Journal of Mathematical Biology最新文献

We study a model of group-structured populations featuring individual-level birth and death events, and group-level fission and extinction events. Individuals play games within their groups, while groups play games against other groups. Payoffs from individual-level games affect birth rates of individuals, and payoffs from group-level games affect group extinction rates. We focus on the evolutionary dynamics of continuous traits with particular emphasis on the phenomenon of evolutionary diversification. Specifically, we consider two-level processes in which individuals and groups play continuous snowdrift or prisoner's dilemma games. Individual game strategies evolve due to selection pressure from both the individual and group level interactions. The resulting evolutionary dynamics turns out to be very complex, including branching and type-diversification at one level or the other. We observe that a weaker selection pressure at the individual level results in more adaptable groups and sometimes group-level branching. Stronger individual-level selection leads to more effective adaptation within each group while preventing the groups from adapting according to the group-level games.

In this study, we develop consistent estimators for key parameters that govern the dynamics of tumor cell populations when subjected to pharmacological treatments. While these treatments often lead to an initial reduction in the abundance of drug-sensitive cells, a population of drug-resistant cells frequently emerges over time, resulting in cancer recurrence. Samples from recurrent tumors present as an invaluable data source that can offer crucial insights into the ability of cancer cells to adapt and withstand treatment interventions. To effectively utilize the data obtained from recurrent tumors, we derive several large number limit theorems, specifically focusing on the metrics that quantify the clonal diversity of cancer cell populations at the time of cancer recurrence. These theorems then serve as the foundation for constructing our estimators. A distinguishing feature of our approach is that our estimators only require a single time-point sequencing data from a single tumor, thereby enhancing the practicality of our approach and enabling the understanding of cancer recurrence at the individual level.

Understanding how genetically encoded rules drive and guide complex neuronal growth processes is essential to comprehending the brain's architecture, and agent-based models (ABMs) offer a powerful simulation approach to further develop this understanding. However, accurately calibrating these models remains a challenge. Here, we present a novel application of Approximate Bayesian Computation (ABC) to address this issue. ABMs are based on parametrized stochastic rules that describe the time evolution of small components-the so-called agents-discretizing the system, leading to stochastic simulations that require appropriate treatment. Mathematically, the calibration defines a stochastic inverse problem. We propose to address it in a Bayesian setting using ABC. We facilitate the repeated comparison between data and simulations by quantifying the morphological information of single neurons with so-called morphometrics and resort to statistical distances to measure discrepancies between populations thereof. We conduct experiments on synthetic as well as experimental data. We find that ABC utilizing Sequential Monte Carlo sampling and the Wasserstein distance finds accurate posterior parameter distributions for representative ABMs. We further demonstrate that these ABMs capture specific features of pyramidal cells of the hippocampus (CA1). Overall, this work establishes a robust framework for calibrating agent-based neuronal growth models and opens the door for future investigations using Bayesian techniques for model building, verification, and adequacy assessment.

Evolutionary graph theory has considerably advanced the process of modelling the evolution of structured populations, which models the interactions between individuals as pairwise contests. In recent years, these classical evolution models have been extended to incorporate more realistic features, e.g. multiplayer games. A recent series of papers have developed a new evolutionary framework including structure, multiplayer interactions, evolutionary dynamics, and movement. However, so far, the developed models have mainly considered independent movement without coordinated behaviour. Although the theory underlying the framework has been developed and explored in various directions, several movement mechanisms have been produced which characterise coordinated movement, for example, herding. By embedding these newly constructed movement distributions, within the evolutionary setting of the framework, we demonstrate that certain levels of aggregation and dispersal benefit specific types of individuals. Moreover, by extending existing parameters within the framework, we are not only able to develop a general process of embedding any of the considered movement distributions into the evolutionary setting on complete graphs but also analytically produce the probability of fixation of a mutant on a complete N-sized network, for the multiplayer Public Goods and Hawk-Dove games. Also, by applying weak selection methods, we extended existing previous analyses on the pairwise Hawk-Dove Game to encompass the multiplayer version considered in this paper. By producing neutrality and equilibrium conditions, we show that hawks generally do worse in our models due to the multiplayer nature of the interactions.

