Effects of constant immigration on the dynamics and persistence of stable and unstable Drosophila populations

Persistence and extinction of species in a disease-induced ecological system under environmental stochasticity

Population extinction is a serious issue both from the theoretical and practical points of view. We explore here how environmental noise influences persistence and extinction of interacting species in presence of a pathogen even when the populations remain stable in its deterministic counterpart. Multiplicative white noise is introduced in a deterministic predator-prey-parasite system by randomly perturbing three biologically important parameters. It is revealed that the extinction criterion of species may be satisfied in multiple ways, indicating various routes to extinction, and disease eradication may be possible with the right environmental noise. Predator population cannot survive, even when its focal prey strongly persists if its growth rate is lower than some critical value, measured by half of the corresponding noise intensity. It is shown that the average extinction time of population decreases with increasing noise intensity and the probability distribution of the extinction time follows the log-normal density curve. A case study on red grouse (prey) and fox (predator) interaction in presence of the parasites trichostrongylus tenuis of grouse is presented to demonstrate that the model well fits the field data.

Complex interaction of resource availability, life-history and demography determines the dynamics and stability of stage-structured populations

The dynamics of stage-structured populations facing stage-specific variability in resource availability and/or demographic factors like unequal sex-ratios, remains poorly understood. We addressed these issues using a stage-structured individual-based model that incorporates life-history parameters common to many holometabolous insects. The model was calibrated using time series data from a 49-generation experiment on laboratory populations of Drosophila melanogaster, subjected to four different combinations of larval and adult nutritional levels. The model was able to capture multiple qualitative and quantitative aspects of the empirical time series across three independent studies. We then simulated the model to explore the interaction of various life-history parameters and nutritional levels in determining population stability. In all nutritional regimes, constancy stability of the populations was reduced upon increasing egg-hatchability, critical mass, and proportion of body resource allocated to female fecundity. However, the effects of increasing sensitivity of female-fecundity to adult density on constancy stability varied across nutrition regimes. The effects of unequal sex-ratio and sex-specific culling were greatly influenced by fecundity but not by levels of juvenile nutrition. Finally, we investigated the implications of some of these insights on the efficiency of the widely-used pest control method, the Sterile Insect Technique (SIT). We show that increasing the amount of juvenile food had no effects on SIT efficiency when the density-independent fecundity is low, but reduces SIT efficiency when the density-independent fecundity is high.

Viability of cyclic populations

Theory on viability of small populations is well developed and has led to the standard methodology of population viability analysis (PVA) to assess vulnerability of single species. However, more complex situations involving community dynamics or environmental change violate theoretical assumptions. Synthesizing concepts from population, community, and conservation ecology, we develop a generic theory on the viability of cyclic populations. The interplay of periodic population decline and demography causes varying risk patterns that aggregate during cycles and modify the temporal structure of viability. This variability is visualized and quantitatively assessed. For two standard viability metrics that summarize immediate extinction risk and the general long-term conditions of populations, we mathematically describe the impact of population cycles. Finally, we suggest and demonstrate PVA for cyclic populations that respond to, e.g., seasonality, interannual variation, or trophic interactions. Our theoretical and methodological advancement opens a route to viability analysis in food webs and trophic meta-communities and equips biodiversity conservation with a long-missing tool.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

A comparison of six methods for stabilizing population dynamics

Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very different concepts of stability, which makes it difficult to compare their relative efficiencies. Moreover, since the dynamics of populations are dependent on the life-history of the species and its environment, it is conceivable that the stabilizing effects of control methods would also be affected by such factors, a complication that has typically not been investigated. In this study, we compare six different control methods with respect to their efficiency at inducing a common level of enhancement (defined as 50% increase) for two kinds of stability (constancy and persistence) under four different life-history/environment combinations. Since these methods have been analytically studied elsewhere, we concentrate on an intuitive understanding of realistic simulations incorporating noise, extinction probability and lattice effect. We show that for these six methods, even when the magnitude of stabilization attained is the same, other aspects of the dynamics like population size distribution can be very different. Consequently, correlated aspects of stability, like the amount of persistence for a given degree of constancy stability (and vice versa) or the corresponding effective population size (a measure of resistance to genetic drift) vary widely among the methods. Moreover, the number of organisms needed to be added or removed to attain similar levels of stabilization also varies for these methods, a fact that has economic implications. Finally, we compare the relative efficiencies of these methods through a composite index of various stability related measures. Our results suggest that Lower Limiter Control (LLC) seems to be the optimal method under most conditions, with the recently proposed Adaptive Limiter Control (ALC) being a close second.

Stabilizing spatially-structured populations through adaptive Limiter Control

Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems are not applicable to real, biological populations. This is because such methods typically require detailed knowledge of system specific parameters and the ability to manipulate them in real time; conditions often not met by most real populations. Moreover, real populations are often noisy and extinction-prone, which can sometimes render such methods ineffective. Here, we investigate a control strategy, which works by perturbing the population size, and is robust to reasonable amounts of noise and extinction probability. This strategy, called the Adaptive Limiter Control (ALC), has been previously shown to increase constancy and persistence of laboratory populations and metapopulations of Drosophila melanogaster. Here, we present a detailed numerical investigation of the effects of ALC on the fluctuations and persistence of metapopulations. We show that at high migration rates, application of ALC does not require a priori information about the population growth rates. We also show that ALC can stabilize metapopulations even when applied to as low as one-tenth of the total number of subpopulations. Moreover, ALC is effective even when the subpopulations have high extinction rates: conditions under which another control algorithm had previously failed to attain stability. Importantly, ALC not only reduces the fluctuation in metapopulation sizes, but also the global extinction probability. Finally, the method is robust to moderate levels of noise in the dynamics and the carrying capacity of the environment. These results, coupled with our earlier empirical findings, establish ALC to be a strong candidate for stabilizing real biological metapopulations.