Journal of Mathematical Biology最新文献

Algebraic techniques in phylogenetics have historically been successful at proving identifiability results and have also led to novel reconstruction algorithms. In this paper, we study the ideal of phylogenetic invariants of the Cavender-Farris-Neyman (CFN) model on a phylogenetic network with the goal of providing a description of the invariants which is useful for network inference. It was previously shown that to characterize the invariants of any level-1 network, it suffices to understand all sunlet networks, which are those consisting of a single cycle with a leaf adjacent to each cycle vertex. We show that the parameterization of an affine open patch of the CFN sunlet model, which intersects the probability simplex, factors through the space of skew-symmetric matrices via Pfaffians. We then show that this affine patch is isomorphic to a determinantal variety and give an explicit Gröbner basis for the associated ideal, which involves only $\left(\begin{array}{c}n\\ 2\end{array}\right)$ coordinates rather than $2^n$ . Lastly, we show that sunlet networks with at least 6 leaves are identifiable using only these polynomials and run extensive simulations, which show that these polynomials can be used to accurately infer the correct network from DNA sequence data.

How does the movement of individuals influence the persistence of a single population? A surprising phenomenon known as dispersal-induced growth (DIG) occurs when the population would become extinct if isolated or well mixed, but migration, at an appropriate rate, can induce the persistence of the population. In this paper, we investigate this phenomenon based on a time-periodic two-patch model incorporating asymmetric migration matrices. Through comprehensive analysis of the qualitative properties of the associated principal eigenvalue, including monotonicity, asymptotic behaviors, and the topological structure of the level sets as a function of the migration rate and frequency, we characterize the important factors driving the occurrence of DIG under fixed environmental oscillation frequencies. Our results provide new insights into how the interplay between spatial connectivity and temporal environmental variation enables the population persistence.

Different from the existing studies on the influence of self-diffusion or cross-diffusion on Turing instability, this paper originally focuses on the effect of nonlocal competition and host-taxis on Turing instability in a more realistic two-dimensional space, and novelly applies it to study the control of pine wilt disease. It turns out that the incorporation of host-taxis is not conducive to the generation of Turing instability, whereas nonlocal competition can promote the formation of pattern structure by facilitating the occurrence of it. The results not only reveal the new mechanism for the emergence of spatial heterogeneity patterns, but also provide an alternative theoretical explanation for the actually observed multi-point aggregation and multiple outbreaks of pine wilt disease. The various spatial patterns induced by nonlocal competition and host-taxis are numerically illustrated. We find that the Turing patterns can preserve the symmetry of the initial distribution, and contrary to the taxis diffusion, the self-diffusion of D. helophoroides promotes the pattern formation. Furthermore, the high consistency between the simulated and actual distribution patterns of pine wilt disease strongly validates the practical reference value of the paper. The most interesting finding is that we obtain the circular aggregation distribution pattern from simulations, which is consistent with the actual spread trend of pine wilt disease, and our study theoretically reveals the intrinsic evolution mechanism behind its occurrence.

We consider a two-component reaction-diffusion system that has previously been developed to model invasion of cells into a resident cell population. The system is an idealised version of models of tumour growth in which tumour cells degrade the surrounding tissue by increasing the acidity of the local environment. By numerically computing families of travelling wave solutions to this problem, we observe that a general initial condition with either compact support, or sufficiently large exponential decay in the far field, tends to the travelling wave solution that has the largest possible decay at its front. Initial conditions with sufficiently slow exponential decay tend to those travelling wave solutions that have the same exponential decay as their initial conditions. We also show that in the limit that the (nondimensional) degradation rate of resident cells is large, the system has similar asymptotic structure as previously observed in perturbed Fisher-KPP models. The asymptotic analysis in this limit explains the formation of an interstitial gap (a region between the invading and receding fronts, in which both cell populations are small), the width of which is logarithmically large in the limit of large degradation rate. These results show that the general mechanism behind the formation of the interstitial gap in reaction-diffusion tumour models is connected to perturbations of the Fisher-KPP system. Biologically, this implies that order of magnitude difference in degradation rate is required to produce appreciably different gap sizes, while the velocity of the invading front is largely determined by the Fisher-KPP velocity, and only very weakly affected by the presence of the interstitial gap.