Faith's Phylogenetic Diversity (PD) on rooted phylogenetic trees satisfies the so-called strong exchange property that guarantees that, for every two sets of leaves of different cardinalities, a leaf can always be moved from the larger set to the smaller set in such a way that the sum of the PD values does not decrease. This strong exchange property entails a simple polynomial-time greedy solution to the PD optimization problem on rooted phylogenetic trees. In this paper we obtain an exchange property for the rooted Phylogenetic Subnet Diversity (rPSD) on rooted phylogenetic networks, which involves a more complicated exchange of leaves. We derive from it a polynomial-time greedy solution to the rPSD optimization problem on rooted semibinary level-2 phylogenetic networks.

Estimation of admixture proportions has become one of the most commonly used computational tools in population genomics. However, there is remarkably little population genetic theory on statistical properties of these variables. We develop theoretical results that can accurately predict means and variances of admixture proportions within a population using models with recombination and genetic drift. Based on established theory on measures of multilocus disequilibrium, we show that there is a set of recurrence relations that can be used to derive expectations for higher moments of the admixture proportions distribution. We obtain closed form solutions for some special cases. Using these results, we develop a method for estimating admixture parameters from estimated admixture proportions obtained from programs such as Structure or Admixture. We apply this method to HapMap 3 data and find that the population history of African Americans, as expected, is not best explained by a single admixture event between people of European and African ancestry. The model of constant gene flow starting at 8 generations and ending at 2 generations before present gives the best fit.

We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph $G=(V,E)$ . The evolution is driven by a linear birth rate, a density dependent logistic death rate and the possibility of mutations along the directed edges in E. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between Bovier et al. (Ann Appl Probab 29(6):3541-358, 2019) and Coquille et al. (Electron J Probab 26:1-37, 2021) we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales, corresponding to the widths of these fitness valleys. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between them. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scales, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

Models with several levels of mixing (households, workplaces), as well as various corresponding formulations for $R_0$ , have been proposed in the literature. However, little attention has been paid to the impact of the distribution of the population size within social structures, effect that can help plan effective interventions. We focus on the influence on the model outcomes of teleworking strategies, consisting in reshaping the distribution of workplace sizes. We consider a stochastic SIR model with two levels of mixing, accounting for a uniformly mixing general population, each individual belonging also to a household and a workplace. The variance of the workplace size distribution appears to be a good proxy for the impact of this distribution on key outcomes of the epidemic, such as epidemic size and peak. In particular, our findings suggest that strategies where the proportion of individuals teleworking depends sublinearly on the size of the workplace outperform the strategy with linear dependence. Besides, one drawback of the model with multiple levels of mixing is its complexity, raising interest in a reduced model. We propose a homogeneously mixing SIR ODE-based model, whose infection rate is chosen as to observe the growth rate of the initial model. This reduced model yields a generally satisfying approximation of the epidemic. These results, robust to various changes in model structure, are very promising from the perspective of implementing effective strategies based on social distancing of specific contacts. Furthermore, they contribute to the effort of building relevant approximations of individual based models at intermediate scales.

Based on the patchy habitats of mistletoes and the mutualistic relationship between mistletoes and birds, we propose a mistletoe-bird model on a weighted network that is described by discrete Laplacian operators. Without considering mistletoes, the dynamics of a model of birds is investigated by a threshold parameter. Under the premise of the persistence of birds, the existence and uniqueness of solutions of a mistletoe-bird model are established, and the stability of solutions of the model is discussed by the ecological reproduction index $R_0^m$ , specifically, mistletoes go extinct when $R_0^m<1$ , and mistletoes coexist with birds when $R_0^m>1$ . Moreover, we show that network weights can induce changes of instantaneous dynamics of birds or mistletoes by the matrix perturbation method. By assuming that the weighted network is a river network and a star network, we simulate the extinction of mistletoes and the coexistence of mistletoes with birds, respectively.

Hand, foot and mouth disease (HFMD) is a Class C infectious disease that carries particularly high risk for preschool children and is a leading cause of childhood death in some countries. We mimic the periodic outbreak of HFMD over a 2-year period-with differing amplitudes-and propose a dynamic HFMD model that differentiates transmission between mature and immature individuals and uses two possible optimal-control strategies to minimize case numbers, total costs and deaths. We parameterized the model by fitting it to HFMD data in mainland China from January 2011 to December 2018, and the basic reproduction number was estimated as 0.9599. Sensitivity analysis demonstrates that transmission between immature and mature individuals contributes substantially to new infections. Increasing the isolation rates of infectious individuals-particularly mature infectious individuals-could greatly reduce the outbreak risk and potentially eradicate the disease in a relatively short time period. It follows that we have a reasonable chance of controlling HFMD if we can reduce transmission in children under 7 and isolate older infectious individuals.