Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

Aggregation pattern of individuals and the outcomes of competition within and between species: Differential equation models

The influence of spatial distribution pattern on the outcomes of intra- and interspecific competition is studied theoretically. The models developed are the generalized logistic andVolterra equations, whereLloyd 's indices of intra- and interspecies mean crowding were incorporated with their assumed linear relationship to mean density in order to express the intensity of crowding which is really effective to the existing individuals. It is shown that while the increasing patchiness of distribution has a pronounced effect of promoting the intraspecific competition and lowering the equilibrium density for individual populations, it generally relaxes the interspecific competition, making it easy for different species sharing the same niche, which would otherwise be incompatible, to coexist stably. These models thus provide a simplest theoretical basis to explain why many insect populations in nature are kept relatively rare in number and why a number of allied species often coexist freely sharing the same resource, against the “competitive exclusion principle” deduced from the originalVolterra equations.     

Hierarchical models of intra-specific competition: scramble versus contest

Hierarchical structured models for scramble and contest intraspecific competition are derived. The dynamical consequences of the two modes of competition are studied under the assumption that both populations divide up the same amount of a limiting resource at equal population levels. A comparison of equilibrium levels and their resiliences is made in order to determine which mode of competition is more advantageous. It is found that the concavity of the resource uptake rate is an important determining factor. Under certain circumstances contest competition is more advantageous for a population while under other circumstances scramble competition is more advantageous.Supported by NSF grant DMS-9306271     

Invasibility and stochastic boundedness in monotonic competition models

We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutual invasibility, as conjectured by Turelli. In the absence of invasibility, a species converges to extinction with large probability if its initial population is small, and extinction of one species must occur with probability one regardless of the initial population sizes. These results are applied to a general symmetric competition model to find conditions under which environmental fluctuations imply coexistence or competitive exclusion.     

Effects of noise on some dynamical models in ecology

We investigate effects of random perturbations on the dynamics of one-dimensional maps (single species difference equations) and of finite dimensional flows (differential equations for n species). In particular, we study the effects of noise on the invariant measure, on the correlation dimension of the attractor, and on the possibility of detecting the nonlinear deterministic component by applying reconstruction techniques to the time series of population abundances. We conclude that adding noise to maps with a stable fixed-point obscures the underlying determinism. This turns out not to be the case for systems exhibiting complex periodic or chaotic motion, whose essential properties are more robust. In some cases, adding noise reveals deterministic structure which otherwise could not be observed. Simulations suggest that similar results hold for flows whose attractor is almost two-dimensional.     

Mathematical models of microbial growth and competition in the chemostat regulated by cell-bound extracellular enzymes

A mathematical model of growth and competitive interaction of microorganisms in the chemostat is analyzed. The growth-limiting nutrient is not in a form that can be directly assimilated by the microorganisms, and must first be transformed into an intermediate product by cell-bound extracellular enzymes. General monotone functions, including Michaelis-Menten and sigmoidal response functions, are used to describe nutrient conversion and growth due to consumption of the intermediate product. It is shown that the initial concentration of the species is an important determining factor for survival or washout. When there are two species whose growth is limited by the same nutrient, three different modes of competition are described. Competitive coexistence steady states are shown to be possible in two of them, but they are always unstable. In all of our numerical simulations, the system approaches a steady state corresponding to the washout of one or both of the species from the chemostat.Research supported by NSF grant DMS-90-96279Research supported by NSERC grant A-9358     

Population dynamic consequences of competition within and between age classes

We investigate the population dynamics of a semivoltine species whose juvenile development takes two years to complete, and is followed by a very short reproductive adult stage. Reproduction is synchronized so at any given time the juvenile population consists of two cohorts. Coexistence of the two cohorts requires that the strength of intea-cohort competition exceeds that of inter-cohort competition, an extension of the competitive exclusion principle. The population may exhibit population cycles with low integer period. We identify two mechanisms for two-year cycles, and note that four-year cycles are a natural consequence of overcompensation. Three year cycles can occur and we discuss the mechanisms involved.     

Population dynamics and competition in chemostat models with adaptive nutrient uptake

 The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative feature of some experimental data which show that the population density of the winning species approaches a positive steady state via transient oscillations while that of the losing species approaches the zero steady state monotonically. Received 4 August 1995; received in revised form 15 December 1995     

Interspecific competition between two field populations of grass-feeding bugs

Abstract. 1. We tested the hypothesis that interspecific competition between two grass-feeding stenodemine bug species ( Notostira elongata Geoffroy and Megaloceraeu recticornis Geoffroy) was capable of causing population-scale mortality in the field.
2. N.elongata nymphs were added to two field enclosures in which the M.recti-cornis population was to hatch. In one of these enclosures the grass Arrhena-therum elatius L., on which only M.recticornis can feed, was also added. Population changes of the bug species were then monitored. An unmanipulated enclosure and an unfenced plot of grassland were used as controls.
3. The results demonstrated that N.elongata lowered the survival of M.recticornis and that this effect was removed by the addition of A.elatius . The results also suggested that N.elongata suffered less from the effects of competition with M.recticornis when the latter had access to the refuge foodplant.
4. Interspecific competition was rare among members of the grass-feeding stenodemine guild in the area studied. Only one out of fifteen possible pairs competed, and this competition occurred only under special circumstances.     

