Hydra Effect Research Articles

Bubbling and hydra effect in a population system with Allee effect

We present a continuous time predator-prey model and predator’s growth subjected to component Allee effect. The model also includes density dependent mortality of predator. We investigate our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect. In our system, we find that a fixed point representing the extinction of predator is always a stable point. When coexistence equilibria exists our system is bistable. We have observed that tristability is possible for our model that includes two stable co-existence fixed point. The most important phenomena which we have observed are hydra effect and cascading effect. Due to component Allee effect in predator the system shows multiple hydra effect. We discuss the phenomenon of bubbling, which indicates increasing and decreasing of amplitudes of cycles. We have presented one-parametric as well as two-parametric bifurcation diagram and also all possible bifurcations that the system could go through.

Bifurcations and hydra effects in Bazykin’s predator–prey model

We consider Bazykin’s model to address harvesting induced stability exchanges through bifurcation analysis. We examine the existence of hydra effects and analyze the stock pattern under predator harvesting. Prey harvesting cannot produce hydra effects in our model, whereas predator harvesting may cause multiple hydra effects. Our study reveals that type II response function and mutual interference among predators jointly induce multiple hydra effects and bistability. Bifurcations such as single Hopf-bifurcation, multiple Hopf-bifurcations and multiple saddle–node bifurcations appear for increasing harvesting rate on the predators. However, over-exploitation of the predators cannot generate any such bifurcation in our study. In simulations, the maximum sustainable yield (MSY) exists at a globally stable state. When predator is culled under increasing effort, basin of attraction of the equilibrium corresponding to the higher predator stock gets expanded, which alternatively is in favor of stock benefit for predators. The ecological theory developed in this study might be useful to understand conservation policy and fishery management.

Stage-specific overcompensation, the hydra effect, and the failure to eradicate an invasive predator

As biological invasions continue to increase globally, eradication programs have been undertaken at significant cost, often without consideration of relevant ecological theory. Theoretical fisheries models have shown that harvest can actually increase the equilibrium size of a population, and uncontrolled studies and anecdotal reports have documented population increases in response to invasive species removal (akin to fisheries harvest). Both findings may be driven by high levels of juvenile survival associated with low adult abundance, often referred to as overcompensation. Here we show that in a coastal marine ecosystem, an eradication program resulted in stage-specific overcompensation and a 30-fold, single-year increase in the population of an introduced predator. Data collected concurrently from four adjacent regional bays without eradication efforts showed no similar population increase, indicating a local and not a regional increase. Specifically, the eradication program had inadvertently reduced the control of recruitment by adults via cannibalism, thereby facilitating the population explosion. Mesocosm experiments confirmed that adult cannibalism of recruits was size-dependent and could control recruitment. Genomic data show substantial isolation of this population and implicate internal population dynamics for the increase, rather than recruitment from other locations. More broadly, this controlled experimental demonstration of stage-specific overcompensation in an aquatic system provides an important cautionary message for eradication efforts of species with limited connectivity and similar life histories.

How intra-stage and inter-stage competition affect overcompensation in density and hydra effects in single-species, stage-structured models

Understanding and predicting responses to increased mortality is important for conservation biology and population management strategies. In stage-structured populations, increased mortality of a particular stage can have the counterintuitive effect of causing increased abundance in one or more stages (called stage-specific overcompensation in density) or the whole population (called a hydra effect). We analyzed an n-stage, single-species, ordinary differential equation model in order to explore the mechanisms driving overcompensation in density and hydra effects in stage-structured populations. We find that in the absence of inter-stage competition, overcompensation in density only occurs if intra-stage competition in one stage is sufficiently strong to cause overcompensation in the maturation or reproductive rate of that stage (i.e., increased input causes decreased output for that stage). When there is inter-stage competition, overcompensation in density can also be driven by sufficiently strong inter-stage competition, even in the absence of overcompensation in any ecological rate. Hydra effects arise under the same conditions and are more likely to be caused by sufficiently strong intra-stage competition. We interpret our results in terms of the direct and indirect effects between stages, which helps clarify the relationships between stage-specific overcompensation in density, overcompensation in ecological rates and hydra effects.

