Modelling the dynamics of genetic algorithms using statistical mechanics

A formalism for modelling the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics, originally due to Prugel-Bennett and Shapiro, is reviewed, generalized and improved upon. This formalism can be used to predict the averaged trajectory of macroscopic statistics describing the GA's population. These macroscopics are chosen to average well between runs, so that fluctuations from mean behaviour can often be neglected. Where necessary, non-trivial terms are determined by assuming maximum entropy with constraints on known macroscopics. Problems of realistic size are described in compact form and finite population effects are included, often proving to be of fundamental importance. The macroscopics used here are cumulants of an appropriate quantity within the population and the mean correlation (Hamming distance) within the population. Including the correlation as an explicit macroscopic provides a significant improvement over the original formulation. The formalism is applied to a number of simple optimization problems in order to determine its predictive power and to gain insight into GA dynamics. Problems which are most amenable to analysis come from the class where alleles within the genotype contribute additively to the phenotype. This class can be treated with some generality, including problems with inhomogeneous contributions from each site, non-linear or noisy fitness measures, simple diploid representations and temporally varying fitness. The results can also be applied to a simple learning problem, generalization in a binary perceptron, and a limit is identified for which the optimal training batch size can be determined for this problem. The theory is compared to averaged results from a real GA in each case, showing excellent agreement if the maximum entropy principle holds. Some situations where this approximation brakes down are identified. In order to fully test the formalism, an attempt is made on the strong sc np-hard problem of storing random patterns in a binary perceptron. Here, the relationship between the genotype and phenotype (training error) is strongly non-linear. Mutation is modelled under the assumption that perceptron configurations are typical of perceptrons with a given training error. Unfortunately, this assumption does not provide a good approximation in general. It is conjectured that perceptron configurations would have to be constrained by other statistics in order to accurately model mutation for this problem. Issues arising from this study are discussed in conclusion and some possible areas of further research are outlined.

GENETIC DIVERSITY AMONG SORGHUM LANDRACES OF SOUTHWESTERN HIGHLANDS OF UGANDA

Sorghum ( Sorghum bicolor L. Moench) is an economic and staple crop in sub-Saharan Africa. The genetic diversity in its germplasm is an invaluable aid for its crop improvement. The objective of this study was to assess the existing genetic diversity among sorghum landraces in the southwestern highlands of Uganda. A total of 47 sorghum landraces, collected from southwestern highlands of Uganda, were characterised using 12 qualitative and 13 quantitative traits. The study was conducted at Kachwekano Research Farm in Kabale District, at an altitude of 2,223 m above sea level, during growing season of December 2014 to August 2015. Panicle shape and compactness were the most varied qualitative traits. Grain yield (1.23 to 11.31 t ha-1) and plant height (144.7 to 351.6 cm) were among quantitative traits that showed high variability. Days to 50% flowering (115 to 130 days) showed the least variability. Results of UPGMA cluster analysis generated a dendrogram with three clusters. Panicle weight, leaf width, stem girth, exertion length, peduncle length, panicle shape and compactness, glume colour and threshability were major traits responsible for the observed clustering (P<0.001). Principal Component Analysis revealed the largest variation contributors.

SSR genetic diversity assessment of popular pigeonpea varieties in Malawi reveals unique fingerprints

Background: Pigeonpea ( Cajanus cajan L. Millsp.) is a drought tolerant legume of the Fabaceae family and the only cultivated species in the genus Cajanus. It is mainly cultivated in the semi-arid tropics of Asia and Oceania, Africa and America. In Malawi, it is grown as a source of food and income and for soil improvement in intercropping systems. However, varietal contamination due to natural outcrossing causes significant quality reduction and yield losses. In this study, 48 polymorphic SSR markers were used to assess the diversity among all pigeonpea varieties cultivated in Malawi to determine if a genetic fingerprint could be identified to distinguish the popular varieties. Results: A total of 212 alleles were observed with an average of 5.58 alleles per marker and a maximum of 14 alleles produced by CCttc019 (Marker 40). Polymorphic information content (PIC), ranged from 0.03 to 0.89 with an average of 0.30. A neighbor-joining tree produced 4 clusters. The most commonly cultivated varieties, which include released varieties and cultivated land races, were well-spread across all the clusters observed, indicating that they generally represented the genetic diversity available in Malawi, although substantial variation was evident that can still be exploited through further breeding. Conclusion: Screening of the allelic data associated with the five most popular cultivated varieties, revealed 6 markers – CCB1, CCB7, Ccac035, CCttc003, Ccac026 and CCttc019 – which displayed unique allelic profiles for each of the five varieties. This genetic fingerprint can potentially be applied for seed certification to confirm the genetic purity of seeds that are delivered to Malawi farmers.

Cooking time of common bean: genetic parameters and selection of elite lines.

The objectives of this study were to investigate the genetic variability and select elite lines for CT, since these lines aggregate essential agronomic traits.

Juvenile-mature genetic correlations in Pinus taeda clones propagated via somatic embryogenesis.

Objetivou-se com o presente trabalho, estimar a correlação genética entre idades de seleção (juvenil-adulta) e eficiência da seleção precoce para as características altura, diâmetro e volume de indivíduos de famílias de Pinus taeda propagados via embriogênese somática. O estudo foi realizado por meio de análise genético-estatística pelo procedimento de estimação de componentes de variância (Reml) e de predição de valores genéticos (Blup), usando-se o software Selegen-Reml/Blup. As correlações genéticas entre idades juvenis e idade de rotação foram realizadas aplicando o modelo linear desenvolvido por Lambeth (1980). Segundo os resultados do modelo estabelecido, a seleção precoce pode ser realizada em clones de Pinus taeda com alta eficiência de seleção. As idades de 4 a 6 anos são suficientes para selecionar clones de Pinus taeda propagados via embriogênese somática para colheita aos 8 e 12 anos e, as idades de 6 a 10 anos são suficientes para selecionar para colheita aos 20 anos. De acordo com as estimativas de correlação genotípicaa partir dos ambientes, a seleção de clones de Pinus taeda propagados via embriogênese somática deve ser praticada de forma específica para cada ambiente. Pode-se realizar a seleção de clones considerando o diâmetro, visto a alta correlação observada entre volume e diâmetro.

Forage peanut (Arachis spp.) genetic evaluation and selection.

Forage peanut improvement for use in grass?legume mixtures is expected to have a great impact on the sustainability of Brazilian livestock production. Eighteen cloned Arachis spp. ecotypes were evaluated under clipping in a Brazilian Cerrado region and results analysed using a mixed model methodology. The objective was to estimate genetic and phenotypic parameters and to select the best ecotypes based on selection index applied on their predicted genotypic value. The traits of total dry-matter (DM) and leaf DM yield presented moderate (0_30 < h2g < 0_50) to high (>0_50) broad-sense heritability, in contrast to the low genetic variability in nutritional quality-associated traits. Ecotypes of Arachis spp. contained average crude protein concentrations of 224 g kg _1 DM in leaves and 138 g kg _1 DM in stems, supporting the potential role of these species to overcome the low protein content in Cerrado pastures. The correlations between yield traits and traits associated with low nutritional value in leaves were consistently significant and positive. Genetic correlations among all the yield traits evaluated during the rainy or dry seasons were significant and positive. The ecotypes were ranked based on selection index. The next step is to validate long-term selection of grass?Arachis in combination with pastures under competition and adjusted grazing in the Cerrado region.