Using Decomposed Error for Reproducing Implicit Understanding of Algorithms.

Reproducibility is important for having confidence in evolutionary machine learning algorithms. Although the focus of reproducibility is usually to recreate an aggregate prediction error score using fixed random seeds, this is not sufficient. Firstly, multiple runs of an algorithm, without a fixed random seed, should ideally return statistically equivalent results. Secondly, it should be confirmed whether the expected behaviour of an algorithm matches its actual behaviour, in terms of how an algorithm targets a reduction in prediction error. Confirming the behaviour of an algorithm is not possible when using a total error aggregate score. Using an error decomposition framework as a methodology for improving the reproducibility of results in evolutionary computation addresses both of these factors. By estimating decomposed error using multiple runs of an algorithm and multiple training sets, the framework provides a greater degree of certainty about the prediction error. Also, decomposing error into bias, variance due to the algorithm (internal variance), and variance due to the training data (external variance) more fully characterises evolutionary algorithms. This allows the behaviour of an algorithm to be confirmed. Applying the framework to a number of evolutionary algorithms shows that their expected behaviour can be different to their actual behaviour. Identifying a behaviour mismatch is important in terms of understanding how to further refine an algorithm as well as how to effectively apply an algorithm to a problem.

A vector-agent approach to (spatiotemporal) movement modelling and reasoning.

Modelling a complex system of autonomous individuals moving through space and time essentially entails understanding the (heterogeneous) spatiotemporal context, interactions with other individuals, their internal states and making any underlying causal interrelationships explicit, a task for which agents (including vector-agents) are specifically well-suited. Building on a conceptual model of agent space-time and reasoning behaviour, a design guideline for an implemented vector-agent model is presented. The movement of football players was chosen as it is appropriately constrained in space, time and individual actions. Sensitivity-variability analysis was applied to measure the performance of different configurations of system components on the emergent movement patterns. The model output varied more when the condition of the contextual actors (players' role-areas) was manipulated. The current study shows how agent-based modelling can contribute to our understanding of movement and how causally relevant evidence can be produced, illustrated through a spatiotemporally constrained football case-study.

Graph-structured populations and the Hill-Robertson effect.

The Hill-Robertson effect describes how, in a finite panmictic diploid population, selection at one diallelic locus reduces the fixation probability of a selectively favoured allele at a second, linked diallelic locus. Here we investigate the influence of population structure on the Hill-Robertson effect in a population of size N. We model population structure as a network by assuming that individuals occupy nodes on a graph connected by edges that link members who can reproduce with each other. Three regular networks (fully connected, ring and torus), two forms of scale-free network and a star are examined. We find that (i) the effect of population structure on the probability of fixation of the favourable allele is invariant for regular structures, but on some scale-free networks and a star, this probability is greatly reduced; (ii) compared to a panmictic population, the mean time to fixation of the favoured allele is much greater on a ring, torus and linear scale-free network, but much less on power-2 scale-free and star networks; (iii) the likelihood with which each of the four possible haplotypes eventually fix is similar across regular networks, but scale-free populations and the star are consistently less likely and much faster to fix the optimal haplotype; (iv) increasing recombination increases the likelihood of fixing the favoured haplotype across all structures, whereas the time to fixation of that haplotype usually increased, and (v) star-like structures were overwhelmingly likely to fix the least fit haplotype and did so significantly more rapidly than other populations. Last, we find that small (N < 64) panmictic populations do not exhibit the scaling property expected from Hill & Robertson (1966 Genet. Res. 8, 269-294. (doi:10.1017/S0016672300010156)).

Managing distance and covariate information with point-based clustering.

