The hydra effect in predator–prey models

The seemingly paradoxical increase of a species population size in response to an increase in its mortality rate has been observed in several continuous-time and discrete-time models. This phenomenon has been termed the “hydra effect”. In light of the fact that there is almost no empirical evidence yet for hydra effects in natural and laboratory populations, we address the question whether the examples that have been put forward are exceptions, or whether hydra effects are in fact a common feature of a wide range of models. We first propose a rigorous definition of the hydra effect in population models. Our results show that hydra effects typically occur in the well-known Gause-type models whenever the system dynamics are cyclic. We discuss the apparent discrepancy between the lack of hydra effects in natural populations and their occurrence in this standard class of predator–prey models.     

Predator–prey system with strong Allee effect in prey

Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

The effect of learning and search images on predator–prey interactions

In dealing with the spatial and temporal variability of prey species, predators may be able to forage optimally if they have flexible and rapid behavioral plasticity rather than predetermined responses. For predators that learn to focus attention on the cryptic prey type most frequently encountered during recent searching (termed a “search image”), rare prey types may be overlooked because of a focus on more common prey. Search imaging reflects biased searching for one of a number of available prey types, and has been studied widely in birds and mammals. Here we discuss the significant implications of this phenomenon for insect predator–prey systems, particularly with respect to parasitic wasps searching for host species using learned olfactory cues. We (1) review studies about perceptual development through individual ontogeny, (2) define the term “search image” and discuss the cognitive mechanisms involved in search-image formation, (3) discuss the role of search images and frequency-dependent predation as a proximate mechanism in the maintenance of prey diversity, (4) examine data on host–parasitoid olfactory search imaging, and (5) conclude by identifying important research areas for future studies in the field of olfactory search images.     

The “acid growth effect” and geotropism

Summary The curvature developed by segments of sunflower hypocotyl exposed to gravitational stimulus was enhanced in buffer solutions between pH 3.4 and 4.0 in the absence of added auxin. This effect was observed both when the segments were submerged during the stimulus and when they floated near the surface of the solution. 5–10 min in a horizontal position was sufficient to induce subsequent curvature.Straight growth of the segments was also promoted in buffers of this pH range.The acid effect on curvature was insensitive to KAsO₂, HgCl₂ and cycloheximide, inhibitors which drastically reduced auxin-induced curvature. Furthermore, acid buffer, but not auxin, restored the ability of segments taken from etiolated and starved plants to respond to gravity. These results suggest that the polarisation following gravistimulus may not be resticted to the asymmetric distribution of auxin and auxin co-factors but may involve a general physiological asymmetry.     

Do stabilimenta in orb webs attract prey or defend spiders?

Orb-weaving spiders are ideal organisms for the study of conflictbetween behavioral investments in foraging and defense becausetheir webs provide physical manifestations of those investments.We examined the impact of including stabilimenta, designs ofbright-white noncapture silk, at the center of orb webs forforaging and defense in Argiope aurantia. Our findings suggestthat stabilimentum building is a defensive behavior, supportingthe "web advertisement" hypothesis that the high visibilityof stabilimenta can prevent birds from flying through webs.Yet, spiders often do not include stabilimenta in their webs,indicating that a serious cost is associated with them. We alsoshow, through comparison of paired webs with and without stabilimenta,that stabilimenta reduce the prey capture success of spidersby almost 30%. This demonstrates the potential impact that defensivebehaviors of spiders can have on their foraging success andsuggests that much of the variation in stabilimenta may be accountedfor by a cost—benefit trade-off made when including stabilimentain webs.     

The role of noise in a predator–prey model with Allee effect

The existence and implications of alternative stable states in ecological systems have been investigated extensively within deterministic models. However, it is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. Thus, in this paper, we study the role of noise on the pattern formation of a spatial predator–prey model with Allee effect. The obtained results show that the spatially extended system exhibits rich dynamic behavior. More specifically, the stationary pattern can be induced to be a stable target wave when the noise intensity is small. As the noise intensity is increased, patchy invasion emerges. These results indicate that the dynamic behavior of predator–prey models may be partly due to stochastic factors instead of deterministic factors, which may also help us to understand the effects arising from the undeniable susceptibility to random fluctuations of real ecosystems.     