Stability switching and hydra effect in a predator–prey metapopulation model

A metapopulation model is investigated to explore how the spatial heterogeneity affects predator–prey interactions. A Rosenzweig–MacArthur (RM) predator–prey model with dispersal of both the prey and predator is formulated. We propose such a system as a well mixed spatial model. Here, partially mixed spatial models are defined in which the dispersal of only one of the communities (prey or predator) is considered. In our study, the spatial heterogeneity is induced by dissimilar (unbalanced) dispersal rates between the patches. A large difference between the predator dispersal rates may stabilize the unstable positive equilibrium of the model. The existence of two ecological phenomena are found under independent harvesting strategy: stability switching and hydra effect. When prey or predator is harvested in a heterogenious environment, a positive stable steady state becomes unstable with increasing the harvesting effort, and a further increase in the effort leads to a stable equilibrium. Thus, a stability switching happens. Furthermore, the predator biomass (at stable state) in both the patches (and hence total predator stock) increases when the patch with a higher predator density is harvested; resulting a hydra effect. These two phenomena do not occur in the non-spatial RM model. Hence, spatial heterogeneity induces stability switching and hydra effect.

DETERMINISTIC PREDATOR–PREY MODELS WITH DISEASE IN THE PREY POPULATION

A class of deterministic predator–prey systems, where the prey population is subject to an infectious disease, is studied. The disease can be transmitted both horizontally and vertically within the host population but cannot be spread between the two trophic levels. Using the mathematical tools of uniform persistence, we derive sufficient conditions for which the interacting populations can coexist. Criteria based on model parameters for which either only the infected prey or healthy prey persists are also provided. It is found through numerical investigations that predation can change competition outcomes between healthy and infected prey populations. Depending on the parameter regimes and initial conditions, predation can either eradicate or promote the disease. As infected prey provides a resource for the predators, disease may promote persistence of the predators. However, infected prey may dominate the predator–prey community if disease is very infectious. In addition, disease in the prey population can mediate a hydra effect in predators and may induce chaotic interactions.

Characterizing the existence of hydra effect in spatial predator-prey models and the influence of functional response types and species dispersal

The hydra effect in ecology corresponds to the increase in the equilibrium or time-averaged density of a population when its mortality rate is augmented. The literature presents examples of the hydra effect in continuous as well as in discrete time population models described by nonlinear systems of ordinary differential and difference equations, respectively. The novelty of this work is that we show by means of numerical simulation the occurrence of the hydra effect in some stationary dynamics of one dimensional reaction-diffusion predator-prey models described by nonlinear systems of partial differential equations with distinct nonlinear functional responses. Reaction-diffusion models are a set of mathematical models that take into account population dynamics and dispersal (diffusivity) within a predefined spatial domain. We show that for a type 2 functional response an increasing diffusivity shortens the range of the hydra effect. Another interesting result concerns the fact that, together with the hydra effect, the prey density also increases with the increase of the per capita density-independent mortality rate of the predator. This result indicates that this top-down disturbance does not necessarily create a trophic cascade in a spatial predator-prey interaction at the steady-state regime.

Disrupting the ethnographic imaginarium: Challenges of immersion in the Silk Road cryptomarket community

This paper is a contemplation of a digital ethnography with the community surrounding Silk Road, the first widely used cryptomarket for drugs on the Dark Web. To position the study within the broader field of illegal anthropology, it provides links between the existing literature on the study of cryptomarkets with relevant anthropological scholarship. A theory of piracy is interrogated for its explanatory capacity of the digital pirates of the Dark Web. The start of the study unexpectedly coincided with the FBI seizure of Silk Road in October 2013. The field site disappearance provoked a practice-based and conceptual rewiring. The paper unpacks how the ‘hydra effect’ introduced to conceptualise resilient innovation within cryptomarkets can also apply to the multiplicity of identities linked to research practice. This effect also raises how the knowledge production within digital ethnographic practice may be reconfigured through notions of opportunism, replication, obsolescence, regeneration, iteration, adaptation and proliferation.

