Periodical cicadas.
The evolution of periodicity and synchronicity of magical cicadas is studied by means of mathematical models.
Animals↗
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Results for “Predatory Behavior”
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Linear stability criteria for population models with periodically perturbed delays.
We examine some simple population models that incorporate a time delay which is not a constant but is instead a known periodic function of time. We examine what effect this periodic variation has on the linear stability of the equilibrium states of scalar population models and of a simple predator prey system. The case when the delay differs from a constant by a small amplitude periodic perturbation can be treated analytically by using two-timing methods. Of particular interest is the case when the system is initially marginally stable. The introduction of variation in the delay can then have either a stabilising effect or a destabilizing one, depending on the frequency of the periodic perturbation. The case when the periodic perturbation has large amplitude is studied numerically. If the fluctuation is large enough the effect can be stabilising.
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Local stability analysis of spatially homogeneous solutions of multi-patch systems.
Multi-patch systems, in which several species interact in patches connected by dispersal, offer a general framework for the description and analysis of spatial ecological systems. This paper describes how to analyse the local stability of spatially homogeneous solutions in such systems. The spatial arrangement of the patches and their coupling is described by a matrix. For a local stability analysis of spatially homogeneous solutions it turns out to be sufficient to know the eigenvalues of this matrix. This is shown for both continuous and discrete time systems. A bookkeeping scheme is presented that facilitates stability analyses by reducing the analysis of a k-species, n-patch system to that of n uncoupled k-dimensional single-patch systems. This is demonstrated in a worked example for a chain of patches. In two applications the method is then used to analyse the stability of the equilibrium of a predator-prey system with a pool of dispersers and of the periodic solutions of the spatial Lotka-Volterra model.
Animals↗
Excitability of an age-structured plankton ecosystem.
We adapt a simple two-component model of a plankton ecosystem to account for the life spans of individual predatory organisms. We investigate the system's short-term dynamics, in particular its excitability, and its long-term dynamics, and show how both can be highly sensitive to initial conditions. We discover that this effect is enhanced by imposing age structure on the system.
Age Distribution↗
The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics.
In the presence of seasonal forcing, the intricate topology of non-integrable Hamiltonian predator-prey models is shown to exercise profound effects on the dynamics and bifurcation structure of more realistic schemes which do not admit a Hamiltonian formulation. The demonstration of this fact is accomplished by writing the more general models as perturbations of a Hamiltonian limit, ℋ, in which are contained infinite numbers of periodic, quasiperiodic and chaotic motions. From ℋ, there emanates a surface, Gamma, of Nejmark-Sacker bifurcations whereby the annual oscillations induced by seasonality are destabilized. Connecting Gamma and ℋ is a bridge of resonance horns within which invariant motions of the Hamiltonian case persist. The boundaries of the resonance horns are curves of tangent (saddle-node) bifurcations corresponding to subharmonics of the yearly cycle. Associated with each horn is a rotation number which determines the dominant frequency, or "color", of attractors within the horn. When viewed through the necessarily coarse filter of ecological data acquisition, and regardless of their detailed topology, these attractors are often indistinguishable from multi-annual cycles. Because the tips of the horns line up monotonically along Gamma, it further follows that the distribution of observable periods in systems subject to fluctuating parameter values induced, for example, by year-to-year variations in the climate, will often exhibit a discernible central tendency. In short, the bifurcation structure is consistent with the observation of multi-annual cycles in Nature. Fundamentally, this is a consequence of the fact that the bridge between ℋ and Gamma is a rainbow bridge. While the present analysis is principally concerned with the two species case (one predator and one prey), Hamiltonian limits are also observed in other ecological contexts: 2n-species (n predators, n prey) systems and periodically-forced three level food chain models. Hamiltonian limits may thus be common in models involving the destruction of one species by another. Given the oft-commented upon structural instability of Hamiltonian systems and the corresponding lack of regard in which they are held as useful caricatures of ecological interactions, the pivotal role assigned here to Hamiltonian limits constitutes a qualitative break with the conventional wisdom.
Animals↗
Dynamics of variable-yield nutrient-phytoplankton-zooplankton models with nutrient recycling and self-shading.
Several nutrient-phytoplankton-zooplankton models with internal nutrient storage by phytoplankton are derived and analyzed. It is shown that there are thresholds beyond which the system is uniformly persistent. Variable-yield models with self-shading of phytoplankton are also considered. With respect to uniform persistence, our result demonstrates that the global dynamics of the system with shading are the same as those for which the self-shading mechanism is ignored.
Animals↗
Generalized monotonicity, integral conditions and partial survival.
An interesting paper of Vance and Coddington concerning the scalar equation x = xf(t, x) is improved by a drastic weakening of the assumptions. Surprising as it may seem, this weakening simplifies the analysis and leads to stronger conclusions. An extension to scalar inequalities of similar structure is applied to a large class of vector equations describing the evolution of n interacting species. Thus we obtain new criteria for extinction and for partial survival, in the sense that each of the separate species may come arbitrarily close to extinction but the population as a whole does not.
