Simultaneous enhancement of multiple stability properties using two-parameter control methods in Drosophila melanogaster

Although a large number of methods have been proposed to control the non-linear dynamics of unstable populations, very few have been verified using biological populations. Here, we investigated the effects of two well-studied control methods (Both Limiter Control and Target-Oriented Control) on the dynamics of unstable populations of Drosophila melanogaster. We also perform biologically realistic simulations to ascertain the generalizability of our results. We show that both methods can significantly reduce population fluctuations, decrease extinction probability and increase effective population size simultaneously. This is in contrast with earlier studies on single parameter control methods that are not able to concurrently achieve multiple aspects of stability. We use the distribution of population sizes to derive biologically intuitive explanations for the mechanisms of how these two control methods attain stability. Finally, we show that non-Drosophila specific biologically realistic simulations are able to capture almost all the trends of our data. This shows that our results are likely generalizable over a wide range of taxa. Therefore, the control methods that incorporate both culling and restocking (like BLC and TOC) can simultaneously achieve multiple kinds of stability and therefore are strong candidates for field applications.     

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.     

Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions

Recent theoretical studies have shown contrasting effects of temporal correlation of environmental fluctuations (red noise) on the risk of population extinction. It is still debated whether and under which conditions red noise increases or decreases extinction risk compared with uncorrelated (white) noise. Here, we explain the opposing effects by introducing two features of red noise time series. On the one hand, positive autocorrelation increases the probability of series of poor environmental conditions, implying increasing extinction risk. On the other hand, for a given time period, the probability of at least one extremely bad year ("catastrophe") is reduced compared with white noise, implying decreasing extinction risk. Which of these two features determines extinction risk depends on the strength of environmental fluctuations and the sensitivity of population dynamics to these fluctuations. If extreme (catastrophic) events can occur (strong noise) or sensitivity is high (overcompensatory density dependence), then temporal correlation decreases extinction risk; otherwise, it increases it. Thus, our results provide a simple explanation for the contrasting previous findings and are a crucial step toward a general understanding of the effect of noise color on extinction risk.     

Local and Regional Determinants of Colonisation-Extinction Dynamics of a Riparian Mainland-Island Root Vole Metapopulation

The role of local habitat geometry (habitat area and isolation) in predicting species distribution has become an increasingly more important issue, because habitat loss and fragmentation cause species range contraction and extinction. However, it has also become clear that other factors, in particular regional factors (environmental stochasticity and regional population dynamics), should be taken into account when predicting colonisation and extinction. In a live trapping study of a mainland-island metapopulation of the root vole (Microtus oeconomus) we found extensive occupancy dynamics across 15 riparian islands, but yet an overall balance between colonisation and extinction over 4 years. The 54 live trapping surveys conducted over 13 seasons revealed imperfect detection and proxies of population density had to be included in robust design, multi-season occupancy models to achieve unbiased rate estimates. Island colonisation probability was parsimoniously predicted by the multi-annual density fluctuations of the regional mainland population and local island habitat quality, while extinction probability was predicted by island population density and the level of the recent flooding events (the latter being the main regionalized disturbance regime in the study system). Island size and isolation had no additional predictive power and thus such local geometric habitat characteristics may be overrated as predictors of vole habitat occupancy relative to measures of local habitat quality. Our results suggest also that dynamic features of the larger region and/or the metapopulation as a whole, owing to spatially correlated environmental stochasticity and/or biotic interactions, may rule the colonisation – extinction dynamics of boreal vole metapopulations. Due to high capacities for dispersal and habitat tracking voles originating from large source populations can rapidly colonise remote and small high quality habitat patches and re-establish populations that have gone extinct due to demographic (small population size) and environmental stochasticity (e.g. extreme climate events).     