The “survivor effect” and the evolution of parthenogenesis and self-fertilization

Parthenogenetic or self-fertilizing species are often reduced to small numbers of survivors or colonists. These types of reproduction may therefore evolve because they eliminate problems of finding a mate. It is argued here that outbreeding populations which are often reduced to a few survivors will experience heavy offspring losses when population expansion occurs. This ‘survivor effect’ results from the production of many individuals homozygous for deleterious mutations (i.e. inbreeding depression). Parthenogenetic and selfing species do not experience a “survivor effect”. This effect together with mate-finding problems will tend to cause the evolution of parthenogenesis and selfing in weedy or colonizing species.     

The effect of alternative prey on the dynamics of imperfect Batesian and Müllerian mimicries

Both Batesian and Müllerian mimicries are considered classical evidence of natural selection where predation pressure has, at times, created a striking similarity between unrelated prey species. Batesian mimicry, in which palatable mimics resemble unpalatable aposematic species, is parasitic and only beneficial to the mimics. By contrast, in classical Müllerian mimicry the cost of predators' avoidance learning is shared between similar unpalatable co-mimics, and therefore mimicry benefits all parties. Recent studies using mathematical modeling have questioned the dynamics of Müllerian mimicry, suggesting that fitness benefits should be calculated in a way similar to Batesian mimicry; that is, according to the relative unpalatability difference between co-mimics. Batesian mimicry is very sensitive to the availability of alternative prey, but the effects of alternative prey for Müllerian dynamics are not known and experiments are rare. We designed two experiments to test the effect of alternative prey on imperfect Batesian and Müllerian mimicry complexes. When alternative prey were scarce, imperfect Batesian mimics were selected out from the population, but abundantly available alternative prey relaxed selection against imperfect mimics. Birds learned to avoid both Müllerian models and mimics irrespective of the availability of alternative prey. However, the rate of avoidance learning of models increased when alternative prey were abundant. This experiment suggests that the availability of alternative prey affects the dynamics of both Müllerian and Batesian mimicry, but in different ways.     

The effect of angiotensin II and indomethacin on immunoreactive prostaglandin “A” levels in man

The effect of angiotensin II on peripheral levels of immunoreactive prostaglandin A₂ (IR-PGA) was determined in 17 normal male volunteers. IR-PGA rose from 338 ± 65 (SE) pg/ml to 635 ± 142 in response to pressor infusions of angiotensin II (p <0.05 on paired analysis). This increase was not observed when indomethacin, 75 mg p.o., was given to 8 patients two hours prior to a repeat infusion. Five patients of the original group were placed on a low sodium diet (10–20 mEq). The response to angiotensin was now exaggerated (278 ±52 pg/ml to 916 ± 284). These five patients were kept on a low sodium intake and given indomethacin 50 mg p.o. q 6 hourly for 4 days. There was no significant rise with angiotensin infusion (106 ± 31 pg/ml to 120 ± 70). Pressor infusions of angiotensin II raise peripheral levels of IR-PGA, and this response is exaggerated by a low sodium diet and blocked by either acute or chronic indomethacin administration. This data supports the concept that vasodilatory prostaglandins may be released by endogenous angiotensin and thus provide a dynamic antagonism to the renin angiotensin system in man.     

Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species

In this paper, a predator–prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.     

Pattern formation in a space- and time-discrete predator–prey system with a strong Allee effect

The spatiotemporal dynamics of a space- and time-discrete predator–prey system is considered theoretically using both analytical methods and computer simulations. The prey is assumed to be affected by the strong Allee effect. We reveal a rich variety of pattern formation scenarios. In particular, we show that, in a predator–prey system with the strong Allee effect for prey, the role of space is crucial for species survival. Pattern formation is observed both inside and outside of the Turing domain. For parameters when the local kinetics is oscillatory, the system typically evolves to spatiotemporal chaos. We also consider the effect of different initial conditions and show that the system exhibits a spatiotemporal multistability. In a certain parameter range, the system dynamics is not self-organized but remembers the details of the initial conditions, which evokes the concept of long-living ecological transients. Finally, we show that our findings have important implications for the understanding of population dynamics on a fragmented habitat.     

