Closing the gap in the Janzen-Connell hypothesis: What determines pathogen diversity?

The high tree diversity in tropical forests has long been a puzzle to ecologists. In the 1970s, Janzen and Connell proposed that tree species (hosts) coexist due to the stabilizing actions of specialized enemies. This Janzen-Connell hypothesis was subsequently supported by theoretical studies. Yet, such studies have taken the presence of specialized pathogens for granted, overlooking that pathogen coexistence also requires an explanation. Moreover, stable ecological coexistence does not necessarily imply evolutionary stability. What are the conditions that allow Janzen-Connell effects to evolve? We link theory from community ecology, evolutionary biology and epidemiology to tackle this question, structuring our approach around five theoretical frameworks. Phenomenological Lotka-Volterra competition models provide the most basic framework, which can be restructured to include (single- or multi-)pathogen dynamics. This ecological foundation can be extended to include pathogen evolution. Hosts, of course, may also evolve, and we introduce a coevolutionary model, showing that host-pathogen coevolution can lead to highly diverse systems. Our work unpacks the assumptions underpinning Janzen-Connell and places theoretical bounds on pathogen and host ecology and evolution. The five theoretical frameworks taken together provide a stronger theoretical basis for Janzen-Connell, delivering a wider lens that can yield important insights into the maintenance of diversity in these increasingly threatened systems.

(Epi)mutation Rates and the Evolution of Composite Trait Architectures.

AbstractMutation rates vary widely along genomes and across inheritance systems. This suggests that complex traits-resulting from the contributions of multiple determinants-might be composite in terms of the underlying mutation rates. Here we investigate through mathematical modeling whether such a heterogeneity may drive changes in a trait's architecture, especially in fluctuating environments, where phenotypic instability can be beneficial. We first identify a convexity principle related to the shape of the trait's fitness function, setting conditions under which composite architectures should be adaptive or, conversely and more commonly, should be selected against. Simulations reveal, however, that applying this principle to realistic evolving populations requires taking into account pervasive epistatic interactions that take place in the system. Indeed, the fate of a mutation affecting the architecture depends on the (epi)genetic background, which itself depends on the current architecture in the population. We tackle this problem by borrowing the adaptive dynamics framework from evolutionary ecology-where it is routinely used to deal with such resident/mutant dependencies-and find that the principle excluding composite architectures generally prevails. Yet the predicted evolutionary trajectories will typically depend on the initial architecture, possibly resulting in historical contingencies. Finally, by relaxing the large population size assumption, we unexpectedly find that not only the strength of selection on a trait's architecture but also its direction depend on population size, revealing a new occurrence of the recently identified phenomenon coined "sign inversion."

Anisogamy Does Not Always Promote the Evolution of Mating Competition Traits in Males.

AbstractAnisogamy has evolved in most sexually reproducing multicellular organisms allowing the definition of male and female sexes, producing small and large gametes. Anisogamy, as the initial sexual dimorphism, is a good starting point to understand the evolution of further sexual dimorphisms. For instance, it is generally accepted that anisogamy sets the stage for more intense mating competition in males than in females. We argue that this idea stems from a restrictive assumption on the conditions under which anisogamy evolved in the first place: the absence of sperm limitation (assuming that all female gametes are fertilized). Here, we relax this assumption and present a model that considers the coevolution of gamete size with a mating competition trait, starting in a population without dimorphism. We vary gamete density to produce different scenarios of gamete limitation. We show that while at high gamete density the evolution of anisogamy always results in male investment in competition, gamete limitation at intermediate gamete densities allows for either females or males to invest more into mating competition. Our results thus suggest that anisogamy does not always promote mating competition among males. The conditions under which anisogamy evolves matter, as does the competition trait.

Larval and Adult Traits Coevolve in Response to Asymmetric Coastal Currents to Shape Marine Dispersal Kernels.

