low-level heuristics. A machine learning mechanism is generally used to decide which low-level heuristic should be applied in each decision step. In this article, we analyse whether sophisticated learning mechanisms are always necessary for HHs to perform well. To this end we consider the most simple HHs from the literature and rigorously analyse their performance for the LeadingOnes benchmark function. Our analysis shows that the standard Simple Random, Permutation, Greedy, and Random Gradient HHs show no signs of learning. While the former HHs do not attempt to learn from the past performance of low-level heuristics, the idea behind the Random Gradient HH is to continue to exploit the currently selected heuristic as long as it is successful. Hence, it is embedded with a reinforcement learning mechanism with the shortest possible memory. However, the probability that a promising heuristic is successful in the next step is relatively low when perturbing a reasonable solution to a combinatorial optimisation problem. We generalise the “simple” Random Gradient HH so success can be measured over a fixed period of time [Formula: see text], instead of a single iteration. For LeadingOnes we prove that the Generalised Random Gradient (GRG) HH can learn to adapt the neighbourhood size of Randomised Local Search to optimality during the run. As a result, we prove it has the best possible performance achievable with the low-level heuristics (Randomised Local Search with different neighbourhood sizes), up to lower-order terms. We also prove that the performance of the HH improves as the number of low-level local search heuristics to choose from increases. In particular, with access to [Formula: see text] low-level local search heuristics, it outperforms the best-possible algorithm using any subset of the [Formula: see text] heuristics. Finally, we show that the advantages of GRG over Randomised Local Search and Evolutionary Algorithms using standard bit mutation increase if the anytime performance is considered (i.e., the performance gap is larger if approximate solutions are sought rather than exact ones). Experimental analyses confirm these results for different problem sizes (up to [Formula: see text]) and shed some light on the best choices for the parameter [Formula: see text] in various situations.

IMPACT OF SPATIAL FILTER ON LAND-USE CHANGES MODELLING USING URBAN CELLULAR AUTOMATA

Urban cellular automata is used vastly in simulating of urban evolutions and dynamics. Finding an appropriate neighbourhood size in urban cellular automata modelling is important because the outputs are strongly influenced by input parameters. This paper investigates the impact of spatial filters on behaviour and outcome of urban cellular automata models. In this study different spatial filters in various sizes including 3*3, 5*5, 7*7, 9*9, 11*11, 13*13, 15*15 and 17*17 cells are used in a scenario of land-use changes. The proposed method is examined changes in size and shape of spatial filter whereas the resolution was kept fixed. The implementation results in Ahvaz city demonstrated that KAPPA index is changed in different shapes and types at the time when different spatial filters are used. However, circular shape with size of 5*5 offers better accuracy.

A comparison of nature inspired algorithms for the quadratic assignment problem

This paper presents an application of the ant algorithm and bees algorithm in optimization of QAP problem as an example of NP-hard optimization problem. The experiments with two types of algorithms: the bees algorithm and the ant algorithm were performed for the test instances of the quadratic assignment problem from QAPLIB, designed by Burkard, Karisch and Rendl. On the basis of the experiments results, an influence of particular elements of algorithms, including neighbourhood size and neighbourhood search method, will be determined.