Dynamical Adaptation of Parental Care

Two models are proposed to simulate population growth of species with mature stage and immature stage in which there are parental cares for immature. It is assumed that the protection of mature to their immature reduces mortality of immature at the cost of reduction of reproduction. Dynamical adaptation of parental care is incorporated into the models, one of which is described with the proportional transition rate from immature to mature (ODE model) and the other one is described with a transition rate from immature to mature according to a fixed age (DDE model). For the ODE model, it is shown that the adaptation of parental care enlarges the possibility of species survival in the sense that population is permanent under the influences of the adaptation, but becomes extinct in the absence of adaptation. It is proved that the outcome of the adaptation makes the population in an optimal state. It is also observed that there are parental care switches, from noncare strategy to care strategy, as the natural death rate of immature individuals increases. The analysis of the DDE model indicates that the adaptation also enlarges the opportunity of population persistence, but the stage delay has the tendency to hinder the movement of population evolution to the optimal state. It is found that the loss rate of immature in the absence of parental care can induce different patterns to disturb the adaptation of population to optimal state. However, it is shown that the adaptation of parental care approaches to the optimal state when parental care is required for the survival of the population, for example, when the loss rate of immature or competition among mature increases or the fecundity decreases. The research was supported by Heiwa–Nakajima Fund and National Science Fund of China (No. 10571143). The research was partly supported by the Sasakawa Scientific Research Grant from The Japan Science Society. The research was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.     

Species' borders and dispersal barriers

Range limits of species are determined by combined effects of physical, historical, ecological, and evolutionary forces. We consider a subset of these factors by using spatial models of competition, hybridization, and local adaptation to examine the effects of partial dispersal barriers on the locations of borders between similar species. Prompted by results from population genetic models and biogeographic observations, we investigate the conditions under which species' borders are attracted to regions of reduced dispersal. For borders maintained by competition or hybridization, we find that dispersal barriers can attract borders whose positions would otherwise be either neutrally stable or moving across space. Borders affected strongly by local adaptation and gene flow, however, are repelled from dispersal barriers. These models illustrate how particular biotic and abiotic factors may combine to limit species' ranges, and they help to elucidate mechanisms by which range limits of many species may coincide.     

Adaptation in auditory-nerve fibers: A revised model

Adaptation of firing rates in auditory-nerve fibers appears to reflect two distinct processes. Rapid adaptation occupies the first few milliseconds of response and is superimposed upon short-term adaptation which has a time constant of about 40 ms. The properties of the two processes are reviewed and compared, and a phenomenological model is developed that successfully accounts for them. The model consists of several stages which have been tentatively associated with underlying physiological processes. In the first stage stimulus intensity is transformed by a static nonlinearity, followed by a low-pass filter. The filtered output may correspond to the hair-cell receptor potential. It modulates the release of a substance that possibly represents synaptic transmitter. Adaptation is produced by the depletion of transmitter which is located in three stores in cascade. A global store with fixed concentration controls the steady-state response and replenishes a local store which is responsible for short-term adaptation. The local store seplenishes a rapidly depleted immediate store. Flow between stores is proportional to concentration gradients with the following exceptions. The immediate store is subdivided into independent volumes or sites and there is no flow among sites or back to the local store. A given site becomes activated only when the receptor potential exceeds its particular activation value and the number of activated sites is proportional to the receptor potential. The flow of transmitter from the immediate store is assumed to be proportional to neural firing rate, with some minor modifications described in the text. The properties of the model are determined from the underlying equations and from a computer simulation. The model produces realistic response properties including PST histograms, onset and steady-state rate-intensity functions, incremental and decremental responses, response modulation for amplitude modulated stimuli, and period histograms for low-frequency tones.     

On visual adaptation: II. The electroretinogram and the bipolar cells

First a model for theb-wave of the electroretinogram is given. The essential part of the model is the diffusion into the rod-bipolar synapse of a transmitter substance, followed by the induction of an inhibitor. Making use of this model, adaptation to an illumination too weak to cause of significant decrease in the concentration of visual pigment is interpreted as due to a decreased effectiveness of the rod impulse in exciting the bipolar cell. The disparity between threshold changes for very small test spots and for relatively large spots is explained simply, without invoking any additional physiological mechanisms. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414 and in part by the United States Public Health Service Training Grant 2G-833.     

