Jomar F. Rabajante

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.

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

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.

Branching and oscillations in the epigenetic landscape of cell-fate determination.

The well-known Waddingtons epigenetic landscape of cell-fate determination is not static but varies because of the dynamic gene regulation during development. However, existing mathematical models with few state variables and fixed parameters are inadequate in characterizing the temporal transformation of the landscape. Here we simulate a decision-switch model of gene regulation with more than two state variables and with time-varying repression among regulatory factors. We are able to demonstrate multi-lineage differentiation at different timescales that portrays the branching canals in Waddingtons illustration. We also present a repressilator-type system that activates suppressed genes via sustained oscillations in a flattened landscape, hence providing an alternative scheme for cellular reprogramming. The time-dependent parameters governed by gradient-based dynamics regulate cell differentiation, dedifferentiation and transdifferentiation. Our prediction integrates the theories of branching and structural oscillations in cell-fate determination, which reveals key temporal patterns of cell differentiation and associated diseases, such as cancer.

Mathematical Programming Models for Determining the Optimal Location of Beehives

Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared to the number of inflorescence that may lead to suboptimal pollination of crops. We hypothesize that optimally distributing the beehives in the apiary can help address the two scenarios stated above. In this paper, we develop quantitative models (specifically using linear programming) for addressing the two given scenarios. We formulate models involving the following factors: (i) fuzzy preference of the beekeeper; (ii) number of available colonies; (iii) unknown-but-bounded strength of colonies; (iv) probabilistic carrying capacity of the plant clusters; and (v) spatial orientation of the apiary.

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.

A Mathematical Model of Intra-Colony Spread of American Foulbrood in European Honeybees (Apis mellifera L.)

American foulbrood (AFB) is one of the severe infectious diseases of European honeybees (Apis mellifera L.) and other Apis species. This disease is caused by a gram-positive, spore-forming bacterium Paenibacillus larvae. In this paper, a compartmental (SI framework) model is constructed to represent the spread of AFB within a colony. The model is analyzed to determine the long-term fate of the colony once exposed to AFB spores. It was found out that without effective and efficient treatment, AFB infection eventually leads to colony collapse. Furthermore, infection thresholds were predicted based on the stability of the equilibrium states. The number of infected cell combs is one of the factors that drive disease spread. Our results can be used to forecast the transmission timeline of AFB infection and to evaluate the control strategies for minimizing a possible epidemic.

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.

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.

Antibiotic-driven escape of host in a parasite-induced Red Queen dynamics

Winnerless coevolution of hosts and parasites could exhibit Red Queen dynamics, which is characterized by parasite-driven cyclic switching of expressed host phenotypes. We hypothesize that the application of antibiotics to suppress the reproduction of parasites can provide an opportunity for the hosts to escape such winnerless coevolution. Here, we formulate a minimal mathematical model of host–parasite interaction involving multiple host phenotypes that are targeted by adapting parasites. Our model predicts the levels of antibiotic effectiveness that can steer the parasite-driven cyclic switching of host phenotypes (oscillations) to a stable equilibrium of host survival. Our simulations show that uninterrupted application of antibiotic with high-level effectiveness (greater than 85%) is needed to escape the Red Queen dynamics. Interrupted and low level of antibiotic effectiveness are indeed useless to stop host–parasite coevolution. This study can be a guide in designing good practices and protocols to minimize the risk of further progression of parasitic infections.

Varroa Destructor: Spatial Distribution over a Modified Cellular Automaton

This study is part of a research endeavor called the UPLB Biomathematics Initiative which aims to help solve biological problems through mathematical modeling. Specifically, we consider here a problem on the management of bee colonies which is done in collaboration with the UPLB Bee Program. This paper focuses on the construction of a cellular automaton model that describes the spatial distribution of mites (Varroa destructor Anderson and Trueman) in honeybee (Apis mellifera Linnaeus) colonies. Through this model, we are able to construct a computer simulation that shows the development of mite infestation through time. The collected data during the early stage of mites spread verify the model constructed.