Revisiting the role of behavior-mediated structuring in the survival of populations in hostile environments.

Increasing the population density of target species is a major goal of ecosystem and agricultural management. This task is especially challenging in hazardous environments with a high abundance of natural enemies such as parasites and predators. Safe locations with lower mortality have been long considered a beneficial factor in enhancing population survival, being a promising tool in commercial fish farming and restoration of threatened species. Here we challenge this opinion and revisit the role of behavior structuring in a hostile environment in shaping the population density. We build a mathematical model, where individuals are structured according to their defensive tactics against natural enemies. The model predicts that although each safe zone enhances the survival of an individual, for an insufficient number of such zones, the entire population experiences a greater overall mortality. This is a result of the interplay of emergent dynamical behavioral structuring and strong intraspecific competition for safe zones. Non-plastic structuring in individuals' boldness reduces the mentioned negative effects. We demonstrate emergence of non-plastic behavioral structuring: the evolutionary branching of a monomorphic population into a dimorphic one with bold/shy strains. We apply our modelling approach to explore fish farming of salmonids in an environment infected by trematode parasites.

Revisiting implementation of multiple natural enemies in pest management.

A major goal of biological control is the reduction and/or eradication of pests using various natural enemies, in particular, via deliberate infection of the target species by parasites. To enhance the biological control, a promising strategy seems to implement a multi-enemy assemblage rather than a single control agent. Although a large body of theoretical studies exists on co-infections in epidemiology and ecology, there is still a big gap in modelling outcomes of multi-enemy biological control. Here we theoretically investigate how the efficiency of biological control of a pest depends on the number of natural enemies used. We implement a combination of eco-epidemiological modelling and the Adaptive Dynamics game theory framework. We found that a progressive addition of parasite species increases the evolutionarily stable virulence of each parasite, and thus enhances the mortality of the target pest. However, using multiple enemies may have only a marginal effect on the success of biological control, or can even be counter-productive when the number of enemies is excessive. We found the possibility of evolutionary suicide, where one or several parasite species go extinct over the course of evolution. Finally, we demonstrate an interesting scenario of coexistence of multiple parasites at the edge of extinction.

Assassin snails (Anentome helena) as a biological model for exploring the effects of individual specialisation within generalist predators.

Quantifying feeding behaviour of generalist predators at the population and individual levels is crucial for understanding the structure and functioning of food webs. Individual predator/consumer feeding niches can be significantly narrower than that of the population across animal taxa. In such species, the population of a generalist predator becomes essentially an ensemble of specialist individuals and this often highly affects the dynamics of the prey-predator interactions. Currently, few experimental systems exist that are both easily technically manipulated in a lab and are reliable to accurately assess effects of individual specialisation within generalist predators. Here we argue that a freshwater predaceous snail, Anentome helena (also known as an 'assassin snail'), is a convenient and reliable experimental system to study feeding of a generalist predator on multiple food types which exhibits well-pronounced specialisation of foraging individuals. Using A. helena we experimentally test: (i) how relative prey abundances in the environment affect the feeding patterns, (ii) whether the feeding patterns are consistent over the duration of the experimental period, and (iii) compare the feeding niche breadth of individuals to that of the laboratory population. By offering four different prey snail species, at a range of relative abundances, we show that there are consistent patterns in feeding. Importantly, the consumption of each prey was independent of the relative abundance at which they were present. Individual predators showed selectivity to a particular prey, i.e. the population of assassin snails seems to be formed of individuals that specialise on different prey. Our findings would contribute to the recent revision and the ongoing debate on the classification of predator species into generalists and specialists.

Bifurcation analysis of the predator-prey model with the Allee effect in the predator.

The use of predator-prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka-Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be subject to an Allee effect, where the per capita growth rate increases with the population density. Including an Allee effect has been shown to fundamentally change predator-prey dynamics and strongly impact species persistence, but previous studies mostly focused on scenarios of an Allee effect in the prey population. Here we explore a predator-prey model with an ecologically important case of the Allee effect in the predator population where it occurs in the numerical response of predator without affecting its functional response. Biologically, this can result from various scenarios such as a lack of mating partners, sperm limitation and cooperative breeding mechanisms, among others. Unlike previous studies, we consider here a generic mathematical formulation of the Allee effect without specifying a concrete parameterisation of the functional form, and analyse the possible local bifurcations in the system. Further, we explore the global bifurcation structure of the model and its possible dynamical regimes for three different concrete parameterisations of the Allee effect. The model possesses a complex bifurcation structure: there can be multiple coexistence states including two stable limit cycles. Inclusion of the Allee effect in the predator generally has a destabilising effect on the coexistence equilibrium. We also show that regardless of the parametrisation of the Allee effect, enrichment of the environment will eventually result in extinction of the predator population.

