Optimizing strategies for slowing the spread of invasive species.

Invasive species are spreading worldwide, causing damage to ecosystems, biodiversity, agriculture, and human health. A major question is, therefore, how to distribute treatment efforts cost-effectively across space and time to prevent or slow the spread of invasive species. However, finding optimal control strategies for the complex spatial-temporal dynamics of populations is complicated and requires novel methodologies. Here, we develop a novel algorithm that can be applied to various population models. The algorithm finds the optimal spatial distribution of treatment efforts and the optimal propagation speed of the target species. We apply the algorithm to examine how the results depend on the species' demography and response to the treatment method. In particular, we analyze (1) a generic model and (2) a detailed model for the management of the spongy moth in North America to slow its spread via mating disruption. We show that, when utilizing optimization approaches to contain invasive species, significant improvements can be made in terms of cost-efficiency. The methodology developed here offers a much-needed tool for further examination of optimal strategies for additional cases of interest.

Optimizing the use of suppression zones for containment of invasive species.

Despite efforts to prevent their establishment, many invasive species continue to spread and threaten food production, human health, and natural biodiversity. Slowing the spread of established species is often a preferred strategy; however, it is also expensive and necessitates treatment over large areas. Therefore, it is critical to examine how to distribute management efforts over space cost-effectively. Here we consider a continuous-space bioeconomic model and we develop a novel algorithm to find the most cost-effective allocation of treatment efforts throughout a landscape. We show that the optimal strategy often comprises eradication in the yet-uninvaded area, and under certain conditions, it also comprises maintaining a "suppression zone," an area between the invaded and the uninvaded areas, where treatment reduces the invading population but without eliminating it. We examine how the optimal strategy depends on the demographic characteristics of the species and reveal general criteria for deciding when a suppression zone is cost effective.

Multiple agents managing a harmful species population should either work together to control it or split their duties to eradicate it.

The management of harmful species, including invasive species, pests, parasites, and diseases, is a major global challenge. Harmful species cause severe damage to ecosystems, biodiversity, agriculture, and human health. In particular, managing harmful species often requires cooperation among multiple agents, such as landowners, agencies, and countries. Each agent may have incentives to contribute less to the treatment, leaving more work for other agents, which may result in inefficient treatment. A central question is, therefore, how should a policymaker allocate treatment duties among the agents? Specifically, should the agents work together in the same area, or should each agent work only in a smaller area designated just for her/him? We consider a dynamic game-theoretic model, where a Nash equilibrium corresponds to a possible set of contributions that the agents could adopt over time. In turn, the allocation by the policymaker determines which of the Nash equilibria could be adopted, which allows us to compare the outcome of various allocations. Our results show that fewer agents can abate the harmful species population faster, but more agents can better control the population to keep its density lower. We prove this result in a general theorem and demonstrate it numerically for two case studies. Therefore, following an outbreak, the better policy would be to split and assign one or a few agents to treat the species in a given location, but if controlling the harmful species population at some low density is needed, the agents should work together in all of the locations.

Combining multiple tactics over time for cost-effective eradication of invading insect populations.

Because of the profound ecological and economic impacts of many non-native insect species, early detection and eradication of newly founded, isolated populations is a high priority for preventing damages. Though successful eradication is often challenging, the effectiveness of several treatment methods/tactics is enhanced by the existence of Allee dynamics in target populations. Historically, successful eradication has often relied on the application of two or more tactics. Here, we examine how to combine three treatment tactics in the most cost-effective manner, either simultaneously or sequentially in a multiple-annum process. We show that each tactic is most efficient across a specific range of population densities. Furthermore, we show that certain tactics inhibit the efficiency of other tactics and should therefore not be used simultaneously; but since each tactic is effective at specific densities, different combinations of tactics should be applied sequentially through time when a multiple-annum eradication programme is needed.

Survivor's dilemma: The evolution of cooperation in volatile environments.

