Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.Comment: 29 page

Evolution of populations expanding on curved surfaces

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.Comment: This preprint has also been posted to http://www.biorxiv.org with doi: 10.1101/406280. Seven pages with 5 figures, plus an appendix containing 3 pages with 1 figur

Metastable Evolutionary Dynamics: Crossing Fitness Barriers or Escaping via Neutral Paths?

We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. One the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a {\em fitness barrier} of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over {\em neutral networks} of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an {\em entropy barrier}: The population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ``landscape'' evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is {\em narrowest}, rather than where the barrier is shallowest.Comment: 32 pages, 7 figures, 1 table; http://www.santafe.edu/projects/evca/med.ps.g

Hidden long evolutionary memory in a model biochemical network

We introduce a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. Starting with a functional core module, random evolutionary drift increases network complexity even in the absence of specific selective pressures. Surprisingly, we uncover a hidden order in sequence space that gives rise to long-term evolutionary memory, implying strong constraints on network evolution due to the topology of accessible sequence space.Comment: 20 Pages, 14 Figure

Evolutionary dynamics of cooperation in neutral populations

Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the formation of homogeneous clusters, which is the hallmark of network reciprocity. Here we go beyond this traditional setup and study the spatiotemporal dynamics of cooperation in a population of populations. We use the prisoner's dilemma game as the mathematical model and show that considering several populations simultaneously give rise to fascinating spatiotemporal dynamics and pattern formation. Even the simplest assumption that strategies between different populations are payoff-neutral with one another results in the spontaneous emergence of cyclic dominance, where defectors of one population become prey of cooperators in the other population, and vice versa. Moreover, if social interactions within different populations are characterized by significantly different temptations to defect, we observe that defectors in the population with the largest temptation counterintuitively vanish the fastest, while cooperators that hang on eventually take over the whole available space. Our results reveal that considering the simultaneous presence of different populations significantly expands the complexity of evolutionary dynamics in structured populations, and it allow us to understand the stability of cooperation under adverse conditions that could never be bridged by network reciprocity alone.Comment: 14 pages, 7 figures; accepted for publication in New Journal of Physic

Evolutionary stability of behavioural types in the continuous double auction

In this paper, we investigate the effectiveness of different types of bidding behaviour for trading agents in the Continuous Double Auction (CDA). Specifically, we consider behavioural types that are neutral (expected profit maximising), passive (targeting a higher profit than neutral) and aggressive (trading off profit for a better chance of transacting). For these types, we employ an evolutionary game-theoretic analysis to determine the population dynamics of agents that use them in different types of environments, including dynamic ones with market shocks. From this analysis, we find that given a symmetric demand and supply, agents are most likely to adopt neutral behaviour in static environments, while there tends to be more passive than neutral agents in dynamic ones. Furthermore, when we have asymmetric demand and supply, agents invariably adopt passive behaviour in both static and dynamic environments, though the gain in so doing is considerably smaller than in the symmetric case