Preventing extinction and outbreaks in chaotic populations

Intermittent instability is widespread in plankton communities

Chaotic dynamics appear to be prevalent in short-lived organisms including plankton and may limit long-term predictability. However, few studies have explored how dynamical stability varies through time, across space and at different taxonomic resolutions. Using plankton time series data from 17 lakes and 4 marine sites, we found seasonal patterns of local instability in many species, that short-term predictability was related to local instability, and that local instability occurred most often in the spring, associated with periods of high growth. Taxonomic aggregates were more stable and more predictable than finer groupings. Across sites, higher latitude locations had higher Lyapunov exponents and greater seasonality in local instability, but only at coarser taxonomic resolution. Overall, these results suggest that prediction accuracy, sensitivity to change and management efficacy may be greater at certain times of year and that prediction will be more feasible for taxonomic aggregates.

Management implications of long transients in ecological systems

The underlying biological processes that govern many ecological systems can create very long periods of transient dynamics. It is often difficult or impossible to distinguish this transient behaviour from similar dynamics that would persist indefinitely. In some cases, a shift from the transient to the long-term, stable dynamics may occur in the absence of any exogenous forces. Recognizing the possibility that the state of an ecosystem may be less stable than it appears is crucial to the long-term success of management strategies in systems with long transient periods. Here we demonstrate the importance of considering the potential of transient system behaviour for management actions across a range of ecosystem organizational scales and natural system types. Developing mechanistic models that capture essential system dynamics will be crucial for promoting system resilience and avoiding system collapses.

Enhancing population stability with combined adaptive limiter control and finding the optimal harvesting-restocking balance

Fluctuations in population size may have negative consequences (e.g., an increased risk of extinction or the occurrence of repeated outbreaks), and many management strategies are aimed at avoiding them by either only restocking or only harvesting the population. Two of these strategies are adaptive limiter control (ALC) and adaptive threshold harvesting (ATH). With ALC the population is controlled by only restocking and with ATH by only harvesting. We propose the strategy of combined adaptive limiter control (CALC) as the combination of ALC and ATH and study the potential advantages of CALC over ALC and ATH. We consider two different population models, namely a stochastic overcompensatory model and a host-pathogen-predator model. For the first model, our results show that the combination of restocking and harvesting under CALC improves the constancy stability of the managed populations when the harvesting and restocking intensities are high enough. Otherwise the effect is marginal or in rare cases negative. For the second model, we show that combining harvesting with restocking reduces the outbreak risk only if the harvesting intensity is low. For medium harvesting intensities the effect is marginal and for high harvesting intensities the risk of outbreaks is increased. In addition, we study the optimal harvesting-restocking balance by considering a proxy of the benefit obtained in terms of the reduction in the outbreak risk and the harvesting and restocking costs.

Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics

A new stage-structured model for the population dynamics of the mosquito (a major vector for numerous vector-borne diseases), which takes the form of a deterministic system of non-autonomous nonlinear differential equations, is designed and used to study the effect of variability in temperature and rainfall on mosquito abundance in a community. Two functional forms of eggs oviposition rate, namely the Verhulst-Pearl logistic and Maynard-Smith-Slatkin functions, are used. Rigorous analysis of the autonomous version of the model shows that, for any of the oviposition functions considered, the trivial equilibrium of the model is locally- and globally-asymptotically stable if a certain vectorial threshold quantity is less than unity. Conditions for the existence and global asymptotic stability of the non-trivial equilibrium solutions of the model are also derived. The model is shown to undergo a Hopf bifurcation under certain conditions (and that increased density-dependent competition in larval mortality reduces the likelihood of such bifurcation). The analyses reveal that the Maynard-Smith-Slatkin oviposition function sustains more oscillations than the Verhulst-Pearl logistic function (hence, it is more suited, from ecological viewpoint, for modeling the egg oviposition process). The non-autonomous model is shown to have a globally-asymptotically stable trivial periodic solution, for each of the oviposition functions, when the associated reproduction threshold is less than unity. Furthermore, this model, in the absence of density-dependent mortality rate for larvae, has a unique and globally-asymptotically stable periodic solution under certain conditions. Numerical simulations of the non-autonomous model, using mosquito surveillance and weather data from the Peel region of Ontario, Canada, show a peak mosquito abundance for temperature and rainfall values in the range [Formula: see text]C and [15-35] mm, respectively. These ranges are recorded in the Peel region between July and August (hence, this study suggests that anti-mosquito control effects should be intensified during this period).