The volatility of an environment significantly impacts cooperative behavior. In environments where viability-threatening events occur on a shorter timescale than reproduction, it is reasonable to measure the costs and benefits of cooperation in terms of their direct effect on survival probability. Then, the number of offspring increases with lifespan. With such a model, is it possible for cooperation to be evolutionarily stable, and how does cooperation depend on the benefit and cost of such interactions, and the volatility of the environment? In this paper, we develop an N-player survivor's dilemma in which prisoner's dilemma payoffs in an iteration are survival rates, and expected lifespan is the measure of reproductive fitness. We investigate cost, benefit, and volatility parameter ranges where various cooperative behaviors may occur. We observe that free-riding results in indirect punishment as the cheated partner's early death leaves the defector vulnerable. For 2- and 3-player versions of the game, we identify parameter regions where the repeated game becomes equivalent to a Harmony, Stag Hunt, or Prisoner's Dilemma static game and discuss evolutionary stability. We find that with two individuals, the initial fraction of cooperators necessary for cooperation to be selected for decreases as the benefit to cost ratio increases and as environmental volatility decreases. With the presence of a third individual, there also exists a parameter region where cooperation can invade an initially all-defecting population.

Information sharing may impede the success of environmental projects.

A major challenge in ecosystem management is to promote cooperation among the multiple agents that manage the ecosystem. In particular, sharing information among the agents is often essential for reaching a desirable collective treatment. However, it is unclear how the sharing of information affects the incentives of selfish agents to cooperate and contribute to the common environmental project. Here, we consider a harmful species population that migrates across lands and causes damages to multiple agents, each of which aims to minimize her/his own costs due to both treatment and damages over time. We use game-theoretical models and compare the resulting collective treatment in three scenarios that differ in the information that agents have about (1) the true contribution of their neighbors to the treatment and (2) the true damages inflicted on their neighbors by the harmful species. We demonstrate that sharing such social information may incentivize the agents to free ride on their neighbors' contributions, thereby reducing the efficiency of the collective treatment. This implies that monitoring and sharing information may have negative consequences, and the extent to which information should be shared in joint projects necessitates a careful examination.

Stability and distribution of predator-prey systems: local and regional mechanisms and patterns.

Explaining the coexistence and distribution of species in time and space remains a fundamental challenge. While species coexistence depends on both local and regional mechanisms, it is sometimes unclear which role each mechanism takes in a given ecosystem. Consequently, it is very hard to predict the response of the ecosystem to environmental changes. Here, we develop a model to study spatial patterns of coexistence, focusing on predator-prey and host-parasite populations. We show, both theoretically and empirically, that these systems may exhibit both local and regional patterns and mechanisms of coexistence. Changes in environmental parameters, such as spatial connectivity, may lead to a transition from regional to local coexistence or it may lead directly to extinction, depending on demographic parameters. This demonstrates the importance of simultaneously analysing interacting mechanisms that act at different spatial scales to understand the response of ecosystems to environmental changes.

Resonance-induced multimodal body-size distributions in ecosystems.

The size of an organism reflects its metabolic rate, growth rate, mortality, and other important characteristics; therefore, the distribution of body size is a major determinant of ecosystem structure and function. Body-size distributions often are multimodal, with several peaks of abundant sizes, and previous studies suggest that this is the outcome of niche separation: species from distinct peaks avoid competition by consuming different resources, which results in selection of different sizes in each niche. However, this cannot explain many ecosystems with several peaks competing over the same niche. Here, we suggest an alternative, generic mechanism underlying multimodal size distributions, by showing that the size-dependent tradeoff between reproduction and resource utilization entails an inherent resonance that may induce multiple peaks, all competing over the same niche. Our theory is well fitted to empirical data in various ecosystems, in which both model and measurements show a multimodal, periodically peaked distribution at larger sizes, followed by a smooth tail at smaller sizes. Moreover, we show a universal pattern of size distributions, manifested in the collapse of data from ecosystems of different scales: phytoplankton in a lake, metazoans in a stream, and arthropods in forests. The demonstrated resonance mechanism is generic, suggesting that multimodal distributions of numerous ecological characters emerge from the interplay between local competition and global migration.

