The dynamics of predation and competition in patchy environments

The model of N. D. Atkinson and B. Shorrocks (J. Anim. Ecol. 50, 461–471 (1981)) as two competing species distributing their progeny amongst patches according to independent negative binomial distributions. The resulting separation of the species increases the likelihood of coexistence. We have assumed a much simpler distribution of the competitors which has enabled us to explore analytically the dynamics of interactions with two competing species and a shared natural enemy in a patchy environment. Two types of natural enemy have been considered: a generalist predator whose dynamics are uncoupled from those of the two prey species, and a specialist (e.g., a parasitoid) whose dynamics are entirely coupled to those of its two prey. The following conclusions emerge. Non-aggregating generalist predators causing random predation across patches are generally destabilizing (although asymmetrical predation may in some case enhance coexistence as a result of preferential predation on the superior competitor). Predator aggregation in patches of high prey density, however, produces a switching effect which tends to promote stability. Coexistence is now even possible with high degrees of correlation in the distribution of the two prey and in situations of extreme competition where the competition coefficients exceed one. The main difference in the models with a specialist parasitoid as the natural enemy is a reduction in stability compared with the equivalent generalist-prey interaction. But stable coexistence can still readily occur if the natural enemies aggregate markedly in patches of high prey density.     

Competition and species packing in patchy environments

In models of competition in which space is treated as a continuum, and population size as continuous, there are no limits to the number of species that can coexist. For a finite number of sites, N, the results are different. The answer will, of course, depend on the model used to ask the question. In the Tilman-May-Nowak ordinary differential equation model, the number of species is asymptotically C log N with most species packed in at the upper end of the competitive hierarchy. In contrast, for metapopulation models with discrete individuals and stochastic spatial systems with various competition neighborhoods, we find a traditional species area relationship CN(a), with no species clumping along the phenotypic gradient. The exponent a is larger by a factor of 2 for spatially explicit models. In words, a spatial distribution of competitors allows for greater diversity than a metapopulation model due to the effects of recruitment limitation in their competition.     

Mating timing,dispersal and local adaptation in patchy environments

Dispersal is a life‐history trait that can evolve under various known selective pressures as identified by a multitude of theoretical and empirical studies. Yet only few of them are considering the succession of mating and dispersal. The sequence of these events influences gene flow and consequently affects the dynamics and evolution of populations. We use individual‐based simulations to investigate the evolution of the timing of dispersal and mating, i.e. mating before or after dispersal. We assume a discrete insect metapopulation in a heterogeneous environment, where populations may adapt to local conditions and only females are allowed to disperse. We run the model assuming different levels of species habitat tolerance, carrying capacity, and temporal environmental variability. Our results show that in species with narrow habitat tolerance, low to moderate dispersal evolves in combination with mating after dispersal (post‐dispersal mating). With such a strategy dispersing females benefit from mating with a resident male, as their offspring will be better adapted to the local habitat conditions. On the contrary, in species with wide habitat tolerance higher dispersal rates in combination with pre‐dispersal mating evolves. In this case individuals are adapted to the ‘average’ habitat where pre‐dispersal mating conveys the benefit of carrying relatives’ genes into a new population. With high dispersal rates and large population size, local adaptation and kin structure both vanish and the temporal sequence of dispersal and mating may become a (nearly) neutral trait.     

Behavioral, Cellular, and Molecular Analysis of Memory in Aplysia II: Long-Term Facilitation

Long-term facilitation (LTF) of Aplysia tail sensory neuron–motorneuron (SN–MN) synapses provides a synaptic correlateof memory for long-term behavioral sensitization of the tail-siphonwithdrawal reflex. LTF can be induced by repeated exposuresof serotonin (5HT) in the isolated pleural-pedal ganglion preparation.In addition, we have shown previously (Sherff and Carew, 1999)that LTF can also be induced by coincident 5HT exposure comprisedof a single 25-min exposure of 5HT at the SN cell body and a5 min pulse of 5HT at the SN-MN synapses. If synaptic 5HT isapplied either 15 min before or after somatic 5HT, LTF is significantlyreduced or is not induced at all. These results show that twoanatomically remote cellular compartments can functionally interactwithin a surprisingly short time period. In this chapter, wediscuss some of the mechanistic implications of this temporalconstraint. We also find that coincident LTF and LTF inducedby repeated pulses of 5HT differ (1) in whether they induceanother temporal phase of facilitation (intermediate-term facilitation,ITF, expressed up to 1.5 hr after 5HT), and (2) in their requirementsfor protein synthesis. The results described both in this paperand in the preceding companion paper show that there are multipleforms of both ITF and LTF that differ in their induction andexpression requirements, and at least in some instances, thedifferent temporal phases of facilitation, and perhaps comparablephases of memory, can be induced independently of each other.     