Mutual exclusion versus coexistence for discrete competitive systems

Using discrete competition models where the density dependent growth functions are either all exponential or all rational, notwithstanding the complex interactions of the species, we establish an exclusion principle. Moreover, in a 2-species discrete competition model where the growth functions are exponential and rational, an example is given illustrating coexistence when our conditions are satisfied. We obtain an exclusion principle for this 2-species model for some choice of parameters.Research partially supported by funds provided by a Science and Education Grant to the USDA-Forest Service, Southeastern Forest Experiment Station, Population Genetics of Forest Trees Research Unit, Raleigh, North Carolina     

An adaptive model for synchrony in the firefly Pteroptyx malaccae

We describe a new model for synchronization of neuronal oscillators that is based on the observation that certain species of fireflies are able to alter their free-running period. We show that by adding adaptation to standard oscillator models it is possible to observe the frequency alteration. One consequence of this is the perfect synchrony between coupled oscillators. Stability and some analytic results are included along with numerical simulations.This work was partially supported by NSF Grant DMS9002028 and the Mathematical Research Branch of The National Institutes of Health     

Models of competition in the chemostat with instantaneous and delayed nutrient recycling

Two models for competition of two populations in a chemostat environment with nutrient recycling are considered. In the first model, the recycling is instantaneous, whereas in the second, the recycling is delayed. For each model an equilibrium analysis is carried out, and persistence criteria are obtained. This paper extends the work done by Beretta et al. (1990) for a single species.Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant NSERC A4823Research carried out at the University of Alberta while on a Canada-China Scholarly Exchange Program     

Response waveforms of vertebrate photoreceptors: What are the underlying mechanisms?

A class of models is investigated using computer simulation in which the inner and outer segments of the vertebrate photoreceptor are coupled through a pump. The outer segment membrane conductance is controlled by an internal transmitter, activated by photolysis of the photosensitive molecules in the cell. Several possibilities for the coupling dynamics are investigated. The analysis favors the conclusion that the hyperpolarizing transient at high intensity stimuli arises from the coupling dynamics, (unless there is an extracellular current shunt path). It predicts, moreover, that the transient shold be observed intracellularly, but not extracellularly to the outer segment, This is, in fact, the case. It also predicts that the trasient should become more marked, as the steady state ratio of inner to outer segment currents decreases. The computer simulations are concerned with the intracellularly recorded responses; the long term adaptation parallel to pigment bleaching and regeneration is not considered explicitly here. In conclusion, it is shown that the state conditions as well as the response waveforms can be related to physiologically significant variables.     

Intracellular mechanisms of adaptation and self-regulation in self-organizing networks: The role of chemical transducers

This paper describes mechanisms of intracellular and intercellular adaptation that are due to spatial or temporal factors. The spatial mechanisms support self-regulating pattern formation that is capable of directing self-organization in a large class of systems, including examples of directed intercellular growth, transmitter production, and intracellular conductance changes. A balance between intracellular flows and counterflows causes adaptation. This balance can be shifted by environmental inputs. The decrease in Ca²⁺-modulated outward K⁺ conductance in certain molluscan nerve cells is a likely example. Examples wherein Ca²⁺ acts as a second messenger that shunts receptor sensitivity can also be discussed from this perspective. The systems differ in basic ways from recent diffusion models. Chemical transducers driven by membrane-bound intracellular signals can establish long-range intercellular interactions that compensate for variable intercellular distances and are invariant under developmental size changes; diffusional signals do not. The intracellular adaptational mechanisms are formally analogous to intercellular mechanisms that include cellular properties which are omitted in recent reaction-diffusion models of pattern formation. The cellular models use these properties to compute size-invariant properties despite wide variations in their intercellular signals. Mechanisms of temporal adaptation can be derived from the simplest laws of chemical transduction by using a correspondence principle. These mechanisms lead to such properties of intercellular signals as transient overshoot, antagonistic rebound, and an inverted U in sensitivity as intracellular signals or adaptation levels shift. Such effects are implicated in studies of behavioral, reinforcement, motor control, and cognitive coding. Supported in part by the National Science Foundation (NSF MCS 77-02958).     

