Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDemographic stochasticity and extinction in populations with Allee effect
116
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.
rate research
Read More
Demographic (shot) noise in population dynamics scales with the square root of the population size. This process is very important, as it yields an absorbing state at zero field, but simulating it, especially on spatial domains, is a non-trivial task. Here we compare the results of two operator-splitting techniques suggested for simulating the corresponding Langevin equation, one by Pechenik and Levine (PL) and the other by Dornic, Chate and Mu~noz (DCM). We identify an anomalously strong bias toward the active phase in the numerical scheme of DCM, a bias which is not present in the alternative scheme of PL. This bias strongly distorts the phase diagram determined via the DCM procedure for the range of time-steps used in such simulations. We pinpoint the underlying cause in the inclusion of the diffusion, treated as an on-site decay with a constant external source, in the stochastic part of the algorithm. Treating the diffusion deterministically is shown to remove this unwanted bias while keeping the simulation algorithm stable, thus a hybrid numerical technique, in which the DCM approach to diffusion is applied but the diffusion is simulated deterministically, appears to be optimal.
In genetic circuits, when the mRNA lifetime is short compared to the cell cycle, proteins are produced in geometrically-distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of switching or escape in stochastic populations, where influx of particles occurs in groups or bursts, sampled from an arbitrary distribution. The fact that the step size of the influx reaction is a-priori unknown, and in general, may fluctuate in time with a given correlation time and statistics, introduces an additional non-demographic step-size noise into the system. Employing the probability generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation. We show that bursty influx exponentially decreases the mean escape time compared to the usual case of single-step influx. In particular, close to bifurcation we find a simple analytical expression for the mean escape time, which solely depends on the mean and variance of the burst-size distribution. Our results are demonstrated on several realistic distributions and compare well with numerical Monte-Carlo simulations.
Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by investigating the effect of bursty influx on the switching dynamics of stochastic populations. Here we extend this formalism to account for bursty reproduction processes, and improve the accuracy of the formalism to include subleading-order corrections. Bursty reproduction appears in various contexts, where notable examples include bursty viral production from infected cells, and reproduction of mammals involving varying number of offspring. The main question we quantitatively address is how bursty reproduction affects the overall fate of the population. We consider two complementary scenarios: population extinction and population survival; in the former a population gets extinct after maintaining a long-lived metastable state, whereas in the latter a population proliferates despite undergoing a deterministic drift towards extinction. In both models reproduction occurs in bursts, sampled from an arbitrary distribution. In the extinction problem, we show that bursty reproduction broadens the quasi-stationary distribution of population sizes in the metastable state, which results in an exponential decrease of the mean time to extinction. In the survival problem, bursty reproduction yields an exponential increase in survival probability of the population. Close to the bifurcation limit our analytical results simplify considerably and are shown to depend solely on the mean and variance of the burst-size distribution. Our formalism is demonstrated on several realistic distributions which all compare well with numerical Monte-Carlo simulations.
We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the populations viability. Slow migration is shown to always increase the populations global extinction risk compared to the isolated case. At fast migration, we demonstrate that synchrony between patches minimizes the populations extinction risk. Moreover, we discover a critical migration rate that maximizes the extinction risk of the population, and identify an early-warning signal when approaching this state. Our theoretical results are confirmed via the highly-efficient weighted ensemble method. Notably, our analysis can also be applied to studying switching in gene regulatory networks with multiple transcriptional states.
Recent collapses of many fisheries across the globe have challenged the mathematical approach to these systems through classic bioeconomic models. Decimated populations did not recover as fast as predicted by these models and depensatory effects were introduced to better fit the dynamics at low population abundances. Alternative to depensation, modeling captures by non-linear harvesting functions produces equivalent outcomes at small abundances, and the dynamics undergoes a bifurcation leading to population collapse and recovery once catching efforts are above or below certain thresholds, respectively. The time that a population takes to undergo these transitions has been mostly overlooked in bioeconomic contexts, though. In this work we quantify analytically and numerically the times associated to these collapse and recovery transitions in a model incorporating non-linear harvesting and immigration in the presence and absence of demographic stochasticity. Counterintuitively, although species at low abundances are prone to extinction due to demographic stochasticity, our results show that stochastic collapse and recovery times are upper bounded by their deterministic estimates. This occurs over the full range of immigration rates. Our work may have relevant quantitative implications in the context of fishery management and rebuilding.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
