Identifying patterning behavior in a plant infestation of insect pests.

In this study, we developed a mechanistic model formulated as a system of reaction-diffusion equations (RDE) to explore the spatiotemporal dynamics of a theoretical pest with a tillering host plant in a controlled rectangular plant field. Local perturbation analysis, a recently developed method of analysis for wave propagation, was utilized to determine patterning regimes resulting from the local and global behaviors of the slow and fast diffusing components of the RDE system, respectively. Turing analysis was done to show that the RDE system does not exhibit Turing patterns. With bug mortality as the bifurcation parameter, regions with oscillations and stable coexistence of the pest and tillers were identified. Numerical simulations illustrate the patterning regimes in 1D and 2D settings. The oscillations suggest that recurrences in pest infestation is possible. Moreover, simulations showed that patterns produced in the model are strongly influenced by the pests' homogeneous dynamics inside the controlled environment.

Optimal strategies and cost-benefit analysis of the [Formula: see text]-player weightlifting game.

The study of cooperation has been extensively studied in game theory. Especially, two-player two-strategy games have been categorized according to their equilibrium strategies and fully analysed. Recently, a grand unified game covering all types of two-player two-strategy games, i.e., the weightlifting game, was proposed. In the present study, we extend this two-player weightlifting game into an [Formula: see text]-player game. We investigate the conditions for pure strategy Nash equilibria and for Pareto optimal strategies, expressed in terms of the success probability and benefit-to-cost ratio of the weightlifting game. We also present a general characterization of [Formula: see text]-player games in terms of the proposed game. In terms of a concrete example, we present diagrams showing how the game category varies depending on the benefit-to-cost ratio. As a general rule, cooperation becomes difficult to achieve as group size increases because the success probability of weightlifting saturates towards unity. The present study provides insights into achieving behavioural cooperation in a large group by means of a cost-benefit analysis.

Using Constrained Optimization for the Allocation of COVID-19 Vaccines in the Philippines.

BACKGROUND: Vaccine allocation is a national concern especially for countries such as the Philippines that have limited resources in acquiring COVID-19 vaccines. As such, certain groups are suggested to be prioritized for vaccination to protect the most vulnerable before vaccinating others. OBJECTIVE: The study aims to determine an optimal and equitable allocation of COVID-19 vaccines in the Philippines that will minimize the projected number of additional COVID-19 deaths while satisfying the priority groups for immediate vaccination. METHODS: In this study, a linear programming model is formulated to determine an allocation of vaccines such that COVID-19 deaths are minimized while the prioritization framework set by the government is satisfied. Data used were collected up to November 2020. Total vaccine supply, vaccine effectiveness, vaccine cost, and projected deaths are analyzed. Results of the model are also compared to other allocation approaches. RESULTS: Results of the model show that a vaccine coverage of around 60-70% of the population can be enough for a community with limited supplies, and an increase in vaccine supply is beneficial if the initial coverage is less than the specified target range. Additionally, among the vaccines considered in the study, the one with 89.9% effectiveness and a 183 Philippine peso price per dose projected the lowest number of deaths. Compared with other model variations and common allocation approaches, the model has achieved both an optimal and equitable allocation. CONCLUSIONS: Having a 100% coverage for vaccination with a 100% effectiveness rate of vaccine is ideal for all countries. However, some countries have limited resources. Therefore, the results of our study can be used by policymakers to determine an optimal and equitable distribution of COVID-19 vaccines for a country/community.

Exaggerated evolution of male armaments via male-male competition.

Males usually compete to gain access to prospective mates. Through this male-male competition, superior males have a higher chance of passing on their traits to the next generation of male offspring. One category of male traits is armaments, which are weapons used during competition, for example, the chelae of fiddler crabs and the antlers of deer. One consequence of intrasexual selection is the exaggerated evolution of armaments, which can be limited by trade-offs, such as trade-offs with male body size. Here, we formulate a game-theoretic sexual selection model to explore the exaggerated evolution of armaments through male-male competition. The model is used to determine how competition affects the evolution of an armament that is subject to trade-offs. Our simulation can be used to support the exaggerated evolution hypothesis, that is, male-male competition escalates the rate of evolution of armaments.