Optimal control of population recovery--the role of economic restoration threshold.

A variety of ecological systems around the world have been damaged in recent years, either by natural factors such as invasive species, storms and global change or by direct human activities such as overfishing and water pollution. Restoration of these systems to provide ecosystem services entails significant economic benefits. Thus, choosing how and when to restore in an optimal fashion is important, but has not been well studied. Here we examine a general model where population growth can be induced or accelerated by investing in active restoration. We show that the most cost-effective method to restore an ecosystem dictates investment until the population approaches an 'economic restoration threshold', a density above which the ecosystem should be left to recover naturally. Therefore, determining this threshold is a key general approach for guiding efficient restoration management, and we demonstrate how to calculate this threshold for both deterministic and stochastic ecosystems.

A reversible mutation in a genomic hotspot saves bacterial swarms from extinction.

Microbial adaptation to changing environmental conditions is frequently mediated by hypermutable sequences. Here we demonstrate that such a hypermutable hotspot within a gene encoding a flagellar unit of Paenibacillus glucanolyticus generated spontaneous non-swarming mutants with increased stress resistance. These mutants, which survived conditions that eliminated wild-type cultures, could be carried by their swarming siblings when the colony spread, consequently increasing their numbers at the spreading edge. Of interest, the hypermutable nature of the aforementioned sequence enabled the non-swarming mutants to serve as "seeds" for a new generation of wild-type cells through reversion of the mutation. Using a mathematical model, we examined the survival dynamics of P. glucanolyticus colonies under fluctuating environments. Our experimental and theoretical results suggest that the non-swarming, stress-resistant mutants can save the colony from extinction. Notably, we identified this hypermutable sequence in flagellar genes of additional Paenibacillus species, suggesting that this phenomenon could be wide-spread and ecologically important.

Decentralized governance may lead to higher infection levels and sub-optimal releases of quarantines amid the COVID-19 pandemic.

The outbreak of the novel Coronavirus (COVID-19) has led countries worldwide to administer quarantine policies. However, each country or state independently decides what mobility restrictions to administer within its borders while aiming to maximize its own citizens' welfare. Since individuals travel between countries and states, the policy in one country affects the infection levels in other countries. Therefore, a major question is whether the policies dictated by multiple governments could be efficient. Here we focus on the decision regarding the timing of releasing quarantines, which were common during the first year of the pandemic. We consider a game-theoretical epidemiological model in which each government decides when to switch from a restrictive to a non-restrictive quarantine and vice versa. We show that, if travel between countries is frequent, then the policy dictated by multiple governments is sub-optimal. But if international travel is restricted, then the policy may become optimal.

A game theoretic approach identifies conditions that foster vaccine-rich to vaccine-poor country donation of surplus vaccines.

Background: Scarcity in supply of COVID-19 vaccines and severe international inequality in their allocation present formidable challenges. These circumstances stress the importance of identifying the conditions under which self-interested vaccine-rich countries will voluntarily donate their surplus vaccines to vaccine-poor countries. Methods: We develop a game-theoretical approach to identify the vaccine donation strategy that is optimal for the vaccine-rich countries as a whole; and to determine whether the optimal strategy is stable (Nash equilibrium or self-enforcing agreement). We examine how the results depend on the following parameters: the fraction of the global unvaccinated population potentially covered if all vaccine-rich countries donate their entire surpluses; the expected emergence rate of variants of concern (VOC); and the relative cost of a new VOC outbreak that is unavoidable despite having surplus doses. Results: We show that full or partial donations of the surplus stock are optimal in certain parameter ranges. Notably, full surplus donation is optimal if the global amount of surplus vaccines is sufficiently large. Within a more restrictive parameter region, these optimal strategies are also stable. Conclusions: Our results imply that, under certain conditions, coordination between vaccine-rich countries can lead to significant surplus donations even by strictly self-interested countries. However, if the global amount that countries can donate is small, we expect no contribution from self-interested countries. The results provide guidance to policy makers in identifying the circumstances in which coordination efforts for vaccine donation are likely to be most effective.