Adaptive threshold harvesting and the suppression of transients

Fluctuations in population size are in many cases undesirable, as they can induce outbreaks and extinctions or impede the optimal management of populations. We propose the strategy of adaptive threshold harvesting (ATH) to control fluctuations in population size. In this strategy, the population is harvested whenever population size has grown beyond a certain proportion in comparison to the previous generation. Taking such population increases into account, ATH intervenes also at smaller population sizes than the strategy of threshold harvesting. Moreover, ATH is the harvesting version of adaptive limiter control (ALC) that has recently been shown to stabilize population oscillations in both experiments and theoretical studies. We find that ATH has similar stabilization properties as ALC and thus offers itself as a harvesting alternative for the control of pests, exploitation of biological resources, or when restocking interventions required from ALC are unfeasible. We present numerical simulations of ATH to illustrate its performance in the presence of noise, lattice effect, and Allee effect. In addition, we propose an adjustment to both ATH and ALC that restricts interventions when control seems unnecessary, i.e. when population size is too small or too large, respectively. This adjustment cancels prolonged transients.

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.

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

Constant immigration can stabilize population size fluctuations but its effects on extinction remain unexplored. We show that constant immigration significantly reduced extinction in fruitfly populations with relatively stable or unstable dynamics. In unstable populations with oscillations of amplitude around 1.5 times the mean population size, persistence and constancy were unrelated. Low immigration enhanced persistence without affecting constancy whereas high immigration increased constancy without enhancing persistence. In relatively stable populations with erratic fluctuations of amplitude close to the mean population size, both low and high immigration enhanced persistence. In these populations, the amplitude of fluctuations relative to mean population size went down due to immigration, and their dynamics were altered to low-period cycles. The effects of immigration on the population size distribution and intrinsic dynamics of stable versus unstable populations differed considerably, suggesting that the mechanisms by which immigration reduced extinction risk depended on underlying dynamics in complex ways.

Stabilizing biological populations and metapopulations through Adaptive Limiter Control

Despite great interest in techniques for stabilizing the dynamics of biological populations and metapopulations, very few practicable methods have been developed or empirically tested. We propose an easily implementable method, Adaptive Limiter Control (ALC), for reducing the magnitude of fluctuation in population sizes and extinction frequencies and demonstrate its efficacy in stabilizing laboratory populations and metapopulations of Drosophila melanogaster. Metapopulation stability was attained through a combination of reduced size fluctuations however, and synchrony at the subpopulation level. Simulations indicated that ALC was effective over a range of maximal population growth rates, migration rates and population dynamics models. Since simulations using broadly applicable, non-species-specific models of population dynamics were able to capture most features of the experimental data, we expect our results to be applicable to a wide range of species.

Optimizing molluscicide treatment strategies in different control stages of schistosomiasis in the People's Republic of China

BACKGROUND

The application of chemical molluscicides is still one of the most effective measures for schistosomiasis control in P. R. China. By applying diverse molluscicide treatment scenarios on different snail densities in the field, we attempted to understand the cost-effectiveness of molluscicide application so as to prescribe an optimal management approach to control intermediate host snail Oncomelania hupensis under acceptable thresholds based on the goal of the National Schistosomiasis Control Programme.

METHODS

The molluscicidal field trial was carried out in the marshland of an island along the Yangtze River, Jiangsu province, P.R. China in October 2010. Three plots in the island representing low-density, medium-density and high-density groups were identified after the baseline survey on snail density. Each snail density plot was divided into four experimental units in which molluscicide (50% niclosamide ethanolamine salt wettable powder) was applied once, twice, trice and four times, respectively. The logistic regression model to correlate snail mortality rate with the covariates of number of molluscicidal treatment and snail density, and a linear regression model to investigate the relationship between cost-effectiveness and number of molluscicidal treatment as well as snail density were established.

RESULTS

The study revealed that increase in the number of molluscicide treatments led to increased snail mortality across all three population density groups. The most cost-effective regimen was seen in the high snail density group with a single molluscicide treatment. For both high and low density groups, the more times molluscicide were applied, the less cost-effectiveness was. However, for the median density group, the level of cost-effectiveness for two applications was slightly higher than that in one time.

CONCLUSIONS

We concluded that different stages of the national schistosomiasis control/elimination programme, namely morbidity control, transmission control and transmission interruption, should utilize different molluscicide treatment strategies to maximize cost-effectiveness.