Demographic consequences of population subdivision on the long-furred woolly mouse opossum (Micoureus paraguayanus) from the Atlantic Forest

Habitat destruction and fragmentation severely affected the Atlantic Forest. Formerly contiguous populations may become subdivided into a larger number of smaller populations, threatening their long-term persistence. The computer package VORTEX was used to simulate the consequences of habitat fragmentation and population subdivision on Micoureus paraguayanus, an endemic arboreal marsupial of the Atlantic Forest. Scenarios simulated hypothetical populations of 100 and 2000 animals being partitioned into 1–10 populations, linked by varying rates of inter-patch dispersal, and also evaluated male-biased dispersal. Results demonstrated that a single population was more stable than an ensemble of populations of equal size, irrespective of dispersal rate. Small populations (10–20 individuals) exhibited high instability due to demographic stochasticity, and were characterized by high rates of extinction, smaller values for metapopulation growth and larger fluctuations in population size and growth rate. Dispersal effects on metapopulation persistence were related to the size of the populations and to the sexes that were capable of dispersing. Male-biased dispersal had no noticeable effects on metapopulation extinction dynamics, whereas scenarios modelling dispersal by both sexes positively affected metapopulation dynamics through higher growth rates, smaller fluctuations in growth rate, larger final metapopulation sizes and lower probabilities of extinction. The present study highlights the complex relationships between metapopulation size, population subdivision, habitat fragmentation, rate of inter-patch dispersal and sex-biased dispersal and indicates the importance of gaining a better understanding of dispersal and its interactions with correlations between disturbance events.     

What happens if density increases? Conservation implications of population influx into refuges

Sudden catastrophic events like fires, hurricanes, tsunamis, landslides and deforestation increase population densities in habitat fragments, as fleeing animals encroach into these refuges. Such sudden overcrowding will trigger transient fluctuations in population size in the refuges, which may expose refuge populations to an increased risk of extinction. Until recently, detailed information about the operation of density dependence in stage-structured populations, and tools for quantifying the effects of transient dynamics, have not been available, so that exploring the extinction risk of such transient fluctuations has been intractable. Here, we use such recently developed tools to show that extinction triggered by overcrowding can threaten populations in refuges. Apart from situations where density dependence acts on survival, our results indicate that short-lived species may be more at risk than longer-lived species. Because dynamics in local populations may be critical for the preservation of metapopulations and rare species, we argue that this aspect warrants further attention from conservation biologists.     

Extinct or still out there? Disentangling influences on extinction and rediscovery helps to clarify the fate of species on the edge

Each year, two or three species that had been considered to be extinct are rediscovered. Uncertainty about whether or not a species is extinct is common, because rare and highly threatened species are difficult to detect. Biological traits such as body size and range size are expected to be associated with extinction. However, these traits, together with the intensity of search effort, might influence the probability of detection and extinction differently. This makes statistical analysis of extinction and rediscovery challenging. Here, we use a variant of survival analysis known as cure rate modelling to differentiate factors that influence rediscovery from those that influence extinction. We analyse a global data set of 99 mammals that have been categorized as extinct or possibly extinct. We estimate the probability that each of these mammals is still extant and thus estimate the proportion of missing (presumed extinct) mammals that are incorrectly assigned extinction. We find that body mass and population density are predictors of extinction, and body mass and search effort predict rediscovery. In mammals, extinction rate increases with body mass and population density, and these traits act synergistically to greatly elevate extinction rate in large species that also occurred in formerly dense populations. However, when they remain extant, larger‐bodied missing species are rediscovered sooner than smaller species. Greater search effort increases the probability of rediscovery in larger species of missing mammals, but has a minimal effect on small species, which take longer to be rediscovered, if extant. By separating the effects of species characteristics on extinction and detection, and using models with the assumption that a proportion of missing species will never be rediscovered, our new approach provides estimates of extinction probability in species with few observation records and scant ecological information.     

