Chaotic provinces in the kingdom of the Red Queen

The Recombination Hotspot Paradox: Co-evolution between PRDM9 and its target sites

Recombination often concentrates in small regions called recombination hotspots where recombination is much higher than the genome's average. In many vertebrates, including humans, gene PRDM9 specifies which DNA motifs will be the target for breaks that initiate recombination, ultimately determining the location of recombination hotspots. Because the sequence that breaks (allowing recombination) is converted into the sequence that does not break (preventing recombination), the latter sequence is over-transmitted to future generations and recombination hotspots are self-destructive. Given their self-destructive nature, recombination hotspots should eventually become extinct in genomes where they are found. While empirical evidence shows that individual hotspots do become inactive over time (die), hotspots are abundant in many vertebrates: a contradiction called the Recombination Hotspot Paradox. What saves recombination hotspots from their foretold extinction? Here we formulate a co-evolutionary model of the interaction among sequence-specific gene conversion, fertility selection, and recurrent mutation. We find that allelic frequencies oscillate leading to stable limit cycles. From a biological perspective this means that when fertility selection is weaker than gene conversion, it cannot stop individual hotspots from dying but can save them from extinction by driving their re-activation (resuscitation). In our model, mutation balances death and resuscitation of hotspots, thus maintaining their number over evolutionary time. Interestingly, we find that multiple alleles result in oscillations that are chaotic and multiple targets in oscillations that are asynchronous between targets thus helping to maintain the average genomic recombination probability constant. Furthermore, we find that the level of expression of PRDM9 should control for the fraction of targets that are hotspots and the overall temperature of the genome. Therefore, our co-evolutionary model improves our understanding of how hotspots may be replaced, thus contributing to solve the Recombination Hotspot Paradox. From a more applied perspective our work provides testable predictions regarding the relation between mutation probability and fertility selection with life expectancy of hotspots.

Eco-evolutionary agriculture: Host-pathogen dynamics in crop rotations

Since its origins, thousands of years ago, agriculture has been challenged by the presence of evolving plant pathogens. Temporal rotations of host and non-host crops have helped farmers to control epidemics among other utilities, but further efforts for strategy assessment are needed. Here, we present a methodology for developing crop rotation strategies optimal for control of pathogens informed by numerical simulations of eco-evolutionary dynamics in one field. This approach can integrate agronomic criteria used in crop rotations—soil quality and cash yield—and the analysis of pathogen evolution in systems where hosts are artificially selected. Our analysis shows which rotation patterns perform better in maximising crop yield when an unspecified infection occurs, with yield being dependent on both soil quality and the strength of the epidemic. Importantly, the use of non-host crops, which both improve soil quality and control the epidemic results in similar rational rotation strategies for diverse agronomic and infection conditions. We test the repeatability of the best rotation patterns over multiple decades, an essential end-user goal. Our results provide sustainable strategies for optimal resource investment for increased food production and lead to further insights into the minimisation of pesticide use in a society demanding ever more efficient agriculture.

The invention of agriculture is a major evolutionary transition in the social evolution of the human race. Transforming the lifestyle from nomadic to sedentary, agriculture provided humankind with the stability necessary to make rapid advancements. However, agriculture, as we know it, is now in danger. While agriculture is a grand artificial selection experiment, it is in a constant battle with the brute force of natural selection, generating highly infectious plant pathogens. Traditional techniques such as slash-burn techniques are not sustainable for feeding the ever-increasing population. Crop rotation, on the other hand, has been developed over thousands of years as a sustainable method. We provide a computational model of how crop rotations can be used to tackle pathogen infection and what properties of rotation patterns make them sustainable in the long run. We hope that this study, together with other sustainable methods such as minimal pesticide use and biocontrol, can make agriculture more efficient.

How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models

Background

Red Queen dynamics are defined as long term co-evolutionary dynamics, often with oscillations of genotype abundances driven by fluctuating selection in host-parasite systems. Much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models that are mostly (i) deterministic, inferring an infinite population size and (ii) evolutionary, thus ecological interactions that change population sizes are excluded. Here, we recall the different mathematical approaches used in the current literature on Red Queen dynamics. We then compare models from game theory (evo) and classical theoretical ecology models (eco-evo), that are all derived from individual interactions and are thus intrinsically stochastic. We assess the influence of this stochasticity through the time to the first loss of a genotype within a host or parasite population.

Results

The time until the first genotype is lost (“extinction time”), is shorter when ecological dynamics, in the form of a changing population size, is considered. Furthermore, when individuals compete only locally with other individuals extinction is even faster. On the other hand, evolutionary models with a fixed population size and competition on the scale of the whole population prolong extinction and therefore stabilise the oscillations. The stabilising properties of intra-specific competitions become stronger when population size is increased and the deterministic part of the dynamics gain influence. In general, the loss of genotype diversity can be counteracted with mutations (or recombination), which then allow the populations to recurrently undergo negative frequency-dependent selection dynamics and selective sweeps.

Conclusion

Although the models we investigated are equal in their biological motivation and interpretation, they have diverging mathematical properties both in the derived deterministic dynamics and the derived stochastic dynamics. We find that models that do not consider intraspecific competition and that include ecological dynamics by letting the population size vary, lose genotypes – and thus Red Queen oscillations – faster than models with competition and a fixed population size.

Computation and Simulation of Evolutionary Game Dynamics in Finite Populations

The study of evolutionary dynamics increasingly relies on computational methods, as more and more cases outside the range of analytical tractability are explored. The computational methods for simulation and numerical approximation of the relevant quantities are diverging without being compared for accuracy and performance. We thoroughly investigate these algorithms in order to propose a reliable standard. For expositional clarity we focus on symmetric 2 × 2 games leading to one-dimensional processes, noting that extensions can be straightforward and lessons will often carry over to more complex cases. We provide time-complexity analysis and systematically compare three families of methods to compute fixation probabilities, fixation times and long-term stationary distributions for the popular Moran process. We provide efficient implementations that substantially improve wall times over naive or immediate implementations. Implications are also discussed for the Wright-Fisher process, as well as structured populations and multiple types.