Facilitation, competition, and vegetation patchiness: from scale free distribution to patterns

A new technique for the modeling of perennial vegetation patchiness in the arid/semiarid climatic zone is suggested. Incorporating the stochasticity that affects life history of seedlings and the deterministic dynamics of soil moisture and biomass, this model is flexible enough to yield qualitatively different forms of spatial organization. In the facilitation-dominated regime, scale free distribution of patch sizes is observed, in correspondence with recent field studies. In the competition controlled case, on the other hand, power-law statistics is valid up to a cutoff, and an intrinsic length scale appears.     

Reinforcement learning for a stochastic automaton modelling predation in stationary model-mimic environments

In this paper we propose a mathematical learning model for the feeding behaviour of a specialist predator operating in a random environment occupied by two types of prey, palatable mimics and unpalatable models, and a generalist predator with additional alternative prey at its disposal. A well known linear reinforcement learning algorithm and its special cases are considered for updating the probabilities of the two actions, eat prey or ignore prey. Each action elicits a probabilistic response from the environment that can be favorable or unfavourable. To assess the performance of the predator a payoff function is constructed that captures the energetic benefit from consuming acceptable prey, the energetic cost from consuming unacceptable prey, and lost benefit from ignoring acceptable prey. Conditions for an improving predator payoff are also explicitly formulated.     

Interspecific competition between Sitophilus zeamais and Sitotroga cerealella in a patchy environment

The maize weevil, Sitophilus zeamais (Motchulsky) (Coleoptera: Curculionidae), and the Angoumois grain moth, Sitotroga cerealella (Olivier) (Lepidoptera: Gelechiidae), are important insect pests of stored products. The coexistence in nature of the two species on maize has been difficult to explain from laboratory set‐ups, as the moth is inevitably eliminated by S. zeamais. However, early laboratory experiments ignored the spatial dimension, while several studies have lately revealed that two competing species may coexist in a spatially divided environment even though one of the species is competitively superior in a simpler universe. Two hypotheses for coexistence were examined by studying the interactions in a system where the resources were spatially divided. It was found that spatial subdivision in the current experiment was insufficient to ensure coexistence between the two species, so neither of the hypotheses could be confirmed. A simple model describing the population dynamics of S. zeamais was fitted to the data. Its parameters provide important information about how resource depletion influences the per capita growth rate. Finally, the study indicates that the mechanism responsible for S. zeamais's rapid elimination of S. cerealella is the superiority of the former species to colonize and monopolize new patches. The design of this study may serve as a template for further laboratory experiments revealing the effect of a spatially divided environment on competitive interactions. However, the present study also indicates that choosing the appropriate spatial scale may be critical for relating the results to natural environments.     

Facilitation and competition influence succession in a subtropical old field

The effects of neighboring vegetation and soil fertility on the establishment, survival and growth of tree species were studied in a subtropical old-field area in south Brazil. Seed damage, germination and seedling establishment of four tree species plus growth and survival of two transplanted tree species were monitored under factorial combinations of the following treatments: (1) pioneer vegetation (presence and absence); (2) soil fertility (addition of NPK and control). Facilitation was the main process affecting plant performance. The presence of pioneer vegetation significantly improved germination, establishment, growth and survival of most study species. Around 90% of sown seeds were damaged and the removal of pioneer vegetation significantly increased seed damage for all species studied, decreased germination in three out of four species, and decreased establishment in one species. Moreover a significantly higher seedling growth rate of Inga virescens was found after the first year of the experiment in plots where vegetation was present. The presence of vegetation significantly increased seedling survival of I. virescens by protecting seedlings from leaf loss due to winter frosts. Competition was detected by the second year when a higher growth of transplanted seedlings of the species Araucaria angustifolia occurred in plots where vegetation was present and fertilizer were applied. A lower growth rate was detected in plots where vegetation was present but fertilizer was not applied. These results indicate a balance between competition for soil nutrients and protection by neighbor vegetation. Damage of seedlings by leaf cutter ants was an important barrier for plant survival. Damage occurred in 80% of the A. angustifolia seedlings and 58% of these damaged seedlings died. The presence of neighboring vegetation tended to protect seedlings from ant damage. Although competition occurred, facilitation seems to be the main process driving early successional changes in this subtropical old field. This was mainly due to the improvement of local microclimatic conditions and protection against herbivores by neighboring vegetation. Facilitation occurred during establishment and growth phases in a subtropical area that is considered a productive, low stress environment. Our results indicate that facilitation may be more frequent in productive environments than previously thought.     

