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PubMed1998

How phenotypic variation and life history trait correlation enhance mean fitness in prey populations.

The relative effects of phenotypic variation and trait correlations on mean population fitness are poorly understood. Moreover, when fitness is evaluated in the context of ecological processes such as predation, theoretical development is lacking. To address this deficiency, we simulate a predator-prey system, where the prey population is composed of three phenotypes that differ in fecundity and predator evasiveness. We use equilibrium population size and allele frequencies to examine the relative effects of trait variation and correlation on mean population fitness. When no correlation is present, increasing variance in either trait increases equilibrium population size. Negative correlations coupled with increasing variance in both traits increases equilibrium population size. Positive correlations are more likely to increase equilibrium population size when variances are inversely related. With respect to allele frequencies, as variance in both traits increases, populations with positive correlations experience greater loss of genetic diversity than those with negative correlations. Thus, selection as a dynamic ecological process (frequency-dependent predation) favors trade-offs, whether they are between trait means (negative correlations) or variances (positive correlations).

Animals↗
PubMed1999

Competition and dispersal in predator-prey waves.

Dispersing predators and prey can exhibit complex spatio-temporal wave-like patterns if the interactions between them cause oscillatory dynamics. We study the effect of these predator-prey density waves on the competition between prey populations and between predator populations with different dispersal strategies. We first describe 1- and 2-dimensional simulations of both discrete and continuous predator-prey models. The results suggest that any population that diffuses faster, disperses farther, or is more likely to disperse will exclude slower diffusing, shorter dispersing, or less likely dispersing populations, everything else being equal. It also appears that it does not matter whether time, space, or state are discrete or continuous, nor what the exact interactions between the predators and prey are. So long as waves exist the competition between populations occurs in a similar fashion. We derive a theory that qualitatively explains the observed behaviour and calculate approximate analytical solutions that describe, to a reasonable extent, these behaviours. Predictions about the cost of dispersal are tested. If strong enough, cost can reverse the populations' relative competitive strengths or lead to coexistence because of the effect of spiral wave cores. The theory is also able to explain previous results of simulations of coexistence in host-parasitoid models (Comins, H. N., and Massell, M. P., 1996, J. Theor. Biol. 183, 19-28).

Animals↗
PubMed1999

The characteristics of epidemics and invasions with thresholds.

In this paper we report the development of a highly efficient numerical method for determining the principal characteristics (velocity, leading edge width, and peak height) of spatial invasions or epidemics described by deterministic one-dimensiohal reaction-diffusion models whose dynamics include a threshold or Allee effect. We prove that this methodology produces the correct results for single-component models which are generalizations of the Fisher model, and then demonstrate by numerical experimentation that analogous methods work for a wide class of epidemic and invasion models including the S-I and S-E-I epidemic models and the Rosenzweig-McArthur predator-prey model. As examplary application of this approach we consider the atto-fox effect in the classic reaction-diffusion model of rabies in the European fox population and show that the appropriate threshold for this model is within an order of magnitude of the peak disease incidence and thus has potentially significant effects on epidemic properties. We then make a careful re-parameterisation of the model and show that the velocities calculated with realistic thresholds differ surprisingly little from those calculated from threshold-free models. We conclude that an appropriately thresholded reaction-diffusion model provides a robust representation of the initial epidemic wave and thus provides a sound basis on which to begin a properly mechanistic modelling enterprise aimed at understanding the long-term persistence of the disease.

Animals↗
PubMed2000

Identifying predator-prey processes from time-series.

The functional response is a key element in predator-prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator-prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.

Algorithms↗
PubMed2000

Optimal Bayesian foraging policies and prey population dynamics-some comments on Rodriguez-Girones and Vasquez.

In this paper we show the density-dependent harvest rates of optimal Bayesian foragers exploiting prey occurring with clumped spatial distribution. Rodríguez-Gironés and Vásquez (1997) recently treated the issue, but they used a patch-leaving rule (current value assessment rule) that is not optimal for the case described here. An optimal Bayesian forager exploiting prey whose distribution follows the negative binomial distribution should leave a patch when the potential (and not instantaneous) gain rate in that patch equals the best long-term gain rate in the environment (potential value assessment rule). It follows that the instantaneous gain rate at which the patches are abandoned is an increasing function of the time spent searching in the patch. It also follows that the proportion of prey harvested in a patch is an increasing sigmoidal function of the number of prey initially present. In this paper we vary several parameters of the model to evaluate the effects on the forager's intake rate, the proportion of prey harvested per patch, and the prey's average mortality rate in the environment. In each case, we study an intake rate maximizing forager's optimal response to the parameter changes. For the potential value assessment rule we find that at a higher average prey density in the environment, a lower proportion of the prey is taken in a patch with a given initial prey density. The proportion of prey taken in a patch of a given prey density also decreases when the variance of the prey density distribution is increased and if the travel time between patches is reduced. We also evaluate the effect of using predation minimization, rather than rate maximization, as the currency. Then a higher proportion of the prey is taken for each given initial prey density. This is related to the assumption that traveling between patches is the most risky activity. Compared to the optimal potential value assessment rule, the current value assessment rule performs worse, in terms of long-term intake rate achieved. The difference in performance is amplified when prey density is high or highly aggregated. These results pertain to the foraging patch spatial scale and may have consequences for the spatial distribution of prey in the environment.

