Effectiveness of Predator Removal for Enhancing Bird Populations

Abstract: Predation pressure on vulnerable bird species has made predator control an important issue for international nature conservation. Predator removal by culling or translocation is controversial, expensive, and time‐consuming, and results are often temporary. Thus, it is important to assess its effectiveness from all available evidence. We used explicit systematic review methodology to determine the impact of predator removal on four measurable responses in birds: breeding performance (hatching success and fledging success) and population size (breeding and postbreeding). We used meta‐analysis to summarize results from 83 predator removal studies from six continents. We also investigated whether characteristics of the prey, predator species, location, and study methodology explained heterogeneity in effect sizes. Removing predators increased hatching success, fledging success, and breeding populations. Removing all predator species achieved a significantly larger increase in breeding population than removing only a subset. Postbreeding population size was not improved on islands, or overall, but did increase on mainlands. Heterogeneity in effect sizes for the four population parameters was not explained by whether predators were native or introduced; prey were declining, migratory, or game species; or by the study methodology. Effect sizes for fledging success were smaller for ground‐nesting birds than those that nest elsewhere, but the difference was not significant. We conclude that current evidence indicates that predator removal is an effective strategy for the conservation of vulnerable bird populations. Nevertheless, the ethical and practical problems associated with predator removal may lead managers to favor alternative, nonlethal solutions. Research is needed to provide and synthesize data to determine whether these are effective management practices for future policies on bird conservation.     

The Effectiveness of Removing Predators to Protect Bird Populations

The control of predators for nature conservation purposes is becoming an increasingly important issue. The growing populations of predator species in some areas and the introduction of predators in other areas have led to concerns about their impact on vulnerable bird species and to the implementation of predator control in some cases. This is set against a background of increasingly fragmented semi-natural habitats and declining populations for many species. To assess the efficiency of predator removal as a conservation measure, the results of 20 published studies of predator removal programs were meta-analyzed. Removing predators had a large, positive effect on hatching success of the target bird species, with removal areas showing higher hatching success, on average, than 75% of the control areas. Similarly, predator removal increased significantly post-breeding population sizes (i.e. autumn densities) of the target bird species. The effect of predator removal on breeding population sizes was not significant, however, with studies differing widely in their reported effects. We conclude that predator removal often fulfills the goal of game management, which is to enhance harvestable post-breeding populations, but that it is much less consistent in achieving the usual aim of conservation managers, which is to maintain and, where appropriate, increase bird breeding population sizes. This may be due to inherent characteristics of avian population regulation, but also to ineffective predator removal and inadequate subsequent monitoring of the prey populations.     

Conservation Strategies for Species Affected by Apparent Competition

Apparent competition is an indirect interaction between 2 or more prey species through a shared predator, and it is increasingly recognized as a mechanism of the decline and extinction of many species. Through case studies, we evaluated the effectiveness of 4 management strategies for species affected by apparent competition: predator control, reduction in the abundances of alternate prey, simultaneous control of predators and alternate prey, and no active management of predators or alternate prey. Solely reducing predator abundances rapidly increased abundances of alternate and rare prey, but observed increases are likely short‐lived due to fast increases in predator abundance following the cessation of control efforts. Substantial reductions of an abundant alternate prey resulted in increased predation on endangered huemul (Hippocamelus bisulcus) deer in Chilean Patagonia, which highlights potential risks associated with solely reducing alternate prey species. Simultaneous removal of predators and alternate prey increased survival of island foxes (Urocyon littoralis) in California (U.S.A.) above a threshold required for population recovery. In the absence of active management, populations of rare woodland caribou (Rangifer tarandus caribou) continued to decline in British Columbia, Canada. On the basis of the cases we examined, we suggest the simultaneous control of predators and alternate prey is the management strategy most likely to increase abundances and probabilities of persistence of rare prey over the long term. Knowing the mechanisms driving changes in species’ abundances before implementing any management intervention is critical. We suggest scientists can best contribute to the conservation of species affected by apparent competition by clearly communicating the biological and demographic forces at play to policy makers responsible for the implementation of proposed management actions. Estrategias de Conservación para Especies Afectadas por Competencia Aparente     

