Populations and Evolution (q-bio.PE)

Abstract: The honeybee plays an extremely important role in ecosystem stability and diversity and in the production of bee pollinated crops. Honey bees and other pollinators are under threat from the combined effects of nutritional stress, parasitism, pesticides, and climate change that impact the timing, duration, and variability of seasonal events. To understand how parasitism and seasonality influence honey bee colonies separately and interactively, we developed a non-autonomous nonlinear honeybee-parasite interaction differential equation model that incorporates seasonality into the egg-laying rate of the queen. Our theoretical results show that parasitism negatively impacts the honey bee population either by decreasing colony size or destabilizing population dynamics through supercritical or subcritical Hopf-bifurcations depending on conditions. Our bifurcation analysis and simulations suggest that seasonality alone may have positive or negative impacts on the survival of honey bee colonies. More specifically, our study indicates that (1) the timing of the maximum egg-laying rate seems to determine when seasonality has positive or negative impacts; and (2) when the period of seasonality is large it can lead to the colony collapsing. Our study further suggests that the synergistic influences of parasitism and seasonality can lead to complicated dynamics that may positively and negatively impact the honey bee colony's survival. Our work partially uncovers the intrinsic effects of climate change and parasites, which potentially provide essential insights into how best to maintain or improve a honey bee colony's health.

Abstract: In this article, we have considered a planar slow-fast modified Leslie-Gower predator-prey model with a weak Allee effect in the predator, based on the natural assumption that the prey reproduces far more quickly than the predator. We present a thorough mathematical analysis demonstrating the existence of homoclinic orbits, heteroclinic orbits, singular Hopf bifurcation, canard limit cycles, relaxation oscillations, the birth of canard explosion by combining the normal form theory of slow-fast systems, Fenichel's theorem and blow-up technique near non-hyperbolic point. We have obtained very rich dynamical phenomena of the model, including the saddle-node, Hopf, transcritical bifurcation, generalized Hopf, cusp point, homoclinic orbit, heteroclinic orbit, and Bogdanov-Takens bifurcations. Moreover, we have investigated the global stability of the unique positive equilibrium, as well as bistability, which shows that the system can display either 'prey extinction', 'stable coexistence', or 'oscillating coexistence' depending on the initial population size and values of the system parameters. The theoretical findings are verified by numerical simulations.

Abstract: It is well known that the confirmed COVID-19 infection is only a fraction of the true fraction. In this paper we use an artificial neural network to learn the connection between the confirmed infection count, the testing data, and the true infection count. The true infection count in the training set is obtained by backcasting from the death count and the infection fatality ratio (IFR). Multiple factors are taken into consideration in the estimation of IFR. We also calibrate the recovered true COVID-19 case count with an SEIR model.

Abstract: We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the stability properties and abundance distributions of large disordered GLV systems depend, in the simplest scenario, solely on the mean and variance of the distribution of species interactions. However, empirical communities deviate from this level of universality. In this article, we present a generalized version of the dynamical mean field theory for non-Gaussian interactions that can be applied to various models, including the GLV equations. Our results show that the generalized mean field equations have solutions which depend on all cumulants of the distribution of species interactions, leading to a breakdown of universality. We leverage on this informative breakdown to extract microscopic interaction details from the macroscopic distribution of densities which are in agreement with empirical data. Specifically, in the case of sparse interactions, which we analytically investigate, we establish a simple relationship between the distribution of interactions and the distribution of species population densities.

Abstract: We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and subsequent immunity is introduced, considering stochasticity at the individual level. By letting the population size going to infinity, we derive a set of equations describing the large scale behavior of the epidemic. The analysis of the model's equilibria reveals a criterion for the existence of an endemic equilibrium, which depends on the rate of immunity loss and the distribution of time between booster doses. The outcome of a vaccination policy in this context is influenced by the efficiency of the vaccine in blocking transmissions and the distribution pattern of booster doses within the population. Strategies with evenly spaced booster shots at the individual level prove to be more effective in preventing disease spread compared to irregularly spaced boosters, as longer intervals without vaccination increase susceptibility and facilitate more efficient disease transmission. We provide an expression for the critical fraction of the population required to adhere to the vaccination policy in order to eradicate the disease, that resembles a well-known threshold for preventing an outbreak with an imperfect vaccine. We also investigate the consequences of unequal vaccine access in a population and prove that, under reasonable assumptions, fair vaccine allocation is the optimal strategy to prevent endemicity.

Abstract: Many-species ecological communities can exhibit persistent fluctuations driven by species interactions. These dynamics feature many interesting properties, such as the emergence of long timescales and large fluctuations, that have remained poorly understood. We look at such dynamics, when species are supported by migration at a small rate. We find that the dynamics are characterized by a single long correlation timescale. We prove that the time and abundances can be rescaled to yield a well-defined limiting process when the migration rate is small but positive. The existence of this rescaled dynamics predicts scaling forms for both abundance distributions and timescales, which are verified exactly in scaling collapse of simulation results. In the rescaled process, a clear separation naturally emerges at any given time between rare and abundant species, allowing for a clear-cut definition of the number of coexisting species. Species move back and forth between the rare and abundant subsets. The dynamics of a species entering the abundant subset starts with rapid growth from rare, appearing as an instantaneous jump in rescaled time, followed by meandering abundances with an overall negative bias. The emergence of the long timescale is explained by another rescaling theory for earlier times. Finally, we prove that the number of abundant species is tuned to remain below and without saturating a well-known stability bound, maintaining the system away from marginality. This is traced back to the perturbing effect of the jump processes of incoming species on the abundant ones.