Cellular transformation by radiation: Induction,promotion, and inhibition

Mammalian cell cultures offer powerful tools for evaluating qualitatively and quantitatively the oncogenic potential of radiation over a wide range of doses with particular importance at the low dose range that is relevant to human exposure and risk. Our studies have shown that early events in the process of radiation induced transformation in both rodent and human cells requires initial replication for fixation of transformation as a hereditary property of the cells and further clonal expansion for full expression. Early events (fixation) are inhibited by cell–cell contact and high cell density but can be modified at low temperature where repair processes are slowed. Cell–cell contact and communication in tissue organization may be in part responsible for our findings that radiation oncogenesis induced in utero in hamsters is expressed at a lower frequency than that induced in vitro. Quantitative studies carried out on hamster embryo cells indicate that neutrons are more effective in their carcinogenic potential than x-rays but also more toxic, that splitting the dose of x-rays at low doses leads to enhanced transformation, but that at high doses protracted radiation has a sparing effect. At all dose ranges survival was increased by protracting the radiation dose, thus suggesting that different repair processes must be involved for survival and transformation. Similar observations were seen when the protease inhibitor Antipain was found to enhance transformation in rodent and human cells when present at the time of radiation, but was protective when added after radiation. Survival was not modified under any of those conditions, and Antipain did not affect DNA replication and repair. In our qualitative studies, once cells are transformed by radiation, they exhibit a wide range of structural and functional phenotypic changes, some of which are membrane-associated and are expressed within days after induction. Our current studies on nutritional and hormonal influences on radiation transformation indicate the following: Pyrolysate products from broiled protein foods act in synergism with radiation to produce transformation, whereas vitamin A analogs are powerful, preventive agents. Retinoids inhibit both x-ray-induced transformation and its promotion by TPA: these modifications (enhancement by TPA, inhibition by retinoids) are not reflected in sister chromatid exchanges, but are reflected in the level of membrane associated enzymes Na/K ATPase. Whereas retinoids modify late events (expression, promotion), we find that thyroid hormone plays a crucial role in the early phases of radiation and chemically induced transformation. Under hypothyroid conditions no transformation is observed. The addition of triiodothyronine at physiological levels results in a transformation rate that is dose-related. Our recent success in transforming human skin fibroblasts will enable quantitative and qualitative studies of radiation carcinogenesis in a system relevant to man.     

Dispersal and competition models for plants

New models for seed dispersal and competition between plant species are formulated and analyzed. The models are integrodifference equations, discrete in time and continuous in space, and have applications to annual and perennial species. The spread or invasion of a single plant species into a geographic region is investigated by studying the travelling wave solutions of these equations. Travelling wave solutions are shown to exist in the single-species models and are compared numerically. The asymptotic wave speed is calculated for various parameter values. The single-species integrodifference equations are extended to a model for two competing annual plants. Competition in the two-species model is based on a difference equation model developed by Pakes and Maller [26]. The two-species model with competition and dispersal yields a system of integrodifference equations. The effects of competition on the travelling wave solutions of invading plant species is investigated numerically.     

The shape of the spatial kernel and its implications for biological invasions in patchy environments

Ecological and epidemiological invasions occur in a spatial context. We investigated how these processes correlate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or epidemiological units. Distance dependence is described by a spatial kernel, characterized by its shape (kurtosis) and width (variance). We also developed a novel method to analyse and generate point-pattern landscapes based on spectral representation. This involves two measures: continuity, which is related to autocorrelation and contrast, which refers to variation in patch density. We also analysed some empirical data where our results are expected to have implications, namely distributions of trees (Quercus and Ulmus) and farms in Sweden. Through a simulation study, we found that kernel shape was not important for predicting the invasion speed in randomly distributed patches. However, the shape may be essential when the distribution of patches deviates from randomness, particularly when the contrast is high. We conclude that the speed of invasions depends on the spatial context and the effect of the spatial kernel is intertwined with the spatial structure. This implies substantial demands on the empirical data, because it requires knowledge of shape and width of the spatial kernel, and spatial structure.     