Mutability as an altruistic trait in finite asexual populations.

Mutation rate (MR) is a crucial determinant of the evolutionary process. Optimal MR may enable efficient evolutionary searching and therefore increase the fitness of the population over time. Nevertheless, individuals may favor MRs that are far from being optimal for the whole population. Instead, each individual may tend to mutate at rates that selfishly increase its own relative fitness. We show that in some cases, undergoing a mutation is altruistic, i.e., it increases the expected fitness of the population, but decreases the expected fitness of the mutated individual itself. In this case, if the population is uniform (completely mixed, undivided), immutability is evolutionary stable and is probably selected for. However, our examination of a segregated population, which is divided into several groups (or patches), shows that the optimal, altruistic MR may out-compete the selfish MR if the coupling between the groups is neither too strong nor too weak. This demonstrates that the population structure is crucial for the succession of the evolutionary process itself. For example, in a uniform population, the evolutionary process may be stopped before the highest fitness is reached, as demonstrated in a one-pick fitness landscape. In addition, we show that the dichotomy between evolutionary stable and optimal MRs can be seen as a special case of a more general phenomenon in which optimal behaviors may be destabilized in finite populations, since optimal sub-populations may become extinct before the benefit of their behavior is expressed.

Over-exploitation of natural resources is followed by inevitable declines in economic growth and discount rate.

A major challenge in environmental policymaking is determining whether and how fast our society should adopt sustainable management methods. These decisions may have long-lasting effects on the environment, and therefore, they depend critically on the discount factor, which determines the relative values given to future environmental goods compared to present ones. The discount factor has been a major focus of debate in recent decades, and nevertheless, the potential effect of the environment and its management on the discount factor has been largely ignored. Here we show that to maximize social welfare, policymakers need to consider discount factors that depend on changes in natural resource harvest at the global scale. Particularly, the more our society over-harvests today, the more policymakers should discount the near future, but the less they should discount the far future. This results in a novel discount formula that implies significantly higher values for future environmental goods.

Where Two Are Fighting, the Third Wins: Stronger Selection Facilitates Greater Polymorphism in Traits Conferring Competition-Dispersal Tradeoffs.

A major conundrum in evolution is that, despite natural selection, polymorphism is still omnipresent in nature: Numerous species exhibit multiple morphs, namely several abundant values of an important trait. Polymorphism is particularly prevalent in asymmetric traits, which are beneficial to their carrier in disruptive competitive interference but at the same time bear disadvantages in other aspects, such as greater mortality or lower fecundity. Here we focus on asymmetric traits in which a better competitor disperses fewer offspring in the absence of competition. We report a general pattern in which polymorphic populations emerge when disruptive selection increases: The stronger the selection, the greater the number of morphs that evolve. This pattern is general and is insensitive to the form of the fitness function. The pattern is somewhat counterintuitive since directional selection is excepted to sharpen the trait distribution and thereby reduce its diversity (but note that similar patterns were suggested in studies that demonstrated increased biodiversity as local selection increases in ecological communities). We explain the underlying mechanism in which stronger selection drives the population towards more competitive values of the trait, which in turn reduces the population density, thereby enabling lesser competitors to stably persist with reduced need to directly compete. Thus, we believe that the pattern is more general and may apply to asymmetric traits more broadly. This robust pattern suggests a comparative, unified explanation to a variety of polymorphic traits in nature.

Optimal approaches for balancing invasive species eradication and endangered species management.

Resolving conflicting ecosystem management goals-such as maintaining fisheries while conserving marine species or harvesting timber while preserving habitat-is a widely recognized challenge. Even more challenging may be conflicts between two conservation goals that are typically considered complementary. Here, we model a case where eradication of an invasive plant, hybrid Spartina, threatens the recovery of an endangered bird that uses Spartina for nesting. Achieving both goals requires restoration of native Spartina. We show that the optimal management entails less intensive treatment over longer time scales to fit with the time scale of natural processes. In contrast, both eradication and restoration, when considered separately, would optimally proceed as fast as possible. Thus, managers should simultaneously consider multiple, potentially conflicting goals, which may require flexibility in the timing of expenditures.