Convergence to stationary distributions in two-species stochastic competition models

Two sets of sufficient conditions are given for convergence to stationary distributions, for some general models of two species competing in a randomly varying environment. The models are nonlinear stochastic difference equations which define Markov chains. One set of sufficient conditions involves strong continuity and -irreducibility of the transition probability for the chain. The second set has a much weaker irreducibility condition, but is only applicable to monotonic models. The results are applied to a stochastic two-species Ricker model, and to Chesson's lottery model with vacant space, to illustrate how the assumptions can be checked in specific models.     

Details of local dispersion improve the fit of neighborhood competition models

I performed a series of greenhouse experiments to explore how patterns in the dispersion of local competitors affect the reproductive performance of Capsella bursa-pastoris, Poa annua and Senecio vulgaris. I manipulated the density and relative frequency of competitors in each of three concentric rings surrounding a central plant, thereby creating a variety patterns by which local competitors were distributed. Neighborhood competition models were used to predict the seed output of these central plants. For both Senecio vulgaris and Capsella bursa-pastoris, I found that models which incorporated the dispersion of competitors, as well as the relative emergence date of plants, performed substantially better than those that considered only the distance between the central plant and each of its competitors. I was unable to measure the seed output of Poa annua but neither emergence data nor the dispersion of competitors were important in determining its final dry-weight.Present address: Department of Biology, Box 1137, Washington University, 1 Brookings Drive, St. Louis, MO 63130, USA     

Local facilitation, bistability and transitions in arid ecosystems

Arid ecosystems are liable to undergo sudden discontinuous transitions from a vegetated to a desert state as a result of human pressure and climate change. A predictive framework about the conditions under which such transitions occur is lacking. Here, we derive and analyze a general model describing the spatial dynamics of vegetation in arid ecosystems considering local facilitation as an essential process. We investigate the conditions under which continuous or discontinuous transitions from a vegetated to a desert state are likely to occur. We focus on arid ecosystems but our approach is sufficiently general to be applied to other ecosystems with severe environmental conditions. The model exhibits bistability and vegetation patchiness. High local facilitation decreases the risk of discontinuous transitions. Moreover, for arid ecosystems where local facilitation is a driving process, vegetation patchiness indicates proximity to a transition point, but does not allow distinguishing between continuous and discontinuous transitions.     

Interactions between freshwater snails and tadpoles: competition and facilitation

Summary Freshwater snails and anuran tadpoles have been suggested to have their highest population densities in ponds of intermediate size where abiotic disturbance (e.g. desiccation) is low and large predators absent. Both snails and tadpoles feed on periphytic algae and, thus, there should be a large potential for competitive interactions to occur between these two distantly related taxa. In a field experiment we examined the relative strength of competition between two closely related snail species, Lymnaea stagnalis and L. peregra, and between L. stagnalis and tadpoles of the common frog, Rana temporaria. Snail growth and egg production and tadpole size at and time to metamorphosis were determined. Effects on the common food source, periphyton, were monitored with the aid of artificial substrates. Periphyton dry weight was dramatically reduced in the presence of snails and/or tadpoles. There were no competitive effects on growth or egg production of the two snail species when they were coexisting. Mortality of L. peregra was high (95%) after reproduction, but independent of treatment. Growth of L. stagnalis was reduced only at the highest tadpole densities, whereas egg production was reduced both by intraspecific competition and by competition with tadpoles. Differences in egg production were retained after tadpole metamorphosis. Tadpole larval period increased, weight of metamorphosing frogs decreased and growth rate was reduced as a function of increasing tadpole density. However, contrary to expectation, snails had a positive effect on tadpole larval period, weight and growth rate. Further, in experimental containers without snails there was a dense growth of the filamentous green alga Cladophora sp. We suggest that the facilitative effects of snails on tadpoles are due to an indirect mutualistic mechanism, involving competition between food sources of different quality (microalgae and Cladophora sp.) and tadpoles being competitively dominant over snails for the preferred food source (microalgae). In the presence of tadpoles snails will be forced to feed on low-quality Cladophora, increasing nutrient turnover rates, which results in enhanced productivity of microalgae, increasing tadpole food resources. Thus, tadpoles have a negative effect on snails through resource depression, while snails facilitate tadpole growth through an indirect enhancement of food availability.     

Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population models predict that a species with a lower dispersal rate always drives a competing species to extinction in the presence of spatial variation of resources. However, the introduction of intrinsic demographic stochasticity can reverse this conclusion. We present a simple model in which competition between the exploitation of resources and stochastic fluctuations leads to victory by either the faster or slower of two species depending on the environmental parameters. A simplified limiting case of the model, analyzed by closing the moment and correlation hierarchy, quantitatively predicts which species will win in the complete model under given parameters of spatial variation and average carrying capacity.     

Effects of competition and shading in planktonic communities

A model for several algal species which compete both for light and for nutrients, and which are also subject to settling and diffusion, is considered. The settling speeds and diffusion coefficients are assumed to be small, in a sense to be made precise later, and a singular perturbation argument is used. In certain cases vertical segregation of the algal species is observed, and the mechanism for this is interpreted biologically.Supported by the Danish Natural Science Research Council (Grant No. 11-8321)     

The theory and application of plant competition models: an agronomic perspective

Many studies of plant competition have been directed towards understanding how plants respond to density in monocultures and how the presence of weeds affects yield in crops. In this Botanical Briefing, the development and current understanding of plant competition is reviewed, with particular emphasis being placed on the theory of plant competition and the development and application of mathematical models to crop-weed competition and the dynamics of weeds in crops. By consolidating the results of past research in this manner, it is hoped to offer a context in which researchers can consider the potential directions for future research in competition studies and its application to integrated weed management.     

Resource partitioning and competition for shells between intertidal hermit crabs on the outer coast of Washington

Summary Resource partitioning was quantified for 6 species of intertidal hermit crabs in the genus Pagurus, that occur on the outer coast of Washington. This, together with field evidence of shell shortage and with laboratory experiments to quantify the mechanism of interactions for shells, allowed estimation of the relative intensities of inter-and intraspecific competition between these species. The findings were that: (1) the magnitude of intraspecific competition was greater than any single interspecific competitive effect for all of the species; and (2) the relative proportion of intraspecific competition was greater for the middle and upper intertidal species than for the lower intertidal species. Studies at several outer coast sites supported these generalizations. Both of these findings are consistent with the hypothesis that competitive divergence has occurred in the past. The structure of the outer coast hermit crab assemblage is compared with that of the San Juan Archipelago hermit crab assemblage. Differences between the two do not seem to be the result of adaptive responses to the presence of more competing species in the former group.     

Pacemaker and network mechanisms of rhythm generation: cooperation and competition

The origin of rhythmic activity in brain circuits and CPG-like motor networks is still not fully understood. The main unsolved questions are (i) What are the respective roles of intrinsic bursting and network based dynamics in systems of coupled heterogeneous, intrinsically complex, even chaotic, neurons? (ii) What are the mechanisms underlying the coexistence of robustness and flexibility in the observed rhythmic spatio-temporal patterns? One common view is that particular bursting neurons provide the rhythmogenic component while the connections between different neurons are responsible for the regularisation and synchronisation of groups of neurons and for specific phase relationships in multi-phasic patterns. We have examined the spatio-temporal rhythmic patterns in computer-simulated motif networks of H-H neurons connected by slow inhibitory synapses with a non-symmetric pattern of coupling strengths. We demonstrate that the interplay between intrinsic and network dynamics features either cooperation or competition, depending on three basic control parameters identified in our model: the shape of intrinsic bursts, the strength of the coupling and its degree of asymmetry. The cooperation of intrinsic dynamics and network mechanisms is shown to correlate with bistability, i.e., the coexistence of two different attractors in the phase space of the system corresponding to different rhythmic spatio-temporal patterns. Conversely, if the network mechanism of rhythmogenesis dominates, monostability is observed with a typical pattern of winnerless competition between neurons. We analyse bifurcations between the two regimes and demonstrate how they provide robustness and flexibility to the network performance.     

Interspecific competition between two species of the bean weevil

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Contributions from the Entomological Laboratory, Kyoto University, No. 110.     

Generalist and specialist predators that mediate permanence in ecological communities

 General dynamic models of systems with two prey and one or two predators are considered. After rescaling the equations so that both prey have the same intrinsic rate of growth, it is shown that there exists a generalist predator that can mediate permanence if and only if there is a population density of a prey at which its per-capita growth rate is positive yet less than its competitor’s invasion rate. In particular, this result implies that if the outcome of competition between the prey is independent of initial conditions, then there exists a generalist predator that mediates permanence. On the other hand, if the outcome of competition is contingent upon initial conditions (i.e., the prey are bistable), then there may not exist a suitable generalist predator. For example, bistable prey modeled by the Ayala–Gilpin (θ-Logistic) equations can be stabilized if and only if θ<1 for one of the prey. It is also shown that two specialist predators always can mediate permanence between bistable prey by creating a repelling heteroclinic cycle consisting of fixed points and limit cycles. Received 10 August 1996; received in revised form 21 March 1997