Journal of Mathematical Biology最新文献

Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate change. To generate new insights into this problem, we present a spatial Markov jump process model of savanna forest fires that integrates key ecological processes, including seed dispersal, fire spread, and non-linear vegetation flammability. In contrast to many models of forest-savanna bistability, we explicitly model both fire dynamics and vegetation regrowth in a mathematically tractable framework. This approach bridges the gap between slow-timescale vegetation models and highly resolved fire dynamics, shedding light on the influence of short-term and transient processes on vegetation cover. In our spatial stochastic model, bistability arises from periodic fires that maintain low forest cover, whereas dense forest areas inhibit fire spread and preserve high tree density. The deterministic mean-field approximation of the model similarly predicts bistability, but deviates quantitatively from the fully spatial model, especially in terms of its transient dynamics. These results also underscore the critical role of timescale separation between fire and vegetation processes in shaping ecosystem structure and resilience.

Horizontal gene transfer (HGT) is an important process in bacterial evolution. Current phylogeny-based approaches to capture it cannot however appropriately account for the fact that HGT can occur between bacteria living in different ecological niches. Due to the fact that arboreal networks are a type of multiple-rooted phylogenetic network that can be thought of as a forest of rooted phylogenetic trees along with a set of additional arcs each joining two different trees in the forest, understanding the combinatorial structure of such networks might therefore pave the way to extending current phylogeny-based HGT-inference methods in this direction. A central question in this context is, how can we construct an arboreal network? Answering this question is strongly informed by finding ways to encode an arboreal network, that is, breaking up the network into simpler combinatorial structures that, in a well defined sense uniquely determine the network. In the form of triplets, trinets and quarnets such encodings are known for certain types of single-rooted phylogenetic networks. By studying the underlying tree of an arboreal network, we complement them here with an answer for arboreal networks.

We look at the interaction of dispersal and environmental stochasticity in n-patch models. We are able to prove persistence and extinction results even in the setting when the dispersal rates are stochastic. As applications we look at Beverton-Holt and Hassell functional responses. We find explicit approximations for the total population size at stationarity when we look at slow and fast dispersal. In particular, we show that if dispersal is small then in the Beverton-Holt setting, if the carrying capacity is random, then environmental fluctuations are always detrimental and decrease the total population size. Instead, in the Hassell setting, if the inverse of the carrying capacity is made random, then environmental fluctuations always increase the population size. Fast dispersal can save populations from extinction and therefore increase the total population size. Using and modifying some approximation results due to Cuello, we find expressions for the total population size in the $n=2$ patch setting when the growth rates, carrying capacities, and dispersal rates are influenced by random fluctuations. We find that there is a complicated interaction between the various terms and that the covariances between the various random parameters (growth rate, carrying capacity, dispersal rate) play a key role in whether we get an increase or a decrease in the total population size. Environmental fluctuations turn to sometimes be beneficial - this shows that not only dispersal, but also environmental stochasticity can lead to an increase in population size.

The diffusion of cholera epidemics and the emergence of drug-resistant strain pose significant challenges to cholera control and treatment, emphasizing the need for more effective interventions. By establishing a reaction-diffusion model of cholera with vaccination and two strains (wild and drug-resistant), we study the spatiotemporal dynamics of cholera transmission in this paper. In a spatially heterogeneous case, we derive $R_0$ and establish a threshold result: the disease-free steady state is globally stable if $R_0<1$ , and the disease persists if $R_0>1$ . In addition, we prove the global stability of the endemic equilibrium by constructing a Lyapunov functional in a spatially homogeneous case. Our model is successfully validated by the cholera data in Zimbabwe via Markov Chain Monte Carlo (MCMC). Using COMSOL Multiphysics software, we display the spatial transmission of cholera in the two-dimensional geographic map via demographic data in Zimbabwe. This offers a novel perspective for investigating the spatiotemporal dynamics of cholera transmission. Our findings indicate that restricted local population diffusion may contribute to the persistence and localized transmission of cholera in certain regions of Zimbabwe. Simulations further indicate that vaccination can serve as an effective intervention under such spatial dynamics.

We introduce several axioms which may or may not hold for any given subgraph of the directed graph of all organisms (past, present and future) where edges represent biological parenthood, with the simplifying background assumption that life does not go extinct. We argue these axioms are plausible for species: if one were to define species based purely on genealogical relationships, it would be reasonable to define them in such a way as to satisfy these axioms. The main axiom we introduce, which we call the identical ancestor point axiom, states that for any organism in any species, either the species contains at most finitely many descendants of that organism, or else the species contains at most finitely many non-descendants of that organism. We show that this (together with a convexity axiom) reduces the subjectivity of species, in a technical sense. We call connected sets satisfying these two axioms "specieslike clusters." We consider the question of identifying a set of biologically plausible constraints that would guarantee every organism inhabits a maximal specieslike cluster subject to those constraints. We provide one such set consisting of two constraints and show that no proper subset thereof suffices.