Genetic management of captive populations: the advantages of circular mating

We performed computer simulations to evaluate the effectiveness of circular mating as a genetic management option for captive populations. As a benchmark, we used the method proposed by Fernández and Caballero according to which parental contributions are set to produce minimum coancestry among the offspring and matings are performed so as to minimize mean pairwise coancestry (referred to as the Gc/mc method). In contrast to other methods, fitness does not vary with population size in the case of circular mating, and can be higher than under random mating. Whether circular mating is an effective method in conserving captive populations depends on the trade-off between different considerations. On the one hand, circular mating shows the highest allelic diversity and the lowest mean pairwise coancestry for all population sizes. It also shows a relatively higher efficiency of purging deleterious alleles. More importantly, circular mating can significantly increase the success probability of populations released to the wild relative to the Gc/mc method. On the other hand, circular mating has the drawback of showing high inbreeding rates and low fitness in early generations, which can result to an increase in the extinction probability of the captive populations. However, this increase is slight unless population size and litter size are both very low. Overall, if the slight increase in extinction probability can be tolerated then circular mating fulfils the primary goals of a captive breeding program, i.e., it maintains high levels of genetic diversity and increases the success probability of reintroduced populations.     

Demographic influences on mitochondrial DNA lineage survivorship in animal populations

Summary Probability models of branching processes and computer simulations of these models are used to examine stochastic survivorship of female lineages under a variety of demographic scenarios. A parameter II, defined as the probability of survival of two or more independent lineages over G generations, is monitored as a function of founding size of a population, population size at carrying capacity, and the frequency distributions of surviving progeny.Stochastic lineage extinction can be very rapid under certain biologically plausible demographic conditions. For stable-sized populations initiated by n females and/or regulated about carrying capacity k=n, it is highly probable that within about 4n generations all descendants will trace their ancestries to a single founder female. For a given mean family size, increased variance decreases lineage survivorship. In expanding populations, however, lineage extinction is dramatically slowed, and the final k value is a far more important determinant of II than is the size of the population at founding. The results are discussed in the context of recent empirical observations of low mitochondrial DNA (mtDNA) sequence heterogeneity in humans and expected distributions of asexually transmitted traits among sexually reproducing species.     

Allee effects and extinction in a lattice model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which the probability of extinction is greatly increased. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.     

Allee effects and extinction in a lattice model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which the probability of extinction is greatly increased. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.     

Scaling of the mean and variance of population dynamics under fluctuating regimes

Theoretical ecologists have long sought to understand how the persistence of populations depends on the interactions between exogenous (biotic and abiotic) and endogenous (e.g., demographic and genetic) drivers of population dynamics. Recent work focuses on the autocorrelation structure of environmental perturbations and its effects on the persistence of populations. Accurate estimation of extinction times and especially determination of the mechanisms affecting extinction times is important for biodiversity conservation. Here we examine the interaction between environmental fluctuations and the scaling effect of the mean population size with its variance. We investigate how interactions between environmental and demographic stochasticity can affect the mean time to extinction, change optimal patch size dynamics, and how it can alter the often-assumed linear relationship between the census size and the effective population size. The importance of the correlation between environmental and demographic variation depends on the relative importance of the two types of variation. We found the correlation to be important when the two types of variation were approximately equal; however, the importance of the correlation diminishes as one source of variation dominates. The implications of these findings are discussed from a conservation and eco-evolutionary point of view.     

Increased outbreak frequency associated with changes in the dynamic behaviour of populations of two aphid species

Sudden changes in the variability of natural populations can result in increased likelihood of extinction or in greater frequency and intensity of pest outbreaks. These changes could be associated with changes in some relevant population parameters such as the equilibrium density or the maximum population growth rate. However, changes in these parameters have very different consequences. An increase in equilibrium density results in a higher variance in population fluctuations according to the relationship between mean and variance described by Taylor's power law, but does not modify the stability properties of the system. On the other hand, changes in the maximum growth rate induce changes in the dynamic regimes and stability properties of the population. In this study, using statistical and mathematical methods borrowed from econometrics and engineering, we identify structural changes to the variance in the population dynamics of the sycamore aphid Drepanosiphum platanoidis and the green spruce aphid Elatobium abietinum in the UK. Some localities showed strong changes in their population parameters, such that their dynamic regime changed completely. These changes in the population dynamic regimes increase the expected frequency of outbreaks, which has enormous economic and ecological consequences. Through this study we show the application of methods that could be helpful to pest and wildlife managers in the task of evaluating changes in the risk of outbreaks or extinction of animal populations under changing global environmental scenarios.     