Dynamics of stage-structure predator-prey systems under density-dependent effect and mortality

We develop a four dimensional predator-prey system in continuous time with stage-structure for both the communities. The reproduction rate of the prey and the transition rate for the predator, in our model, are assumed to be density-dependent. The stability results for the coexisting equilibrium are obtained by making use of Routh–Hurwitz criteria. Because of the density-dependent effects, numerical simulations are applied in complex situations. We observe that increasing values of the coefficients linked with density-dependent term promote the stability of the coexisting steady state. Our main focus is to understand the variation of stocks when mortality rates on different stage classes are increased. We verified that stable stock on mature predator increases with its increasing mortality rate in three different modeling frameworks. However, no such positive effect on the biomass of the immature predator occurs when immature predators are removed, culled or harvested. Therefore, we could conclude that the appearance of hydra effect on many unstructured predator-prey models is due to the mortality of the mature predator only. No hydra effect is also detected when mature prey is removed in several situations we discussed. Overall, the obtained results are new and could be interesting contribution in theoretical ecology.

Hydra effects in stable food chain models

In this paper, we explore the occurrence of the hydra effect in food chains, a popular research theme in the current decade. The hydra effect, one of the paradoxical results in theoretical and applied ecology refers to the fact where increasing mortality rate on a population enhances its own stock. The main focus is to propose a dynamical system model of food chain showing a stable steady state and estimate the variation of stock of targeted species with increasing mortality. In our model, the per capita growth rate of any predator trophic level does not depend upon its density. The prey–predator model incorporating such a feature for predator growth is referred to as ‘pure predator system’ (see Sieber and Hilker (2012), J. Math. Biol. (2012) 64: 341–360, Journal of Mathematical Biology). Keeping the above feature in mind, we study a Rosenweig-MacArthur food chain model with logistic prey growth and Holling type II functional responses. It is shown that hydra effect at stable state appears on (a) prey in a four-trophic system, (b) first predator in a five-trophic system, and (c) prey and second predator in a six-trophic system. Xiao and Cao (2009) (Mathematical and Computer Modelling 50 (2009) 360–379) established that limit cycle may be observed due to harvesting in a system with the ratio-dependent prey-predator system (example of a non “non-pure predator system”). Therefore, if harvesting causes instability on some range of mortality rate, the hydra effect cannot occur at a stable state. Some results show that the unique stable steady state in our model remains stable under harvesting of either trophic level. As a whole, our investigations have some contribution in understanding population interactions, fishery management and biological pest control tactic.

How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects.

Population responses to environmental change depend on both the ecological interactions between species and the evolutionary responses of all species. In this study, we explore how evolution in prey, predators, or both species affect the responses of predator populations to a sustained increase in mortality. We use an eco-evolutionary predator-prey model to explore how evolution alters the predator extinction threshold (defined as the minimum mortality rate that prevents population growth at low predator densities) and predator hydra effects (increased predator abundance in response to increased mortality). Our analysis identifies how evolutionary responses of prey and predators individually affect the predator extinction threshold and hydra effects, and how those effects are altered by interactions between the evolutionary responses. Based on our theoretical results, we predict that it is common in natural systems for evolutionary responses in one or both species to allow predators to persist at higher mortality rates than would be possible in the absence of evolution (i.e., evolution increases the predator mortality extinction threshold). We also predict that evolution-driven hydra effects occur in a minority of natural systems, but are not rare. We revisited published eco-evolutionary models and found that evolution causes hydra effects and increases the predator extinction threshold in many studies, but those effects have been overlooked. We discuss the implications of these results for species conservation, predicting population responses to environmental change, and the possibility of evolutionary rescue.

Hydra effect and paradox of enrichment in discrete-time predator-prey models

We develop three discrete-time predator-prey models from the Nicholson–Bailey host-parasitoid framework, assuming a type II functional response and logistic prey growth in form of the Beverton–Holt map. Our models show many similarities with the continuous-time Rosenzweig–MacArthur model, not only the same equilibria and sequence of bifurcations, but also phenomena such as the hydra effect and paradox of enrichment. Our three models differ in the order of events, in which the processes of density-dependent prey regulation and predation take place. When their order is reversed, but their relative order remains the same such that only census timing is changed, we observe quantitative differences in population size, but no differences in qualitative behaviour. When a modified order of events induces delayed density dependence, we observe increased stability of population dynamics, which is somewhat contrary to conventional expectation. Overall, our models exhibit behaviour analogous to the Rosenzweig–MacArthur model and highlight the importance of the order of events in discrete-time models.

