The resident strikes back: invader-induced switching of resident attractor

The aim of this paper is two-fold: (a) by way of example, we elucidate the phenomenon of invader-induced switches in a resident attractor; (b) we expose in detail how resonance and phase have a strong impact when semelparous organisms (as, e.g. Pacific salmon) with different life-cycle lengths compete in a self-induced periodically fluctuating environment. We analyse a simple model for the competition between annuals and biennials, focusing on the situation that the annual population in isolation converges to a two-cycle. Well-timed biennial mutants sample the periodically varying environment more efficiently than the annual resident. They can invade successfully even when they are inferior to the resident, in the sense that they have lower viability and/or fertility. Successful invasion can lead to resonance-mediated coexistence if the invader is rather inferior to the resident. Remarkably, for mutants that are less inferior to the resident, successful invasion by a mutant strategy will inevitably be followed by the extinction of the former invader and concurrent re-establishment of the resident. The expulsion of the invader is brought about by an invasion-induced phase shift or attractor switch. We call this phenomenon "the resident strikes back" and say that the resident strategy is invasible, yet invincible. After the resident has struck back, other mutants can successfully invade again. On a longer time-scale, this might lead to an intermittent occurrence of ultimately inferior strategies. The results show that even in a deterministic setting, successful invasion does not necessarily lead to establishment and that mutual invasibility is not always sufficient for coexistence.     

The evolution of enzyme specificity in the metabolic replicator model of prebiotic evolution

The chemical machinery of life must have been catalytic from the outset. Models of the chemical origins have attempted to explain the ecological mechanisms maintaining a minimum necessary diversity of prebiotic replicator enzymes, but little attention has been paid so far to the evolutionary initiation of that diversity. We propose a possible first step in this direction: based on our previous model of a surface-bound metabolic replicator system we try to explain how the adaptive specialization of enzymatic replicator populations might have led to more diverse and more efficient communities of cooperating replicators with two different enzyme activities. The key assumptions of the model are that mutations in the replicator population can lead towards a) both of the two different enzyme specificities in separate replicators: efficient "specialists" or b) a "generalist" replicator type with both enzyme specificities working at less efficiency, or c) a fast-replicating, non-enzymatic "parasite". We show that under realistic trade-off constraints on the phenotypic effects of these mutations the evolved replicator community will be usually composed of both types of specialists and of a limited abundance of parasites, provided that the replicators can slowly migrate on the mineral surface. It is only at very weak trade-offs that generalists take over in a phase-transition-like manner. The parasites do not seriously harm the system but can freely mutate, therefore they can be considered as pre-adaptations to later, useful functions that the metabolic system can adopt to increase its own fitness.     

Invasion under a trade-off between density dependence and maximum growth rate

The invasion of alien species and genotypes is an increasing concern in contemporary ecology. A central question is, what life-history traits enable invasion amidst populations of wild species and conventional cultivars? In order to invade, the initially rare species must perform better than their resident competitors. We conducted a mathematical analysis and simulation of a two-species extension of the Maynard Smith and Slatkin model for population dynamics in discrete time to study the role of density dependence as different types of competition in the invasion of new species. The type of density dependence ranged from scramble to contest competition. This led to intrinsic dynamics of the species range from point equilibrium to cycles and chaos. The traits were treated either as free parameters or constrained by a trade-off resulting from a common fixed strength of density dependence or equilibrium density. Resident and intruder traits had up to ten-fold differences in all of the parameters investigated. Higher equilibrium density of the intruder allowed invasion. Under constrained equilibrium density, an intrinsically stable intruder could invade an unstable resident population. Scramble competition made a population more susceptible to invasion than contest competition (e.g., limitation by light or territory availability). This predicts that a population which is mainly limited by food (or nutrients in plants) is more likely to be invaded than a population limited by a hierarchical competition, such as light among plants. The intruder population may have an effect on the resident population's dynamics, which makes the traditional invasion analysis unable to predict invasion outcome.     