Metapopulation dynamics in a regional population of the blue-winged grasshopper (Oedipoda caerulescens; Linnaeus, 1758)

For two consecutive years we registered the presence (or absence) of blue winged grasshoppers (Oedipoda caerulescens; Linnaeus, 1758) on 312 habitat patches of differing size in a region of more than 3000 ha. The data show that presence of grasshoppers on a habitat patch is dependent on patch size as well as on patch isolation. We used an ecological incidence model to describe the metapopulation dynamics of the regional population and derived the parameters for this model from presence-absence data and observations of Oedipoda dispersion. The analysis shows that local extinction of grasshopper populations is influenced by strong fluctuations of environmental conditions and that for a number of small patches in our region recolonization is important for the presence of O. caerulescens. Colonization probability, as derived using the incidence model, is in good agreement with estimates from a population genetical analysis.     

Allee effects in stochastic populations

The Allee effect, or inverse density dependence at low population sizes, could seriously impact preservation and management of biological populations. The mounting evidence for widespread Allee effects has lately inspired theoretical studies of how Allee effects alter population dynamics. However, the recent mathematical models of Allee effects have been missing another important force prevalent at low population sizes: stochasticity. In this paper, the combination of Allee effects and stochasticity is studied using diffusion processes, a type of general stochastic population model that accommodates both demographic and environmental stochastic fluctuations. Including an Allee effect in a conventional deterministic population model typically produces an unstable equilibrium at a low population size, a critical population level below which extinction is certain. In a stochastic version of such a model, the probability of reaching a lower size a before reaching an upper size b , when considered as a function of initial population size, has an inflection point at the underlying deterministic unstable equilibrium. The inflection point represents a threshold in the probabilistic prospects for the population and is independent of the type of stochastic fluctuations in the model. In particular, models containing demographic noise alone (absent Allee effects) do not display this threshold behavior, even though demographic noise is considered an "extinction vortex". The results in this paper provide a new understanding of the interplay of stochastic and deterministic forces in ecological populations.     

Chaotic dynamics may determine the effect of inter-patch migration on metapopulation survival

A simple, strategic model of a system of habitat fragments connected by conservation corridors is presented. The intrinsic dynamics of the population on each fragment are stochastic. In addition, at each generation there is a probability of a catastrophic event occurring which affects all the habitat fragments by greatly reducing the size of the population on each. Global extinction is considered to occur when all the populations simultaneously fall below a threshold value. If the intrinsic dynamics on each fragment are simple cycles or a stable equilibrium, then the addition of conservation corridors does not reduce the frequency of global extinction. This is because migration between fragments induces their populations to have values which are similar to each other. However, if the intrinsic population dynamics are chaotic then the probability of global extinction is greatly reduced by the introduction of conservation corridors. Although local extinction is likely, the chaos acts to oppose the synchronising effect of migration. Often a subset of the populations survive a catastrophe and can recolonize the other patches.     

Effects of climate on population fluctuations of ibex

Predicting the effects of the expected changes in climate on the dynamics of populations require that critical periods for climate‐induced changes in population size are identified. Based on time series analyses of 26 Swiss ibex (Capra ibex) populations, we show that variation in winter climate affected the annual changes in population size of most of the populations after accounting for the effects of density dependence and demographic stochasticity. In addition, precipitation during early summer also influenced the population fluctuations. This suggests that the major influences of climate on ibex population dynamics operated either through loss of individuals during winter or early summer, or through an effect on fecundity. However, spatial covariation in these climate variables was not able to synchronize the population fluctuations of ibex over larger distances, probably due to large spatial heterogeneity in the effects of single climate variables on different populations. Such spatial variation in the influence of the same climate variable on the local population dynamics suggests that predictions of influences of climate change need to account for local differences in population dynamical responses to climatic conditions.     

