Accelerated crossing of fitness valleys through division of labor and cheating in asexual populations

Time scales and wave formation in non-linear spatial public goods games

The co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and spatial population structure. As co-evolving populations grow into a spatial domain, their initial spatial arrangement and their growth rate differences are important factors that determine the long-term outcome. We here model producer and free-rider co-evolution in the context of a diffusive public good (PG) that is produced by the producers at a cost but evokes local concentration-dependent growth benefits to all. The benefit of the PG can be non-linearly dependent on public good concentration. We consider the spatial growth dynamics of producers and free-riders in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by the processes of birth, death and diffusion (cell movement and public good distribution). Typically, one population goes extinct, but the time-scale of this process varies with initial conditions and the growth rate functions. We establish that spatial variation is transient regardless of dimensionality, and that structured initial conditions lead to increasing times to get close to an extinction state, called ε-extinction time. Further, we find that uncorrelated initial spatial structures do not influence this ε-extinction time in comparison to a corresponding well-mixed (non-spatial) system. In order to estimate the ε-extinction time of either free-riders or producers we derive a slow manifold solution. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated. Our results provide quantitative predictions for the transient spatial dynamics of cooperative traits under pressure of extinction.

Evolutionary public good (PG) games capture the essence of production of growth-beneficial factors that are vulnerable to exploitation by free-riders who do not carry the cost of production. PGs emerge in cellular populations, for example in growing bacteria and cancer cells. We study the eco-evolutionary dynamics of a PG in populations that grow in space. In our model, PG-producer cells and free-rider cells can grow according to their own birth and death rates. Co-evolution occurs due to public good-driven surplus in the intrinsic growth rates at a cost to producers. A net growth rate-benefit to free-riders leads to the well-known tragedy of the commons in which producers go extinct. What is often omitted from discussions is the time scale on which this extinction can occur, especially in spatial populations. Here, we derive analytical estimates of the ε-extinction time in different spatial settings. As we do not consider a stochastic process, the ε-extinction time captures the time needed to approach an extinction state. We identify spatial scenarios in which extinction takes long enough such that the tragedy of the commons never occurs within a meaningful lifetime of the system. Using numerical simulations we analyze the deviations from our analytical predictions.

Passenger mutations can accelerate tumour suppressor gene inactivation in cancer evolution

Carcinogenesis is an evolutionary process whereby cells accumulate multiple mutations. Besides the 'driver mutations' that cause the disease, cells also accumulate a number of other mutations with seemingly no direct role in this evolutionary process. They are called passenger mutations. While it has been argued that passenger mutations render tumours more fragile due to reduced fitness, the role of passenger mutations remains understudied. Using evolutionary computational models, we demonstrate that in the context of tumour suppressor gene inactivation (and hence fitness valley crossing), the presence of passenger mutations can accelerate the rate of evolution by reducing overall population fitness and increasing the relative fitness of intermediate mutants in the fitness valley crossing pathway. Hence, the baseline rate of tumour suppressor gene inactivation might be faster than previously thought. Conceptually, parallels are found in the field of turbulence and pattern formation, where instabilities can be driven by perturbations that are damped (disadvantageous), but provide a richer set of pathways such that a system can achieve some desired goal more readily. This highlights, through a number of novel parallels, the relevance of physical sciences in oncology.

Cooperation-based branching as a mechanism of evolutionary speciation

When performing complex tasks, coexistence of organisms in a shared environment can be achieved by means of different strategies. For example, individuals can evolve to complete all parts of the complex task, choosing self-sufficiency over cooperation. On the other hand, they may choose to split parts of the task and share the products for mutual benefit, such that distinct groups of the organisms specialize on a subset of elementary tasks. In contrast to the existing theory of specialization and task sharing for cells in multicellular organisms (or colonies of social insects), here we describe a mechanism of evolutionary branching which is based on cooperation and division of labor, and where selection happens at the individual level. Using a class of mathematical models and the methodology of adaptive dynamics, we investigate the conditions for such branching into distinct cooperating subgroups to occur. We show that, as long as performing multiple tasks is associated with additional cost, branching occurs for a wide parameter range, and this scenario is stable against the invasion of cheaters. We hypothesize that over time, this can lead to evolutionary speciation. Examples from bacterial evolution and the connection with the Black Queen Hypothesis are discussed. It is our hope that the theory of diversification rooted in cooperation may inspire further ecological research to identify more evolutionary examples consistent with this speciation mechanism.

