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.     

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.     

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.     

When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect

The phenomenon of a population increasing in response to an increase in its per-capita mortality rate has recently been termed the 'hydra effect'. This article reviews and unifies previous work on this phenomenon. Some discrete models of density-dependent growth were shown to exhibit hydra effects in 1954, but the topic was then ignored for decades. Here the history of research on the hydra effect is reviewed, and the key factors producing it are explored. Mortality that precedes overcompensatory density dependence always has the potential to produce hydra effects. Even when mortality follows density dependence, hydra effects may occur in unstable systems due to changes in the amplitude and/or form of population cycles. An increase in resource productivity due to lower consumption rates following increased consumer mortality can also produce a hydra effect. Lower consumption can come about as the result of increased satiation of the consumers or changes in behaviour of either consumer or resource species that reduce the mean attack rate. Changes in species composition of a resource community may also decrease the average attack rate. Population structure can promote hydra effects by allowing separation of the timing of density dependence and mortality, although stage-specific density dependence usually decreases hydra effects.     

Interaction strength revisited—clarifying the role of energy flux for food web stability

Interaction strength (IS) has been theoretically shown to play a major role in governing the stability and dynamics of food webs. Nonetheless, its definition has been varied and problematic, including a range of recent definitions based on biological rates associated with model parameters (e.g., attack rate). Results from food web theory have been used to argue that IS metrics based on energy flux ought to have a clear relationship with stability. Here, we use simple models to elucidate the actual relationship between local stability and a number of common IS metrics (total flux and per capita fluxes) as well as a more recently suggested metric. We find that the classical IS metrics map to stability in a more complex way than suggested by existing food web theory and that the new IS metric has a much clearer, and biologically interpretable, relationship with local stability. The total energy flux metric falls off existing theoretical predictions when the total resource productivity available to the consumer is reduced despite increased consumer attack rates. The density of a consumer can hence decrease when its attack rate increases. This effect, called the paradox of attack rate, is similar to the well-known hydra effect and can even cascade up a food chain to exclude a predator when consumer attack rate is increased.     

pH值对大乳头水螅种群增长、无性生殖及3种抗氧化酶活力的影响

应用种群累积培养法,就培养液pH值对大乳头水螅（Hydra magnipapillata）的生存、种群增长、无性生殖以及水螅的超氧化物歧化酶（SOD）、过氧化氢酶（CAT）、谷胱甘肽过氧化物酶（GSH—PX）3种抗氧化酶活力的影响进行了探讨。结果表明,水螅存活的pH上限为10．5,下限为4．0,水螅存活的最适pH范围为5．5～9．5;pH值对水螅种群增长有显著影响,种群密度及种群瞬时增长率均随pH的不同而明显改变。培养15d后,除了pn4．0时水螅种群为负增长外,其他pH梯度下的水螅种群为正增长,其中pH6．5时水螅种群密度最高。以pH6．5为起始点,随着培养液酸性或碱性的增强,水螅种群密度整体都呈递减趋势。水螅SOD活力的转折点在pH6．5,当pH值偏离6．5时（酸性或碱性增强）,水螅SOD活力整体呈明显上升趋势;但水螅GSH—PX和CAT活力的转折点却在pH7．0,当pH值偏离7．0时（酸性或碱性增强）GSH—PX和CAT活力整体呈明显下降趋势。pH6．5时水螅SOD活力最低与pH6．5实验组水螅的无性出芽生殖率最高之间可能存在一定的内在联系。本文研究结果可为实验室培养水螅提供适宜的pH值指标。     

The Visually Mediated Escape Response in Fish: Predicting Prey Responsiveness and the Locomotor Behaviour of Predators and Prey

The outcome of predator-prey encounters is determined by a number of factors related to the locomotor and sensory performance of the animals. Escape responses can be triggered visually, i.e. by the magnifying retinal image of an approaching object (i.e. a predator), called the looming effect, and calculated as the rate of change of the angle subtended by the predator frontal profile as seen by the prey. A threshold of looming angle (ALT, the Apparent Looming Threshold) determines the reaction distance of a startled fish, which is proportional to the attack speed of the predator and its apparent frontal profile. Optimal tactics for predator attacks as well as consideration on their functional morphology are discussed in relation to ALT. Predator optimal attack speeds depend on predator morphology as well as the prey ALT. Predictions on the scaling of ALT suggest that ALT may increase (i.e. implying a decrease in reaction distance) with prey size in cases in which predator attack speeds are high (i.e. > 4 L/s in a 1-m long predator), while it may be relatively independent of prey size when predators attack at lower speeds. The issue of scaling of ALT is discussed using examples from field and laboratory studies. While the timing of the escape is a crucial issue for avoiding being preyed upon, the direction of escape manoeuvres may also determine the success of the escape. A simple theoretical framework for optimal escape trajectories is presented here and compared with existing data on escape trajectories of fish reacting to startling stimuli.     