Intraguild predation and mesopredator release effect on long-lived prey

Complete extirpation of a species can generate cascading effects throughout an ecosystem, yet are precisely the goal of island eradications of pest species. “Mesopredator release effect”, an asymmetrical special case of intraguild predation, has been hypothesised as a possible indirect effect from eradications, where superpredator removal can generate a mesopredator increase which may increase the impact on their shared prey. Theoretically this suggests that for intraguild predators, the superpredator may protect the shared prey from mesopredation, and removal of superpredators alone is not recommended. We create a model of long-lived age-structured shared prey and explore the non-equilibrium dynamics of this system. The superpredator can impact all prey life-stages (adult survival and reproductive success) whereas the smaller mesopredator can only impact early life-stages (reproductive success). This model is independently tested with data from a closed oceanic island system where eradication of introduced intraguild predators is possible for conservation of threatened birds. Mesopredator release only occurs in strongly top-down moderated (resource-abundant) systems. Even when mesopredator release can occur, the negative impact of more mesopredators is outweighed by the benefit of superpredator removal, allowing recovery of the prey population. Results are robust to 10% variation in model parameters. The consideration of age-structured prey contradicts previous theoretical results for mesopredator release effect and intraguild predation. Superpredator eradication is vital for population recovery of long-lived insular species. Nonetheless island conservation must retain a whole-ecosystem perspective given the complex trophic relationships among multiple species on islands.     

The Paradox of the Long‐Term Positive Effects of a North American Crayfish on a European Community of Predators

Abstract: Invasions of non‐native species are one of the major causes of losses of native species. In some cases, however, non‐natives may also have positive effects on native species. We investigated the potential facilitative effects of the North American red swamp crayfish (Procambarus clarkii) on the community of predators in southwestern Spain. To do so, we examined the diets of predators in the area and their population trends since introduction of the crayfish. Most predator species consumed red swamp crayfish, which sometimes occurred in over 50% of their diet samples. Moreover, the abundance of species preying on crayfish increased significantly in the area as opposed to the abundance of herbivores and to predator populations in other areas of Europe, where those predators are even considered threatened. Thus, we report the first case in which one non‐native species is both beneficial because it provides prey for threatened species and detrimental because it can drive species at lower trophic levels to extinction. Increases in predator numbers that are associated with non‐native species of prey, especially when some of these predators are also invasive non‐natives, may increase levels of predation on other species and produce cascading effects that threaten native biota at longer temporal and larger spatial scales. Future management plans should include the complexity of interactions between invasive non‐natives and the entire native community, the feasibility of successful removal of non‐native species, and the potential social and economic interests in the area.     

Geographical gradients in diet affect population dynamics of Canada lynx

Geographical gradients in the stability of cyclic populations of herbivores and their predators may relate to the degree of specialization of predators. However, such changes are usually associated with transition from specialist to generalist predator species, rather than from geographical variation in dietary breadth of specialist predators. Canada lynx (Lynx canadensis) and snowshoe hare (Lepus americanus) populations undergo cyclic fluctuations in northern parts of their range, but cycles are either greatly attenuated or lost altogether in the southern boreal forest where prey diversity is higher. We tested the influence of prey specialization on population cycles by measuring the stable carbon and nitrogen isotope ratios in lynx and their prey, estimating the contribution of hares to lynx diet across their range, and correlating this degree of specialization to the strength of their population cycles. Hares dominated the lynx diet across their range, but specialization on hares decreased in southern and western populations. The degree of specialization correlated with cyclic signal strength indicated by spectral analysis of lynx harvest data, but overall variability of lynx harvest (the standard deviation of natural-log-transformed harvest numbers) did not change significantly with dietary specialization. Thus, as alternative prey became more important in the lynx diet, the fluctuations became decoupled from a regular cycle but did not become less variable. Our results support the hypothesis that alternative prey decrease population cycle regularity but emphasize that such changes may be driven by dietary shifts among dominant specialist predators rather than exclusively through changes in the predator community.     

Influence of prey reserve capacity on predator–prey dynamics

In this article the dynamics of a predator and prey population has been modelled when a reserve is created to protect a certain number of prey population from predation. This investigation is essential to derive some guiding principles to conserve the prey population and also to understand the behaviour and dependence of predator population on the reserve capacity. The present study concerns analysis of a fairly general model and hence some of the existing results based on specific explicit models, like Lotka–Volterra model and Rosenzweig–MacArthur model, can be derived from this work. In this study, conditions have been derived for coexistence of predator and prey, and extinction of predators. Results are obtained for global stability of required equilibrium of the model. Also, a method is suggested to compute reserve capacity in order to drive the ecosystem state to a required level. The key results developed in this article have been illustrated using numerical simulation. These results can be interpreted in different contexts like resource conservation, pest management, bio-economics of a renewable resource, etc.     