Effects of stochasticity on the length and behaviour of ecological transients.

There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system's transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.

How does feedback from phage infections influence the evolution of phase variation in Campylobacter?

Campylobacter jejuni (C. jejuni) causes gastroenteritis following the consumption of contaminated poultry meat, resulting in a large health and economic burden worldwide. Phage therapy is a promising technique for eradicating C. jejuni from poultry flocks and chicken carcasses. However, C. jejuni can resist infections by some phages through stochastic, phase-variable ON/OFF switching of the phage receptors mediated by simple sequence repeats (SSR). While selection strength and exposure time influence the evolution of SSR-mediated phase variation (PV), phages offer a more complex evolutionary environment as phage replication depends on having a permissive host organism. Here, we build and explore several continuous culture bacteria-phage computational models, each analysing different phase-variable scenarios calibrated to the experimental SSR rates of C. jejuni loci and replication parameters for the F336 phage. We simulate the evolution of PV rates via the adaptive dynamics framework for varying levels of selective pressures that act on the phage-resistant state. Our results indicate that growth reducing counter-selection on a single PV locus results in the stable maintenance of the phage, while compensatory selection between bacterial states affects the evolutionary stable mutation rates (i.e. very high and very low mutation rates are evolutionarily disadvantageous), whereas, in the absence of either selective pressure the evolution of PV rates results in mutation rates below the basal values. Contrastingly, a biologically-relevant model with two phase-variable loci resulted in phage extinction and locking of the bacteria into a phage-resistant state suggesting that another counter-selective pressure is required, instance, the use of a distinct phage whose receptor is an F336-phage-resistant state. We conclude that a delicate balance between counter-selection and phage-attack can result in both the evolution of phase-variable phage receptors and persistence of PV-receptor-specific phage.

Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling.

Understanding CRISPR-Cas systems-the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks-is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical 'rich-get-richer' mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.

Revisiting the Role of Hyperparasitism in the Evolution of Virulence.

AbstractHyperparasitism denotes the natural phenomenon where a parasite infecting a host is in turn infected by its own parasite. Hyperparasites can shape the dynamics of host-parasite interactions and often have a deleterious impact on pathogens, an important class of parasites, causing a reduction in their virulence and transmission rate. Hyperparasitism thus could be an important tool of biological control. However, host-parasite-hyperparasite systems have so far been outside the mainstream of modeling studies, especially those dealing with eco-evolutionary aspects of species interactions. Here, we theoretically explore the evolution of life-history traits in a generic host-parasite-hyperparasite system, focusing on parasite virulence and the positive impact that hyperparasitism has on the host population. We also explore the coevolution of life-history traits of the parasite and hyperparasite, using adaptive dynamics and quantitative genetics frameworks to identify evolutionarily singular strategies. We find that in the presence of hyperparasites, the evolutionarily optimal pathogen virulence generally shifts toward more virulent strains. However, even in this case the use of hyperparasites in biocontrol could be justified, since overall host mortality decreases. An intriguing possible outcome of the evolution of the hyperparasite can be its evolutionary suicide.

Modelling the spatiotemporal complexity of interactions between pathogenic bacteria and a phage with a temperature-dependent life cycle switch.

We apply mathematical modelling to explore bacteria-phage interaction mediated by condition-dependent lysogeny, where the type of the phage infection cycle (lytic or lysogenic) is determined by the ambient temperature. In a natural environment, daily and seasonal variations of the temperature cause a frequent switch between the two infection scenarios, making the bacteria-phage interaction with condition-dependent lysogeny highly complex. As a case study, we explore the natural control of the pathogenic bacteria Burkholderia pseudomallei by its dominant phage. B. pseudomallei is the causative agent of melioidosis, which is among the most fatal diseases in Southeast Asia and across the world. We assess the spatial aspect of B. pseudomallei-phage interactions in soil, which has been so far overlooked in the literature, using the reaction-diffusion PDE-based framework with external forcing through daily and seasonal parameter variation. Through extensive computer simulations for realistic biological parameters, we obtain results suggesting that phages may regulate B. pseudomallei numbers across seasons in endemic areas, and that the abundance of highly pathogenic phage-free bacteria shows a clear annual cycle. The model predicts particularly dangerous soil layers characterised by high pathogen densities. Our findings can potentially help refine melioidosis prevention and monitoring practices.