Inducible defenses: continuous reaction norms or threshold traits?

Phenotypically plastic traits can be expressed as continuous reaction norms or as threshold traits, but little is known about the selective conditions that favor one over the other. We study this question using a model of prey defenses in which prey can induce any level of defense conditional on cues that are informative of local predator density. The model incorporates a trade-off between defense expression and fecundity and feedback between the defense level of prey and predator attack rates. Both continuous reaction norms and threshold traits can emerge as evolutionarily stable solutions of defense induction, and we show that the shape of the trade-off curve plays a key role in determining the outcome. Threshold traits are favored when selection is disruptive. Ecological conditions that favor defense dimorphisms in the absence of cues will favor threshold traits in the presence of slightly informative cues. We caution that continuous reaction norms and threshold traits may result in similar patterns of defense expression at the population level, and we discuss potential pitfalls of inferring reaction norm type from observational data.     

光周期对中国水螅种群增长、无性出芽生殖及抗氧化酶活力的影响

单细胞真核绿藻在中国水螅(Hydra sinensis)内胚层皮肌细胞中共生是有较高科研价值的特殊生物学现象。水螅宿主细胞为共生藻提供CO2、氮源及矿物质,而共生藻通过光合作用可能为宿主提供碳水化合物等有机物营养,因此水螅与共生藻间代谢流是以共生藻光合作用为中心,但基于代谢流二者间的互作机制目前尚未阐明。水螅通过营养积累进行出芽生殖,从母体脱落的芽体数量间接反映水螅营养积累的相对量。而光暴露时长能影响共生绿藻光合作用,如果共生藻的确能向水螅细胞转移光合作用产物,那光暴露时长应该能间接影响水螅的营养积累、从而进一步影响水螅无性出芽生殖。为证实该假说,本研究应用种群累积培养法,观察了光周期对中国水螅种群增长、无性出芽生殖及抗氧化酶(SOD和CAT)活力的影响。结果显示,光周期对中国水螅种群增长具有明显的影响。培养15 d后,所有实验组水螅的种群密度均为正增长,其中8L∶16D(在一个24h周期内光暴露8 h、黑暗16 h)实验组种群密度最大、而0L∶24D(持续黑暗)实验组种群密度最小。另外,随着光暴露时长的增加,中国水螅SOD及CAT活力整体均呈下降趋势。结果表明,从光周期对中国水螅无性出芽生殖及两种抗氧化酶活力的影响来看,中国水螅对光周期的生理学响应较为敏感,这个现象可能源于共生绿藻能通过向宿主细胞转移光合作用产物的方式为水螅提供营养补充。     

Habitat heterogeneity and mammalian predator–prey interactions

• 1 In predator–prey theory, habitat heterogeneity can affect the relationship between kill rates and prey or predator density through its effect on the predator's ability to search for, encounter, kill and consume its prey. Many studies of predator–prey interactions include the effect of spatial heterogeneity, but these are mostly based on species with restricted mobility or conducted in experimental settings.
• 2 Here, we aim to identify the patterns through which spatial heterogeneity affects predator–prey dynamics and to review the literature on the effect of spatial heterogeneity on predator–prey interactions in terrestrial mammalian systems, i.e. in freely moving species with high mobility, in non‐experimental settings. We also review current methodologies that allow the study of the predation process within a spatial context.
• 3 When the functional response includes the effect of spatial heterogeneity, it usually takes the form of predator‐dependent or ratio‐dependent models and has wide applicability.
• 4 The analysis of the predation process through its different stages may further contribute towards identifying the spatial scale of interest and the specific spatial mechanism affecting predator–prey interactions.
• 5 Analyzing the predation process based on the functional response theory, but separating the stages of predation and applying a multiscale approach, is likely to increase our insight into how spatial heterogeneity affects predator–prey dynamics. This may increase our ability to forecast the consequences of landscape transformations on predator–prey dynamics.