ASSORTATIVE MATE CHOICE AND DOMINANCE MODIFICATION: ALTERNATIVE WAYS OF REMOVING HETEROZYGOTE DISADVANTAGE

In genetic polymorphisms of two alleles, heterozygous individuals may contribute to the next generation on average more or fewer descendants than the homozygotes. Two different evolutionary responses that remove a disadvantageous heterozygote phenotype from the population are the evolution of strictly assortative mate choice, and that of a modifier making one of the two alleles completely dominant. We derive invasion fitness of mutants introducing dominance or assortative mate choice in a randomly mating population with a genetic polymorphism for an ecological trait. Mutations with small effects as well as mutants introducing complete dominance or perfect assorting are considered. Using adaptive dynamics techniques, we are able to calculate the ratio of fitness gradients for the effects of a dominance modifier and a mate choice locus, near evolutionary branching points. With equal resident allele frequencies, selection for mate choice is always stronger. Dominance is more strongly selected than assortative mating when the resident (common) alleles have very unequal frequencies at equilibrium. With female mate choice the difference in frequencies where dominance is more strongly selected is smaller than when mutants of both sexes can choose without costs. A symmetric resource-competition model illustrates the results.     

Delayed maturation in temporally structured populations with non-equilibrium dynamics

In this paper we study the evolutionary dynamics of delayed maturation in semelparous individuals. We model this in a two-stage clonally reproducing population subject to density-dependent fertility. The population dynamical model allows multiple — cyclic and/or chaotic — attractors, thus allowing us to illustrate how (i) evolutionary stability is primarily a property of a population dynamical system as a whole, and (ii) that the evolutionary stability of a demographic strategy by necessity derives from the evolutionary stability of the stationary population dynamical systems it can engender, i.e., its associated population dynamical attractors. Our approach is based on numerically estimating invasion exponents or “mutant fitnesses”. The invasion exponent is defined as the theoretical long-term average relative growth rate of a population of mutants in the stationary environment defined by a resident population system. For some combinations of resident and mutant trait values, we have to consider multi-valued invasion exponents, which makes the evolutionary argument more complicated (and more interesting) than is usually envisaged. Multi-valuedness occurs (i) when more than one attractor is associated with the values of the residents' demographic parameters, or (ii) when the setting of the mutant parameters makes the descendants of a single mutant reproduce exclusively either in even or in odd years, so that a mutant population is affected by either subsequence of the fluctuating resident densities only. Non-equilibrium population dynamics or random environmental noise selects for strategists with a non-zero probability to delay maturation. When there is an evolutionarily attracting pair of such a strategy and a population dynamical attractor engendered by it, this delaying probability is a Continuously Stable Strategy, that is an Evolutionarily Unbeatable Strategy which is also Stable in a long term evolutionary sense. Population dynamical coexistence of delaying and non-delaying strategists is possible with non-equilibrium dynamics, but adding random environmental noise to the model destroys this coexistence. Adding random noise also shifts the CSS towards a higher probability of delaying maturation.     

Species diversity reduces invasion success in pathogen‐regulated communities

The loss of natural enemies is thought to explain why certain invasive species are so spectacularly successful in their introduced range. However, if losing natural enemies leads to unregulated population growth, this implies that native species are themselves normally subject to natural enemy regulation. One possible widespread mechanism of natural enemy regulation is negative soil feedbacks, in which resident species growing on home soils are disadvantaged because of a build‐up of species‐specific soil pathogens. Here we construct simple models in which pathogens cause resident species to suffer reduced competitive ability on home soils and consider the consequences of such pathogen regulation for potential invading species. We show that the probability of successful invasion and its timescale depend strongly on the competitive ability of the invader on resident soils, but are unaffected by whether or not the invader also suffers reduced competitive ability on home soils (i.e. pathogen regulation). This is because, at the start of an invasion, the invader is rare and hence mostly encounters resident soils. However, the lack of pathogen regulation does allow the invader to achieve an unusually high population density. We also show that increasing resident species diversity in a pathogen‐regulated community increases invasion resistance by reducing the frequency of home‐site encounters. Diverse communities are more resistant to invasion than monocultures of the component species: they preclude a greater range of potential invaders, slow the timescale of invasion and reduce invader population size. Thus, widespread pathogen regulation of resident species is a potential explanation for the empirical observation that diverse communities are more invasion resistant.     