Functional responses: a question of alternative prey and predator density

Throughout the study of ecology, there has been a growing realization that indirect effects among species cause complexity in food webs. Understanding and predicting the behavior of ecosystems consequently depends on our ability to identify indirect effects and their mechanisms. The present study experimentally investigates indirect interactions arising between two prey species that share a common predator. In a natural field experiment, we introduced different densities of mealworms (Tenebrio molitor), an alternative prey, to a previously studied predator-prey system in which paper wasps (Polistes dominulus) preyed on shield beetle larvae (Cassida rubiginosa). We tested if alternative prey affects predation on the first prey (i.e., the predator-dependent functional response of paper wasps) by modifying either interference among predators or the effective number of predators foraging on shield beetles. Presence of mealworms significantly reduced the effective number of predators, whereas predator interference was not affected. In this way, the experimentally introduced alternative prey altered the wasps' functional response and thereby indirectly influenced C. rubiginosa density. In all prey-density combinations offered, paper wasps constantly preferred T. molitor. This led to an asymmetrical, indirect interaction between both prey species: an increase in mealworm density significantly relaxed predation on C. rubiginosa, whereas an increase in C. rubiginosa density intensified predation on mealworms. Such asymmetrical outcomes of a fixed food preference can significantly affect the population dynamics of the species involved. In spite of the repeated finding of a Type III functional response in this system, our experiment did not reveal switching behavior in paper wasps. The variety of mechanisms underlying direct and indirect interactions within our study system exemplifies the importance of incorporating alternative prey when investigating the impact of a generalist predator on a focal prey population under realistic field conditions.     

The growth-predation risk trade-off under a growing gape-limited predation threat

Growth is a critical ecological trait because it can determine population demography, evolution, and community interactions. Predation risk frequently induces decreased foraging and slow growth in prey. However, such strategies may not always be favored when prey can outgrow a predator's hunting ability. At the same time, a growing gape-limited predator broadens its hunting ability through time by expanding its gape and thereby creates a moving size refuge for susceptible prey. Here, I explore the ramifications of growing gape-limited predators for adaptive prey growth. A discrete demographic model for optimal foraging/growth strategies was derived under the realistic scenario of gape-limited and gape-unconstrained predation threats. Analytic and numerical results demonstrate a novel fitness minimum just above the growth rate of the gape-limited predator. This local fitness minimum separates a slow growth strategy that forages infrequently and accumulates low but constant predation risk from a fast growth strategy that forages frequently and experiences a high early predation risk in return for lower future predation risk and enhanced fecundity. Slow strategies generally were advantageous in communities dominated by gape-unconstrained predators whereas fast strategies were advantageous in gape-limited predator communities. Results were sensitive to the assumed relationships between prey size and fecundity and between prey growth and predation risk. Predator growth increased the parameter space favoring fast prey strategies. The model makes the testable predictions that prey should not grow at the same rate as their gape-limited predator and generally should grow faster than the fastest growing gape-limited predator. By focusing on predator constraints on prey capture, these results integrate the ecological and evolutionary implications of prey growth in diverse predator communities and offer an explanation for empirical growth patterns previously viewed to be anomalies.     

Do mountain log skinks (<Emphasis Type="Italic">Pseudemoia entrecasteauxii</Emphasis>) modify their behaviour in the presence of two predators?