Grass-to-grass protection from grazing in a semi-arid steppe. Facilitation, competition, and mass effect

Plants of low palatability often serve as biotic refuges from grazing to palatable plants. Evidence for this facilitation comes from cases where the interacting species have different life form, which may minimize competition. Protected plants act as remnant seed sources that may maintain the palatable populations locally viable through mass effects. Here, we assess (1) the spatial association between a highly palatable Patagonian grass (Bromus pictus) and less preferred tussock grasses, (2) the role played by seed sources in maintaining the population in the face of heavy grazing by sheep, and (3) the facilitative and competitive components of the interaction. We quantified B. pictus density and its distance to nearest tussocks inside and outside a grazing exclosure. We also considered different distances from the exclosure, both leeward and windward, because strong westerly winds may be critical for dispersal. Additionally, we quantified several attributes of protected and unprotected B. pictus plants with and without grazing. Density of B. pictus was about 20 times greater inside the exclosure than outside. However, this difference was less pronounced in the leeward vicinity of the exclosure than in the windward one, which suggests a mass effect. B. pictus was significantly associated to less palatable tussocks, and the association became stronger under grazing and as distance from the exclosure edge increased. Protection under grazing was associated with a significant increase in plant biomass, height, tiller number, and panicle number, whereas protection in the absence of grazing, which could evidence competition, resulted in reductions of tiller number and panicle number, and an increase of height. These results suggest that in areas under grazing pressure on palatable grasses, other less palatable grasses may provide a protection from grazing that outweighs competitive effects. Such protection may generate small-scale mass effects that maintain the population at relatively high density.     

Searching efficiency of the lady beetleCoccinella septempunctata larvae in uniform and patchy environments

Experiments were conducted on the searching behavior and searching efficiency of the lady beetleCoccinella septempunctata bruckii Mulsant under conditions of various prey distributions and prey densities. The larvae changed their searching behavior before and after feeding. Before feeding the larvae moved quickly and the searching paths were nearly linear. But after feeding the speed decreased and turning angle increased. The speed and turning angle reverted gradually and recovered the initial pattern 95 s after feeding. The searching efficiency differed depending on the prey distribution. At low prey density, searching was most efficient when prey were distributed uniformly. But at middle and high prey densities, searching was most efficient when prey items were highly aggregated. The observed searching behavior of 4th instarC. septempunctata larvae was likely to be optimal considering the natural distribution of colonies of their prey, aphids.     

Theoretical perspectives on the statics and dynamics of species' borders in patchy environments

Understanding range limits is a fundamental problem in ecology and evolutionary biology. In 1963, Mayr argued that "contaminating" gene flow from central populations constrained adaptation in marginal populations, preventing range expansion, while in 1984, Bradshaw suggested that absence of genetic variation prevented species from occurring everywhere. Understanding stability of range boundaries requires unraveling the interplay of demography, gene flow, and evolution of populations in concrete landscape settings. We walk through a set of interrelated spatial scenarios that illustrate interesting complexities of this interplay. To motivate our individual-based model results, we consider a hypothetical zooplankter in a landscape of discrete water bodies coupled by dispersal. We examine how patterns of dispersal influence adaptation in sink habitats where conditions are outside the species' niche. The likelihood of observing niche evolution (and thus range expansion) over any given timescale depends on (1) the degree of initial maladaptation; (2) pattern (pulsed vs. continuous, uni- vs. bidirectional), timing (juvenile vs. adult), and rate of dispersal (and hence population size); (3) mutation rate; (4) sexuality; and (5) the degree of heterogeneity in the occupied range. We also show how the genetic architecture of polygenic adaptation is influenced by the interplay of selection and dispersal in heterogeneous landscapes.     

