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PubMed1995

Indirect effects in ecological interaction networks. II. The conjugate variable approach.

A new method called the conjugate variable approach for the analysis of indirect effects propagating through an ecosystem network is developed. For a given ecosystem of n species, the 2n variables representing the inflows and abundances of the n species are related in the n equations that define the system's steady states. There are 2n alternative ways of designating, for each species, either an inflow or an abundance variable as an independent variable and the other (i.e., its conjugate variable) as a dependent variable. Each of these alternative ways defines a unique configuration of constraints in the influence propagation through the ecosystem network. In particular, designating as independent variables the inflow variables of all but two focal species leaves their abundance variables free to change, thus leading to the evaluation of the total effect between the two focal species. On the other hand, choosing their abundance variables as independent variables to fix prohibits influence to pass through any of these intermediate species, thus selectively evaluating the direct effect between the two focal species. Any other way between these two extreme cases sets partial constraints on influence propagation, thus evaluating a partial effect between the two species. Four categories of effects between two species--inflow to abundance, abundance to abundance, inflow to inflow, and abundance to inflow--can be distinguished and explicitly evaluated in terms of community matrix elements.

Animals↗
PubMed1995

Indirect effects in ecological interaction networks. I. The chain rule approach.

A mathematical method for evaluating indirect effects propagated through ecosystems consisting of multiple species is developed. The time-backward expansion of the sensitivity matrix of a system at steady state represents the tracking back of the total effects received by species. Aggregating those portions of the total effect between two species that travel through a common path with various schedules gives the path partitioning of the total effect. From this path partitioning, a chain rule is derived that expresses the indirect effect transmitted through an individual path as the products of direct effects associated with the links constituting the path. The evaluation of indirect effects by this chain rule is applied to example systems to reveal the entire structure of influence propagation through the systems. The results of this application suggest three basic mechanisms through which indirect effects contribute to the complexity and contingency of species interactions: (i) the globalization of influence by bundles of long indirect paths, (ii) the amplification (or reduction) of effects by positive (or negative) cycles, and (iii) the alteration in sign of interactions between a pair of species due to the change in dominance among the effects carried by parallel paths connecting the species.

Animals↗
PubMed1994

Chaos in one-predator, two-prey models: general results from bifurcation theory.

We show that chaos is the expected outcome of the dynamics of a class of one-predator, two-prey models. This generalizes results of previous studies of Lotka-Volterra models. We examine dynamics near a state in which a high codimension bifurcation occurs, considering all possible nearby dynamics in both parameter and state space by doing an unfolding analysis of the model's normal form. In this way, we argue that realistic predator-prey systems that can be closely modeled by the general models discussed here must exhibit chaotic dynamics.

Animals↗
PubMed1994

Multiple cyclic sets connecting saddle points and limit cycles of a four-species system and its uniform persistence.

Considering a model of a generalized Gause-type four-species system of two predator-prey pairs linked by competition, the authors derive sufficient conditions for the existence of three different invariant cyclic sets connecting saddle points and limit cycle(s) on the boundary of its state space. Also discussed is the uniform persistence of the model in the presence of such cycle sets.

Animals↗
PubMed1996

Spatially heterogeneous discrete waves in predator-prey communities over a patchy environment.

A model motivated by the earlier work of J. D. Murray and D. Stirzaker is proposed to describe the dynamics of predator-prey communities over a patchy environment. The model is a system of delay differential equations. It is shown that if only one time lag is incorporated into the model, then a branch of spatially homogeneous periodic solutions occur as a primary Hopf bifurcation. However, if two time lags are used to measure different delayed factors in the process of growth, decay, and predator consumption of the prey population, then stable spatially heterogeneous periodic solutions (discrete waves or phase-locked oscillations) may exist. The utilized method is based on center manifold, normal form, and equivariant Hopf bifurcation theory.

Animals↗
PubMed1996

An exact analytical solution of a three-component model for competitive coexistence.

A three-component competition system is modeled as a reaction-diffusion process. An exact analytical solution has been found that indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra-type equations are no longer valid. Cases with one or both predators diffuse are analyzed, and the stability question is discussed.

Animals↗
PubMed1996

Bionomic equilibrium of two-species system. I.

The concept of bionomic equilibrium is used to obtain limits of cost per unit effort and maximum value of effort for the joint harvesting of three types of two-species system: (1) a logistic growth model of two ecologically independent species, (2) a logistic growth model of two species that have competitive interactions, and (3) a Lotka-Volterra model of one prey and one predator. In each case, the existence of feasible bionomic equilibrium points and that of partially feasible bionomic equilibrium points are considered separately. First it is shown that cost per unit effort has both upper and lower threshold values if feasible bionomic equilibrium points occur, whereas it has only the upper threshold values if partially feasible bionomic equilibrium points occur. Further, the threshold values depend solely on the catchability coefficients, the selling prices of unit biomasses, and the parameters of the given model, namely the biotic potentials, carrying capacities, etc. Next, it is proven that for the first type of feasible point, if the cost per unit effort is kept under proper threshold values, then corresponding to each such value, the maximum value of the efforts exerted can be calculated in terms of the given parameters only. Moreover, the set of all such maximum values of the efforts for different choices of cost per unit effort is always bounded and the supremum of these maximum efforts is independent of the choice of cost per unit effort.