Both population size and patch quality affect local extinctions and colonizations

Currently, the habitat of many species is fragmented, resulting in small local populations with individuals occasionally dispersing between the remaining habitat patches. In a solitary bee metapopulation, extinction probability was related to both local bee population sizes and pollen resources measured as host plant population size. Patch size, on the other hand, had no additional predictive power. The turnover rate of local bee populations in 63 habitat patches over 4 years was high, with 72 extinction events and 31 colonization events, but the pollen plant population was stable with no extinctions or colonizations. Both pollen resources and bee populations had strong and independent effects on extinction probability, but connectivity was not of importance. Colonizations occurred more frequently within larger host plant populations. For metapopulation survival of the bee, large pollen plant populations are essential, independent of current bee population size.     

The genetic underpinnings of population cyclicity: establishing expectations for the genetic anatomy of cycling populations

Despite extensive research into the mechanisms underlying population cyclicity, we have little understanding of the impacts of numerical fluctuations on the genetic variation of cycling populations. Thus, the potential implications of natural and anthropogenically‐driven variation in population cycle dynamics on the diversity and evolutionary potential of cyclic populations is unclear. Here, we use Canada lynx Lynx canadensis matrix population models, set up in a linear stepping‐stone, to generate demographic replicates of biologically realistic cycling populations. Overall, increasing cycle amplitude predictably reduced genetic diversity and increased genetic differentiation, with cyclic effects increased by population synchrony. Modest dispersal rates (1–3% of the population) between high and low amplitude cyclic populations did not diminish these effects suggesting that spatial variation in cyclic amplitude should be reflected in patterns of genetic diversity and differentiation at these rates. At high dispersal rates (6%) groups containing only high amplitude cyclic populations had higher diversity and lower differentiation than those mixed with low amplitude cyclic populations. Negative density‐dependent dispersal did not impact genetic diversity, but did homogenize populations by reducing differentiation and patterns of isolation by distance. Surprisingly, temporal changes in diversity and differentiation throughout a cycle were not always consistent with population size. In particular, negative density‐dependent dispersal simultaneously decreased differences in genetic diversity while increasing differences in genetic differentiation between numerical peaks and nadirs. Combined, our findings suggest demographic changes at fine temporal scales can impact genetic variation of interacting populations and provide testable predictions relating population cyclicty to genetic variation. Further, our results suggest that including realistic demographic and dispersal parameters in population genetic models and using information from temporal changes in genetic variation could help to discern complex demographic scenarios and illuminate population dynamics at fine temporal scales.     

EVOLUTIONARY RESPONSES TO ENVIRONMENTAL CHANGES: HOW DOES COMPETITION AFFECT ADAPTATION?

The role and importance of ecological interactions for evolutionary responses to environmental changes is to large extent unknown. Here it is shown that interspecific competition may slow down rates of adaptation substantially and fundamentally change patterns of adaptation to long-term environmental changes. In the model investigated here, species compete for resources distributed along an ecological niche space. Environmental change is represented by a slowly moving resource maximum and evolutionary responses of single species are compared with responses of coalitions of two and three competing species. In scenarios with two and three species, species that are favored by increasing resource availability increase in equilibrium population size whereas disfavored species decline in size. Increased competition makes it less favorable for individuals of a disfavored species to occupy a niche close to the maximum and reduces the selection pressure for tracking the moving resource distribution. Individual-based simulations and an analysis using adaptive dynamics show that the combination of weaker selection pressure and reduced population size reduces the evolutionary rate of the disfavored species considerably. If the resource landscape moves stochastically, weak evolutionary responses cause large fluctuations in population size and thereby large extinction risk for competing species, whereas a single species subject to the same environmental variability may track the resource maximum closely and maintain a much more stable population size. Other studies have shown that competitive interactions may amplify changes in mean population sizes due to environmental changes and thereby increase extinction risks. This study accentuates the harmful role of competitive interactions by illustrating that they may also decrease rates of adaptation. The slowdown in evolutionary rates caused by competition may also contribute to explain low rates of morphological change in spite of large environmental fluctuations found in fossil records.