Animals↗
PubMed2000

Diffusion-limited predator-prey dynamics in Euclidean environments: an allometric individual-based model.

We claim that diffusion-limited rates of reaction can be an explanation for the altered population dynamics predicted by models incorporating local interactions and limited individual mobility. We show that the predictions of a spatially explicit, individual-based model result from reduced rates of predation and reproduction caused by limited individual mobility and patchiness. When these reduced rates are used in a mean-field model, there is better agreement with the predictions of the simulation model incorporating local interactions. We also explain previous findings regarding the effects of dimensionality on population dynamics in light of diffusion-limited reactions and Pólya random walks. In particular, we demonstrate that 3D systems are better "stirred" than 2D systems and consequently have a reduced tendency for diffusion-limited interaction rates.

Animals↗
PubMed2001

Directed movement of predators and the emergence of density-dependence in predator-prey models.

We consider a bitrophic spatially distributed community consisting of prey and actively moving predators. The model is based on the assumption that the spatial and temporal variations of the predators' velocity are determined by the prey gradient. Locally, the populations follow the simple Lotka-Volterra interaction. We also assume predator reproduction and mortality to be negligible in comparison with the time scale of migration. The model demonstrates heterogeneous oscillating distributions of both species, which occur because of the active movements of predators. One consequence of this heterogeneity is increased viability of the prey population, compared to the equivalent homogeneous model, and increased consumption. Further numerical analysis shows that, on the spatially aggregated scale, the average predator density adversely affects the individual consumption, leading to a nonlinear predator-dependent trophic function, completely different from the Lotka-Volterra rule assumed at the local scale.

Animals↗
PubMed2002

Habitat destruction in a simple predator-prey patch model: how predators enhance prey persistence and abundance.

We model a metapopulation of predator-prey patches using both spatially implicit or mean-field (MF) and spatially explicit (SE) approaches. We show that in the MF model there are parameter regimes for which prey cannot persist in the absence of predators, but can in their presence. In addition, there are parameter regimes for which prey may persist in isolation, but the presence of predators will increase prey patch density. Predators may thus enhance prey persistence and overall abundance. The key mechanism responsible for this effect is the occurrence of prey dispersal from patches that are occupied by both prey and predators. In addition, these patches should be either long-lived, such as that occurs when predators keep prey from overexploiting its local resource, or the presence of a predator on a patch should significantly enhance the prey dispersal out of that patch. In the SE approach these positive effects of predators on prey persistence and abundance occur for even larger parameter ranges than in the MF model. Prey dispersal from predator-prey patches may thus be important for persistence of both species as a community, independent of the modeling framework studied. Comparison of the MF and SE approaches shows that local dispersal constraints can have the edge over global dispersal for the persistence of the metapopulation in regimes where the two species have a beneficial effect on each other. In general, our model provides an example of feedback in multiple-species metapopulations that can make the implementation of conservation schemes based on single-species arguments very risky.

Animals↗
PubMed2002

The impact of resource limitation and the phenology of parasitoid attack on the duration of insect herbivore outbreaks.

Fluctuations in resource quality and quantity, and changes in mortality due to predators and parasites are thought to be of prime importance in the regular fluctuations of forest insects. We examine how food limitation and parasitoids with different phenologies of attack regulate the population cycles of insect hosts. Our analysis of the limit cycle of a model with a biologically realistic form of density dependence in the host yields two novel predictions. First, outbreaks will typically last for only 2 generations after parasitoids begin to reduce the host population below the maximum density. Second, host growth rate is important in determining cycle length only when parasitoids attack before the impacts of resource limitation affect the host. The robustness of these predictions are tested using a more general form of density dependence in the host, revealing that our predictions are valid as long as density dependence in the host is not too overcompensatory.

Animals↗
PubMed1987

Mathematical model and simulation of retina and tectum opticum of lower vertebrates.