Synchronization-induced persistence versus selection for habitats in spatially coupled ecosystems.

Critical population phase transitions, in which a persistent population becomes extinction-prone owing to environmental changes, are fundamentally important in ecology, and their determination is a key factor in successful ecosystem management. To persist, a species requires a suitable environment in a sufficiently large spatial region. However, even if this condition is met, the species does not necessarily persist, owing to stochastic fluctuations. Here, we develop a model that allows simultaneous investigation of extinction due to either stochastic or deterministic reasons. We find that even classic birth-death processes in spatially extended ecosystems exhibit phase transitions between extinction-prone and persistent populations. Sometimes these are first-order transitions, which means that environmental changes may result in irreversible population collapse. Moreover, we find that higher migration rates not only lead to higher robustness to stochastic fluctuations, but also result in lower sustainability in heterogeneous environments by preventing efficient selection for suitable habitats. This demonstrates that intermediate migration rates are optimal for survival. At low migration rates, the dynamics are reduced to metapopulation dynamics, whereas at high migration rates, the dynamics are reduced to a multi-type branching process. We focus on species persistence, but our results suggest a unique method for finding phase transitions in spatially extended stochastic systems in general.

The weak shall inherit: bacteriocin-mediated interactions in bacterial populations.

BACKGROUND: Evolutionary arms race plays a major role in shaping biological diversity. In microbial systems, competition often involves chemical warfare and the production of bacteriocins, narrow-spectrum toxins aimed at killing closely related strains by forming pores in their target's membrane or by degrading the target's RNA or DNA. Although many empirical and theoretical studies describe competitive exclusion of bacteriocin-sensitive strains by producers of bacteriocins, the dynamics among producers are largely unknown. METHODOLOGY/PRINCIPAL FINDINGS: We used a reporter-gene assay to show that the bacterial response to bacteriocins' treatment mirrors the inflicted damage Potent bacteriocins are lethal to competing strains, but at sublethal doses can serve as strong inducing agents, enhancing their antagonists' bacteriocin production. In contrast, weaker bacteriocins are less toxic to their competitors and trigger mild bacteriocin expression. We used empirical and numerical models to explore the role of cross-induction in the arms race between bacteriocin-producing strains. We found that in well-mixed, unstructured environments where interactions are global, producers of weak bacteriocins are selectively advantageous and outcompete producers of potent bacteriocins. However, in spatially structured environments, where interactions are local, each producer occupies its own territory, and competition takes place only in "no man's lands" between territories, resulting in much slower dynamics. CONCLUSION/SIGNIFICANCE: The models we present imply that producers of potent bacteriocins that trigger a strong response in neighboring bacteriocinogenic strains are doomed, while producers of weak bacteriocins that trigger a mild response in bacteriocinogenic strains flourish. This counter-intuitive outcome might explain the preponderance of weak bacteriocin producers in nature. However, the described scenario is prolonged in spatially structured environments thus promoting coexistence, allowing migration and evolution, and maintaining bacterial diversity.

Density-dependent cooperation as a mechanism for persistence and coexistence.

To overcome stress, such as resource limitation, an organism often needs to successfully mediate competition with other members of its own species. This may favor the evolution of defective traits that are harmful to the species population as a whole, and that may lead to its dilution or even to its extinction (the tragedy of the commons). Here, we show that this phenomenon can be circumvented by cooperation plasticity, in which an individual decides, based on environmental conditions, whether to cooperate or to defect. Specifically, we analyze the evolution of density-dependent cooperation. In our model, the population is spatially subdivided, periodically remixed, and comprises several species. We find that evolution pushes individuals to be more cooperative when their own species is at lower densities, and we show that not only could this cooperation prevent the tragedy of the commons, but it could also facilitate coexistence between many species that compete for the same resource.