Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Stochastic Adaptive Dynamics Model for Bacterial Populations with Mutation, Dormancy and Transfer
167
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper introduces a stochastic adaptive dynamics model for the interplay of several crucial traits and mechanisms in bacterial evolution, namely dormancy, horizontal gene transfer (HGT), mutation and competition. In particular, it combines the recent model of Champagnat, Meleard and Tran (2021) involving HGT with the model for competition-induced dormancy of Blath and Tobias (2020). Our main result is a convergence theorem which describes the evolution of the different traits in the population on a `doubly logarithmic scale as piece-wise affine functions. Interestingly, even for a relatively small trait space, the limiting process exhibits a non-monotone dependence of the success of the dormancy trait on the dormancy initiation probability. Further, the model establishes a new `approximate coexistence regime for multiple traits that has not been observed in previous literature.
rate research
Read More
We investigate the interplay between two fundamental mechanisms of microbial population dynamics and evolution called dormancy and horizontal gene transfer. The corresponding traits come in many guises and are ubiquitous in microbial communities, affecting their dynamics in important ways. Recently, they have each moved (separately) into the focus of stochastic individual-based modelling (Billiard et al. 2016, 2018; Champagnat, Meleard and Tran, 2021; Blath and Tobias 2020). Here, we examine their combined effects in a unified model. Indeed, we consider the (idealized) scenario of two sub-populations, respectively carrying trait 1 and trait 2, where trait 1 individuals are able to switch (under competitive pressure) into a dormant state, and trait 2 individuals are able to execute horizontal gene transfer, turning trait 1 individuals into trait 2 ones, at a rate depending on the frequency of individuals. In the large-population limit, we examine the fate of a single trait i individual (a mutant) arriving in a trait j resident population living in equilibrium, for $i,j=1,2,i eq j$. We provide a complete analysis of the invasion dynamics in all cases where the resident population is individually fit and the initial behaviour of the mutant population is non-critical. We identify parameter regimes for the invasion and fixation of the new trait, stable coexistence of the two traits, and founder control (where the initial resident always dominates, irrespective of its trait). The most striking result is that stable coexistence occurs in certain scenarios even if trait 2 (which benefits from transfer at the cost of trait 1) would be unfit when being merely on its own. In the case of founder control, the limiting dynamical system has an unstable coexistence equilibrium. In all cases, we observe the classical (up to 3) phases of invasion dynamics `a la Champagnat (2006).
251 -
Fernando Cordero
, Adrian Gonzalez Casanova
, Jason Schweinsberg andn Maite Wilke-Berenguer
2020
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake, it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, $N$ individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a $Lambda$-coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all $Lambda$-coalescents that can arise in this framework.
We consider a spatial model of cancer in which cells are points on the $d$-dimensional torus $mathcal{T}=[0,L]^d$, and each cell with $k-1$ mutations acquires a $k$th mutation at rate $mu_k$. We will assume that the mutation rates $mu_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire $k$ mutations as the torus volume tends to infinity. This paper generalizes results on waiting for $kgeq 3$ mutations by Foo, Leder, and Schweinsberg, who considered the case in which all of the mutation rates $mu_k$ were the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating environmental conditions. To this end, we compare the long term behaviour of `1-type Bienayme-Galton-Watson branching processes (describing populations consisting of `active individuals only) with that of a class of `2-type branching processes, describing populations consisting of `active and `dormant individuals. All processes are embedded in an environment changing randomly between `harsh and `healthy conditions, affecting the reproductive behaviour of the populations accordingly. For the 2-type branching processes, we consider several different switching regimes between active and dormant states. We also impose overall resource limitations which incorporate the potentially different `production costs of active and dormant offspring, leading to the notion of `fair comparison between different populations, and allow for a reproductive trade-off due to the maintenance of the dormancy trait. Our switching regimes include the case where switches from active to dormant states and vice versa happen randomly, irrespective of the state of the environment (`spontaneous switching), but also the case where switches are triggered by the environment (`responsive switching), as well as combined strategies. It turns out that there are rather natural scenarios under which either switching strategy can be super-critical, while the others, as well as complete absence of a seed bank, are strictly sub-critical, even under `fair comparison wrt. available resources. In such a case, we see a clear selective advantage of the super-critical strategy, which is retained even under the presence of a (potentially small) reproductive trade-off. [...]
In this paper, we consider a mean-reverting stochastic volatility equation with regime switching, and present some sufficient conditions for the existence of global positive solution, asymptotic boundedness in pth moment, positive recurrence and existence of stationary distribution of this equation. Some results obtained in this paper extend the ones in literature. Example is given to verify the results by simulation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
