The Effect of Mating Complexity on Gene Drive Dynamics.

AbstractGene drive technology promises to deliver on some of the global challenges humanity faces today in health care, agriculture, and conservation. However, there is a limited understanding of the consequences of releasing self-perpetuating transgenic organisms into wild populations under complex ecological conditions. In this study, we analyze the impact of three such complexities-mate choice, mating systems, and spatial mating network-on the population dynamics for two distinct classes of modification gene drive systems. All three factors had a high impact on the modeling outcome. First, we demonstrate that distortion-based gene drives appear to be more robust against mate choice than viability-based gene drives. Second, we find that gene drive spread is much faster for higher degrees of polygamy. Including a fitness cost, the drive is fastest for intermediate levels of polygamy. Finally, the spread of a gene drive is faster and more effective when the individuals have fewer connections in a spatial mating network. Our results highlight the need to include mating complexities when modeling the properties of gene drives, such as release thresholds, timescales, and population-level consequences. This inclusion will enable a more confident prediction of the dynamics of engineered gene drives and possibly even inform about the origin and evolution of natural gene drives.

Memory shapes microbial populations.

Correct decision making is fundamental for all living organisms to thrive under environmental changes. The patterns of environmental variation and the quality of available information define the most favourable strategy among multiple options, from randomly adopting a phenotypic state to sensing and reacting to environmental cues. Cellular memory-the ability to track and condition the time to switch to a different phenotypic state-can help withstand environmental fluctuations. How does memory manifest itself in unicellular organisms? We describe the population-wide consequences of phenotypic memory in microbes through a combination of deterministic modelling and stochastic simulations. Moving beyond binary switching models, our work highlights the need to consider a broader range of switching behaviours when describing microbial adaptive strategies. We show that memory in individual cells generates patterns at the population level coherent with overshoots and non-exponential lag times distributions experimentally observed in phenotypically heterogeneous populations. We emphasise the implications of our work in understanding antibiotic tolerance and, in general, bacterial survival under fluctuating environments.

On the fitness of informative cues in complex environments.

To be able to deal with uncertainty is of primary importance to most living organisms. When cues provide information about the state of the environment, organisms can use them to respond flexibly. Life forms have evolved complex adaptations and sensory mechanisms to use these environmental cues and extract valuable information about the environment. Previous work has shown a theoretical limit to the amount of fitness benefit possible to be extracted from the cues. We show that the previously used information theoretical approaches can be generalised to scenarios involving any potential relationship between the number of possible phenotypes and environmental states. Such cases are relevant when physiological constraints or complex ecological scenarios lead to the number of environmental states exceeding potential phenotypes. We illustrate cases in which these scenarios can emerge: along environmental gradients, such as geographical transects or complex environments, where organisms adopt different bet-hedging strategies, switching stochastically between phenotypes or developing intermediate ones. In conclusion, we develop an information-theoretic extensible approach for investigating and quantifying fitness in ecological studies.

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.

Cellular hysteresis as a principle to maximize the efficacy of antibiotic therapy.

Antibiotic resistance has become one of the most dramatic threats to global health. While novel treatment options are urgently required, most attempts focus on finding new antibiotic substances. However, their development is costly, and their efficacy is often compromised within short time periods due to the enormous potential of microorganisms for rapid adaptation. Here, we developed a strategy that uses the currently available antibiotics. Our strategy exploits cellular hysteresis, which is the long-lasting, transgenerational change in cellular physiology that is induced by one antibiotic and sensitizes bacteria to another subsequently administered antibiotic. Using evolution experiments, mathematical modeling, genomics, and functional genetic analysis, we demonstrate that sequential treatment protocols with high levels of cellular hysteresis constrain the evolving bacteria by (i) increasing extinction frequencies, (ii) reducing adaptation rates, and (iii) limiting emergence of multidrug resistance. Cellular hysteresis is most effective in fast sequential protocols, in which antibiotics are changed within 12 h or 24 h, in contrast to the less frequent changes in cycling protocols commonly implemented in hospitals. We found that cellular hysteresis imposes specific selective pressure on the bacteria that disfavors resistance mutations. Instead, if bacterial populations survive, hysteresis is countered in two distinct ways, either through a process related to antibiotic tolerance or a mechanism controlled by the previously uncharacterized two-component regulator CpxS. We conclude that cellular hysteresis can be harnessed to optimize antibiotic therapy, to achieve both enhanced bacterial elimination and reduced resistance evolution.

Evolutionary dynamics of complex multiple games.

Evolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behaviour. However, it has typically focused on a single game describing the interactions between individuals. Organisms are simultaneously involved in many intraspecies and interspecies interactions. Therefore, there is a need to move from single games to multiple games. However, these interactions in nature involve many players. Shifting from 2-player games to multiple multiplayer games yield richer dynamics closer to natural settings. Such a complete picture of multiple game dynamics (MGD), where multiple players are involved, was lacking. For multiple multiplayer games-where each game could have an arbitrary finite number of players and strategies, we provide a replicator equation for MGD having many players and strategies. We show that if the individual games involved have more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Expected dynamics from single games is no longer valid, and trajectories can possess different limiting behaviour. In the case of finite populations, we formulate and calculate an essential and useful stochastic property, fixation probability. Our results highlight that studying a set of interactions defined by a single game can be misleading if we do not take the broader setting of the interactions into account. Through our results and analysis, we thus discuss and advocate the development of evolutionary game(s) theory, which will help us disentangle the complexity of multiple interactions.

Unravelling the complexity and redundancy of carbon catabolic repression in Pseudomonas fluorescens SBW25.

The two-component system CbrAB is the principal regulator for cellular metabolic balance in Pseudomonas fluorescens SBW25 and is necessary for growth on many substrates including xylose. To understand the regulatory linkage between CbrAB and genes for xylose utilization (xut), we performed transposon mutagenesis of ΔcbrB to select for Xut+ suppressors. This led to identification of crc and hfq. Subsequent genetic and biochemical analysis showed that Crc and Hfq are key mediators of succinate-provoked carbon catabolite repression (CCR). Specifically, Crc/Hfq sequentially bind to mRNAs of both the transcriptional activator and structural genes involved in xylose catabolism. However, in the absence of succinate, repression is relieved through competitive binding by two ncRNAs, CrcY and CrcZ, whose expression is activated by CbrAB. These findings provoke a model for CCR in which it is assumed that crc and hfq are functionally complementary, whereas crcY and crcZ are genetically redundant. Inactivation of either crcY or crcZ produced no effects on bacterial fitness in laboratory media, however, results of mathematical modelling predict that the co-existence of crcY and crcZ requires separate functional identity. Finally, we provide empirical evidence that CCR is advantageous in nutrient-complex environments where preferred carbon sources are present at high concentrations but fluctuate in their availability.

Disentangling eco-evolutionary effects on trait fixation.

In population genetics, fixation of traits in a demographically changing population under frequency-independent selection has been extensively analysed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. A combination of demographic fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics has received comparatively little attention. We consider a stochastic, competitive Lotka-Volterra model with higher order interactions between two traits. The emerging individual-based model allows for stochastic fluctuations in the frequencies of the two traits and the total population size. We calculate the fixation probability of a trait under differing competition coefficients. This fixation probability resembles, qualitatively, the deterministic evolutionary dynamics. Furthermore, we partially disentangle the selection effects into their ecological and evolutionary components. We find that changing the evolutionary selection strength also changes the population dynamics and vice versa. Thus, a clean separation of the ecological and evolutionary effects is not possible. Instead, our results imply a nested interaction of the evolutionary and ecological effects. The entangled eco-evolutionary processes thus cannot be ignored when determining fixation properties in a co-evolutionary system.

Chaotic provinces in the kingdom of the Red Queen.

The interplay between parasites and their hosts is found in all kinds of species and plays an important role in understanding the principles of evolution and coevolution. Usually, the different genotypes of hosts and parasites oscillate in their abundances. The well-established theory of oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the different types within each species. So far, it is unclear under what conditions Red Queen dynamics persists, especially when the number of types per species increases. Some models show that with many types of hosts and parasites or more species chaotic dynamics occur. In our analysis, an arbitrary number of types within two species are examined in a deterministic framework with constant or changing population size and very simple interactions. This general framework allows for analytical solutions for internal fixed points and their stability. The numerical analysis shows that for two species, once more than two types are considered per species, irregular dynamics in their frequencies can be observed in the long run. The nature of the dynamics depends strongly on the initial configuration of the system; the usual regular Red Queen oscillations are only observed when all types initially have similar abundance.

Eco-evolutionary dynamics of social dilemmas.

Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved-as captured by idioms such as 'too many cooks spoil the broth' where additional contributions are discounted, or 'two heads are better than one' where cooperators synergistically enhance the group benefit. Interaction group sizes may depend on the size of the population and hence on ecological processes. This results in feedback mechanisms between ecological and evolutionary processes, which jointly affect and determine the evolutionary trajectory. Only recently combined eco-evolutionary processes became experimentally tractable in microbial social dilemmas. Here we analyse the evolutionary dynamics of non-linear social dilemmas in settings where the population fluctuates in size and the environment changes over time. In particular, cooperation is often supported and maintained at high densities through ecological fluctuations. Moreover, we find that the combination of the two processes routinely reveals highly complex dynamics, which suggests common occurrence in nature.

Host-parasite coevolution in populations of constant and variable size.