AbstractDispersal emerges as an outcome of organismal traits and external forcings. However, it remains unclear how the emergent dispersal kernel evolves as a by-product of selection on the underlying traits. This question is particularly compelling in coastal marine systems, where dispersal is tied to development and reproduction and where directional currents bias larval dispersal downstream, causing selection for retention. We modeled the dynamics of a metapopulation along a finite coastline using an integral projection model and adaptive dynamics to understand how asymmetric coastal currents influence the evolution of larval (pelagic larval duration) and adult (spawning frequency) life history traits, which indirectly shape the evolution of marine dispersal kernels. Selection induced by alongshore currents favors the release of larvae over multiple time periods, allowing long pelagic larval durations and long-distance dispersal to be maintained in marine life cycles in situations where they were previously predicted to be selected against. Two evolutionarily stable strategies emerged: one with a long pelagic larval duration and many spawning events, resulting in a dispersal kernel with a larger mean and variance, and another with a short pelagic larval duration and few spawning events, resulting in a dispersal kernel with a smaller mean and variance. Our theory shows how coastal ocean flows are important agents of selection that can generate multiple, often co-occurring evolutionary outcomes for marine life history traits that affect dispersal.

The impact of sterility-mortality tolerance and recovery-transmission trade-offs on host-parasite coevolution.

Understanding the coevolutionary dynamics of hosts and their parasites remains a major focus of much theoretical literature. Despite empirical evidence supporting the presence of sterility-mortality tolerance trade-offs in hosts and recovery-transmission trade-offs in parasites, none of the current models have explored the potential outcomes when both trade-offs are considered within a coevolutionary framework. In this study, we consider a model where the host evolves sterility tolerance at the cost of increased mortality and the parasite evolves higher transmission rate at the cost of increased recovery rate (reduced infection duration), and use adaptive dynamics to predict the coevolutionary outcomes under such trade-off assumptions. We particularly aim to understand how our coevolutionary dynamics compare with single species evolutionary models. We find that evolutionary branching in the host can drive the parasite population to branch, but that cycles in the population dynamics can prevent the coexisting strains from reaching their extremes. We also find that varying crowding does not impact the recovery rate when only the parasite evolves, yet coevolution reduces recovery as crowding intensifies. We conclude by discussing how different host and parasite trade-offs shape coevolutionary outcomes, underscoring the pivotal role of trade-offs in coevolution.

A mathematical framework for evo-devo dynamics.

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

The impact of dormancy on evolutionary branching.

In this paper, we investigate the consequences of dormancy in the 'rare mutation' and 'large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second 'small mutations' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the 'speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.

Parasite evolution of host manipulation strategies with fluctuating ecological dynamics.

Trophically transmitted parasites often infect an intermediate prey host and manipulate their behaviour to make predation more likely, thus facilitating parasite transmission to the definitive host. However, it is unclear when such a manipulation strategy should be expected to evolve. We develop the first evolutionary invasion model to explore the evolution of manipulation strategies that are in a trade-off with parasite production of free-living spores. We find that the size of the susceptible prey population together with the threat of predation drives manipulation evolution. We find that it is only when the susceptible prey population is large and the threat of predation is relatively small that selection favours manipulation strategies over spore production. We also confirm that the system exhibits cyclic population dynamics, and this can influence the qualitative direction of selection.

Metamicrobiome diversity promotes the evolution of host-microbial mutualisms.

Ecological theory suggests that a host organism's internal spatial structure can promote the persistence of mutualistic microbes by allowing for the turnover of tissue occupied by non-beneficial or cheating microbes. This type of regulation, whereby a host preferentially rewards tissue occupied by beneficial members of its microbiome but sanctions tissue occupied by non-beneficial cheaters, is expected to generate a competition-extinction trade-off by allowing beneficial microbes to experience a lower extinction rate than competitively dominant cheaters. Using an adaptive dynamics approach, we demonstrate that although ecologically stable, microbial regulation via sanctioning is not stable in any evolutionary sense, as each individual host will be under pressure to reduce the costs incurred from cheater suppression in order to maximize its own fitness at the expense of the rest of the host population. However, increasing the diversity of non-beneficial cheaters in the host population metamicrobiome can lead to an increase in the relative fitness of hosts that actively sanction non-performing tissue, thus facilitating the evolutionary emergence and persistence of such strategies in host-microbial systems. These counter-intuitive results demonstrate how diversity at multiple levels of biological organization and spatiotemporal scales can interact to facilitate the establishment and maintenance of mutualistic relationships.