Prey often adopt antipredator strategies to reduce the likelihood of predation. In the presence of predators, prey may use antipredator strategies that are effective against a single predator (specific) or that are effective against several predators (nonspecific). Most studies have been confined to single predator environments although prey are often faced with multiple predators. When more than one predator is present, specific antipredator behaviours can conflict and avoidance of one predator may increase vulnerability to another. To test how prey cope with this dilemma, I recorded the behaviours of lizards responding to the nonlethal cues of a bird and snake presented singly and simultaneously. Lizards use specific and conflicting antipredator tactics when confronted with each predator, as evidenced by refuge use. However, when both predators were present, lizards refuge use was the same as in the predator-free environment, indicating that they abandoned refuge use as a primary mechanism for predator avoidance. In the presence of both predators, they reduced their overall movement and time spent thermoregulating. This shift in behaviour may represent a compromise to minimize overall risk, following a change in predator exposure. This provides evidence of plasticity in lizard antipredator behaviour and shows that prey responses to two predators cannot be accurately predicted from what is observed when only one predator is present.Communicated by W. Cooper     

Species identity dominates the relationship between predator biodiversity and herbivore suppression

Agricultural pest suppression is an important ecosystem service that may be threatened by the loss of predator diversity. This has stimulated interest in the relationship between predator biodiversity and biological control. Multiple-predator studies have shown that predators may complement or interfere with one another, but few experiments have determined if the resulting effects on prey are caused by changes in predator abundance, identity, species richness, or some combination of these factors. We experimentally isolated the effect of predator species richness on the biological control of an important agricultural pest, the green peach aphid. We found no evidence that increasing predator species richness affects aphid biological control; overall there was no strong complementarity or interference among predator species that altered the strength of aphid suppression. Instead, our experiments revealed strong effects of predator species identity, because predators varied dramatically in their per capita consumption rates. Our results are consistent with other multiple-predator studies finding strong species-identity effects and suggest that, for the biological control of aphids, conservation strategies that directly target key species will be more effective than those targeting predator biodiversity more broadly.     

The value of flexibility in conservation financing

Land‐acquisition strategies employed by conservation organizations vary in their flexibility. Conservation‐planning theory largely fails to reflect this by presenting models that are either extremely inflexible—parcel acquisitions are irreversible and budgets are fixed—or extremely flexible—previously acquired parcels can readily be sold. This latter approach, the selling of protected areas, is infeasible or problematic in many situations. We considered the value to conservation organizations of increasing the flexibility of their land‐acquisition strategies through their approach to financing deals. Specifically, we modeled 2 acquisition‐financing methods commonly used by conservation organizations: borrowing and budget carry‐over. Using simulated data, we compared results from these models with those from an inflexible fixed‐budget model and an extremely flexible selling model in which previous acquisitions could be sold to fund new acquisitions. We then examined 3 case studies of how conservation organizations use borrowing and budget carry‐over in practice. Model comparisons showed that borrowing and budget carry‐over always returned considerably higher rewards than the fixed‐budget model. How they performed relative to the selling model depended on the relative conservation value of past acquisitions. Both the models and case studies showed that incorporating flexibility through borrowing or budget carry‐over gives conservation organizations the ability to purchase parcels of higher conservation value than when budgets are fixed without the problems associated with the selling of protected areas.     

Evaluating impacts of forage fish abundance on marine predators

Forage fish—small, low trophic level, pelagic fish such as herrings, sardines, and anchovies—are important prey species in marine ecosystems and also support large commercial fisheries. In many parts of the world, forage fish fisheries are managed using precautionary principles that target catch limits below the maximum sustainable yield. However, there are increasing calls to further limit forage fish catch to safeguard their fish, seabird, and marine mammal predators. The effectiveness of these extra-precautionary regulations, which assume that increasing prey abundance increases predator productivity, are under debate. In this study, we used prey-linked population models to measure the influence of forage fish abundance on the population growth rates of 45 marine predator populations representing 32 fish, seabird, and mammal species from 5 regions around the world. We used simulated data to confirm the ability of the statistical model to accurately detect prey influences under varying levels of influence strength and process variability. Our results indicate that predator productivity was rarely influenced by the abundance of their forage fish prey. Only 6 predator populations (13% of the total) were positively influenced by increasing prey abundance and the model exhibited high power to detect prey influences when they existed. These results suggest that additional limitation of forage fish harvest to levels well below sustainable yields would rarely result in detectable increases in marine predator populations.     