Population genetic processes, such as the adaptation of a quantitative trait to directional selection, may occur on longer time scales than the sweep of a single advantageous mutation. To study such processes in finite populations, approximations for the time course of the distribution of a beneficial mutation were derived previously by branching process methods. The application to the evolution of a quantitative trait requires bounds for the probability of survival $S^{\left(n\right)}$ up to generation n of a single beneficial mutation. Here, we present a method to obtain a simple, analytically explicit, either upper or lower, bound for $S^{\left(n\right)}$ in a supercritical Galton-Watson process. We prove the existence of an upper bound for offspring distributions including Poisson, binomial, and negative binomial. They are constructed by bounding the given generating function, $\phi$ , by a fractional linear one that has the same survival probability $S^{\infty }$ and yields the same rate of convergence of $S^{\left(n\right)}$ to $S^{\infty }$ as $\phi$ . For distributions with at most three offspring, we characterize when this method yields an upper bound, a lower bound, or only an approximation. Because for many distributions it is difficult to get a handle on $S^{\infty }$ , we derive an approximation by series expansion in s, where s is the selective advantage of the mutant. We briefly review well-known asymptotic results that generalize Haldane's approximation 2s for $S^{\infty }$ , as well as less well-known results on sharp bounds for $S^{\infty }$ . We apply them to explore when bounds for $S^{\left(n\right)}$ exist for a family of generalized Poisson distributions. Numerical results demonstrate the accuracy of our and of previously derived bounds for $S^{\infty }$ and $S^{\left(n\right)}$ . Finally, we treat an application of these results to determine the response of a quantitative trait to prolonged directional selection.

In recent years, the application of fractional derivatives in mathematical models has gained significant popularity. In the case of time-fractional derivatives, one of the main reasons for their use lies in their nonlocal property, which can overcome the limitations of ordinary differential equation models that are purely local and might fail to describe memory-dependent processes. The most common approach, often called fractionalisation, is based on the direct replacement of the classical derivatives in the ODE models, with fractional ones. When they are compared to real data, fractionalised models are often shown to provide better fitting results. The most common interpretation of this is that fractionalised models keep track of the history, while local models do not. However, while the physical meaning of a classical derivative is clear, the same cannot be said for fractional derivatives. Therefore, the relationship between modelling assumptions and mathematical equations remains unclear. Here, we introduce and critically discuss the fractionalisation approach by considering two representative examples of fractionalised biomathematical models. In our discussion, we address several properties of fractional operators that may impose significant limitations in their applications. However, the key question on which we would like to reflect is: is a fractionalised model still a model?

A survey of the literature reveals notable discrepancies among the purported exact results for the spectra of stochastic gene expression models. For self-repressing gene circuits, previous studies ([Phys. Rev. Lett. 99, 108103 (2007)], [Phys. Rev. E 83,062902 (2011)], [J. Chem. Phys. 160, 074105 (2024)], and [bioRxiv 2025.02.05.635946 (2025)]) have provided different exact solutions for the eigenvalues of the generator matrix. In this work, we propose a unified Hilbert space framework for the spectral theory of stochastic gene expression. Based on this framework, we analytically derive the spectra for models of constitutive, bursty, and autoregulated gene expression. The eigenvalues and eigenvectors obtained are then used to construct an exact spectral representation of the time-dependent distribution of gene product numbers. The spectral gap between the zero eigenvalue and the first nonzero eigenvalue, which reflects the relaxation rate of the system towards its steady state, is then compared with the prediction of the deterministic model, and we find that deterministic modeling fails to capture the relaxation rate when autoregulation is strong. In particular, our results demonstrate that for infinite-dimensional operators such as in stochastic gene expression models, many conclusions in linear algebra do not apply, and one must rely on the modern theory of functional analysis.

The large-scale use of insecticides remains a cornerstone of malaria vector control, but its long-term effectiveness is undermined by the evolution of quantitative insecticide resistance (qIR) in mosquito populations. We develop and analyze a mathematical model to identify optimal deployment strategies for two insecticides that differ only in their relative efficacy against target mosquito populations. Resistance is represented as a continuous phenotypic trait influencing mosquito fecundity and mortality, and the model accounts for successive deployment periods. Our results show that when mutational variance is high, the optimal strategy is to deploy the most effective insecticide at full coverage, regardless of its relative efficacy or pre-deployment exposure history. By contrast, when mutational variance is low, optimal deployment requires a transient reduction in coverage during early periods, with a threshold effect driven by both relative efficacy and initial exposure rates. Crucially, we find that, under the hypothesis that the first insecticide is ineffective against mosquitoes, simultaneous use of both insecticides is rarely optimal. Instead, sequential deployment-using one insecticide until resistance reaches a critical threshold, followed by optimal use of the second-delays resistance evolution and improves long-term control. These findings provide a theoretical foundation for adaptive qIR management strategies aimed at prolonging the effectiveness of insecticides in malaria vector control.

Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Autocatalysis was recently defined stoichiometrically for reaction networks; five types of minimal autocatalytic networks, termed autocatalytic cores were identified. A necessary and sufficient stoichiometric criterion was later established for dynamical autocatalysis in diluted regimes, ensuring a positive growth rate of autocatalytic species starting from infinitesimal concentrations, given that degradation rates are sufficiently low. Here, we show that minimal autocatalytic networks in the dynamical sense, in the diluted regime, follow the same classification as autocatalytic cores in the stoichiometric sense. We further prove the uniqueness of the stationary regimes of autocatalytic cores, with and without degradation, for all types, except types II with three catalytic loops or more, for which the question remains open. These results indicate that the stationary point is robust under perturbation at low concentrations. More complex behaviours require additional non-linear couplings.