The evolutionary dynamics of hyperparasites.

Evolutionary theory has typically focused on pairwise interactions, such as those between hosts and parasites, with relatively little work having been carried out on more complex interactions including hyperparasites: parasites of parasites. Hyperparasites are common in nature, with the chestnut blight fungus virus CHV-1 a well-known natural example, but also notably include the phages of important human bacterial diseases. We build a general modeling framework for the evolution of hyperparasites that highlights the central role that the ability of a hyperparasite to be transmitted with its parasite plays in their evolution. A key result is that hyperparasites which transmit with their parasite hosts (hitchhike) will be selected for lower virulence, trending towards hypermutualism or hypercommensalism. We examine the impact on the evolution of hyperparasite systems of a wide range of host and parasite traits showing, for example, that high parasite virulence selects for higher hyperparasite virulence resulting in reductions in parasite virulence when hyperparasitized. Furthermore, we show that acute parasite infection will also select for increased hyperparasite virulence. Our results have implications for hyperparasite research, both as biocontrol agents and for their role in shaping community ecology and evolution and moreover emphasize the importance of understanding evolution in the context of multitrophic interactions.

Separation of evolutionary timescales in coevolving species.

Many coevolutionary processes, including host-parasite and host-symbiont interactions, involve one species or trait which evolves much faster than the other. Whether or not a coevolutionary trajectory converges depends on the relative rates of evolutionary change in the two species, and so current adaptive dynamics approaches generally either determine convergence stability by considering arbitrary (often comparable) rates of evolutionary change or else rely on necessary or sufficient conditions for convergence stability. We propose a method for determining convergence stability in the case where one species is expected to evolve much faster than the other. This requires a second separation of timescales, which assumes that the faster evolving species will reach its evolutionary equilibrium (if one exists) before a new mutation arises in the more slowly evolving species. This method, which is likely to be a reasonable approximation for many coevolving species, both provides straightforward conditions for convergence stability and is less computationally expensive than traditional analysis of coevolution models, as it reduces the trait space from a two-dimensional plane to a one-dimensional manifold. In this paper, we present the theory underlying this new separation of timescales and provide examples of how it could be used to determine coevolutionary outcomes from models.

The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective.

We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug administration and distribution, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic and global sensitivity analyses, as well as numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour tissues and drug dose on the development of chemoresistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastases may be less impacted by the chemotherapeutic agent.

Evolutionary branching in multi-level selection models.

We study a model of group-structured populations featuring individual-level birth and death events, and group-level fission and extinction events. Individuals play games within their groups, while groups play games against other groups. Payoffs from individual-level games affect birth rates of individuals, and payoffs from group-level games affect group extinction rates. We focus on the evolutionary dynamics of continuous traits with particular emphasis on the phenomenon of evolutionary diversification. Specifically, we consider two-level processes in which individuals and groups play continuous snowdrift or prisoner's dilemma games. Individual game strategies evolve due to selection pressure from both the individual and group level interactions. The resulting evolutionary dynamics turns out to be very complex, including branching and type-diversification at one level or the other. We observe that a weaker selection pressure at the individual level results in more adaptable groups and sometimes group-level branching. Stronger individual-level selection leads to more effective adaptation within each group while preventing the groups from adapting according to the group-level games.

The impact of harvesting on the evolutionary dynamics of prey species in a prey-predator systems.

Matsuda and Abrams (Theor Popul Biol 45(1):76-91, 1994) initiated the exploration of self-extinction in species through evolution, focusing on the advantageous position of mutants near the extinction boundary in a prey-predator system with evolving foraging traits. Previous models lacked theoretical investigation into the long-term effects of harvesting. In our model, we introduce constant-effort prey and predator harvesting, along with individual logistic growth of predators. The model reveals two distinct evolutionary outcomes: (i) Evolutionary suicide, marked by a saddle-node bifurcation, where prey extinction results from the invasion of a lower forager mutant; and (ii) Evolutionary reversal, characterized by a subcritical Hopf bifurcation, leading to cyclic prey evolution. Employing an innovative approach based on Gröbner basis computation, we identify various bifurcation manifolds, including fold, transcritical, cusp, Hopf, and Bogdanov-Takens bifurcations. These contrasting scenarios emerge from variations in harvesting parameters while keeping other factors constant, rendering the model an intriguing subject of study.