The epithelial-mesenchymal transition (EMT), a key stage in tumor metastasis and invasion, depends on many micro-environmental factors, including oxygen levels. In this article, we use a continuum partial differential equations (PDEs) framework comprising coupled equations for the epithelial, mesenchymal, and necrotic cell densities and oxygen concentration to unravel the mysteries of how oxygen heterogeneity affects EMT. A distinguishing feature of the model is that the rates of EMT and MET (mesenchymal-epithelial transition) depend on the oxygen concentration. We assume EMT occurs when oxygen concentration drops below a critical level, and MET occurs when it rises above the critical value. We begin by studying EMT dynamics in an in vitro scenario, where oxygen levels are assumed to be spatially uniform and fluctuate over time between normoxia and hypoxia. This setup mimics aspects of the in vivo phenomenon of cyclic hypoxia. Numerical simulations indicate that the tumor cells adopt a single phenotype based on the oxygen levels: under normoxic conditions, the cells exhibit an epithelial phenotype, while under hypoxic conditions, they transition to a mesenchymal phenotype. We also observe that temporal changes in oxygen levels affect the tumor's overall growth rate. Specifically, our investigations reveal that as the timescale of the oxygen fluctuations decreases, the tumor's growth rate increases. We then use the model to study an in vivo scenario in which we account for oxygen diffusion in order to investigate the effect of spatial heterogeneity in oxygen levels on the EMT dynamics. Simulation results indicate that spatial oxygen heterogeneity generates a heterogeneous population within the tumor, with epithelial cells localized on the outer rim of the tumor and mesenchymal cells concentrated at the tumor center. We perform additional simulations which show further that an increase in mesenchymal diffusivity increases the density of the epithelial cells and the tumor's volume.

Starvation driven diffusion (SDD) describes a cognitive strategy that starvation of a species leads to its stronger movement. In this paper, to better understand the effects of SDD, we propose and analyze a type of predator-prey systems with predator and prey both obeying SDD. By analyzing the linearized eigenvalue problem, we investigate the stability and instability of a semi-trivial steady state, which depends on the conversion efficiency of prey to predator as well as on the predator's minimum motility rate when conversion efficiency is properly large. Predator and prey coexist if the unique semi-trivial steady state is unstable. Utilizing Crandall-Rabinowitz bifurcation theorem, we investigate the local existence, stability, and structure of a bifurcating nontrivial steady state. There exists only one critical conversion efficiency guaranteeing the occurrence of steady-state bifurcation at the unique semi-trivial steady state. The global existence and structure of a bifurcating nontrivial steady state are proven by the global bifurcation theorem. One nontrivial steady state always exists for sufficiently large conversion efficiency. As examples, we apply theoretical results to predator-prey models with Holling type II/IV functional response involving SDD, and verify them via numerical simulations. We numerically observe spatially inhomogeneous periodic solutions, which should arise from nontrivial steady states via Hopf bifurcation, or even via homoclinic bifurcation in the case of Holling type IV functional response. Notably, these solutions consistently mirror resource distribution patterns, aligning conceptually with the ideal free distribution.

In areas infested with Aedes aegypti mosquitoes it may be possible to control dengue, and some other vector-borne diseases, by introducing Wolbachia-infected mosquitoes into the wildtype population. Thus far, empirical and theoretical studies of Wolbachia release have tended to focus on the dynamics at the community scale. However, Ae. aegypti mosquitoes typically dwell in and around the same houses as the people they bite and it can be insightful to explore what happens at the household scale where small population sizes lead to inherently stochastic dynamics. Here we use a continuous-time Markov framework to develop a stochastic household model for small populations of wildtype and Wolbachia-infected mosquitoes. We investigate the transient and long term dynamics of the system, in particular examining the impact of stochasticity on the Wolbachia invasion threshold and bistability between the wildtype-only and Wolbachia-only steady states previously observed in deterministic models. We focus on the influence of key parameters which determine the fitness cost of Wolbachia infection and the probability of Wolbachia vertical transmission. Using Markov and matrix population theory, we derive salient characteristics of the system including the probability of successful Wolbachia invasion, the expected time until invasion and the probability that a Wolbachia-infected population reverts to a wildtype population. These attributes can inform strategies for the release of Wolbachia-infected mosquitoes. In addition, we find that releasing the minimum number of Wolbachia-infected mosquitoes required to displace a resident wildtype population according to the deterministic model, only results in that outcome about 20% of the time in the stochastic model; a significantly larger release is required to reach a steady state composed entirely of Wolbachia-infected mosquitoes 90% of the time.