Improving environment drives dynamical change in social game structure.

The development of cooperation in human societies is a major unsolved problem in biological and social sciences. Extensive studies in game theory have shown that cooperative behaviour can evolve only under very limited conditions or with additional complexities, such as spatial structure. Non-trivial two-person games are categorized into three types of games, namely, the prisoner's dilemma game, the chicken game and the stag hunt game. Recently, the weight-lifting game has been shown to cover all five games depending on the success probability of weight lifting, which include the above three games and two trivial cases (all cooperation and all defection; conventionally not distinguished as separate classes). Here, we introduce the concept of the environmental value of a society. Cultural development and deterioration are represented by changes in this probability. We discuss cultural evolution in human societies and the biological communities of living systems.

Author Correction: Grazing enhances species diversity in grassland communities.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Grazing enhances species diversity in grassland communities.

In grassland studies, an intermediate level of grazing often results in the highest species diversity. Although a few hypotheses have been proposed to explain this unimodal response of species diversity to grazing intensity, no convincing explanation has been provided. Here, we build a lattice model of a grassland community comprising multiple species with various levels of grazing. We analyze the relationship between grazing and plant diversity in grasslands under variable intensities of grazing pressure. The highest species diversity is observed at an intermediate grazing intensity. Grazers suppress domination by the most superior species in birth rate, resulting in the coexistence of inferior species. This unimodal grazing effect disappears with the introduction of a small amount of nongrazing natural mortality. Unimodal patterns of species diversity may be limited to the case where grazers are the principal source of natural mortality.

Resistance of a terrestrial plant community to local microhabitat changes.

The number of plant and animal species that exist today is estimated to be around 8.7 million. Approximately 300,000 of these species are flora. This extremely high species diversity has been puzzling scientist since the beginning of ecological research because most of these species compete for limited resources that should lead to the exclusion of all but few superior species. This can be seen in a number of coexistence model today that can only maintain at most four species at a time. We have shown recently that by incorporating minute differences in microhabitat to a lattice competition model, about 13 species can coexist from an initial number of 20. Here, we improve the model further by considering that microhabitat differences are not fixed but can change over time which can affect coexistence. A primary driver to this alteration is climate change, both natural and human induced. To show the resistance of a lattice plant community model, a dynamic microhabitat locality is incorporated by changing the spatial and species-specific heterogeneity of each lattice site. We show that even if the microhabitat locality of each plant species is dynamic, diversity can still be maintained in a lattice plant ecosystem model. This shows that natural communities of terrestrial plants can be resistant to the stress of microhabitat locality changes to a certain extent.

Asymptotic stability of a modified Lotka-Volterra model with small immigrations.

Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.

From epigenetic landscape to phenotypic fitness landscape: Evolutionary effect of pathogens on host traits.

The epigenetic landscape illustrates how cells differentiate through the control of gene regulatory networks. Numerous studies have investigated epigenetic gene regulation but there are limited studies on how the epigenetic landscape and the presence of pathogens influence the evolution of host traits. Here, we formulate a multistable decision-switch model involving several phenotypes with the antagonistic influence of parasitism. As expected, pathogens can drive dominant (common) phenotypes to become inferior through negative frequency-dependent selection. Furthermore, novel predictions of our model show that parasitism can steer the dynamics of phenotype specification from multistable equilibrium convergence to oscillations. This oscillatory behavior could explain pathogen-mediated epimutations and excessive phenotypic plasticity. The Red Queen dynamics also occur in certain parameter space of the model, which demonstrates winnerless cyclic phenotype-switching in hosts and in pathogens. The results of our simulations elucidate the association between the epigenetic and phenotypic fitness landscapes and how parasitism facilitates non-genetic phenotypic diversity.

Host-parasite Red Queen dynamics with phase-locked rare genotypes.