A general multi-scale description of metastable adaptive motion across fitness valleys.

We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph G = ( V , E ) . The evolution is driven by a linear birth rate, a density dependent logistic death rate and the possibility of mutations along the directed edges in E. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between Bovier et al. (Ann Appl Probab 29(6):3541-358, 2019) and Coquille et al. (Electron J Probab 26:1-37, 2021) we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales, corresponding to the widths of these fitness valleys. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between them. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scales, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

Spatial social dilemmas promote diversity.

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

Evolutionary double suicide in symbiotic systems.

Mutualism is thought to face a threat of coextinction cascade because the loss of a member species could lead to the extinction of the other member. Despite this common emphasis on the perils of such knock-on effect, hitherto, the evolutionary causes leading to extinction have been less emphasised. Here, we examine how extinction could be triggered in mutualism and whether an evolutionary response to partner loss could prevent collateral extinctions, by theoretically examining the coevolution of the host exploitation by symbionts and host dependence on symbiosis. Our model reveals that mutualism is more vulnerable to co-extinction through adaptive evolution (evolutionary double suicide) than parasitism. Additionally, it shows that the risk of evolutionary double suicide rarely promotes the backward evolution to an autonomous (non-symbiotic) state. Our results provide a new perspective on the evolutionary fragility of mutualism and the rarity of observed evolutionary transitions from mutualism to parasitism.

Evolutionary emergence of alternative stable states in shallow lakes.

Ecosystems under stress may respond abruptly and irreversibly through tipping points. Although mechanisms leading to alternative stable states are much studied, little is known about how such ecosystems could have emerged in the first place. We investigate whether evolution by natural selection along resource gradients leads to bistability, using shallow lakes as an example. There, tipping points occur between two alternative states dominated by either submersed or floating macrophytes depending on nutrient loading. We model the evolution of macrophyte depth in the lake, identify the conditions under which the ancestor population diversifies and investigate whether alternative stable states dominated by different macrophyte phenotypes occur. We find that eco-evolutionary dynamics may lead to alternative stable states, but under restrictive conditions. Such dynamics require sufficient asymmetries in the acquisition of both light and nutrient. Our analysis suggests that competitive asymmetries along opposing resource gradients may allow bistability to emerge by natural selection.

Complex life cycles drive community assembly through immigration and adaptive diversification.

Most animals undergo ontogenetic niche shifts during their life. Yet, standard ecological theory builds on models that ignore this complexity. Here, we study how complex life cycles, where juvenile and adult individuals each feed on different sets of resources, affect community richness. Two different modes of community assembly are considered: gradual adaptive evolution and immigration of new species with randomly selected phenotypes. We find that under gradual evolution complex life cycles can lead to both higher and lower species richness when compared to a model of species with simple life cycles that lack an ontogenetic niche shift. Thus, complex life cycles do not per se increase the scope for gradual adaptive diversification. However, complex life cycles can lead to significantly higher species richness when communities are assembled trough immigration, as immigrants can occupy isolated peaks of the dynamic fitness landscape that are not accessible via gradual evolution.

Maximal ecological diversity exceeds evolutionary diversity in model ecosystems.

Understanding community saturation is fundamental to ecological theory. While investigations of the diversity of evolutionary stable states (ESSs) are widespread, the diversity of communities that have yet to reach an evolutionary endpoint is poorly understood. We use Lotka-Volterra dynamics and trait-based competition to compare the diversity of randomly assembled communities to the diversity of the ESS. We show that, with a large enough founding diversity (whether assembled at once or through sequential invasions), the number of long-time surviving species exceeds that of the ESS. However, the excessive founding diversity required to assemble a saturated community increases rapidly with the dimension of phenotype space. Additionally, traits present in communities resulting from random assembly are more clustered in phenotype space compared to random, although still markedly less ordered than the ESS. By combining theories of random assembly and ESSs we bring a new viewpoint to both the saturation and random assembly literature.