The adaptation ability of neuronal models subject to a current step stimulus

Three neuronal models of the spike initiating process were investigated with respect to their ability to show adaptation to a current step: (i) the perfect integrator model (PIM), (ii) the leaky integrator model (LIM), and (iii) the Hodgkin-Huxley (HH-) model. It was found that although each neuronal model will generate different response spike trains to a given stimulus, all responses fulfilled the criteria of a deterministic neural response (Awiszus 1988). The results show that both PIM and LIM are unable to show adaptation regardless of the choice of model parameters whereas the HH-model shows a clear rate of discharge adaptation. The reason for this adaptation lies in the fact that there are conditions for the HH-model where a step stimulus is highly effective. These conditions are investigated by means of a phase plane analysis. Consequences of these results for the explanation of neuronal adaptation and the validity of the neuronal models investigated are discussed.     

Selection on phenotypic plasticity of morphological traits in response to flooding and competition in the clonal shore plant Ranunculus reptans

Adaptive evolution of phenotypic plasticity requires that plastic genotypes have the highest global fitness. We studied selection by spatial heterogeneity of interspecific competition and flooding, and by temporal heterogeneity of flooding on morphological plasticity of 52 genotypes of the clonal shore plant Ranunculus reptans. Competition reduced clone size, rosette size, leaf length and stolon internode thickness. Flooding had similar effects and reduced competition. Differences in selection between environments imply potential for either local adaptation or for indirect evolution of phenotypic plasticity. We also detected direct selection for plastic reductions in internode length in response to flooding and for a plastic increase in internode length in response to competition. Plastic responses of some morphological traits to flooding were in line with selection thereon, suggesting that they indeed are adaptive and might have evolved in response to direct selection on plasticity.     

Interspecific competition counteracts negative effects of dispersal on adaptation of an arthropod herbivore to a new host

Dispersal and competition have both been suggested to drive variation in adaptability to a new environment, either positively or negatively. A simultaneous experimental test of both mechanisms is however lacking. Here, we experimentally investigate how population dynamics and local adaptation to a new host plant in a model species, the two‐spotted spider mite (Tetranychus urticae), are affected by dispersal from a stock population (no‐adapted) and competition with an already adapted spider mite species (Tetranychus evansi). For the population dynamics, we find that competition generally reduces population size and increases the risk of population extinction. However, these negative effects are counteracted by dispersal. For local adaptation, the roles of competition and dispersal are reversed. Without competition, dispersal exerts a negative effect on adaptation (measured as fecundity) to a novel host and females receiving the highest number of immigrants performed similarly to the stock population females. By contrast, with competition, adding more immigrants did not result in a lower fecundity. Females from populations with competition receiving the highest number of immigrants had a significantly higher fecundity than females from populations without competition (same dispersal treatment) and than the stock population females. We suggest that by exerting a stronger selection on the adapting populations, competition can counteract the migration load effect of dispersal. Interestingly, adaptation to the new host does not significantly reduce performance on the ancestral host, regardless of dispersal rate or competition. Our results highlight that assessments of how species can adapt to changing conditions need to jointly consider connectivity and the community context.     

Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

Summary We present models of adaptive change in continuous traits for the following situations: (1) adaptation of a single trait within a single population in which the fitness of a given individual depends on the population's mean trait value as well as its own trait value; (2) adaptation of two (or more) traits within a single population; (3) adaptation in two or more interacting species. We analyse a dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient (i.e. the rate of increase of individual fitness with the individual's trait value). Such models have been employed in evolutionary game theory and are often appropriate both for the evolution of quantitative genetic traits and for the behavioural adjustment of phenotypically plastic traits. The dynamics of the adaptation of several different ecologically important traits can result in characters that minimize individual fitness and can preclude evolution towards characters that maximize individual fitness. We discuss biological circumstances that are likely to produce such adaptive failures for situations involving foraging, predator avoidance, competition and coevolution. The results argue for greater attention to dynamical stability in models of the evolution of continuous traits.     