Management implications of long transients in ecological systems.

The underlying biological processes that govern many ecological systems can create very long periods of transient dynamics. It is often difficult or impossible to distinguish this transient behaviour from similar dynamics that would persist indefinitely. In some cases, a shift from the transient to the long-term, stable dynamics may occur in the absence of any exogenous forces. Recognizing the possibility that the state of an ecosystem may be less stable than it appears is crucial to the long-term success of management strategies in systems with long transient periods. Here we demonstrate the importance of considering the potential of transient system behaviour for management actions across a range of ecosystem organizational scales and natural system types. Developing mechanistic models that capture essential system dynamics will be crucial for promoting system resilience and avoiding system collapses.

Coevolution of female fidelity and male help in populations with alternative reproductive tactics.

In socially monogamous species, pair-bonded males often continue to provide care to all offspring in their nests despite some degree of paternity loss due to female extra-pair copulation. Previous theoretical models suggested that females can use their within-pair offspring as 'hostages' to blackmail their social mates, so that they continue to provide care to the brood at low levels of cuckoldry. These models, however, rely on the assumption of sufficiently accurate male detection of cuckoldry and the reduction of parental effort in case of suspicion. Therefore, they cannot explain the abundant cases where cuckolded males continue to provide extensive care to the brood. Here we use an analytical population genetics model and an individual-based simulation model to explore the coevolution of female fidelity and male help in populations with two genetically determined alternative reproductive tactics (ARTs): sneakers that achieve paternity solely via extra-pair copulations and bourgeois that form a mating pair and spend some efforts in brood care. We show that when the efficiency of mate guarding is intermediate, the bourgeois males can evolve to 'specialize' in providing care by spending more than 90% of time in helping their females while guarding them as much as possible, despite frequent cuckoldry by the sneakers. We also show that when sneakers have tactic-specific adaptations and thus are more competitive than the bourgeois in gaining extra-pair fertilizations, the frequency of sneakers and the degrees of female fidelity and male help can fluctuate in evolutionary cycles. Our theoretical predictions highlight the need for further empirical tests in species with ARTs.

Identifying the sources of structural sensitivity in partially specified biological models.

Biological systems are characterised by a high degree of uncertainty and complexity, which implies that exact mathematical equations to describe biological processes cannot generally be justified. Moreover, models can exhibit sensitivity to the precise formulations of their component functions-a property known as structural sensitivity. Structural sensitivity can be revealed and quantified by considering partially specified models with uncertain functions, but this goes beyond well-established, parameter-based sensitivity analysis, and currently presents a mathematical challenge. Here we build upon previous work in this direction by addressing the crucial question of identifying the processes which act as the major sources of model uncertainty and those which are less influential. To achieve this goal, we introduce two related concepts: (1) the gradient of structural sensitivity, accounting for errors made in specifying unknown functions, and (2) the partial degree of sensitivity with respect to each function, a global measure of the uncertainty due to possible variation of the given function while the others are kept fixed. We propose an iterative framework of experiments and analysis to inform a heuristic reduction of structural sensitivity in a model. To demonstrate the framework introduced, we investigate the sources of structural sensitivity in a tritrophic food chain model.

Exploring the role of spatial and stoichiometric heterogeneity in the top-down control in eutrophic planktonic ecosystems.

