Adaptive dynamics of regulatory networks: size matters

A Boolean gene regulatory model of heterosis and speciation

BACKGROUND

Modelling genetic phenomena affecting biological traits is important for the development of agriculture as it allows breeders to predict the potential of breeding for certain traits. One such phenomenon is heterosis or hybrid vigor: crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance. Heterosis has become a very useful tool in global agriculture, but its genetic basis remains controversial and its effects hard to predict. We have taken a computational approach to studying heterosis, developing a simulation of evolution, independent reassortment of alleles and hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework. These artificial regulatory networks exhibit topological properties that reflect those observed in biology, and fitness is measured as the ability of a network to respond to external inputs in a pre-defined way.

RESULTS

Our model reproduced common experimental observations on heterosis using only biologically justified parameters, such as mutation rates. Hybrid vigor was observed and its extent was seen to increase as parental populations diverged, up until a point of sudden collapse of hybrid fitness. Thus, the model also describes a process akin to speciation due to genetic incompatibility of the separated populations. We also reproduce, for the first time in a model, the fact that hybrid vigor cannot easily be fixed by within a breeding line, currently an important limitation of the use of hybrid crops. The simulation allowed us to study the effects of three standard models for the genetic basis of heterosis: dominance, over-dominance, and epistasis.

CONCLUSION

This study describes the most detailed simulation of heterosis using gene regulatory networks to date and reproduces several phenomena associated with heterosis for the first time in a model. The level of detail in our model allows us to suggest possible warning signs of the impending collapse of hybrid vigor in breeding. In addition, the simulation provides a framework that can be extended to study other aspects of heterosis and alternative evolutionary scenarios.

Gene networks and metacommunities: dispersal differences can override adaptive advantage

Dispersal is an important mechanism contributing to both ecological and evolutionary dynamics. In metapopulation and metacommunity ecology, dispersal enables new patches to be colonized; in evolution, dispersal counter-acts local selection, leading to regional homogenization. Here, I consider a three-patch metacommunity in which two species, each with a limiting quantitative trait underlain by gene networks of 16 to 256 genes, compete with one another and disperse among patches. Incorporating dispersal among heterogeneous patches introduces a tradeoff not observed in single-patch simulations: if the difference between gene network size of the two species is greater than the difference in dispersal ability (e.g., if the ratio of network sizes is larger than the ratio of dispersal abilities), then genetic architecture drives community outcome. However, if the difference in dispersal abilities is greater than gene network differences, then any adaptive advantages afforded by genetic architecture are over-ridden by dispersal. Thus, in addition to the selective pressures imposed by competition that shape the genetic architecture of quantitative traits, dispersal among patches creates an escape that may further alter the effects of different genetic architectures. These results provide a theoretical expectation for what we may observe as the field of ecological genomics develops.

Smaller gene networks permit longer persistence in fast-changing environments

The environments in which organisms live and reproduce are rarely static, and as the environment changes, populations must evolve so that phenotypes match the challenges presented. The quantitative traits that map to environmental variables are underlain by hundreds or thousands of interacting genes whose allele frequencies and epistatic relationships must change appropriately for adaptation to occur. Extending an earlier model in which individuals possess an ecologically-critical trait encoded by gene networks of 16 to 256 genes and random or scale-free topology, I test the hypothesis that smaller, scale-free networks permit longer persistence times in a constantly-changing environment. Genetic architecture interacting with the rate of environmental change accounts for 78% of the variance in trait heritability and 66% of the variance in population persistence times. When the rate of environmental change is high, the relationship between network size and heritability is apparent, with smaller and scale-free networks conferring a distinct advantage for persistence time. However, when the rate of environmental change is very slow, the relationship between network size and heritability disappears and populations persist the duration of the simulations, without regard to genetic architecture. These results provide a link between genes and population dynamics that may be tested as the -omics and bioinformatics fields mature, and as we are able to determine the genetic basis of ecologically-relevant quantitative traits.

Evolution of competitive ability: an adaptation speed vs. accuracy tradeoff rooted in gene network size

Ecologists have increasingly come to understand that evolutionary change on short time-scales can alter ecological dynamics (and vice-versa), and this idea is being incorporated into community ecology research programs. Previous research has suggested that the size and topology of the gene network underlying a quantitative trait should constrain or facilitate adaptation and thereby alter population dynamics. Here, I consider a scenario in which two species with different genetic architectures compete and evolve in fluctuating environments. An important trade-off emerges between adaptive accuracy and adaptive speed, driven by the size of the gene network underlying the ecologically-critical trait and the rate of environmental change. Smaller, scale-free networks confer a competitive advantage in rapidly-changing environments, but larger networks permit increased adaptive accuracy when environmental change is sufficiently slow to allow a species time to adapt. As the differences in network characteristics increase, the time-to-resolution of competition decreases. These results augment and refine previous conclusions about the ecological implications of the genetic architecture of quantitative traits, emphasizing a role of adaptive accuracy. Along with previous work, in particular that considering the role of gene network connectivity, these results provide a set of expectations for what we may observe as the field of ecological genomics develops.

Smaller, scale-free gene networks increase quantitative trait heritability and result in faster population recovery

One of the goals of biology is to bridge levels of organization. Recent technological advances are enabling us to span from genetic sequence to traits, and then from traits to ecological dynamics. The quantitative genetics parameter heritability describes how quickly a trait can evolve, and in turn describes how quickly a population can recover from an environmental change. Here I propose that we can link the details of the genetic architecture of a quantitative trait--i.e., the number of underlying genes and their relationships in a network--to population recovery rates by way of heritability. I test this hypothesis using a set of agent-based models in which individuals possess one of two network topologies or a linear genotype-phenotype map, 16-256 genes underlying the trait, and a variety of mutation and recombination rates and degrees of environmental change. I find that the network architectures introduce extensive directional epistasis that systematically hides and reveals additive genetic variance and affects heritability: network size, topology, and recombination explain 81% of the variance in average heritability in a stable environment. Network size and topology, the width of the fitness function, pre-change additive variance, and certain interactions account for ∼75% of the variance in population recovery times after a sudden environmental change. These results suggest that not only the amount of additive variance, but importantly the number of loci across which it is distributed, is important in regulating the rate at which a trait can evolve and populations can recover. Taken in conjunction with previous research focused on differences in degree of network connectivity, these results provide a set of theoretical expectations and testable hypotheses for biologists working to span levels of organization from the genotype to the phenotype, and from the phenotype to the environment.