     

Organelle survival in a foreign organism: Hydra nematocysts in the flatworm Microstomum lineare

Nematocysts are characteristic organelles of the phylum cnidaria. They are designated kleptocnidae when sequestered in animals that feed on cnidaria. Kleptocnidae are known for more than a century. Nevertheless it is still enigmatic how selected nematocyst types survive in the predator and how they reach their final destination in the foreign body. In the free-living Platyhelminth Microstomum lineare the fate of nematocysts of the prey Hydra oligactis was analyzed at the ultrastructural level and by fluorescence microscopy using hydra polyps that had been stained in vivo with the fluorescent dyes TROMI and TRITC. M. lineare digested hydra tissue in its intestine within 30?min and all nematocyst types were phagocytosed without adherent cytoplasm by intestinal cnidophagocytes. Desmoneme and isorhiza nematocysts were digested whereas cnidophagocytes containing the venom-loaded stenotele nematocysts started to migrate out of the intestinal epithelia through the parenchyma to the epidermis thereby traversing the subintestinal and subepidermal muscle layer. Within one to two days, M. lineare began to form a muscle layer basolateral around epidermal cnidophagocytes. Epidermal stenoteles survived in M. lineare for at least four weeks. The ability of epidermal stenotele nematocysts to discharge suggest that this hydra organelle preserved its physiological properties in the new host.     

Harvesting,census timing and “hidden” hydra effects

Population control in some form of harvesting might be expected to reduce population size, but quite the opposite can happen due to the hydra effect. This phenomenon describes an increase in population size with increased mortality. One mechanism causing hydra effects is the temporal separation of (i) harvesting and (ii) density-dependent reproduction. Here we consider discrete-time models of these two processes. It is commonly believed that harvesting needs to precede reproduction for a hydra effect to occur. We show that, by contrast, hydra effects also take place for harvest after reproduction. Due to the timing of population census, however, the hydra effect will not be measured and thus remains ‘hidden’. As a consequence, managers may miss out on the opportunity to increase both the yield and the remaining stock of renewable resources. If harvesting aims at controlling pest species, management interventions may backfire in the sense that the pest increases rather than decreases—and, to make things even worse, this may actually go unnoticed. To remedy these undesirable consequences, we propose a modelling framework that can reveal hidden hydra effects. Our results are based on rigorous mathematical proofs that the order of two events does not matter for standard harvesting/hunting strategies.     

Predator selectivity alters the effect of dispersal on coexistence among apparent competitors

While the majority of studies on dispersal effects on patterns of coexistence among species in a metacommunity have focused on resource competitors, dispersal in systems with predator–prey interactions may provide very different results. Here, we use an analytical model to study the effect of dispersal rates on coexistence of two prey species sharing a predator (apparent competition), when the traits of that predator vary. Specifically, we explore the range in immigration rates where apparent competitors are able to coexist, and how that range changes with predator selectivity and efficiency. We find that if the inferior apparent competitor has a higher probability of being consumed, it will require less immigration to invade and to exclude the superior prey as the predator becomes more opportunistic. However, if the inferior apparent competitor has a lower probability of being consumed (and lower growth rates), higher immigration is required for the inferior prey to invade and exclude the superior prey as the predator becomes more opportunistic. We further find that the largest range of immigration rates where prey coexist occurs when predator selectivity is intermediate (i.e. they do not show much bias towards consuming one species or the other). Increasing predator efficiency generally reduces the immigration rates necessary for the inferior apparent competitor to invade and exclude the superior apparent competitor, but also reduces the range of immigration rates where the two apparent competitors can coexist. However, when the superior apparent competitor has a higher probability of being consumed, increased predator efficiency can increase the range of parameters where the species can coexist. Our results are consistent with some of the variation observed in the effect of dispersal on prey species richness in empirical systems with top predators.     

Predator Inspection: Closer Approach as a Way to Improve Assessment of Potential Threats

When detecting a predator, some prey animals respond in a counterintuitive fashion by approaching, rather than fleeing, that potential threat of extinction. This seemingly paradoxical behaviour, known as predator inspection, has been reported for a wide variety of taxa-and therefore can be assumed to be adaptive. However, the view of predator inspection as a paradoxical behaviour rests on two implicit assumptions: (a) initial predator detecting is unambiguous, with no uncertainty in discriminating between hunting and non hunting members of predator species, or members of predator species and unrelated phenomena; (b) the costs of flight are negligible relative to the risk of predation. Upon reflection assumption (a) is not really tenable. Whereas assumption (b) is not consistent with experimental evidence [Godin & Crossman (1994) Behav. Ecol. Sociobiol.34, 359-366]. Given that predator detection is ambiguous and the costs of flight are not negligible, a prey individual may benefit by a closer approach to the source of the alarming signals, thus improving its assessment of the situation-despite the increased risk of predation. In this paper, the above statement is given rigor by reformulating the problem in game theoretical terms. The results indicate that a prey will minimize its costs by performing predator inspection whenever its degree of certainty regarding predator identification and/or assessment of its intentions is less than a threshold, which is determined by the model's parameters. Copyright 1999 Academic Press.     