Facilitation and competition in the high Arctic: the importance of the experimental approach

In the last decade, plant ecologists have focussed more on the occurrence of positive plant–plant interactions than ever before. Especially in severe environments, such as the Arctic, species removal experiments tend to find facilitative rather than competitive effects, casting doubt on the importance of competition under extreme growing conditions. Two approaches to measure plant–plant interactions presented here reveal that competition affects plant growth even in the high Arctic. Luzula confusa and Salix polaris show a reduced growth in mixed stands compared with pure. This competition effect is not detected in a removal experiment, which inevitably also alters site microclimate. Indeed, in the latter experiment, facilitative effects of Luzula on Salix were found. Evidently, both facilitation and competition are acting and important. Causes and implications are discussed using a conceptual model derived from that of Brooker and Callaghan (1998).     

Search mechanism of a stream grazer in patchy environments: the role of food abundance

Summary The search behavior of the grazing stream insect Baetis tricaudatus (Ephemeroptera: Baetidae) was examined in field and laboratory experiments. Regardless of food abundance in experimental habitats, nymphs spent significantly more time in food patches than predicted if they had moved randomly with respect to patches. A significant reduction in movement rate within patches relative to movement rate between patches largely accounted for these results. The movement pattern within patches was highly systematic and in agreement with predictions of optimal foraging theory since food was uniformly distributed within patches. Between-patch search movements were affected by food abundance in the most recently grazed patch. Search intensity after departure from a patch was positively related to food abundance in the patch while movement rate after patch departure was inversely related to patch food level. These effects produced between-patch movement patterns that were suboptimal in the experimental habitats because they resulted in revisitation of previously depleted patches. However, differences between experimental and natural habitats in the spatial occurrence of patch types suggest that Baetis between-patch search behavior may be adaptive in natural habitats.     

Comparative dynamics of three models for host-parasitoid interactions in a patchy environment

Phenomenological models represent a simplified approach to the study of complex systems such as host-parasitoid interactions. In this paper we compare the dynamics of three phenomenological models for host-parasitoid interactions developed by May (1978), May and Hassell (1981) and May et al. (1981). The essence of the paper by May and Hassell (1981) was to define a minimum number of parameters that would describe the interactions, avoiding the technical difficulties encountered when using models that involve many parameters, yet yielding a system of equations that could capture the essence of real world interactions in patchy environments. Those studies dealt primarily with equilibrium and coexistence phenomena. Here we study the dynamics through bifurcation analysis and phase portraits in a much wider range of parameter values, carrying the models beyond equilibrium states. We show that the dynamics can be either stable or chaotic depending on the location of a damping term in the equations. In the case of the stable system, when host density dependence acts first, a stable point is reached, followed by a closed invariant curve in phase space that first increases then decreases, finally returning to an asymptotically stable point. Chaos is not seen. On the other hand, when parasitoid attack occurs before host density dependence, chaos is inevitably apparent. We show, as did May et al. (1981) and stated earlier byWang and Gutierrez (1980), that the sequence of events in host-parasitoid interactions is crucial in determining their stability. In a chaotic state the size of the host (e.g., insect pests) population becomes unpredictable, frequently becoming quite large, a biologically undesirable outcome. From a mathematical point of view the system is of interest because it reveals how a strategically placed damping term can dramatically alter the outcome. Our study, reaching beyond equilibrium states, suggests a strategy for biological control different from that of May et al. (1981).     

Stochastic automaton models for interaction of excitatory and inhibitory impulse sequences in neurons

The mechanisms by which excitatory and inhibitory input impulse sequences interact in changing the spike probability in neurons are examined in the two mathematical neuron models; one is a real-time neuron model which is close to physiological reality, and the other a stochastic automaton model for the temporal pattern discrimination proposed in the previous paper (Tsukada et al., 1976), which is developed in this paper as neuron models for interaction of excitatory and inhibitory input impulse sequences. The interval distributions of the output spike train from these models tend to be multimodal and are compared with those used for experimental data, reported by Bishop et al. (1964) for geniculate neuron activity and Poisson process deleting model analyzed by Ten Hoopen et al. (1966). Special attention, moreover, should be paid to how different forms of inhibitory input are transformed into the output interval distributions through these neuron models. These results exhibit a clear correlation between inhibitory input form and output interval distribution. More detailed information on this mechanism is obtained from the computations of recurrence-time under the stationary condition to go from active state to itself for the first time, each of which is influenced by the inhibitory input forms. In addition to these facts, some resultant characteristics on interval histogram and serial correlation are discussed in relation to physiological data from the literature.