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.     

Consumer functional response and competition in consumer-resource systems

This study investigates the effect of the functional response of resource consumers on the relationship between resource overlap and competition for some two-consumer, two-resource models. Two measures of competition are examined: α, the competition coefficient, and β, an index of the ease of invasion by the second consumer species when the first is at its carrying capacity. A comparison of systems with linear (type-1) and decelerating (type-2) functional responses shows that: (1) Competition coefficients are functions of the population densities of consumers or resources in systems with type-2 responses. (2) Competition coefficients may differ substantially in magnitude between systems with type-1 and type-2 functional responses. (3) The relative handling time of different resources is important in determining the relationship between overlap and competition. Positive correlations between capture rates (per unit resource) and handling times cause the system with type-2 functional responses to exhibit a higher level of competition for a given level of overlap than for the case of negative correlation. (4) If the functional response is type-2 it may be possible to obtain a priority effect in which either consumer species can exclude the other. (5) Invasion may be easier in a system with type-1 functional responses than in a similar system with type-2 functional responses, even when competition coefficients are larger in the former. Accelerating functional responses also affect the relationship between overlap and competition, but realistic models of such responses are likely to be very complex. Several currently accepted ideas in competition theory depend upon the assumption of a linear functional response, and are unlikely to be generally valid.     

Is the shape of the density-growth relationship for stream salmonids evidence for exploitative rather than interference competition?

1. Empirical studies show that average growth of stream-dwelling salmon and trout often declines with increasing density in a characteristic concave relationship. However, the mechanisms that generate negative density-growth relationships in populations in natural streams are not certain. 2. In a recent study, Imre, Grant & Cunjak (2005; Journal of Animal Ecology, 74, 508-516) argue that density-dependent growth due to exploitative competition for prey causes the negative density-growth relationships for stream salmonids. They argue that the concave shape of empirical density-growth relationships is consistent with a simple model of exploitative competition and not consistent with interference competition for space. 3. We use a simple model to show that competition for space can yield concave density-growth relationships consistent with the empirical pattern when individuals compete for foraging sites that vary spatially in quality and lower-quality sites predominate. Thus, the predictions of the exploitative competition and spatial competition models overlap. 4. The shape of the density-growth relationship does not differentiate between candidate mechanisms underlying density-dependent growth for stream salmonids. Our results highlight the general problem with determining the mechanism driving an ecological process from patterns in observational data within the context of linking population demographics to habitat structure and animal behaviour.     

Balance between noise and adaptation in competition models of perceptual bistability

Perceptual bistability occurs when a physical stimulus gives rise to two distinct interpretations that alternate irregularly. Noise and adaptation processes are two possible mechanisms for switching in neuronal competition models that describe the alternating behaviors. Either of these processes, if strong enough, could alone cause the alternations in dominance. We examined their relative role in producing alternations by studying models where by smoothly varying the parameters, one can change the rhythmogenesis mechanism from being adaptation-driven to noise-driven. In consideration of the experimental constraints on the statistics of the alternations (mean and shape of the dominance duration distribution and correlations between successive durations) we ask whether we can rule out one of the mechanisms. We conclude that in order to comply with the observed mean of the dominance durations and their coefficient of variation, the models must operate within a balance between the noise and adaptation strength—both mechanisms are involved in producing alternations, in such a way that the system operates near the boundary between being adaptation-driven and noise-driven.     

Neuroglandular contacts between vasopressin-reactive fibers and cells of the pars tuberalis in the rat

Summary In electron micrographs fibers containing vasopressin-immunoreactive elementary granules 100–120 nm in diameter are observed within the basal lamina of the adenohypophyseal pars tuberalis adjacent to the rostral portion of the median eminence. The concept of a neuroglandular transmitter function of vasopressin is discussed.Supported by the Deutsche Forschungsgemeinschaft (Grant Nr. Kr. 569/2) and the Stiftung VolkswagenwerkThe excellent technical assistance of Mrs. Helga Prien is thankfully acknowledged