Animals↗
Predator-prey models with delay and prey harvesting.
It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions.
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Rich dynamics of a ratio-dependent one-prey two-predators model.
The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1). competitive exclusion; 2). total extinction, i.e., collapse of the whole system; 3). coexistence in the form of positive steady state; 4). coexistence in the form of oscillatory solutions; and 5). introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed.
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From chaos to chaos. An analysis of a discrete age-structured prey-predator model.
Discrete age-structured density-dependent one-population models and discrete age-structured density-dependent prey-predator models are considered. Regarding the former, we present formal proofs of the nature of bifurcations involved as well as presenting some new results about the dynamics in unstable and chaotic parameter regions. Regarding the latter, we show that increased predation may act both as a stabilizing and a destabilizing effect. Moreover, we find that possible periodic dynamics of low period, either exact or approximate, may not be generated by the predator, but it may be generated by the prey. Finally, what is most interesting from the biological point of view, is that given that the prey, in absence of the predator, exhibits periodic or almost periodic oscillations of low period, then the introduction of the predator does not alter this periodicity in any substantial way until the stabilizing effect of increased predation becomes so strong that a stable equilibrium is achieved.
Aging↗
Predator migration in response to prey density: what are the consequences?
A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically.
Animals↗
On the option interpretation of rational harvesting planning.
We consider the determination of the harvesting strategy maximizing the present expected value of the cumulative yield from the present up to extinction. By relying on a combination of stochastic calculus, ordinary nonlinear programming, and the classical theory of diffusions, we show that if the underlying population evolves according to a logistic diffusion subject to a general diffusion coefficient, then there is a single threshold density at which harvesting should be initiated in a singular fashion. We derive the condition which uniquely determines the threshold and show that harvesting should be initiated only when the option value of further preserving another individual falls below its opportunity cost. In this way, we present a real option interpretation of rational harvesting planning. We also consider the comparative static properties of the value of the harvesting opportunity and state a set of usually satisfied conditions under which increased stochastic fluctuations (demographic or environmental) decrease the expected cumulative yield from harvesting and increase the optimal harvesting threshold, thus postponing the rational exercise of the irreversible harvesting decision.
Animals↗
Ultraviolet properties of Australian mammal urine.
The exploitation of predator signals by potential prey is well researched, but relatively little is known about how predators exploit chemical cues (either deliberate signals or waste by-products) produced by their prey. In Finland, the urine of some small rodents ( Microtus spp. and Clethrionomys spp.) is reflective in the ultraviolet range of wavelengths, and diurnal raptors with ultraviolet vision use these urine marks to track their rodent prey. This study examines the potential for such a phenomenon in Australian systems by studying the ultraviolet properties of urine from 13 native and introduced mammal species that are variously preyed upon by raptors. Urine from all 13 species displayed various levels of ultraviolet absorbance in their urine and fluorescence in the ultraviolet range. However, no signs of ultraviolet hyper-reflectance were detected, suggesting that the urine of European voles have unique ultraviolet properties. Ultraviolet-sensitive predators in Australia may be able to distinguish between species based on variation in the ultraviolet absorbance of their urine, but ultraviolet properties did not differ between prey and non-prey species, nor marsupial and placental groups. Moreover, because many natural surfaces are ultraviolet absorbing, it is unlikely that raptors could rely upon the ultraviolet properties of urine to target key prey species.
Animal Communication↗
Ambient temperature affects mechanosensory host location in a parasitic wasp.
Certain parasitic wasps (Ichneumonidae, Pimplinae) use self-produced vibrations transmitted on plant substrate to locate their immobile concealed hosts (i.e. lepidopteran pupae). This mechanosensory mechanism, called the vibrational sounding, depends both on physical cues of the environment and physical activity of the parasitoid and is postulated to depend on ambient temperature. We analysed the influences of temperature on vibrational sounding by choice experiments using plant-stem models with hidden host mimics in the temperate species Pimpla turionellae. The results show a significant effect of temperature on host-location activity and on the success of this process. Outside an optimum range, the performance of the wasps decreased both at low and high temperatures. Below 10 degrees C and beyond 24 degrees C, the wasps displayed (1) substantial reduction in responsiveness, i.e. proportion of females showing ovipositor insertions, (2) reduction of quantitative activity with ovipositor insertions in the individuals, and (3) reduced precision of mechanosensory host location. Nevertheless, female wasps were able to locate their host over a surprisingly broad range of ambient temperatures which indicates that the wasps are able to compensate for temperature effects on vibrational sounding.
Animals↗
Sensory ecology of predator-prey interactions: responses of the AN2 interneuron in the field cricket, Teleogryllus oceanicus to the echolocation calls of sympatric bats.