Consequences of asymmetric competition between resident and invasive defoliators: A novel empirically based modelling approach

Invasive species can have profound effects on a resident community via indirect interactions among community members. While long periodic cycles in population dynamics can make the experimental observation of the indirect effects difficult, modelling the possible effects on an evolutionary time scale may provide the much needed information on the potential threats of the invasive species on the ecosystem. Using empirical data from a recent invasion in northernmost Fennoscandia, we applied adaptive dynamics theory and modelled the long term consequences of the invasion by the winter moth into the resident community. Specifically, we investigated the outcome of the observed short-term asymmetric preferences of generalist predators and specialist parasitoids on the long term population dynamics of the invasive winter moth and resident autumnal moth sharing these natural enemies. Our results indicate that coexistence after the invasion is possible. However, the outcome of the indirect interaction on the population dynamics of the moth species was variable and the dynamics might not be persistent on an evolutionary time scale. In addition, the indirect interactions between the two moth species via shared natural enemies were able to cause asynchrony in the population cycles corresponding to field observations from previous sympatric outbreak areas. Therefore, the invasion may cause drastic changes in the resident community, for example by prolonging outbreak periods of birch-feeding moths, increasing the average population densities of the moths or, alternatively, leading to extinction of the resident moth species or to equilibrium densities of the two, formerly cyclic, herbivores.     

On the (dis) advantages of cannibalism

Cannibalism is an interaction between individuals that can produce counter- intuitive effects at the population level. A striking effect is that a population may persist under food conditions such that the non-cannibalistic variant is doomed to go extinct. This so-called life boat mechanism has received considerable attention. Implicitly, such studies sometimes suggest, that the life boat mechanism procures an evolutionary advantage to the cannibalistic trait. Here we compare, in the context of a size structured population model, the conditions under which the life boat mechanism works, with those that guarantee, that a cannibalistic mutant can invade successfully under the steady environmental conditions as set by a non-cannibalistic resident. We find qualitative agreement and quantitative difference. In particular, we find that a prerequisite for the life boat mechanism is, that cannibalistic mutants are successful invaders. Roughly speaking, our results show that cannibalism brings advantages to both the individuals and the population when adult food is limiting.     

Modelling invasibility in endogenously oscillating tree populations: timing of invasion matters

The timing of introduction of a new species into an ecosystem can be critical in determining the invasibility (i.e. the sensitivity to invasion) of a resident population. Here, we use an individual-based model to test how (1) the type of competition (symmetric versus asymmetric) and (2) seed masting influence the success of invasion by producing oscillatory dynamics in resident tree populations. We focus on a case where two species (one resident, one invader introduced at low density) do not differ in terms of competitive abilities. By varying the time of introduction of the invader, we show that oscillations in the resident population favour invasion, by creating “invasibility windows” during which resource is available for the invader due to transiently depressed resident population density. We discuss this result in the context of current knowledge on forest dynamics and invasions, emphasizing the importance of variability in population dynamics.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the "competitive exclusion" principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.     

EVOLUTION OF DISPERSAL RATES IN METAPOPULATION MODELS: BRANCHING AND CYCLIC DYNAMICS IN PHENOTYPE SPACE

We study the evolution of dispersal rates in a two patch metapopulation model. The local dynamics in each patch are given by difference equations, which, together with the rate of dispersal between the patches, determine the ecological dynamics of the metapopulation. We assume that phenotypes are given by their dispersal rate. The evolutionary dynamics in phenotype space are determined by invasion exponents, which describe whether a mutant can invade a given resident population. If the resident metapopulation is at a stable equilibrium, then selection on dispersal rates is neutral if the population sizes in the two patches are the same, while selection drives dispersal rates to zero if the local abundances are different. With non-equilibrium metapopulation dynamics, non-zero dispersal rates can be maintained by selection. In this case, and if the patches are ecologically identical, dispersal rates always evolve to values which induce synchronized metapopulation dynamics. If the patches are ecologically different, evolutionary branching into two coexisting dispersal phenotypes can be observed. Such branching can happen repeatedly, leading to polymorphisms with more than two phenotypes. If there is a cost to dispersal, evolutionary cycling in phenotype space can occur due to the dependence of selection pressures on the ecological attractor of the resident population, or because phenotypic branching alternates with the extinction of one of the branches. Our results extend those of Holt and McPeek (1996), and suggest that phenotypic branching is an important evolutionary process. This process may be relevant for sympatric speciation.     

Disease-induced stabilization of predator-prey oscillations

Parasites are an integral part of virtually all food webs and species communities. Here we consider the invasion of a resident predator-prey system by an infectious disease with frequency-dependent transmission spreading within the predator population. We derive biologically plausible and insightful quantities (demographic and epizootiological reproduction numbers) that allow us to completely determine community composition. Successful disease invasion can have two contrary effects in driving its host population to extinction or in stabilizing predator-prey cycles. Our findings contradict predictions from previous models suggesting a destabilizing effect of parasites. We show that predator infection counteracts the paradox of enrichment. In turn, parasite removal from food webs can have catastrophic effects. We discuss the implications for biological control and resource management on more than one trophic level.     

