Journal of Biological Dynamics最新文献

The turnover rate of producer biomass in aquatic ecosystems is generally faster than in terrestrial. That is, aquatic producer biomass grows, is consumed, and is replaced considerably faster than terrestrial. The WKL model describes the flow of phosphorus and carbon through a grazer-producer system, hence varying the model parameters allows for analysis of different ecosystems of this type. Here we explore the impacts of the intrinsic growth rate of the producer and the maximal ingestion rate of the grazer on these dynamics because these parameters determine turnover rate. Simulations show that for low intrinsic growth rate and maximal ingestion rate, the grazer goes extinct; for higher values of these parameters, coexistence occurs in oscillations. Sensitivity analysis reveals the relative importance of all parameters on asymptotic dynamics. Lastly, the impacts of changing these two parameters in the LKE model appears to be quantitatively similar to the impacts in the WKL model.

We use a mixed time model to study the dynamics of a system consisting of two consumers that reproduce only in annual birth pulses, possibly at different times, with interaction limited to competition for a resource that reproduces continuously. Ecological theory predicts competitive exclusion; this expectation is met under most circumstances, the winner being the species with the greater 'power', defined as the time average consumer level at the fixed point. Instability of that fixed point for the stronger competitor slightly weakens its domination, so that a resident species with an unstable fixed point can sometimes be invaded by a slightly weaker species, leading ultimately to coexistence. Differences in birth pulse times can lead to qualitatively different long-term coexistence behaviour, including cycles of different lengths or chaos. We also determine conditions under which the timing of an annual pulse of a toxin can change the balance of power.

We prove bifurcation theorems for evolutionary game theoretic (Darwinian dynamic) versions of nonlinear matrix equations for structured population dynamics. These theorems generalize existing theorems concerning the bifurcation and stability of equilibrium solutions when an extinction equilibrium destabilizes by allowing for the general appearance of the bifurcation parameter. We apply the theorems to a Darwinian model designed to investigate the evolutionary selection of reproductive strategies that involve either low or high post-reproductive survival (semelparity or iteroparity). The model incorporates the phenotypic trait dependence of two features: population density effects on fertility and a trade-off between inherent fertility and post-reproductive survival. Our analysis of the model determines conditions under which evolution selects for low or for high reproductive survival. In some cases (notably an Allee component effect on newborn survival), the model predicts multiple attractor scenarios in which low or high reproductive survival is initial condition dependent.

In Nature, species coexistence is much more frequent than what the classical competition model predicts, so that scientists look for mechanisms that explain such a coexistence. We revisit the classical competition model assuming that individuals invest time in competing individuals of the other species. This assumption extends the classical competition model (that becomes a particular case of the model presented) under the form of a Holling type II term, that we call competitive response to interfering time. The resulting model expands the outcomes allowed by the classical model by (i) enlarging the range of parameter values that allow coexistence scenarios and (ii) displaying dynamical scenarios not allowed by the classical model: namely, bi-stable conditional coexistence in favour of i (either species coexist or species i wins) or tri-stable conditional coexistence (either species coexist or any of them goes extinct), being exclusion in both cases due to priority effects.

Vector-borne infectious diseases may involve both horizontal transmission between hosts and transmission from infected vectors to susceptible hosts. In this paper, we incorporate these two transmission modes into a vector-borne disease model that includes general nonlinear incidence rates and the age of infection for both hosts and vectors. We show the existence, uniqueness, nonnegativity, and boundedness of solutions for the model. We study the existence and local stability of steady states, which is shown to be determined by the basic reproduction number. By showing the existence of a global compact attractor and uniform persistence of the system, we establish the threshold dynamics using the Fluctuation Lemma and the approach of Lyapunov functionals. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable and otherwise the disease will be established when there is initial infection force for the hosts. We also study a model with the standard incidence rate and discuss the effect of different incidence rates on the disease dynamics.

In this paper, we consider a nonautonomous predator-prey system with Beddington-DeAngelis functional response and explore the global stability of boundary solution. Based on the dynamics of logistic equation, some new sufficient conditions on the global asymptotic stability of boundary solution are presented for general time-dependence case. Our main results indicate that (i) the long-term ineffective predation behaviour or high mortality of predator species will lead the predator species to extinction, even if the intraspecies competition of predator species is weak or no intraspecies competition; (ii) the long-term intense intraspecific competition may lead the predator species to extinction, even though the long-term accumulative predation benefit is higher than the death lose. When all parameters are periodic functions with common period, a necessary and sufficient condition on the global stability of boundary periodic solution is obtained. In addition, some numerical simulations are performed to illustrate the theoretical results.

We present a systematic comparison and analysis of four discrete-time, host-parasitoid models. For each model, we specify that density-dependent effects occur prior to parasitism in the life cycle of the host. We compare density-dependent growth functions arising from the Beverton-Holt and Ricker maps, as well as parasitism functions assuming either a Poisson or negative binomial distribution for parasitoid attacks. We show that overcompensatory density-dependence leads to period-doubling bifurcations, which may be supercritical or subcritical. Stronger parasitism from the Poisson distribution leads to loss of stability of the coexistence equilibrium through a Neimark-Sacker bifurcation, resulting in population cycles. Our analytic results also revealed dynamics for one of our models that were previously undetected by authors who conducted a numerical investigation. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete-time model in order to promote communication and broader understanding.

We model the extent to which age-targeted protective sequestration can be used to reduce ICU admissions caused by novel coronavirus COVID-19. Using demographic data from New Zealand, we demonstrate that lowering the age threshold to 50 years of age reduces ICU admissions drastically and show that for sufficiently strict isolation protocols, sequestering one-third of the countries population for a total of 8 months is sufficient to avoid overwhelming ICU capacity throughout the entire course of the epidemic. Similar results are expected to hold for other countries, though some minor adaption will be required based on local age demographics and hospital facilities.

In this paper, we first investigate a stochastic two-predators one-prey model with Lévy noise and distributed delays. The global dynamical behaviour is discussed. The criteria on the existence of global positive solutions, stochastic boundedness, extinction and global asymptotic stability in the mean with probability one are established. And then, the harvesting for each species is introduced to the model. The optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY, for short) are further established.