Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects

Assessing the information-content of messy data to reconstruct population recovery dynamics for the world's rarest primate

Understanding the dynamics of population recovery in threatened species requires robust longitudinal monitoring datasets. However, evidence-based decision-making is often impeded by variable data collection approaches, necessitating critical evaluation of restricted available baselines. The Hainan gibbon, the world's rarest primate, had possibly declined to only seven or eight individuals in 1978 at Bawangling National Nature Reserve but has experienced subsequent population growth. Past population estimates lack detailed reporting of survey effort, and multiple conflicting estimates are available, hindering assessment of gibbon recovery. We investigated all reported estimates of Bawangling gibbon population size from 1978 to 2022, to evaluate the biological signal of population trends and the extent to which noise associated with varying survey effort, reporting and estimation may mask or misrepresent any underlying signal. This longitudinal dataset demonstrates that the Bawangling population experienced a series of bottlenecks and recoveries, with three successive periods of growth interspersed by population crashes (1978-1989, 1989-2000 and 2000-2022). The rate of gibbon population recovery was progressively slower over time in each successive period of growth, and this potential decline in recovery rate following serial bottlenecks suggests that additional management strategies may be required alongside "nature-based solutions" for this species. However, population viability analysis suggests the 1978 founder population is unlikely to have been as low as seven individuals, raising concerns for interpreting reported historical population counts and understanding the dynamics of the species' recovery. We caution against overinterpreting potential signals within "messy" conservation datasets, and we emphasise the crucial importance of standardised replicable survey methods and transparent reporting of data and effort in all future surveys of Hainan gibbons and other highly threatened species.

Unraveling the forces shaping foraging dynamics in harvester ant colonies: Recruitment efficiency and environmental variability

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

Controlling smoking: A smoking epidemic model with different smoking degrees in deterministic and stochastic environments

Engaging in smoking not only leads to substantial health risks but also imposes considerable financial burdens. To deepen our understanding of the mechanisms behind smoking transmission and to address the tobacco epidemic, we examined a five-dimensional smoking epidemic model that accounts for different degrees of smoking under both deterministic and stochastic conditions. In the deterministic case, we determine the basic reproduction number, analyze the stability of equilibria with and without smoking, and investigate the existence of saddle-node bifurcation. Our analysis reveals that the basic reproduction number cannot completely determine the existence of smoking, and the model possesses bistability, indicating its dynamic is susceptible to interference from environmental noises. In the stochastic case, we establish sufficient conditions for the ergodic stationary distribution and the elimination of smokers by constructing appropriate Lyapunov functions. Numerical simulations suggest that the effects of inevitable random fluctuations in the natural environment on controlling the smoking epidemic may be beneficial, harmful, or negligible, which are closely related to the noise intensities, initial smoking population sizes, and the effective exposure rate of smoking transmission (β). Given the uncontrollable nature of environmental random effects, effective smoking control strategies can be achieved by: (1) accurate monitoring of initial smoking population sizes, and (2) implementing effective measures to reduce β. Therefore, it is both effective and feasible to implement a complete set of strong MPOWER measures to control smoking prevalence.

Noise-induced dynamics in a single species model with Allee effect driven by correlated colored noises

In this paper, a single species model with Allee effect driven by correlated colored noises is proposed and investigated. The stationary probability density of the model is obtained using the approximative Fokker-Planck equation, and its shape is discussed in detail. P-bifurcation and noise-induced bistability are explored, followed by the observation of noise-enhanced stability through mean first passage time analysis. Our findings demonstrate that: (i) noise can induce P-bifurcation, causing the structure of a stationary probability distribution to shift from unimodal to monotonic under positive correlation and switch from unimodal to bimodal under negative correlation; (ii) correlation time promotes population growth, leading to a higher probability of large population size and delaying the extinction process; (iii) noise-enhanced stability induced by multiplicative noise depends on both additive noise and correlation time, while it always exists for additive noise.

Global dynamics of an SIS compartment model with resource constraints

This paper formulates a mathematical framework to describe the dynamics of SIS-type infectious diseases with resource constraints. We first define the basic reproduction number that determines disease prevalence and analyze the existence and local stability of the equilibria. Subsequently, we analyze the global dynamics of the model, excluding periodic solutions and heteroclinic orbits, using the compound matrix approach. The analysis implies that the model can undergo forward and backward bifurcations depending on critical parameters. In the former scenario, the disease persists when the basic reproduction number under resource constraints exceeds one. In the latter scenario, the backward bifurcation creates bistability dynamics in which the disease may persist or become extinct depending on the initial level of infected individuals and the resource abundance.