Interactions between hosts and parasites have been hypothesized to cause winnerless coevolution, called Red Queen dynamics. The canonical Red Queen dynamics assume that all interacting genotypes of hosts and parasites undergo cyclic changes in abundance through negative frequency-dependent selection, which means that any genotype could become frequent at some stage. However, this prediction cannot explain why many rare genotypes stay rare in natural host-parasite systems. To investigate this, we build a mathematical model involving multihost and multiparasite genotypes. In a deterministic and controlled environment, Red Queen dynamics occur between two genotypes undergoing cyclic dominance changes, whereas the rest of the genotypes remain subordinate for long periods of time in phase-locked synchronized dynamics with low amplitude. However, introduction of stochastic noise in the model might allow the subordinate cyclic host and parasite types to replace dominant cyclic types as new players in the Red Queen dynamics. The factors that influence such evolutionary switching are interhost competition, specificity of parasitism, and degree of stochastic noise. Our model can explain, for the first time, the persistence of rare, hardly cycling genotypes in populations (for example, marine microbial communities) undergoing host-parasite coevolution.

Microhabitat locality allows multi-species coexistence in terrestrial plant communities.

Most terrestrial plant communities exhibit relatively high species diversity and many competitive species are ubiquitous. Many theoretical studies have been carried out to investigate the coexistence of a few competitive species and in most cases they suggest competitive exclusion. Theoretical studies have revealed that coexistence of even three or four species can be extremely difficult. It has been suggested that the coexistence of many species has been achieved by the fine differences in suitable microhabitats for each species, attributing to niche-separation. So far there is no explicit demonstration of such a coexistence in mathematical and simulation studies. Here we built a simple lattice Lotka-Volterra model of competition by incorporating the minute differences of suitable microhabitats for many species. By applying the site variations in species-specific settlement rates of a seedling, we achieved the coexistence of more than 10 species. This result indicates that competition between many species is avoided by the spatial variations in species-specific microhabitats. Our results demonstrate that coexistence of many species becomes possible by the minute differences in microhabitats. This mechanism should be applicable to many vegetation types, such as temperate forests and grasslands.

Red Queen dynamics in multi-host and multi-parasite interaction system.

In host-parasite systems, dominant host types are expected to be eventually replaced by other hosts due to the elevated potency of their specific parasites. This leads to changes in the abundance of both hosts and parasites exhibiting cycles of alternating dominance called Red Queen dynamics. Host-parasite models with less than three hosts and parasites have been demonstrated to exhibit Red Queen cycles, but natural host-parasite interactions typically involve many host and parasite types resulting in an intractable system with many parameters. Here we present numerical simulations of Red Queen dynamics with more than ten hosts and specialist parasites under the condition of no super-host nor super-parasite. The parameter region where the Red Queen cycles arise contracts as the number of interacting host and parasite types increases. The interplay between inter-host competition and parasite infectivity influences the condition for the Red Queen dynamics. Relatively large host carrying capacity and intermediate rates of parasite mortality result in never-ending cycles of dominant types.

The paradox of enrichment in phytoplankton by induced competitive interactions.

The biodiversity loss of phytoplankton with eutrophication has been reported in many aquatic ecosystems, e.g., water pollution and red tides. This phenomenon seems similar, but different from the paradox of enrichment via trophic interactions, e.g., predator-prey systems. We here propose the paradox of enrichment by induced competitive interactions using multiple contact process (a lattice Lotka-Volterra competition model). Simulation results demonstrate how eutrophication invokes more competitions in a competitive ecosystem resulting in the loss of phytoplankton diversity in ecological time. The paradox is enhanced under local interactions, indicating that the limited dispersal of phytoplankton reduces interspecific competition greatly. Thus, the paradox of enrichment appears when eutrophication destroys an ecosystem either by elevated interspecific competition within a trophic level and/or destabilization by trophic interactions. Unless eutrophication due to human activities is ceased, the world's aquatic ecosystems will be at risk.