Understanding the impact of eutrophication on the dynamics of aquatic food webs, remains a long-term challenge in ecology. Mathematical models generally predict the destabilisation of such webs, under increasing eutrophication levels, with large oscillations of species densities that can result in their extinction. This is at odds with a number of ecological observations that show stable dynamics even for high nutrient loads. The apparent discrepancy between theory and observations is known as the Rosenzweig's 'paradox of enrichment' and various solutions to the problem have been proposed over the years. In this study, we explore the stabilisation of dynamics of a tri-trophic plankton model in a eutrophic environment which occurs as a result of interplay of space heterogeneity, ecological stoichiometry, and food taxis of predators. We build a variety of models of increasing complexity, to explore various scenarios of phytoplankton growth, zooplankton food-dependent vertical movement, and different stoichiometric limitations of zooplankton. We show that the synergy among the vertical gradient in phytoplankton growth, phytoplankton structuring in terms of their stoichiometric ratio, and food-dependent vertical movement of zooplankton, would result in a postponing of destabilisation of eutrophic systems as compared to a well-mixed system. Our approach reveals a high complexity of the bifurcation structure of the system when key model parameters, such as the degree of eutrophication and light shading, are varied. We find coexistence of limit cycles and stable equilibria and that the possibility of multiple attractors in the system can result in hysteresis phenomena when the nutrient load is manipulated. These results are relevant and should be taken into account in lake restoration programs.

Long transients in ecology: Theory and applications.

This paper discusses the recent progress in understanding the properties of transient dynamics in complex ecological systems. Predicting long-term trends as well as sudden changes and regime shifts in ecosystems dynamics is a major issue for ecology as such changes often result in population collapse and extinctions. Analysis of population dynamics has traditionally been focused on their long-term, asymptotic behavior whilst largely disregarding the effect of transients. However, there is a growing understanding that in ecosystems the asymptotic behavior is rarely seen. A big new challenge for theoretical and empirical ecology is to understand the implications of long transients. It is believed that the identification of the corresponding mechanisms along with the knowledge of scaling laws of the transient's lifetime should substantially improve the quality of long-term forecasting and crisis anticipation. Although transient dynamics have received considerable attention in physical literature, research into ecological transients is in its infancy and systematic studies are lacking. This text aims to partially bridge this gap and facilitate further progress in quantitative analysis of long transients in ecology. By revisiting and critically examining a broad variety of mathematical models used in ecological applications as well as empirical facts, we reveal several main mechanisms leading to the emergence of long transients and hence lays the basis for a unifying theory.

Exploring Evolutionary Fitness in Biological Systems Using Machine Learning Methods.

Here, we propose a computational approach to explore evolutionary fitness in complex biological systems based on empirical data using artificial neural networks. The essence of our approach is the following. We first introduce a ranking order of inherited elements (behavioral strategies or/and life history traits) in considered self-reproducing systems: we use available empirical information on selective advantages of such elements. Next, we introduce evolutionary fitness, which is formally described as a certain function reflecting the introduced ranking order. Then, we approximate fitness in the space of key parameters using a Taylor expansion. To estimate the coefficients in the Taylor expansion, we utilize artificial neural networks: we construct a surface to separate the domains of superior and interior ranking of pair inherited elements in the space of parameters. Finally, we use the obtained approximation of the fitness surface to find the evolutionarily stable (optimal) strategy which maximizes fitness. As an ecologically important study case, we apply our approach to explore the evolutionarily stable diel vertical migration of zooplankton in marine and freshwater ecosystems. Using machine learning we reconstruct the fitness function of herbivorous zooplankton from empirical data and predict the daily trajectory of a dominant species in the northeastern Black Sea.

Modelling evolution of virulence in populations with a distributed parasite load.

Modelling evolution of virulence in host-parasite systems is an actively developing area of research with ever-growing literature. However, most of the existing studies overlook the fact that individuals within an infected population may have a variable infection load, i.e. infected populations are naturally structured with respect to the parasite burden. Empirical data suggests that the mortality and infectiousness of individuals can strongly depend on their infection load; moreover, the shape of distribution of infection load may vary on ecological and evolutionary time scales. Here we show that distributed infection load may have important consequences for the eventual evolution of virulence as compared to a similar model without structuring. Mathematically, we consider an SI model, where the dynamics of the infected subpopulation is described by a von Förster-type equation, in which the infection load plays the role of age. We implement the adaptive dynamics framework to predict evolutionary outcomes in this model. We demonstrate that for simple trade-off functions between virulence, disease transmission and parasite growth rates, multiple evolutionary attractors are possible. Interestingly, unlike in the case of unstructured models, achieving an evolutionary stable strategy becomes possible even for a variation of a single ecological parameter (the parasite growth rate) and keeping the other parameters constant. We conclude that evolution in disease-structured populations is strongly mediated by alterations in the overall shape of the parasite load distribution.