水螅异常极性体轴的形成及矫正进程的观察

目的:如何建立和维持体轴是一个基本的发育生物学问题,而淡水水螅是适合进行形态发生和个体发育调控机制研究的重要模式生物。本文观察了大乳头水螅异常极性体轴的形成及矫正进程,初步探讨水螅极性体轴的维持和调控机制。方法:先切取水螅的整个头部,再获得带二根触手的口区组织。通过ABTS细胞化学染色法检测水螅基盘分子标志物过氧化物酶的表达,判别水螅基盘组织(水螅足区的末端)是否形成。结果:从40块口区组织再生得到的水螅个体中有1例极性体轴发育异常的个体,其身体两端均发育成头区,且两端的头区均具有捕食能力。随后水螅其中一端头区的触手逐渐萎缩、退化,最终该端头区转化成具有吸附能力的基盘组织。结论:水螅组织的再生涉及极性体轴的重建,而一些特殊因素可能造成临时性的水螅极性体轴调控紊乱。本研究表明水螅具备自我矫正异常极性体轴的能力。另外,本研究结果显示水螅触手可以萎缩直至退化,该现象涉及的细胞学过程可能是非常复杂的,有可能涉及到触手细胞的凋亡转化过程,也可能是触手的高度分化细胞仍然具备去分化能力、去分化后再转移到身体其他地方,其具体机制值得进一步探究。     

The role of nerve cell density in the regulation of bud production in hydra

Summary The role of nerve cell density in the regulation of bud production in hydra was examined. Animals with different rates of bud production were produced by altering the temperature, population density and illumination of their cultures. When the distribution of cell types was examined in animals with different rates of bud production, the density of nerve cells in those animals was found to be correlated with their rate of bud production. Transfer of animals from one environment to another resulted in immediate changes in the rate of differentiation of large interstitial cells into nerve cells. This suggests that the density of nerve cells may play a role in regulating the rate of bud production in hydra.     

The impact of mortality on predator population size and stability in systems with stage-structured prey

The relationships between a predator population's mortality rate and its population size and stability are investigated for several simple predator-prey models with stage-structured prey populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's population growth; the nature of stage-transitions; and the stage-selectivity of the predator. Instability occurs at high, rather than low predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable predator population to increase in abundance as its own mortality rate increases in stable systems, provided that the predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in predator population size with increasing predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.     

Efficiency evaluation of two competing foraging modes under different conditions

Various foraging modes are employed by predators in nature, ranging from ambush to active predation. Although the foraging mode may be limited by physiological constraints, other factors, such as prey behavior and distribution, may come into play. Using a simulation model, we tested to what extent the relative success of an ambush and an active predator changes as a function of the relative velocity and movement directionality of prey and active predator. In accordance with previous studies, we found that when both active predator and prey use nondirectional movement, the active mode is advantageous. However, as movement becomes more directional, this advantage diminishes gradually to 0. Previous theoretical studies assumed that animal movement is nondirectional; however, recent field observations show that in fact animal movement usually has some component of directionality. We therefore suggest that our simulation is a better predictor of encounter rates than previous studies. Furthermore, we show that as long as the active predator cannot move faster than its prey, it has little or no advantage over the ambush predator. However, as the active predator's velocity increases, its advantage increases sharply.     

The escape response of the zebra danio (Brachydanio rerio) II. The effect of experience

Naïve zebra danios (Brachydanio rerio) flee from an approaching predator when the angle subtended at the danio's eye by the predator changes at a rate greater than some characteristic threshold value. The hypothesis was tested that this value declines, and hence reactive distance increases, as a function of the number of past experiences with the predator. Artificial predators of two types, a model and a film of an approaching object, were presented to the danios daily and changes in behaviour recorded. The rate of change of visual angle at the time of response to the predator (dα/dt threshold) declined asymptotically with increasing experience. Consequently, flight distance increased asymptotically. The change was not due to growth, maturation, or increased familiarity with the testing situation. The danios apparently associated the visual characteristics of the predator with its subsequent high rate of angular growth and began to respond to these visual characteristics prior to dα/dt exceeding the threshold. The angle of escape was not affected by experience. Escape velocity increased with experience of the film predator, but not with experience of the model predator. No decrement of the learned change in reactive distance was evident after 10 days without experience with the film predator.