Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the

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Community assembly is affected by environmental filtering that restricts viable phenotypes and by species interactions that impose limits on interspecific trait similarity.Relative influences of these processes should vary according to habitat features and dispersal. Species dispersion within assemblage trait space also should vary in relation to species richness, strength of competition, and the spatiotemporal scale of analysis. We examined ecomorphological diversity of two freshwater fish families (Neotropical Cichlidae, Nearctic Centrarchidae) to test theories of local assembly from regional species pools and theories of species packing within mesohabitat patches. Cichlid and centrarchid assemblages were surveyed in four floodplain rivers (two in South America and two in North America) during low-water periods when fish densities are highest. Surveys were conducted in four mesohabitat types (submerged wood, leaf litter, rocks, sand bank) within river channels and floodplain lakes. We measured 23 morphological traits associated with locomotion and feeding. Principal components analysis was performed on the species 3 traits matrix, and species axis scores were used to calculate species pairwise Euclidean distances and indices of dispersion within assemblage morphospace: mean nearest-neighbor distance (indicating similarity), mean distance to centroid (assemblage morphospace size), and standard deviation of nearestneighbor distance (evenness of dispersion within assemblage morphospace). A null model was used to assess whether patterns were significantly nonrandom. When data for all mesohabitat types were combined for each river, species were significantly overdispersed and the assemblage morphospace was larger than predicted at random in every case. Analysis of assemblages within mesohabitat patches of different types revealed, in every case, significant overdispersion of species in morphospace indicative of limiting similarity. The total assemblage morphospace was greater than expected for tropical cichlids, but not for temperate centrarchids. Trends of species dispersion with assemblage morphospace in relation to species richness within mesohabitat patches were not consistent among or within river systems, possibly indicating that patches were already saturated with these perciform fishes. Interregional comparisons suggest an influence from both adaptive diversification and environmental filtering at broad spatial scales. At the scale of mesohabitat patches in lowland rivers, cichlid and centrarchid assemblages revealed patterns of trait complementarity that imply limiting similarity and strong influence of biotic interactions.

Hill climbing algorithms are at the core of many approaches to solve optimization problems. Such algorithms usually require the complete enumeration of a neighborhood of the current solution. In the case of problems defined over binary strings of length n, we define the r-ball neighborhood as the set of solutions at Hamming distance r or less from the current solution. For r n this neighborhood contains Θ(n r ) solutions. In this paper efficient methods are introduced to locate improving moves in the r-ball neighborhood for problems that can be written as a sum of a linear number of subfunctions depending on a bounded number of variables. NK-landscapes and MAX-kSAT are examples of these problems. If the number of subfunctions depending on any given variable is also bounded, then we prove that the method can explore the neighborhood in constant time, despite the fact that the number of solutions in the neighborhood is polynomial in n. We develop a hill climber based on our exploration method and we analyze its efficiency and efficacy using experiments with NKq-landscapes instances.

Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound their runtime. We analyze the runtime in dependence of the number of inner points k. In the first part of the paper, we study a [Formula: see text] EA in a strictly black box setting and show that it can solve the Euclidean TSP in expected time [Formula: see text] where A is a function of the minimum angle [Formula: see text] between any three points. Based on insights provided by the analysis, we improve this upper bound by introducing a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps. This strategy improves the upper bound to [Formula: see text]. In the second part of the paper, we use the information gained in the analysis to incorporate domain knowledge to design two fixed-parameter tractable (FPT) evolutionary algorithms for the planar Euclidean TSP. We first develop a [Formula: see text] EA based on an analysis by M. Theile, 2009, ”Exact solutions to the traveling salesperson problem by a population-based evolutionary algorithm,” Lecture notes in computer science, Vol. 5482 (pp. 145–155), that solves the TSP with k inner points in [Formula: see text] generations with probability [Formula: see text]. We then design a [Formula: see text] EA that incorporates a dynamic programming step into the fitness evaluation. We prove that a variant of this evolutionary algorithm using 2-opt mutation solves the problem after [Formula: see text] steps in expectation with a cost of [Formula: see text] for each fitness evaluation.