Key issues review: evolution on rugged adaptive landscapes

Adaptive landscapes represent a mapping between genotype and fitness. Rugged adaptive landscapes contain two or more adaptive peaks: allele combinations with higher fitness than any of their neighbors in the genetic space. How do populations evolve on such rugged landscapes? Evolutionary biologists have struggled with this question since it was first introduced in the 1930s by Sewall Wright. Discoveries in the fields of genetics and biochemistry inspired various mathematical models of adaptive landscapes. The development of landscape models led to numerous theoretical studies analyzing evolution on rugged landscapes under different biological conditions. The large body of theoretical work suggests that adaptive landscapes are major determinants of the progress and outcome of evolutionary processes. Recent technological advances in molecular biology and microbiology allow experimenters to measure adaptive values of large sets of allele combinations and construct empirical adaptive landscapes for the first time. Such empirical landscapes have already been generated in bacteria, yeast, viruses, and fungi, and are contributing to new insights about evolution on adaptive landscapes. In this Key Issues Review we will: (i) introduce the concept of adaptive landscapes; (ii) review the major theoretical studies of evolution on rugged landscapes; (iii) review some of the recently obtained empirical adaptive landscapes; (iv) discuss recent mathematical and statistical analyses motivated by empirical adaptive landscapes, as well as provide the reader with instructions and source code to implement simulations of evolution on adaptive landscapes; and (v) discuss possible future directions for this exciting field.

Contribution of HIV-1 genomes that do not integrate to the basic reproductive ratio of the virus

Recent experimental data indicate that HIV-1 DNA that fails to integrate (from now on called uDNA) can by itself successfully produce infectious offspring virions in resting T cells that become activated after infection. This scenario is likely important at the initial stages of the infection. We use mathematical models to calculate the relative contribution of unintegrated and integrated viral DNA to the basic reproductive ratio of the virus, R0, and the models are parameterized with preliminary data. This is done in the context of both free virus spread and transmission of the virus through virological synapses. For free virus transmission, we find that under preliminary parameter estimates, uDNA might contribute about 20% to the total R0. This requires that a single copy of uDNA can successfully replicate. If the presence of more than one uDNA copy is required for replication, uDNA does not contribute to R0. For synaptic transmission, uDNA can contribute to R0 regardless of the number of uDNA copies required for replication. The larger the number of viruses that are successfully transmitted per synapse, however, the lower the contribution of uDNA to R0 because this increases the chances that at least one virus integrates. Using available parameter values, uDNA can maximally contribute 20% to R0 in this case. We argue that the contribution of uDNA to virus reproduction might also be important for continued low level replication of HIV-1 in the presence of integrase inhibitor therapy. Assuming a 20% contribution of uDNA to the overall R0, our calculations suggest that R0=1.6 in the absence of virus integration. While these are rough estimates based on preliminary data that are currently available, this analysis provides a framework for future experimental work which should directly measure key parameters.

Collapse of cooperation in evolving games

Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner's Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as a robust outcome in evolving populations. Here we extend evolutionary game theory by allowing players' payoffs as well as their strategies to evolve in response to selection on heritable mutations. In nature, many organisms engage in mutually beneficial interactions and individuals may seek to change the ratio of risk to reward for cooperation by altering the resources they commit to cooperative interactions. To study this, we construct a general framework for the coevolution of strategies and payoffs in arbitrary iterated games. We show that, when there is a tradeoff between the benefits and costs of cooperation, coevolution often leads to a dramatic loss of cooperation in the Iterated Prisoner's Dilemma. The collapse of cooperation is so extreme that the average payoff in a population can decline even as the potential reward for mutual cooperation increases. Depending upon the form of tradeoffs, evolution may even move away from the Iterated Prisoner's Dilemma game altogether. Our work offers a new perspective on the Prisoner's Dilemma and its predictions for cooperation in natural populations; and it provides a general framework to understand the coevolution of strategies and payoffs in iterated interactions.

Spatial interactions and cooperation can change the speed of evolution of complex phenotypes

Complex traits arise from the interactions among multiple gene products. In the case where the complex phenotype is separated from the wild type by a fitness valley or a fitness plateau, the generation of a complex phenotype may take a very long evolutionary time. Interestingly, the rate of evolution depends in nontrivial ways on various properties of the underlying stochastic process, such as the spatial organization of the population and social interactions among cells. Here we review some of our recent work that investigates these phenomena in asexual populations. The role of spatial constraints is quite complex: there are realistic cases where spatial constrains can accelerate or delay evolution, or even influence it in a nonmonotonic fashion, where evolution works fastest for intermediate-range constraints. Social interactions among cells can be studied in the context of the division-of-labor games. Under a range of circumstances, cooperation among cells can lead to a relatively fast creation of a complex phenotype as an emerging (distributed) property. If we further assume the presence of cheaters, we observe the emergence of a fully mutated population of cells possessing the complex phenotype. Applications of these ideas to cancer initiation and biofilm formation in bacteria are discussed.