The processing of information within the retino-tectal visual system of amphibians is decomposed into five major operational stages, three of them taking place in the retina and two in the optic tectum. The stages in the retina involve (i) a spatially local high-pass filtering in connection to the perception of moving objects, (ii) separation of the receptor activity into ON- and OFF-channels regarding the distinction of objects on both light and dark backgrounds, (iii) spatial integration via near excitation and far-reaching inhibition. Variation of the spatial range of excitation and inhibition allows to account for typical activities observed in a variety of classes of retina ganglion cells. Mathematical description of the operations in the tectum opticum include (i) spatial summation of retinal output (mainly of class-2 and class-3 retina ganglion cells), and (ii) direct or indirect lateral inhibition between tectal cells. In the computer simulation, first the output of the mathematical retina model is computed which, then, is used as the input to the tectum model. The full spatio-temporal dynamics is taken into account. The simulations show that different combinations of strength of lateral inhibition on the one side and the response properties of the retina ganglion cells on the other side determine the response properties of tectal cell types involved in object recognition.

Amphibians↗
PubMed1991

A stochastic model for predator-prey systems: basic properties, stability and computer simulation.

A simple stochastic description of a model of a predator-prey system is given. The evolution of the system is described by means of Itô's stochastic differential equations (SDEs), which are the natural stochastic generalization of the Lotka-Volterra deterministic differential equations. Since these SDEs do not satisfy the usual conditions for the existence and uniqueness of the solution, we state a theorem of existence; moreover we study the stability of the equilibrium point and perform a computer simulation to study the behaviour of the trajectories of solutions with given initial data and to estimate first and second moments.

Animals↗
PubMed1993

Visual performance of the toad (Bufo bufo) at low light levels: retinal ganglion cell responses and prey-catching accuracy.

The accuracy of toad snapping towards moving worm dummies under various levels of dim illumination (from absolute threshold to "moonlight") was video-recorded and related to spike responses of retinal ganglion cells exposed to equivalent stimuli. Some toads (at ca. 16 degrees C) successfully snapped at dummies that produced only one photoisomerization per 50 rods per second in the retina, in good agreement with thresholds of sensitive retinal ganglion cells. One factor underlying such high sensitivity is extensive temporal summation by the ganglion cells. This, however, is inevitably accompanied by very long response latencies (around 3 s near threshold), whereby the information reaching the brain shows the dummy in a position where it was several seconds earlier. Indeed, as the light was dimmed, snaps were displaced successively further to the rear of the dummy, finally missing it. The results in weak but clearly supra-threshold illumination indicate that snaps were aimed at the advancing head as seen by the brain, but landed further backwards in proportion to the retinal latency. Near absolute threshold, however, accuracy was "too good", suggesting that the animal had recourse to a neural representation of the regularly moving dummies to correct for the slowness of vision.

Animals↗
PubMed1991

Action of the octavolateralis efferent system upon the lateral line of free-swimming toadfish, Opsanus tau.

The activation and action of the octavolateralis efferent system was studied by chronic recordings of discharge patterns from putative efferent and single primary afferent neurons in alert, free-swimming toadfish. Efferent axons isolated in the anterior lateral line nerve showed phasic discharges following touch stimuli applied to the head or trunk and demonstrated sustained discharges to visual stimuli. Resting discharge patterns of primary afferents were categorized into irregular, burster, regular, and silent classes. Afferent discharges were often modulated by low frequency (less than 1 Hz) water movement around the head generated during respiratory movements. When fish with recording electrodes implanted in the lateral line nerve were visually stimulated, modulated peak discharges and average (DC) firing rates were inhibited in irregular-type units only. Inhibition of irregular-type afferent neurons also followed visual presentation of natural prey and persisted long after prey stimuli were removed from view. The inhibitory action upon lateralis afferents when activated by biologically significant visual stimuli leads to the hypothesis that the octavolateralis efferent system functions in the peripheral processing of information carried by the lateral line in natural settings.

Animals↗
PubMed1993

Passive sound localization of prey by the pallid bat (Antrozous p. pallidus).