Ecological bistability and evolutionary reversals under asymmetrical competition

Abstract How does the process of life‐history evolution interplay with population dynamics? Almost all models that have addressed this question assume that any combination of phenotypic traits uniquely determine the ecological population state. Here we show that if multiple ecological equilibria can exist, the evolution of a trait that relates to competitive performance can undergo adaptive reversals that drive cyclic alternation between population equilibria. The occurrence of evolutionary reversals requires neither environmentally driven changes in selective forces nor the coevolution of interactions with other species. The mechanism inducing evolutionary reversals is twofold. First, there exist phenotypes near which mutants can invade and yet fail to become fixed; although these mutants are eventually eliminated, their transitory growth causes the resident population to switch to an alternative ecological equilibrium. Second, asymmetrical competition causes the direction of selection to revert between high and low density. When ecological conditions for evolutionary reversals are not satisfied, the population evolves toward a steady state of either low or high abundance, depending on the degree of competitive asymmetry and environmental parameters. A sharp evolutionary transition between evolutionary stasis and evolutionary reversals and cycling can occur in response to a smooth change in ecological parameters, and this may have implications for our understanding of size‐abundance patterns.     

Anomalous invasion dynamics due to dispersal polymorphism and dispersal–reproduction trade-offs

Dispersal polymorphism and mutation play significant roles during biological invasions, potentially leading to evolution and complex behaviour such as accelerating or decelerating invasion fronts. However, life-history theory predicts that reproductive fitness—another key determinant of invasion dynamics—may be lower for more dispersive strains. Here, we use a mathematical model to show that unexpected invasion dynamics emerge from the combination of heritable dispersal polymorphism, dispersal-fitness trade-offs, and mutation between strains. We show that the invasion dynamics are determined by the trade-off relationship between dispersal and population growth rates of the constituent strains. We find that invasion dynamics can be ‘anomalous’ (i.e. faster than any of the strains in isolation), but that the ultimate invasion speed is determined by the traits of, at most, two strains. The model is simple but generic, so we expect the predictions to apply to a wide range of ecological, evolutionary, or epidemiological invasions.     

Evolution of virulence: triggering host inflammation allows invading pathogens to exclude competitors

Virulence is generally considered to benefit parasites by enhancing resource-transfer from host to pathogen. Here, we offer an alternative framework where virulent immune-provoking behaviours and enhanced immune resistance are joint tactics of invading pathogens to eliminate resident competitors (transferring resources from resident to invading pathogen). The pathogen wins by creating a novel immunological challenge to which it is already adapted. We analyse a general ecological model of 'proactive invasion' where invaders not adapted to a local environment can succeed by changing it to one where they are better adapted than residents. However, the two-trait nature of the 'proactive' strategy (provocation of, and adaptation to environmental change) presents an evolutionary conundrum, as neither trait alone is favoured in a homogenous host population. We show that this conundrum can be resolved by allowing for host heterogeneity. We relate our model to emerging empirical findings on immunological mediation of parasite competition.     

The impact of interactions on invasion and colonization resistance in microbial communities

In human microbiota, the prevention or promotion of invasions can be crucial to human health. Invasion outcomes, in turn, are impacted by the composition of resident communities and interactions of resident members with the invader. Here we study how interactions influence invasion outcomes in microbial communities, when interactions are primarily mediated by chemicals that are released into or consumed from the environment. We use a previously developed dynamic model which explicitly includes species abundances and the concentrations of chemicals that mediate species interaction. Using this model, we assessed how species interactions impact invasion by simulating a new species being introduced into an existing resident community. We classified invasion outcomes as resistance, augmentation, displacement, or disruption depending on whether the richness of the resident community was maintained or decreased and whether the invader was maintained in the community or went extinct. We found that as the number of invaders introduced into the resident community increased, disruption rather than augmentation became more prevalent. With more facilitation of the invader by the resident community, resistance outcomes were replaced by displacement and augmentation. By contrast, with more facilitation among residents, displacement outcomes shifted to resistance. When facilitation of the resident community by the invader was eliminated, the majority of augmentation outcomes turned into displacement, while when inhibition of residents by invaders was eliminated, invasion outcomes were largely unaffected. Our results suggest that a better understanding of interactions within resident communities and between residents and invaders is crucial to predicting the success of invasions into microbial communities.     