We observed the responses of the AN2 interneuron in the Pacific field cricket, Teleogryllus oceanicus, a cell implicated in eliciting avoidance flight away from bats, to acoustic stimuli representing the echolocation calls of bats as well as field recordings of search and gleaning attack calls of six species of insectivorous sympatric bats (West Australia, Australia: Tadarida australis, Chalinolobus goudii, Nyctophilus geoffroyi; Queensland, Australia: Vespadelus pumilus, Myotis adversus; Kaua'i, Hawai'i: Lasiurus cinereus). The broad frequency sensitivity of the AN2 cell indicates that T. oceanicus has evolved to detect a wide range of echolocation call frequencies. The reduced sensitivity of this cell at frequencies higher than 70 kHz suggests that some bats (e.g., the gleaning species, N. geoffroyi) may circumvent this insect's auditory defences by using frequency-mismatched (allotonic) calls. The calls of the freetail bat, T. australis evoked the strongest response in the AN2 cell but, ironically, this may allow this bat to prey upon T. oceanicus as previous studies report that under certain conditions, flying crickets exhibit ambiguous directional responses towards frequencies similar to those emitted by this bat. Short duration calls (1--2 ms) are sufficient to evoke AN2 responses with instantaneous spike periods capable of causing defensive flight behaviours; most bats tested emit calls of durations greater than this. The short calls of N. geoffroyi produced during gleaning attacks may reduce this species' acoustic conspicuousness to this cricket.
Acoustic Stimulation↗
GABA-mediated echo duration selectivity of inferior collicular neurons of Eptesicus fuscus, determined with single pulses and pulse-echo pairs.
When insectivorous bats such as Eptesicus fuscus emit ultrasonic signals and analyze the returning echoes to hunt insects, duration selectivity of auditory neurons plays an important role in echo recognition. The success of prey capture indicates that they can effectively encode progressively shortened echo duration throughout the hunting process. The present study examines the echo duration selectivity of neurons in the central nucleus of the bat inferior colliculus (IC) under stimulation conditions of single pulses and pulse-echo (P-E) pairs. This study also examines the role of gamma-aminobutyric acid (GABA)ergic inhibition in shaping echo duration selectivity of IC neurons. The data obtained show that the echo duration selectivity of IC neurons is sharper when determined with P-E pairs than with single pulses. Echo duration selectivity also sharpens with shortening of pulse duration and P-E gap. Bicuculline application decreases and GABA application increases echo duration selectivity of IC neurons. The degree of change in echo duration selectivity progressively increases with shortening of pulse duration and P-E gap during bicuculline application while the opposite is observed during the GABA application. These data indicate that the GABAergic inhibition contributes to sharpening of echo duration selectivity of IC neurons and facilitates echo recognition by bats throughout different phases of hunting.
Acoustic Stimulation↗
The role of echolocation in the hunting of terrestrial prey--new evidence for an underestimated strategy in the gleaning bat, Megaderma lyra.
The observation that gleaning bats detect prey by its noises, together with difficulties in recording their faint sonar calls, have led some authors to conclude that gleaning bats may not use echolocation in certain hunting situations. In particular, it is conjectured that echolocation plays no role in the classification and tracking of prey. In the present study, we show that the gleaning bat, Megaderma lyra, is able to find silent and motionless prey on the ground. The significance of sonar for catching a variety of terrestrial prey is established in a standardized situation. Sonar calls were found to be emitted during all stages, i.e. approach, hovering above the prey, and return to the roost, of every hunting flight. The harmonic pattern of the calls differed significantly between these stages, calls with three or more prominent components prevailing during hovering. Bats identified prey and rejected dummies while hovering above them. During this stage, increased call rates and reduced call durations were found. Echolocation activity during, and the duration of, the hovering phase depended on prey type, in particular on prey movement. The prey-dependent shifts in sonar activity, the broadband call structure with an emphasis on higher harmonics, and a systematic shift of the calls' peak frequencies during hovering, are discussed as adaptations to identifying prey by sonar.
Animals↗
A circadian pacemaker in free-living chipmunks: essential for survival?
The importance of circadian timing was evaluated for 18 months from late-April 1997 through October 1998 in a high-density population of free-living eastern chipmunks, Tamias striatus, at a 4-ha forest site in the Allegheny Mountains. Included in the radiocollared field group were 30 chipmunks with supra-chiasmatic nucleus-targeted lesions, 24 surgical controls, and 20 intact controls. An additional 17 chipmunks were used in a laboratory study as lesion-calibration controls to correlate degree of circadian arrhythmicity with extent of supra-chiasmatic nucleus deletion. Survival was documented in the field by daily radio tracking and by regular trapping censuses except during winter hibernation. A significantly higher proportion of supra-chiasmatic nucleus-lesioned than surgical control chipmunks or intact controls were killed by weasel predation during the first 80 days after repatriation. A 28-h continuous census found no surface activity of any chipmunks during hours of darkness. However, episodes of nocturnal movement were detected within the permanent dens by radio telemetric data logging, especially in supra-chiasmatic nucleus-lesioned animals. Excavation and mapping of six chipmunk burrow systems aided in the interpretation of the telemetric activity data. Nighttime restlessness of supra-chiasmatic nucleus-lesioned animals may have acted as a clue to the predator for locating its prey.
Animals↗