The pallid bat (Antrozous p. pallidus) uses passive sound localization to capture terrestrial prey. This study of captive pallid bats examined the roles of echolocation and passive sound localization in prey capture, and focused on their spectral requirements for accurate passive sound localization. Crickets were used as prey throughout these studies. All tests were conducted in dim, red light in an effort to preclude the use of vision. Hunting performance did not differ significantly in red light and total darkness, nor did it differ when visual contrast between the terrestrial prey and the substrate was varied, demonstrating that the bats did not use vision to locate prey. Our bats apparently used echolocation for general orientation, but not to locate prey. They did not increase their pulse emission rate prior to prey capture, suggesting that they were not actively scanning prey. Instead, they required prey-generated sounds for localization. The bats attended to the sound of walking crickets for localization, and also attacked small, inanimate objects dragged across the floor. Stationary and/or anesthetized crickets were ignored, as were crickets walking on substrates that greatly attenuated walking sounds. Cricket communication sounds were not used in prey localization; the bats never captured stationary, calling crickets. The accuracy of their passive sound localization was tested with an open-loop passive sound localization task that required them to land upon an anesthetized cricket tossed on the floor. The impact of a cricket produced a single 10-20 ms duration sound, yet with this information, the bats were able to land within 7.6 cm of the cricket from a maximum distance of 4.9 m. This performance suggests a sound localization accuracy of approximately +/- 1 degree in the horizontal and vertical dimensions of auditory space. The lower frequency limit for accurate sound localization was between 3-8 kHz. A physiological survey of frequency representation in the pallid bat inferior colliculus suggests that this lower frequency limit is around 5 kHz.

Animals↗
PubMed1994

Substrate-gleaning versus aerial-hawking: plasticity in the foraging and echolocation behaviour of the long-eared bat, Myotis evotis.

The foraging and echolocation behaviour of Myotis evotis was investigated during substrate-gleaning and aerial-hawking attacks. Bats gleaned moths from both the ground and a bark-covered trellis, however, they were equally adept at capturing flying moths. The calls emitted by M. evotis during substrate-gleaning sequences were short, broadband, and frequency-modulated (FM). Three behavioural phases were identified: search, hover, and attack. Gleaning search calls were significantly longer in duration, lower in highest frequency, and larger in bandwidth than hover/attack calls. Calls were detected in only 68% of gleaning sequences, and when they were emitted, bats ceased calling approximately 200 ms before attacking. Terminal feeding buzzes, the rapid increase in pulse repetition rate associated with an attempted prey capture, were never recorded during gleaning attacks. The echolocation calls uttered by M. evotis during aerial-hawking foraging sequences were also short duration, high frequency, FM calls. Two distinct acoustic phases were identified: approach and terminal. Approach calls were significantly different from terminal calls in all variables measured. Calls were detected in 100% of aerial-hawking attacks and terminal feeding buzzes were invariably produced. Gleaning hover/attack calls were spectrally similar to aerial approach calls, but were shorter in duration and emitted at a significantly lower (but constant) repetition rate than aerial signals. Although the foraging environment (flight cage contents) remained unchanged between tasks (substrate-gleaning vs. aerial-hawking), bats emitted significantly lower amplitude calls while gleaning. We conclude that M. evotis adjusts its echolocation behaviour to meet the perceptual demands (acoustical constraints) imposed by each foraging situation.

Animals↗
PubMed1992

Differential sensitivity of Dugesia dorotocephala and Cheumatopsyche pettiti to water acidification: ecological implication for predator-prey interactions.

The initial hypothesis that predation pressure should decrease with decreasing pH in aquatic macrobenthic communities if predatory invertebrates are more sensitive to water acidification than prey invertebrates is tested. Short-term toxicity bioassays were conducted in soft water (average value of total hardness 38.0 mg CaCO3/L) to determine the differential sensitivity of the predator, Dugesia dorotocephala (Turbellaria, Tricladida), and the prey, larvae of Cheumatopsyche pettiti (Insecta, Trichoptera), to low pH. Test pH solutions were prepared with sulfuric acid (H2SO4). Test species were also exposed to high concentrations of sulfate ion (95 mg SO4 =/L for D. dorotocephala and 340 mg SO4 =/L for C. pettiti) as sulfate toxicity controls, using potassium sulfate (K2SO4). No mortality was observed during these toxicity controls, indicating that toxic effects generated by low pH were fundamentally due to H+ ions. The 72 and 96-h LC50s (as pH values) and their 95% confidence limits were 4.88 (4.72-5.05) and 5.04 (4.89-5.21) for D. dorotocephala, and 3.25 (3.00-3.51) and 3.48 (3.24-3.73) for C. pettiti. Net-spinning caddis-fly larvae migrated from their retreat nets and protruded their anal papillae before dying. After short-term bioassays, predation-pressure laboratory experiments were performed for 6 days. The cumulative mortality of C. pettiti by predation of D. dorotocephala decreased with decreasing sublethal pH values. The average predation rates at mean pH values of 7.7, 7.7, 6.6, 6.5, 6.2 and 6.0 were 2.5, 2.0, 1.33, 1.17, 0.67 and 0.33 larvae/day, respectively. The major biotic factor affecting predation pressure appears to be the reduction in the physiological activity of triclads at low pH.(ABSTRACT TRUNCATED AT 250 WORDS)

Acids↗