BACKGROUND: Geographic perspectives of disease and the human condition often involve point-based observations and questions of clustering or dispersion within a spatial context. These problems involve a finite set of point observations and are constrained by a larger, but finite, set of locations where the observations could occur. Developing a rigorous method for pattern analysis in this context requires handling spatial covariates, a method for constrained finite spatial clustering, and addressing bias in geographic distance measures. An approach, based on Ripley's K and applied to the problem of clustering with deliberate self-harm (DSH), is presented. METHODS: Point-based Monte-Carlo simulation of Ripley's K, accounting for socio-economic deprivation and sources of distance measurement bias, was developed to estimate clustering of DSH at a range of spatial scales. A rotated Minkowski L1 distance metric allowed variation in physical distance and clustering to be assessed. Self-harm data was derived from an audit of 2 years' emergency hospital presentations (n = 136) in a New Zealand town (population ~50,000). Study area was defined by residential (housing) land parcels representing a finite set of possible point addresses. RESULTS: Area-based deprivation was spatially correlated. Accounting for deprivation and distance bias showed evidence for clustering of DSH for spatial scales up to 500 m with a one-sided 95 % CI, suggesting that social contagion may be present for this urban cohort. CONCLUSIONS: Many problems involve finite locations in geographic space that require estimates of distance-based clustering at many scales. A Monte-Carlo approach to Ripley's K, incorporating covariates and models for distance bias, are crucial when assessing health-related clustering. The case study showed that social network structure defined at the neighbourhood level may account for aspects of neighbourhood clustering of DSH. Accounting for covariate measures that exhibit spatial clustering, such as deprivation, are crucial when assessing point-based clustering.

Matrix matters: differences of grand skink metapopulation parameters in native tussock grasslands and exotic pasture grasslands.

Modelling metapopulation dynamics is a potentially very powerful tool for conservation biologists. In recent years, scientists have broadened the range of variables incorporated into metapopulation modelling from using almost exclusively habitat patch size and isolation, to the inclusion of attributes of the matrix and habitat patch quality. We investigated the influence of habitat patch and matrix characteristics on the metapopulation parameters of a highly endangered lizard species, the New Zealand endemic grand skink (Oligosoma grande) taking into account incomplete detectability. The predictive ability of the developed zxmetapopulation model was assessed through cross-validation of the data and with an independent data-set. Grand skinks occur on scattered rock-outcrops surrounded by indigenous tussock (bunch) and pasture grasslands therefore implying a metapopulation structure. We found that the type of matrix surrounding the habitat patch was equally as important as the size of habitat patch for estimating occupancy, colonisation and extinction probabilities. Additionally, the type of matrix was more important than the physical distance between habitat patches for colonisation probabilities. Detection probability differed between habitat patches in the two matrix types and between habitat patches with different attributes such as habitat patch composition and abundance of vegetation on the outcrop. The developed metapopulation models can now be used for management decisions on area protection, monitoring, and the selection of translocation sites for the grand skink. Our study showed that it is important to incorporate not only habitat patch size and distance between habitat patches, but also those matrix type and habitat patch attributes which are vital in the ecology of the target species.

Neighbourhood deprivation and access to alcohol outlets: a national study.

People living in poor areas suffer higher mortality than those in wealthy areas. Environmental factors partly explain this association, including exposure to pollutants and accessibility of healthcare. We sought to determine whether proximity to alcohol outlets varied by area deprivation in New Zealand. Roadway travel distance from each census unit to the nearest alcohol outlet was summarised according to socioeconomic deprivation for each area. Analyses were conducted by license type (pubs/bars, clubs, restaurants, off-licenses) and community urban-rural status. Strong associations were found between proximity to the nearest alcohol outlet and deprivation, there being greater access to outlets in more-deprived urban areas.

Genetic drift on networks: ploidy and the time to fixation.

Genetic drift in finite populations ultimately leads to the loss of genetic variation. This paper examines the rate of neutral gene loss for a range of population structures defined by a graph. We show that, where individuals reside at fixed points on an undirected graph with equal degree nodes, the mean time to loss differs from the panmictic value by a positive additive term that depends on the number of individuals (not genes) in the population. The effect of these spatial structures is to slow the time to fixation by an amount that depends on the way individuals are distributed, rather than changing the apparent number of genes available to be sampled. This relationship breaks down, however, for a broad class of spatial structures such as random, small-world and scale-free networks. For the latter structures there is a counter-intuitive acceleration of fixation proportional to the level of ploidy.