The E(NK) model: extending the NK model to incorporate gene-by-environment interactions and epistasis for diploid genomes

The haploid NK model developed by Kauffman can be extended to diploid genomes and to incorporate gene-by-environment interaction effects in combination with epistasis. To provide the flexibility to include a wide range of forms of gene-by-environment interactions, a target population of environment types (TPE) is defined. The TPE consists of a set of E different environment types, each with their own frequency of occurrence. Each environment type conditions a different NK gene network structure or series of gene effects for a given network structure, providing the framework for defining gene-by-environment interactions. Thus, different NK models can be partially or completely nested within the E environment types of a TPE, giving rise to the E(NK) model for a biological system. With this model it is possible to examine how populations of genotypes evolve in context with properties of the environment that influence the contributions of genes to the fitness values of genotypes. We are using the E(NK) model to investigate how both epistasis and gene-by-environment interactions influence the genetic improvement of quantitative traits by plant breeding strategies applied to agricultural systems. © 2002 Wiley Periodicals, Inc.

Heritability and gene-environment interactions for melanocytic nevus density examined in a U.K. adolescent twin study

Risk factors for melanoma include environmental (particularly ultraviolet exposure) and genetic factors. In rare families, susceptibility to melanoma is determined by high penetrance mutations in the genes CDKN2A or CDK4, with more common, less penetrant genes also postulated. A further, potent risk factor for melanoma is the presence of large numbers of melanocytic nevi so that genes controlling nevus phenotype could be such melanoma susceptibility genes. A large Australian study involving twins aged 12 y of predominantly U.K. ancestry showed strong evidence for genetic influence on nevus number and density. We carried out essentially the same study in the U.K. to gain insight into gene-environment interactions for nevi. One hundred and three monozygous (MZ) and 118 dizygous (DZ) twin pairs aged 10-18 y were examined in Yorkshire and Surrey, U.K. Nevus counts were, on average, higher in boys (mean = 98.6) than girls (83.8) (p = 0.009) and higher in Australia (110.4) than in the U.K. (79.2, adjusted to age 12 y, p < 0.0001), and nevus densities were higher on sun-exposed sites (92 per m(2)) than sun-protected sites (58 per m(2)) (p < 0.0001). Correlations in sex and age adjusted nevus density were higher in MZ pairs (0.94, 95% CI 0.92-0.96) than in DZ pairs (0.61, 95%CI 0.49-0.72), were notably similar to those of the Australian study (MZ = 0.94, DZ = 0.60), and were consistent with high heritability (65% in the U.K., 68% in Australia). We conclude that emergence of nevi in adolescents is under strong genetic control, whereas environmental exposures affect the mean number of nevi.

Evaluating plant breeding strategies by simulating gene action and dryland environment effects

Functional genomics is the systematic study of genome-wide effects of gene expression on organism growth and development with the ultimate aim of understanding how networks of genes influence traits. Here, we use a dynamic biophysical cropping systems model (APSIM-Sorg) to generate a state space of genotype performance based on 15 genes controlling four adaptive traits and then search this spice using a quantitative genetics model of a plant breeding program (QU-GENE) to simulate recurrent selection. Complex epistatic and gene X environment effects were generated for yield even though gene action at the trait level had been defined as simple additive effects. Given alternative breeding strategies that restricted either the cultivar maturity type or the drought environment type, the positive (+) alleles for 15 genes associated with the four adaptive traits were accumulated at different rates over cycles of selection. While early maturing genotypes were favored in the Severe-Terminal drought environment type, late genotypes were favored in the Mild-Terminal and Midseason drought environment types. In the Severe-Terminal environment, there was an interaction of the stay-green (SG) trait with other traits: Selection for + alleles of the SG genes was delayed until + alleles for genes associated with the transpiration efficiency and osmotic adjustment traits had been fixed. Given limitations in our current understanding of trait interaction and genetic control, the results are not conclusive. However, they demonstrate how the per se complexity of gene X gene X environment interactions will challenge the application of genomics and marker-assisted selection in crop improvement for dryland adaptation.

Genotype-by-management interactions for grain yield and grain protein concentration of wheat

The magnitude of genotype-by-management (G x M) interactions for grain yield and grain protein concentration was examined in a multi-environment trial (MET) involving a diverse set of 272 advanced breeding lines from the Queensland wheat breeding program. The MET was structured as a series of management-regimes imposed at 3 sites for 2 years. The management-regimes were generated at each site-year as separate trials in which planting time, N fertiliser application rate, cropping history, and irrigation were manipulated. irrigation was used to simulate different rainfall regimes. From the combined analysis of variance, the G x M interaction variance components were found to be the largest source of G x E interaction variation for both grain yield (0.117 +/- 0.005 t(2) ha(-2); 49% of total G x E 0.238 +/- 0.028 t(2) ha(-2)) and grain protein concentration (0.445 +/- 0.020%(2); 82% of total G x E 0.546 +/- 0.057%(2)), and in both cases this source of variation was larger than the genotypic variance component (grain yield 0.068 +/- 0.014 t(2) ha(-2) and grain protein 0.203 +/- 0.026%(2)). The genotypic correlation between the traits varied considerably with management-regime, ranging from -0.98 to -0.31, with an estimate of 0.0 for one trial. Pattern analysis identified advanced breeding lines with improved grain yield and grain protein concentration relative to the cultivars Hartog, Sunco and Meteor. It is likely that a large component of the previously documented G x E interactions for grain yield of wheat in the northern grains region are in part a result of G x M interactions. The implications of the strong influence of G x M interactions for the conduct of wheat breeding METs in the northern region are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