Spatial Models of Prebiotic Evolution: Soup Before Pizza?

The problem of information integration andresistance to the invasion of parasitic mutants in prebiotic replicator systemsis a notorious issue of research on the origin of life.Almost all theoretical studies published so far havedemonstrated that some kind of spatial structure is indispensable forthe persistence and/or the parasite resistance of any feasible replicator system.Based on a detailed critical survey of spatial models on prebiotic informationintegration, we suggest a possible scenario for replicator system evolution leadingto the emergence of the first protocells capable of independent life.We show that even the spatial versions of the hypercycle model are vulnerable toselfish parasites in heterogeneous habitats. Contrary, the metabolic system remainspersistent and coexistent with its parasites both on heterogeneous surfaces andin chaotically mixing flowing media. Persistent metabolic parasites can beconverted to metabolic cooperators, or they can gradually obtain replicase activity.Our simulations show that, once replicase activity emerged, a gradual and simultaneousevolutionary improvement of replicase functionality (speed and fidelity) andtemplate efficiency is possible only on a surface that constrains the mobility ofmacromolecule replicators. Based on the results of the models reviewed, we suggestthat open chaotic flows (`soup') and surface dynamics (`pizza') both played keyroles in the sequence of evolutionary events ultimately concluding in theappearance of the first living cell on Earth.     

Identification of mutations that decrease the stability of a fragment of Saccharomyces cerevisiae chromosome III lacking efficient replicators

Eukaryotic chromosomes are duplicated during S phase and transmitted to progeny during mitosis with high fidelity. Chromosome duplication is controlled at the level of replication initiation, which occurs at cis-acting replicator sequences that are spaced at intervals of approximately 40 kb along the chromosomes of the budding yeast Saccharomyces cerevisiae. Surprisingly, we found that derivatives of yeast chromosome III that lack known replicators were replicated and segregated properly in at least 96% of cell divisions. To gain insight into the mechanisms that maintain these "originless" chromosome fragments, we screened for mutants defective in the maintenance of an "originless" chromosome fragment, but proficient in the maintenance of the same fragment that carries its normal complement of replicators (originless fragment maintenance mutants, or ofm). We show that three of these Ofm mutations appear to disrupt different processes involved in chromosome transmission. The OFM1-1 mutant seems to disrupt an alternative initiation mechanism, and the ofm6 mutant appears to be defective in replication fork progression. ofm14 is an allele of RAD9, which is required for the activation of the DNA damage checkpoint, suggesting that this checkpoint plays a key role in the maintenance of the "originless" fragment.     

Resident-invader dynamics and the coexistence of similar strategies

We study the resident-invader dynamics for a given class of models of unstructured populations of finite-dimensional strategies. We prove various results on the existence and uniqueness of -limit sets in the interior of the resident-invader population state space, and we classify the generically possible types of dynamics in terms of the invasion conditions when the resident and invader strategies are similar to one another.This work was supported by the Academy of Finland     

Relative nonlinearity and permanence

We modify the commonly used invasibility concept for coexistence of species to the stronger concept of uniform invasibility. For two-species discrete-time competition and predator-prey models, we use this concept to find broad easily checked sufficient conditions for the rigorous concept of permanent coexistence. With these results, permanent coexistence becomes a tractable concept for many discrete-time population models. To understand how these conditions apply to nonpoint attractors, we generalize the concept of relative nonlinearity and use it to show how population fluctuations affect the long-term low-density growth rate (“the invasion rate”) of a species when it is invading the system consisting of the other species (“the resident”) at a single-species attractor. The concept of relative nonlinearity defines circumstances when this invasion rate is increased or decreased by resident population fluctuations arising from a nonpoint attractor. The presence and sign of relative nonlinearity is easily checked in models of interacting species. When relative nonlinearity is zero or positive, fluctuations cannot decrease the invasion rate. It follows that permanence is then determined by invasibility of the resident’s fixed points. However, when relative nonlinearity is negative, invasibility, and hence permanent coexistence, can be undermined by resident population fluctuations. These results are illustrated with specific two-species competition and predator-prey models of generic forms.