Effects of larval density on a natural population of Culex restuans (Diptera: Culicidae): No evidence of compensatory mortality.

1. We investigated the effects of strong density-dependence on larval growth, development, and survival of the mosquito Culex restuans (Theobald). We tested the hypothesis that density reduction early in larval development could result in as many or more individuals surviving to adulthood (compensation or overcompensation, respectively), or increased reproductive performance via rapid development and greater adult size. 2. In a field study of a natural population of C. restuans we tested for the effects of a 75% lower density on percent survivorship to adulthood, number of adults, development time, adult size, adult longevity, and size dependent fecundity. 3. We found no evidence for compensation or overcompensation in adult production, nor for effects of lower density on percent survivorship. Low density yielded significant increases in adult size, adult longevity, and size-dependent fecundity, and a decrease in development time. 4. Estimated per capita population growth rate was significantly greater in the low-density treatment than in the high-density treatment. We infer this difference resulted from greater per capita resources increasing female size and fecundity, and reducing development time. Greater per capita population growth could therefore result from early mortality of larvae, meaning that the hydra effect, which predicts greater equilibrium population with, as opposed to without, extrinsic mortality, may be possible for these mosquitoes.

Mode change in the dynamics of exploited limited population with age structure

This study focuses on the dynamics of exploited limited population with age structure and compares dynamic modes of population models with and without exploitation while considering age-specific harvesting. Transcritical, period-doubling, and Neimark–Sacker bifurcations occur in the population models. In the case of juvenile harvest, the way of stability loss does not depend on the harvest rate. However, in the case of adult harvest, the hydra effect occurs, which is an increase in harvest rate that subsequently increases the stationary size of the young group. As a rule, harvesting leads to dynamics stabilization. However, the models reveal multistability. Hence, in the case of exploitation, different dynamic modes can occur with their attraction basins at the same population parameter values. Irregular harvesting or a changing harvest rate may also result in fluctuations in exploited population size because the current population size can shift from one attraction basin to another. Controlling exploited population dynamics is sufficient to shift and retain the population number to within the attraction basin of the dynamic mode selected.

How can mortality increase population size? A test of two mechanistic hypotheses.

Overcompensation occurs when added mortality increases survival to the next life-cycle stage. Overcompensation can contribute to the Hydra effect, wherein added mortality increases equilibrium population size. One hypothesis for overcompensation is that added mortality eases density dependence, increasing survival to adulthood ("temporal separation of mortality and density dependence"). Mortality early in the life cycle is therefore predicted to cause overcompensation, whereas mortality later in the life cycle is not. Another hypothesis for overcompensation is that threat of mortality (e.g., from predation) causes behavioral changes that reduce overexploitation of resources, allowing resource recovery, and increasing production of adults ("prudent resource exploitation"). Behaviorally active predation cues alone are therefore predicted to cause overcompensation. We tested these predictions in two experiments with larvae of two species of Aedes. As predicted, early mortality yielded greater production of adults, and of adult females, and greater estimated rate of population increase than did later mortality. Addition of water-borne predation cues usually reduced browsing on surfaces in late-stage larvae, but contrary to prediction, resulted in neither significantly greater production of adult mosquitoes nor significantly greater estimated rate of increase. Thus we have strong evidence that timing of mortality contributes to overcompensation and the Hydra effect in mosquitoes. Evidence that predation cues alone can result in overcompensation via prudent resource exploitation is lacking. We expect the overcompensation in response to early mortality will be common in organisms with complex life cycles, density dependence among juveniles, and developmental control of populations.

Multiple hydra effect in a predator–prey model with Allee effect and mutual interference in the predator

In this work we show by means of numerical bifurcation analysis that two alternative stable states exhibit a hydra effect in a continuous time predator-prey model with Allee effect and mutual interference in the predator. We denote this behavior as multiple hydra effect. In addition, it is also shown that there are no cascading effects along the multiple hydra effect interval. In other words, besides the multiple hydra effect, there is a positive correlation between predator and prey densities when the density independent per capita mortality rate of the predator is increased.