BACKGROUND: The matching-allele and gene-for-gene models are widely used in mathematical approaches that study the dynamics of host-parasite interactions. Agrawal and Lively (Evolutionary Ecology Research 4:79-90, 2002) captured these two models in a single framework and numerically explored the associated time discrete dynamics of allele frequencies. RESULTS: Here, we present a detailed analytical investigation of this unifying framework in continuous time and provide a generalization. We extend the model to take into account changing population sizes, which result from the antagonistic nature of the interaction and follow the Lotka-Volterra equations. Under this extension, the population dynamics become most complex as the model moves away from pure matching-allele and becomes more gene-for-gene-like. While the population densities oscillate with a single oscillation frequency in the pure matching-allele model, a second oscillation frequency arises under gene-for-gene-like conditions. These observations hold for general interaction parameters and allow to infer generic patterns of the dynamics. CONCLUSION: Our results suggest that experimentally inferred dynamical patterns of host-parasite coevolution should typically be much more complex than the popular illustrations of Red Queen dynamics. A single parasite that infects more than one host can substantially alter the cyclic dynamics.

Modes of migration and multilevel selection in evolutionary multiplayer games.

The evolution of cooperation in group-structured populations has received much attention, but little is known about the effects of different modes of migration of individuals between groups. Here, we have incorporated four different modes of migration that differ in the degree of coordination among the individuals. For each mode of migration, we identify the set of multiplayer games in which the cooperative strategy has higher fixation probability than defection. The comparison shows that the set of games under which cooperation may evolve generally expands depending upon the degree of coordination among the migrating individuals. Weak altruism can evolve under all modes of individual migration, provided that the benefit to cost ratio is high enough. Strong altruism, however, evolves only if the mode of migration involves coordination of individual actions. Depending upon the migration frequency and degree of coordination among individuals, conditions that allow selection to work at the level of groups can be established.

Dynamics of a combined Medea-underdominant population transformation system.

BACKGROUND: Transgenic constructs intended to be stably established at high frequencies in wild populations have been demonstrated to "drive" from low frequencies in experimental insect populations. Linking such population transformation constructs to genes which render them unable to transmit pathogens could eventually be used to stop the spread of vector-borne diseases like malaria and dengue. RESULTS: Generally, population transformation constructs with only a single transgenic drive mechanism have been envisioned. Using a theoretical modelling approach we describe the predicted properties of a construct combining autosomal Medea and underdominant population transformation systems. We show that when combined they can exhibit synergistic properties which in broad circumstances surpass those of the single systems. CONCLUSION: With combined systems, intentional population transformation and its reversal can be achieved readily. Combined constructs also enhance the capacity to geographically restrict transgenic constructs to targeted populations. It is anticipated that these properties are likely to be of particular value in attracting regulatory approval and public acceptance of this novel technology.

Effects of time spent in pregnancy or brooding on immunocompetence.

Sexes of a species may show different characteristics beyond the differences in their sexual organs and such sexual dimorphism often occurs in the level of immune response when exposed to pathogens (immunocompetence). In general, females have increased longevity relative to males, which is associated with higher immunocompetence. However, males have higher immunocompetence in some species, such as pipefishes and seahorses. Experimental evidence suggests that this could be because males, rather than females, carry fertilized eggs to birth in these species. This observation suggests that an increase in immunocompetence may be related to the level of parental investment and not to a particular sex. We use state-dependent life-history theory to study optimal investment in offspring production relative to parent immunocompetence, varying the relative time that a parent spends in brooding or pregnancy within a breeding cycle. When offspring is dependent on a parent's survival for a large part of the breeding cycle, we predict higher investments in immunity and longer life expectancies.

Lotka-Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host-parasite coevolution.

BACKGROUND: Host-parasite coevolution is generally believed to follow Red Queen dynamics consisting of ongoing oscillations in the frequencies of interacting host and parasite alleles. This belief is founded on previous theoretical work, which assumes infinite or constant population size. To what extent are such sustained oscillations realistic? RESULTS: Here, we use a related mathematical modeling approach to demonstrate that ongoing Red Queen dynamics is unlikely. In fact, they collapse rapidly when two critical pieces of realism are acknowledged: (i) population size fluctuations, caused by the antagonism of the interaction in concordance with the Lotka-Volterra relationship; and (ii) stochasticity, acting in any finite population. Together, these two factors cause fast allele fixation. Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants. CONCLUSION: Our results call for a paradigm shift in our understanding of host-parasite coevolution, strongly suggesting that these are driven by recurrent selective sweeps rather than continuous allele oscillations.

Evolutionary games in the multiverse.

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may, in fact, take place between a number of individuals and not just between two. Here we address one-shot games with multiple players. As long as we have only two strategies, many results from two-player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions no longer hold. For two-player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players with any number of strategies , there can be at most isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied to specific cases, such as public goods games or multiplayer stag hunts.

Theoretical assessment of persistence and adaptation in weeds with complex life cycles.