Wolves-coyotes-foxes: a cascade among carnivores

Due to the widespread eradication of large canids and felids, top predators in many terrestrial ecosystems are now medium-sized carnivores such as coyotes. Coyotes have been shown to increase songbird and rodent abundance and diversity by suppressing populations of small carnivores such as domestic cats and foxes. The restoration of gray wolves to many parts of North America, however, could alter this interaction chain. Here we use a 30-year time series of wolf, coyote, and fox relative abundance from the state of Minnesota, USA, to show that wolves suppress coyote populations, which in turn releases foxes from top-down control by coyotes. In contrast to mesopredator release theory, which has often considered the consequence of top predator removal in a three-species interaction chain (e.g., coyote-fox-prey), the presence of the top predator releases the smaller predator in a four-species interaction chain. Thus, heavy predation by abundant small predators might be more similar to the historical ecosystem before top-predator extirpation. The restructuring of predator communities due to the loss or restoration of top predators is likely to alter the size spectrum of heavily consumed prey with important implications for biodiversity and human health.     

Predators choosing between patches with standing crop: the influence of switching rules and input types

Where prey arriving in a patch are not consumed immediately, they will accumulate. Predators are then presented with a prey density or standing crop that increases through further input, and decreases through the consumption by predators. Firstly, I show that the switching rule of predators has a significant influence on the expected predator equilibrium distribution in such a dynamic system. Three rules are compared; for all rules, analytical solutions are calculated (where possible). To test their plausibility for natural situations, predator distributions are simulated given the assumption that each predator obtains individual patch profitability estimates by using a common learning rule. As long as prey arrive in the patches in constant numbers per time unit, the first rule leads to input matching because predators stop switching when consumption in the two patches is equal. The other two rules, where predators continue to sample both patches even in the equilibrium state, lead to predator distributions where the more profitable patch is underused. The final equilibrium depends on the exact assumptions of the switching rule; however, it is independent of interference. But if the input delivered into a patch is a function of the current prey standing crop (for example in a reproducing prey population), predator and prey distributions will not reach an equilibrium in most cases: either standing crops increase indefinitely, or they approach zero, with all predators concentrating on the better patch. Only a small number of parameter sets show intermediate crops that are reasonably stable. With this input type, only up to 54% of the simulations reach the expected distribution. In a system with competition for dynamic standing crop, it is therefore essential to know the type of input and the switching-rule used by predators to be able to predict equilibrium predator distributions. Received: 17 March 1995/Accepted after revision: 5 November 1995     

Drivers of Seabird Population Recovery on New Zealand Islands after Predator Eradication

Eradication of introduced mammalian predators from islands has become increasingly common, with over 800 successful projects around the world. Historically, introduced predators extirpated or reduced the size of many seabird populations, changing the dynamics of entire island ecosystems. Although the primary outcome of many eradication projects is the restoration of affected seabird populations, natural population responses are rarely documented and mechanisms are poorly understood. We used a generic model of seabird colony growth to identify key predictor variables relevant to recovery or recolonization. We used generalized linear mixed models to test the importance of these variables in driving seabird population responses after predator eradication on islands around New Zealand. The most influential variable affecting recolonization of seabirds around New Zealand was the distance to a source population, with few cases of recolonization without a source population ≤25 km away. Colony growth was most affected by metapopulation status; there was little colony growth in species with a declining status. These characteristics may facilitate the prioritization of newly predator‐free islands for active management. Although we found some evidence documenting natural recovery, generally this topic was understudied. Our results suggest that in order to guide management strategies, more effort should be allocated to monitoring wildlife response after eradication. Conductores de la Recuperación de Poblaciones de Aves Marinas en Islas de Nueva Zelanda después de la Erradicación de Depredadores     

A review of predator diet effects on prey defensive responses

Numerous studies have examined how predator diets influence prey responses to predation risk, but the role predator diet plays in modulating prey responses remains equivocal. We reviewed 405 predator–prey studies in 109 published articles that investigated changes in prey responses when predators consumed different prey items. In 54 % of reviewed studies, prey responses were influenced by predator diet. The value of responding based on a predator’s recent diet increased when predators specialized more strongly on particular prey species, which may create patterns in diet cue use among prey depending upon whether they are preyed upon by generalist or specialist predators. Further, prey can alleviate costs or accrue greater benefits using diet cues as secondary sources of information to fine tune responses to predators and to learn novel risk cues from exotic predators or alarm cues from sympatric prey species. However, the ability to draw broad conclusions regarding use of predator diet cues by prey was limited by a lack of research identifying molecular structures of the chemicals that mediate these interactions. Conclusions are also limited by a narrow research focus. Seventy percent of reviewed studies were performed in freshwater systems, with a limited range of model predator–prey systems, and 98 % of reviewed studies were performed in laboratory settings. Besides identifying the molecules prey use to detect predators, future studies should strive to manipulate different aspects of prey responses to predator diet across a broader range of predator–prey species, particularly in marine and terrestrial systems, and to expand studies into the field.     