Global stabilization of fixed points using predictive control

We analyze the global stability properties of some methods of predictive control. We particularly focus on the optimal control function introduced by de Sousa Vieira and Lichtenberg [Phys. Rev. E 54, 1200 (1996)]. We rigorously prove that it is possible to use this method for the global stabilization of a discrete system x(n+1)=f(x(n)) into a positive equilibrium for a class of maps commonly used in population dynamics. Moreover, the controlled system is globally stable for all values of the control parameter for which it is locally asymptotically stable. Our study highlights the difficulty of obtaining global stability results for other methods of predictive control, where higher iterations of f are used in the control scheme.

Predicting the timing and magnitude of tropical mosquito population peaks for maximizing control efficiency

The transmission of mosquito-borne diseases is strongly linked to the abundance of the host vector. Identifying the environmental and biological precursors which herald the onset of peaks in mosquito abundance would give health and land-use managers the capacity to predict the timing and distribution of the most efficient and cost-effective mosquito control. We analysed a 15-year time series of monthly abundance of Aedes vigilax, a tropical mosquito species from northern Australia, to determine periodicity and drivers of population peaks (high-density outbreaks). Two sets of density-dependent models were used to examine the correlation between mosquito abundance peaks and the environmental drivers of peaks or troughs (low-density periods). The seasonal peaks of reproduction (r) and abundance () occur at the beginning of September and early November, respectively. The combination of low mosquito abundance and a low frequency of a high tide exceeding 7 m in the previous low-abundance (trough) period were the most parsimonious predictors of a peak's magnitude, with this model explaining over 50% of the deviance in . Model weights, estimated using AIC_c, were also relatively high for those including monthly maximum tide height, monthly accumulated tide height or total rainfall per month in the trough, with high values in the trough correlating negatively with the onset of a high-abundance peak. These findings illustrate that basic environmental monitoring data can be coupled with relatively simple density feedback models to predict the timing and magnitude of mosquito abundance peaks. Decision-makers can use these methods to determine optimal levels of control (i.e., least-cost measures yielding the largest decline in mosquito abundance) and so reduce the risk of disease outbreaks in human populations.

Mosquitoes carry several diseases that are potentially fatal to people. The risk of disease transmission is high when mosquitoes are abundant in an area, and it is therefore the job of health professionals to control or prevent mosquito outbreaks in certain areas, especially those close to human habitation. Biologists that study mosquito populations have the ability to predict peaks in mosquito population abundance by relating measures of these with environmental variables, such as tidal events and rainfall. Here we analysed data of mosquito (Aedes vigilax) populations from northern Australia over 15 years. We compared the highs and lows in mosquito numbers to possible drivers of these, such as tides. We found that low tide events prior to the mosquito peaks were followed by a boom in mosquito numbers. We also found the highest population growth rate is in September, which is two months earlier than the peak of mosquito abundance. Thus, following low tide events in the dry season, targeted control (such as spraying in earlier September) of mosquito breeding areas may allow for more effective control of mosquitoes close to human settlement, and therefore reduce the likelihood of disease outbreaks.

Endogenous and exogenous factors controlling temporal abundance patterns of tropical mosquitoes

The growing demand for efficient and effective mosquito control requires a better understanding of vector population dynamics and how these are modified by endogenous and exogenous factors. A long-term (11-year) monitoring data set describing the relative abundance of the saltmarsh mosquito (Aedes vigilax) in the greater Darwin region, northern Australia, was examined in a suite of Gompertz-logistic (GL) models with and without hypothesized environmental correlates (high tide frequency, rainfall, and relative humidity). High tide frequency and humidity were hypothesized to influence saltmarsh mosquito abundance positively, and rainfall was hypothesized to correlate negatively by reducing the availability of suitable habitats (moist substrata) required by ovipositing adult female mosquitoes. We also examined whether environmental correlates explained the variance in seasonal carrying capacity (K) because environmental stochasticity is hypothesized to modify population growth rate (r), carrying capacity, or both. Current and lagged-time effects were tested by comparing alternative population dynamics models using three different information criteria (Akaike's Information Criterion [corrected; AIC(c)], Bayesian Information Criterion [BIC], and cross-validation [C-V]). The GL model with a two-month lag without environmental effects explained 31% of the deviance in population growth rate. This increased to > 70% under various model combinations of high tide frequency, rainfall, and relative humidity, of which, high tide frequency and rainfall had the highest contributions. Temporal variation in K was explained weakly by high tide frequency, and there was some evidence that the filling of depressions to reduce standing water availability has reduced Aedes vigilax carrying capacity over the study period. This study underscores the need to consider simultaneously both types of drivers (endogenous and exogenous) when predicting mosquito abundance and population growth patterns. This work also indicates that climate change, via continued increases in rainfall and higher expected frequencies and intensities of high tide events with sea level rise, will alter mosquito abundance trends in northern Australia.