Herbicide-resistant weeds pose a substantial threat to global food security. Perennial weed species are particularly troublesome. Such perennials as Sorghum halepense spread quickly and are difficult to manage due to their ability to reproduce sexually via seeds and asexually through rhizomes. Our theoretical study of S. halepense incorporates this complex life cycle with control measures of herbicide application and tillage. Rooted in the biology and experimental data of S. halepense, our population-based model predicts population dynamics and target-site resistance evolution in this perennial weed. We found that the resistance cost determines the standing genetic variation for herbicide resistance. The sexual phase of the life cycle, including self-pollination and seed bank dynamics, contributes substantially to the persistence and rapid adaptation of S. halepense. While self-pollination accelerates target-site resistance evolution, seed banks considerably increase the probability of escape from control strategies and maintain genetic variation. Combining tillage and herbicide application effectively reduces weed densities and the risk of control failure without delaying resistance adaptation. We also show how mixtures of different herbicide classes are superior to rotations and mono-treatment in controlling perennial weeds and resistance evolution. Thus, by integrating experimental data and agronomic views, our theoretical study synergistically contributes to understanding and tackling the global threat to food security from resistant weeds.

Optimizing crop rotations via Parrondo's paradox for sustainable agriculture.

Crop rotation, a sustainable agricultural technique, has been at humanity's disposal since time immemorial and is practised globally. Switching between cover crops and cash crops helps avoid the adverse effects of intensive farming. Determining the optimum cash-cover rotation schedule for maximizing yield has been tackled on multiple fronts by agricultural scientists, economists, biologists and computer scientists, to name a few. However, considering the uncertainty due to diseases, pests, droughts, floods and impending effects of climate change is essential when designing rotation strategies. Analysing this time-tested technique of crop rotations with a new lens of Parrondo's paradox allows us to optimally use the rotation technique in synchrony with uncertainty. While previous approaches are reactive to the diversity of crop types and environmental uncertainties, we make use of the said uncertainties to enhance crop rotation schedules. We calculate optimum switching probabilities in a randomized cropping sequence and suggest optimum deterministic sequences and judicious use of fertilizers. Our methods demonstrate strategies to enhance crop yield and the eventual profit margins for farmers. Conforming to translational biology, we extend Parrondo's paradox, where two losing situations can be combined eventually into a winning scenario, to agriculture.

Ecological Drivers of Community Cohesion.

From protocellular to societal, networks of living systems are complex and multiscale. Discerning the factors that facilitate assembly of these intricate interdependencies using pairwise interactions can be nearly impossible. To facilitate a greater understanding, we developed a mathematical and computational model based on a synthetic four-strain Saccharomyces cerevisiae interdependent system. Specifically, we aimed to provide a greater understanding of how ecological factors influence community dynamics. By leveraging transiently structured ecologies, we were able to drive community cohesion. We show how ecological interventions could reverse or slow the extinction rate of a cohesive community. An interconnected system first needs to persist long enough to be a subject of natural selection. Our emulation of Darwin's "warm little ponds" with an ecology governed by transient compartmentalization provided the necessary persistence. Our results reveal utility across scales of organization, stressing the importance of cyclic processes in major evolutionary transitions, engineering of synthetic microbial consortia, and conservation biology. IMPORTANCE We are facing unprecedented disruption and collapse of ecosystems across the globe. To have any hope of mitigating this phenomenon, a much greater understanding of ecosystem dynamics is required. However, ecosystems are typically composed of highly dynamic networks of individual species. These interactions are further modulated by abiotic and biotic factors that vary temporally and spatially. Thus, ecological dynamics are obfuscated by this complexity. Here, we developed a theoretical model, informed by a synthetic experimental system, of Darwin's "warm little ponds." This cycling four-species system seeks to elucidate the ecological factors that drive or inhibit interaction. We show that these factors could provide an essential tool for avoiding the accelerating ecological collapse. Our study also provides a starting point to develop a more encompassing model to inform conservation efforts.

Mutualism and evolutionary multiplayer games: revisiting the Red King.

Coevolution of two species is typically thought to favour the evolution of faster evolutionary rates helping a species keep ahead in the Red Queen race, where 'it takes all the running you can do to stay where you are'. In contrast, if species are in a mutualistic relationship, it was proposed that the Red King effect may act, where it can be beneficial to evolve slower than the mutualistic species. The Red King hypothesis proposes that the species which evolves slower can gain a larger share of the benefits. However, the interactions between the two species may involve multiple individuals. To analyse such a situation, we resort to evolutionary multiplayer games. Even in situations where evolving slower is beneficial in a two-player setting, faster evolution may be favoured in a multiplayer setting. The underlying features of multiplayer games can be crucial for the distribution of benefits. They also suggest a link between the evolution of the rate of evolution and group size.