The GP problem: quantifying gene-to-phenotype relationships

In this paper we refer to the gene-to-phenotype modeling challenge as the GP problem. Integrating information across levels of organization within a genotype-environment system is a major challenge in computational biology. However, resolving the GP problem is a fundamental requirement if we are to understand and predict phenotypes given knowledge of the genome and model dynamic properties of biological systems. Organisms are consequences of this integration, and it is a major property of biological systems that underlies the responses we observe. We discuss the E(NK) model as a framework for investigation of the GP problem and the prediction of system properties at different levels of organization. We apply this quantitative framework to an investigation of the processes involved in genetic improvement of plants for agriculture. In our analysis, N genes determine the genetic variation for a set of traits that are responsible for plant adaptation to E environment-types within a target population of environments. The N genes can interact in epistatic NK gene-networks through the way that they influence plant growth and development processes within a dynamic crop growth model. We use a sorghum crop growth model, available within the APSIM agricultural production systems simulation model, to integrate the gene-environment interactions that occur during growth and development and to predict genotype-to-phenotype relationships for a given E(NK) model. Directional selection is then applied to the population of genotypes, based on their predicted phenotypes, to simulate the dynamic aspects of genetic improvement by a plant-breeding program. The outcomes of the simulated breeding are evaluated across cycles of selection in terms of the changes in allele frequencies for the N genes and the genotypic and phenotypic values of the populations of genotypes.

The branching gene RAMOSUS1 mediates interactions among two novel signals and auxin in pea

In Pisum sativium, the RAMOSUS genes RMS1, RMS2, and RMS5 regulate shoot branching via physiologically defined mobile signals. RMS1 is most likely a carotenoid cleavage enzyme and acts with RMS5 to control levels of an as yet unidentified mobile branching inhibitor required for auxin inhibition of branching. Our work provides molecular, genetic, and physiological evidence that RMS1 plays a central role in a shoot-to-root-to-shoot feedback system that regulates shoot branching in pea. Indole-3-acetic acid (IAA) positively regulates RMS1 transcript level, a potentially important mechanism for regulation of shoot branching by IAA. In addition, RMS1 transcript levels are dramatically elevated in rms3, rms4, and rms5 plants, which do not contain elevated IAA levels. This degree of upregulation of RMS1 expression cannot be achieved in wild-type plants by exogenous IAA application. Grafting studies indicate that an IAA-independent mobile feedback signal contributes to the elevated RMS1 transcript levels in rms4 plants. Therefore, the long-distance signaling network controlling branching in pea involves IAA, the RMS1 inhibitor, and an IAA-independent feedback signal. Consistent with physiological studies that predict an interaction between RMS2 and RMS1, rms2 mutations appear to disrupt this IAA-independent regulation of RMS1 expression.

Analysis of line x environment interactions for yield in navy beans. 2. Pattern analysis of lines and environment within years

Seven years of multi-environment yield trials of navy bean (Phaseolus vulgaris L.) grown in Queensland were examined. As is common with plant breeding evaluation trials, test entries and locations varied between years. Grain yield data were analysed for each year using cluster and ordination analyses (pattern analyses). These methods facilitate descriptions of genotype performance across environments and the discrimination among genotypes provided by the environments. The observed trends for genotypic yield performance across environments were partly consistent with agronomic and disease reactions at specific environments and also partly explainable by breeding and selection history. In some cases, similarities in discrimination among environments were related to geographic proximity, in others management practices, and in others similarities occurred between geographically widely separated environments which differed in management practices. One location was identified as having atypical line discrimination. The analysis indicated that the number of test locations was below requirements for adequate representation of line x environment interaction. The pattern analyses methods used were an effective aid in describing the patterns in data for each year and illustrated the variations in adaptive patterns from year to year. The study has implications for assessing the number and location of test sites for plant breeding multi-environment trials, and for the understanding of genetic traits contributing to line x environment interactions.

Male-by-female interactions influence fertilization success and mediate the benefits of polyandry in the sea urchin Heliocidaris erythrogramma

Numerous studies have reported that females benefit from mating with multiple males (polyandry) by minimizing the probability of fertilization by genetically incompatible sperm. Few, however, have directly attributed variation in female reproductive success to the fertilizing capacity of sperm. In this study we report on two experiments that investigated the benefits of polyandry and the interacting effects of males and females at fertilization in the free-spawning Australian sea urchin Heliocidaris erythrogramma. In the first experiment we used a paired (split clutch) experimental design and compared fertilization rates within female egg clutches under polyandry (eggs exposed to the sperm from two males simultaneously) and monandry (eggs from the same female exposed to sperm from each of the same two males separately). Our analysis revealed a significant fertilization benefit of polyandry and strong interacting effects of males and females at fertilization. Further analysis of these data strongly suggested that the higher rates of fertilization in the polyandry treatment were due to an overrepresentation of fertilizations due to the most compatible male. To further explore the interacting effects of males and females at fertilization we performed a second factorial experiment in which four mates were crossed with two females (in all eight combinations). In addition to confirming that fertilization success is influenced by male X female interactions, this latter experiment revealed that both sexes contributed significant variance to the observed patterns of fertilization. Taken together, these findings highlight the importance of male X female interactions at fertilization and suggest that polyandry will enable females to reduce the cost of fertilization by incompatible gametes.