In order to investigate the spatial distribution and evolution dynamics of populations exhibiting synchronized reproduction and two stage long-distance dispersal modes, in this paper we propose an impulsive integro-differential model with non-local pulse. Firstly, we establish the extinction and persistence dynamics on the bounded domain with Dirichlet boundary of non-local type. Secondly, we derive the existence and characterization of the spreading speed in the whole space as well as the consistency with the minimum wave speed of the traveling waves. Finally, numerical simulations are presented to study the effects of different dispersal patterns and dispersal allocation strategy on population persistence and spreading speed under a constant measure of total dispersal. Our results show that under the same overall variance, the non-local diffusion pattern has both higher steady-state density and greater spreading speed than the local diffusion pattern. Moreover, under the fixed total dispersal, the optimal state for both population persistence and spreading speed is usually achieved through a stage-concentrated dispersal strategy, where dispersal occurs in a single life stage and the other stages remain sedentary. Additionally, we numerically investigate the impact of overcompensation on threshold and propagation dynamics, serving as a complement to the theoretical results in the non-monotonic case. This work provides new insights into the understanding of non-local interactions in biology and ecology.

Both virus-to-cell and cell-to-cell transmission modes play a crucial role in the long-term dynamics of HIV infection. Additionally, the immune response - particularly the activity of cytotoxic T lymphocytes (CTLs) - can significantly influence the threshold conditions for viral persistence. By incorporating age-structured within-host virus dynamics and the immune response, we develop a dynamical model to explore the intricacies of HIV transmission and progression within a detailed mathematical framework. Specifically, by analyzing the characteristic equations, we establish the local stability of the feasible steady states. Using Lyapunov functionals and LaSalle's invariance principle, we demonstrate that the global threshold dynamics of the model can be described by the immune-inactivated and immune-activated reproduction rates. This study provides a more accurate representation of the complex interplay between HIV and the immune system, offering valuable insights for potential therapeutic strategies.

In biological systems, cooperative behavior forms the foundation for the survival and prosperity of many organisms. However, the finite nature of resources often drives selfish individuals to exploit resources through deceptive tactics, thereby instigating conflicts between collective and individual interests. These strategic interactions not only alter the availability of environmental resources but also feedback on the strategic choices of populations, leading to the co-evolution of environmental resources and behavioral strategies. By integrating population dynamics with replicator dynamics, we develop models for both well-mixed and spatially heterogeneous distributions that incorporate resource feedback mechanisms to analyze the intricate interplay between cooperative behavior and resource dynamics across temporal and spatial scales. Our findings reveal complex evolutionary dynamics, including rich multistability, transcritical and Hopf bifurcations in the temporal system, alongside spatial stability, Turing instability, Turing-Hopf bifurcation, and chaotic behavior in the spatial diffusion system. In homogeneous distributions, payoffs result in stable periodic solutions, while heterogeneous distributions disrupt stable periodicity and lead to chaotic dynamics. Notably, increasing the initial density of cooperators, the rate of resource growth, and reducing the initial resource stock are favorable for sustaining cooperation. Interestingly, high payoffs for cooperators and low payoffs for defectors do not necessarily promote cooperative behavior, as evolutionary outcomes also depend on resource abundance. We provide the conditions that sustain cooperation, revealing the critical role of resource dynamics and spatial diffusion in shaping the evolution of cooperative strategies. Our findings have important implications for studying ecosystem management, conservation biology, and animal social behavior.