Prey–predator dynamics with predator switching regulated by a catabolic repression control mode

Since many predators can live under certain circumstances as saprophytes or consume more than one prey, and different enzymes are generally required for each prey or nutrient digestion, the predator must be sufficiently adaptive for effective utilization of the prey mass. Control modes as induction and repression, however, act at the level of genes and cause changes in the biosynthesis rate of these enzymes. In this work, an extension of the catabolic repression control mode from the level of genes to the level of the behavior of the predator is proposed, in order to model the balanced attack of the predator on the prey. It is demonstrated that, when the prey population has the competitive advantage over the predator (in using the common substrate), the catabolic repression mechanism favors the prey population, which dominates over the predator even at low specific dilution rate values, whereas, the stable steady or periodic coexistence state is not favored. When the predator has the competitive advantage at low substrate concentrations and the prey at high substrate concentrations, the introduction of the catabolic repression mechanism in the model again favors the stable steady state of the prey, while the coexistence region is dramatically reduced. Conversely, when the prey population has the competitive advantage at low and the predator at high substrate concentrations, dominance of prey and coexistence steady state could be favored by the catabolic repression mechanism. It is concluded that the catabolic repression control favors dominance of the prey population and, under certain circumstances, coexistence of both prey and predator populations.     

Conservation of Marine Megafauna through Minimization of Fisheries Bycatch

Abstract: Many populations of marine megafauna, including seabirds, sea turtles, marine mammals, and elasmobranchs, have declined in recent decades due largely to anthropogenic mortality. To successfully conserve these long‐lived animals, efforts must be prioritized according to feasibility and the degree to which they address threats with the highest relative impacts on population dynamics. Recently, Wilcox and Donlan (2007, Frontiers in Ecology and the Environment) and Donlan and Wilcox (2008, Biological Invasions) proposed a conservation strategy of “compensatory mitigation” in which fishing industries offset bycatch of seabirds and sea turtles by funding eradication of invasive mammalian predators from the terrestrial reproductive sites of these marine animals . Although this is a creative and conceptually compelling approach, we find it flawed as a conservation tool because it has narrow applicability among marine megafauna, it does not address the most pervasive threats to marine megafauna, and it is logistically and financially infeasible. Invasive predator eradication does not adequately offset the most pressing threat to most marine megafauna populations—fisheries bycatch. For seabird populations, fisheries bycatch and invasive predators infrequently are overlapping threats. Invasive predators have limited population‐level impacts on sea turtles and marine mammals and no impacts on elasmobranchs, all of which are threatened by bycatch. Implementing compensatory mitigation in marine fisheries is unrealistic due to inadequate monitoring, control, and surveillance in the majority of fleets. Therefore, offsetting fisheries bycatch with eradication of invasive predators would be less likely to reverse population declines than reducing bycatch. We recommend that efforts to mitigate bycatch in marine capture fisheries should address multiple threats to sensitive bycatch species groups, but these efforts should first institute proven bycatch avoidance and reduction methods before considering compensatory mitigation.     

A predator-prey model with satiation and intraspecific competition

We present a new predator-prey model where, except for the prey growth, assumed to be logistic, we endeavor to give some behavioral justification to all elements of the predator-prey interaction. The functional response takes account of predator satiation and predator competition. It is supported by some experimental evidence. We distinguish two contributions to the numerical response: the positive part, proportional to the functional response, is the birth rate of predators; the negative part is the death rate due to hunger.Two outcomes are possible. If the prey are unable to grow fast enough to replace the amount killed by the predators, both species become extinct. In the opposite case, both populations stabilize at a constant population. At this equilibrium level, the prey are not abundant enough to satiate the predators.The predation rate that allows the highest predator population is one half of the ideal prey growth rate. A higher exploitation rate can allow higher populations only temporarily. Evolved predator behavior, reguges for the prey, or other mechanisms can explain this regulation.Two more population behaviors (cycles and predator extinction) can be obtained with a time-lag in one of the responses. This is shown in a separate paper.The model is structurally stable. It can thus withstand small environmental perturbations.