The effect of prolonged “bleaching” on skeletal banding and stable isotopic composition in Montastrea annularis

X-radiography and carbon and oxygen stable isotope analysis have been used to examine the effects of prolonged bleaching on the growth rate and chemical composition of the skeleton of the massive reef coral, Montastrea annularis. The post-bleaching linear growth of one colony that remained bleached for 10 to 12 months following the 1987 Caribbean-wide bleaching event was only 37% of mean annual growth from pre-bleaching years, and was manifest as a loss of the following year's low density band. Two colonies that did not bleach (normal) and two that bleached and regained their coloration (recovered) had linear growth rates over the same period that were 81 to 98% of mean pre-bleaching annual growth. Linear growth by a third recovered coral was 66% of pre-bleaching growth. No sub-annual stress bands were associated with the bleaching. The skeleton of the bleached colony had carbon and oxygen isotopic compositions that were reduced in range and enriched (increased) in both ¹³C and ¹⁸O in the post-bleaching year. The skeletons of two of the nine colonies, one bleached and one recovered, had depleted (reduced) ¹⁸O values (-5.3 and -4.8%., respectively) during the bleaching episode that agree with the suggestion that positive temperature anomalies occurred during, and may have caused, the bleaching event. The range and values for all other normal and recovered corals, however, were not different between the post-bleaching year and previous years. Our data suggest that stress bands and isotopic analysis of coral skeletons may not always be reliable tools for examining the occurrence, cause or effects of certain discrete stress events that may interrupt skeletal growth.     

The effect of prior experience on a prey’s current perceived risk

The prior experience of prey may influence how they assess the level of predation risk associated with an information source. Here, I present the results from a set of experiments that demonstrate how the prior experience of green frog (Rana clamitans) tadpoles can influence their risk assessment during exposure to the chemical cue of predatory larval dragonflies (Anax spp.) consuming conspecific tadpoles. At the short-term scale, green frog tadpoles perceived a higher level of risk when consecutive cue exposures overlapped, but only when the total chemical cue concentration was weak. Weaker chemical cue concentrations may be less reliable than stronger cue concentrations, and overlapping cue exposures may increase the degree of certainty that tadpoles have in their perceived risk. When consecutive cue exposures did not overlap, tadpoles assessed the risk associated with each cue exposure independently. Predator-conditioned tadpoles responded longer during exposure to the Anax chemical cue than nonconditioned tadpoles, which suggests that a tadpole’s long-term experience eventually does influence its risk assessment. In general, the results suggest that a prey’s prior experience may influence its current perceived risk by influencing either the degree of certainty in or the level of its perceived risk. Understanding how the prior experience of prey influences their current risk assessment requires that the rate of decay of the value of prior experience should be identified at two timescales as an indicator of the current level of predation risk.     

Predator–prey systems in streams and rivers

Many predator–prey systems are found in environments with a predominantly unidirectional flow such as streams and rivers. Alterations of natural flow regimes (e.g., due to human management or global warming) put biological populations at risk. The aim of this paper is to devise a simple method that links flow speeds (currents) with population retention (persistence) and wash-out (extinction). We consider systems of prey and specialist, as well as generalist, predators, for which we distinguish the following flow speed scenarios: (a) coexistence, (b) persistence of prey only or (c) predators only (provided they are generalists), and (d) extinction of both populations. The method is based on a reaction–advection–diffusion model and traveling wave speed approximations. We show that this approach matches well spread rates observed in numerical simulations. The results from this paper can provide a useful tool in the assessment of instream flow needs, estimating the flow speed necessary for preserving riverine populations.     

Gloom and doom? The future of marine capture fisheries

Predicting global fisheries is a high-order challenge but predictions have been made and updates are needed. Past forecasts, present trends and perspectives of key parameters of the fisheries--including potential harvest, state of stocks, supply and demand, trade, fishing technology and governance--are reviewed in detail, as the basis for new forecasts and forecasting performance assessment. The future of marine capture fisheries will be conditioned by the political, social and economic evolution of the world within which they operate. Consequently, recent global scenarios for the future world are reviewed, with the emphasis on fisheries. The main driving forces (e.g. global economic development, demography, environment, public awareness, information technology, energy, ethics) including aquaculture are described. Outlooks are provided for each aspect of the fishery sector. The conclusion puts these elements in perspective and offers the authors' personal interpretation of the possible future pathway of fisheries, the uncertainty about it and the still unanswered questions of direct relevance in shaping that future.