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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. Supplementary Information The online version contains supplementary material available at 10.1007/s40258-021-00667-z.

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.

In response to the need to derive empirical data on the status of pollinators, we have developed a protocol to assess the pollinator population in managed and natural ecosystems, especially in Asia where there is no harmonized initiative for pollination research. This protocol is helpful in assessing organic and non-organic farming since pollinator persistence can be an indicator of good and sustainable practices. The three important steps in the protocol are planning, implementation of the survey, and computation of indices. In the planning step, experts rank and classify the pollinator hotspots in various ecosystem types based on the seasonality and likelihood of having high number of flowers and pollinators. Two-stage sampling and mapping of each hotspots are designed. The number of sample hotspots is computed according to sampling precision and confidence levels assigned per class per ecosystem type. In each sample hotspot, sample survey sites are randomly selected according to the agreed sampling precision and confidence levels. In the second step, for orchard or agroecosystem, a grid map with 100 m2 divisions is surveyed. For natural vegetation, survey sites are randomly selected according to the location of pollinator nesting sites. All sampling surveys are conducted during the blooming period of the plants, with consideration of the peak of anthesis, because this is the period when the pollinators are actively foraging, the pollen viability is high, and the nectar secretion is at its peak. Moreover, a template is created to compute for diversity measures and our proposed pollination matching measures (P-to-P ratio and index).

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.

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.

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. Our model suggests an allocation of vaccines such that COVID-19 deaths are minimized while the prioritization framework is satisfied. Results of the model show that a vaccine coverage of at least 50 to 70% of the population can be enough for a community with limited supplies, and an increase in vaccine supply is beneficial if initial coverage is less than the specified target range. Also, among the vaccines considered in the study, the one with 89.9% effectiveness and has a 183 Philippine peso (Php) price per dose projected the least number of deaths. Compared to other model variations and common allocation approaches, the model has achieved both an optimal and equitable allocation. This will be helpful for policymakers in determining a vaccine distribution for a resource-constrained community.

The epigenetic landscape illustrates how cells differentiate into different types 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 many possible phenotypes with the antagonistic influence of parasitism. As expected, pathogens can drive dominant (common) phenotypes to become inferior, such as 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 how epigenetic landscape is associated with the phenotypic fitness landscape and how parasitism facilitates non-genetic phenotypic diversity.

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.

Human activities in aquatic and terrestrial ecosystems can cause the depletion of coastal resources. The study aimed to develop a decision support system for the municipality of Palauig, Zambales as the basis for coastal resource management. Water use allocation was done in a systems approach, using Gurobi® - mathematical optimization solver, considering priority goals of Palauig, goal 1 is to maximize mangrove use in minimizing disaster risk, goal 2 is maximizing water suitability and goal 3 is maximizing the total economic value of resources. The municipal water map was divided into 1-ha grids. Optimization run results showed that disaster risk fronting shoreline would be canceled by mangrove allocated on those areas. The area allocation of 331 ha mangrove, 1 ha coral, 1,573 ha seagrass, 50 ha fish cage, 33 ha MPA and 17,942 ha fishing area, the water uses would have economic values of Php 2.9B, Php 20.8M, Php 1.7B, Php 4.1B, Php 323M, and Php 33.9B, respectively. The area allocated for the fish cage did not exceed the allowable area set hence, its environmental impacts would be manageable. Production of 2.3MT would meet Palauig’s consumption requirement for fish.

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.

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.

Red Queen dynamics are observed in selected genotypes, whereas the rest of the genotypes remain subordinate in synchronized dynamics., 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.

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.

Modern biology will never be the same without mathematical and computational tools. Using mind map with “epigenetics” as the root, we discuss the current advancement in the field of biomathematics for modeling cell-fate specification. In the discussions, we also present possible directions for future research.

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.

A fuzzy goal programming (FGP) model for biodiesel production in the Philippines was formulated with Coconut (Cocos nucifera) and Jatropha (Jatropha curcas) as sources of biodiesel. Objectives were maximization of feedstock production and overall revenue and, minimization of energy used in production and working capital for farming subject to biodiesel and non-biodiesel requirements, and availability of land, labor, water and machine time. All these objectives and constraints were assumed to be fuzzy. Model was tested for different sets of weights. Results for all sets of weights showed the same optimal allocation. Coconut alone can satisfy the biodiesel requirement of 2% per volume.

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.