Population extinctions can increase metapopulation persistence.

Metapopulations persist when local populations are rapidly recolonized following local extinctions. Such persistence requires asynchrony; simultaneous crashes of all populations would leave no source of recolonization. We show theoretically and experimentally that catastrophic population extinctions themselves can promote metapopulation persistence, by preventing spatial synchrony and thus enhancing recolonization. We refer to this behaviour as the 'spatial hydra effect': as with the mythical hydra that grows two new heads when one is removed, extinctions can increase recolonization. The effect is robust, occurring in a wide range of theoretical models exhibiting cyclic or quasi-cyclic population dynamics. In a laboratory microcosm experiment using cyclic protist predator-prey metapopulations, catastrophic perturbations wiping out populations but leaving the patch otherwise unchanged increased metapopulation persistence when high dispersal rates would otherwise have led to spatially synchronous extinctions of all populations. We discuss several candidate examples of the spatial hydra effect in nature.

When Predators Help Prey Adapt and Persist in a Changing Environment.

To persist in a changing world, populations must adapt. The ability to adapt is influenced by interactions with other species, such as predators. Recent experiments and theory suggest that selective pressures arising from predation may help prey adapt phenotypically to changing environments, but how this influences persistence remains unclear. In particular, it has not yet been shown whether predator-induced adaptation can outweigh predator-imposed reductions in population size, allowing prey to persist when they would otherwise go extinct. Here we examine if (and if so, how) predation can enhance the ability of prey to persist in a directionally changing environment. To do so, we extend a single-species quantitative-genetics framework that predicts rates of environmental change beyond which populations go extinct. While we assume predation decreases prey density, we find that predators can indeed help prey persist if they sufficiently increase prey adaptedness (decrease phenotypic lag). We show two ways this can occur: (1) the selective push, in which predators consume maladapted individuals and thus add selection that pushes the mean prey trait toward its optimum; and (2) the evolutionary hydra effect, when predation reduces prey density and thereby increases prey birthrate, allowing more selective events per unit time and effectively reducing generation time. We also discuss how our results apply more broadly to sources of mortality beyond predation.

Prey dynamics under generalist predator culling in stage structured models

In this paper, by means of mathematical dynamical models we investigate the impacts of predator culling on a prey population structured in two stage classes, juveniles and adults, assuming stage specific predation by two generalist predators with functional responses types 2 and 3 in all possible combinations. According to the chosen set of parameter values, these impacts can manifest through possible demographic Allee effects, sustained population oscillations, alternative stable states (e.g., predator-pit-like behavior) and Hydra effect, which are all discussed, in turn, in terms of species conservation, harvest yield and pest biological control

Effects of strength and timing of harvest on seasonal population models: stability switches and catastrophic shifts

Population abundance of many species is controlled by a combination of density-dependent processes during different periods of the annual cycle. In the context of population exploitation or conservation programs, sequential density dependence has the potential to dramatically change population responses to harvesting. Looking for a better understanding of the potential effects of harvesting on the dynamics of seasonal populations, we carry out a theoretical analysis of a discrete model for a semelparous population with an annual cycle involving three discrete density-dependent events: breeding, natural mortality, and harvesting. Our study reveals how the interplay between the model parameters determines the importance of harvest timing on stability and population abundance, especially when two nontrivial stable equilibria coexist. We address the possibility for compensatory mortality and report different forms of the hydra effect, including non-smooth ones due to catastrophic shifts. These drastic switches may include hysteresis, which has important implications for conservation goals. Regarding variability, we show that increasing the harvesting effort may either stabilize or destabilize the population, and these effects strongly depend on harvest timing and natural mortality rates. Our results also emphasize the importance of sampling populations after every discrete event occurs during one cycle. Indeed, though the dynamics are not affected by census timing, the model shows that changes in population abundance in response to changes in harvesting pressure are substantially different depending on when population is sampled. Thus, a manager would receive different (and sometimes contradictory) messages depending on census time, which could lead to managing mistakes.