Animals↗
PubMed1995

Lateralization of predator-evasion response in a teleost fish (Girardinus falcatus).

Evidence of lateral asymmetries in the direction of turning during escape behaviour in a species of poeciliid fish, Girardinus falcatus, is reported. When repeatedly faced with a simulated predator (in five successive sessions, spaced 7 days apart), immature Girardinus falcatus exhibited a significant population bias to turn right on the first session and a progressive bias to turn left in subsequent sessions. Mature Girardinus were then tested to check whether the shift in the direction of turn with repeated sessions depended on maturation or habituation. It was found that adult Girardinus showed a slight population bias to turn right in the first session and a strong subsequent bias to turn left after repeated sessions. The implications of these findings to our current understanding of the evolution of brain lateralization are discussed.

Animals↗
PubMed1987

The anterior basal lobe and control of prey-capture in the cuttlefish (Sepia officinalis).

The predatory behaviour of the cuttlefish comprises several stages: prey-detection, orientation, translation and prey-seizing. In this neuroethological study, lesions to the anterior basal lobe were made by an electrolytic method and the animals were allowed to attack their prey in an unrestricted way so that motor defects, functional recovery and the emergence of new adaptative behavioural strategies could be studied. Lesions to the central region of the anterior basal lobe suppress the orientating behaviour, thus only prey situated in the frontal visual field can be seized. Less extensive lesions in this region are associated with similar defects. Without head orientation, the cuttlefish still rotates with its fins. This rotation, however, is usually underestimated, tentacular ejection thus missing the prey. Dorsal lesions cause an underestimation of tentacular strike often associated with defects in maintaining ocular convergence. These results demonstrate the heterogenous function of the anterior basal lobe and its complex role in the control of predatory behaviour.

Animals↗
PubMed1988

Seasonal and environmental influences upon the diurnal heart-rate pattern in wild rabbits living under seminatural conditions.

Diurnal patterns in the heart-rates (HR) of 16 wild European rabbits have been studied, based on more than 1200 days of radiotelemetrical HR recordings. HR shows a distinct diurnal rhythm which is closely coupled to the diurnal pattern of activity for free ranging animals. The rabbits' activity phase, accompanied by high HRs extends from late afternoon to early morning. It is followed by diurnal rest with low HRs, irrespective of burrow utilization. This diurnal resting phase is often interrupted by short excursions outside the burrow. The duration of the activity phase and the times of onset and cessation of activity are very stable across different individuals and over three years of measurement. Disturbances of this stable seasonal pattern are by predation and by weather influences. The importance of light cycle and human disturbances as synchronizers for diurnal HR pattern in wild rabbits is discussed.

Animals↗
PubMed1991

The calls of murine predators activate endogenous analgesia mechanisms in laboratory mice.

In view of the suggested role of endogenous analgesia mechanisms as an antipredator defense mechanism, the effects on nociception of exposure to the calls of various murine predatory and nonpredatory species were assessed. Data revealed that the calls of the Tawny Owl, Barn Owl and Common Gull all induced significant analgesia following exposure to 2 min of birdsong. Time course analysis revealed the analgesia induced by the Tawny Owl call to have a duration in excess of 40 min while the Barn Owl and Gull call-induced analgesias were much shorter lasting (approximately 10 min or less). Five mg/kg naloxone was found to attenuate the analgesia induced by the Tawny and Barn Owls but not the Common Gull. Together, these data suggest that brief exposure to the calls of night-hunting, aerial predators activate endogenous opioid-mediated analgesia mechanisms in mice.

Animal Communication↗
PubMed1991

Twenty-two kHz alarm cries to presentation of a predator, by laboratory rats living in visible burrow systems.

When a cat was presented to groups of 3 male and 2 female laboratory rats in the open area of a visible burrow system, the rats retreated to the burrow system and showed high levels of 18-24 kHz ultrasonic cries during the cat presentation and for 30 min following removal of the cat. Latency to make ultrasonic vocalizations, durations of these vocalizations, and duration in the burrow systems were all strikingly and reliably different during and after cat exposure in comparison to similar periods with a control (stuffed cat toy) stimulus. However, when individual rats were exposed to a cat in an open area of similar size, ultrasonic cry production was minimal. Also rats exposed individually to a cat in an apparatus providing an escape chamber similarly showed no ultrasonic cries, indicating that concealment per se is not a sufficient condition for their appearance. These results suggest that the production of ultrasonic vocalizations during and after exposure to a predator is greatly facilitated by the presence of familiar conspecifics, and may serve as alarm cries. While the alarm cry hypothesis also suggests a possible function for 18-24 kHz ultrasounds in the context of copulation and intraspecies aggression, the sonographic and functional relationships among the cries emitted in these different situations remain to be analyzed.

Animals↗