Effects of density-restricted food encounter on some single-level competition models

A family of two-species competition models in which density-restricted rates of food enounter are explicitly incorporated generates the following results:

1. 1. Sigmoidal growth. A new model for sigmoidal single-species growth is produced, but one whose inflection point always falls below half the carrying capacity.

2. 2. Comparison with simpler models. In models having shared and exclusive resources, the one or two stable nodes of simpler models may no longer occur in the first quadrant. Such models can simulate how one species by consuming enough overlapping resource can cause another species, unable to maintain itself on its exclusive resources, to go extinct. In models for interspecific interference competition (resource competition purely intraspecific), one or even two more intersections of the zero-isoclines may occur, or the isoclines may intersect once, but with different relative slopes than in the simpler models.

3. 3. Alternative communities. A new model is produced for alternative communities. Conditions for this situation, phrased in terms of parameters measuring feeding and competitive abilities, are rather narrow.

     

Effects of nutrient and soil moisture on competition between shape Carex stricta,shape Phalaris arundinacea,and shape Typha latifolia

We investigated the importance of nutrients, soil moisture, arbuscular mycorrhizal fungi (AMF), and interspecific competition levels on the biomass allocation patterns of three wetland perennial plant species, Carex stricta Lam., Phalaris arundinacea L., and Typha latifolia L. A factorial experiment was conducted with high-low nutrient levels, high-low soil moisture levels, and with and without AMF inoculation. Under the experimental conditions, plant inoculation by AMF was too low to create a treatment and the AMF treatment was dropped from the total analysis. P. arundinacea and T. latifolia biomass were 73% and 77% higher, respectively, in the high nutrient treatment compared to the low nutrient treatment. Biomass allocation between shoots and roots remained relatively constant between environmental treatments, although shoot:root ratios of P. arundinacea declined in the low nutrient treatment. For C. stricta, the high nutrient and soil moisture treatments resulted in an increase in biomass of 50% and 15%, respectively. Shoot:root ratios were nearly constant among all environmental conditions. Biomass of T. latifolia and C. stricta was greatly decreased when grown with P. arundinacea. The rapid, initial height growth of P. arundinacea produced a spreading, horizontal canopy that overshadowed the vertical leaves of T. latifolia and C. stricta throughout the study. This pattern was repeated in both high and low nutrient and soil moisture treatments. When grown with P. arundinacea, C. stricta and T. latifolia significantly increased their mean shoot height, regardless of the nutrient or soil moisture level. The results of this experiment suggest that C. stricta and T. latifolia were light limited when growing with P. arundinacea and that canopy architecture is more important for biomass allocation than the other environmental conditions tested. The results also suggest that Phalaris arundinacea is an inherently better competitor (sensu Grime 1979) than C. stricta or T. latifolia.     

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.     

Density compensation in New World bat communities

Understanding the role of competitive interactions in shaping the structure of communities has been one the most unrelenting challenges to ecology. Traditionally, competitive interactions were assumed to be the most important agent of deterministic structure, with overdispersed morphological patterns based on body size and trophic status as their hallmark. However, models of community organization based solely on morphology have yielded only equivocal results for many taxa. Fortunately, morphological patterns may not be the only indications of competitively induced deterministic structure. Herein, we explore the degree to which the structure of five feeding guilds (aerial insectivores, frugivores, gleaning animalivores, molossid insectivores, and nectarivores) from 15 New World bat communities reflects density compensation. Nonrandom associations between abundance and morphological distance were detected in five communities, in three feeding guilds, and with respect to four competitive scenarios. Nonetheless, patterns consistent with the hypothesis of density compensation were neither pervasive nor consistent in New World bat communities. Competitively induced community structure may exist under only narrow temporal and environmental conditions, and may not be characteristic of organization in most situations.     

Species packing in nonsmooth competition models

Despite the potential for competition to generate equilibrium coexistence of infinitely tightly packed species along a trait axis, prior work has shown that the classical expectation of system-specific limits to the similarity of stably coexisting species is sound. A key reason is that known instances of continuous coexistence are fragile, requiring fine-tuning of parameters: A small alteration of the parameters leads back to the classical limiting similarity predictions. Here we present, but then cast aside, a new theoretical challenge to the expectation of limiting similarity. Robust continuous coexistence can arise if competition between species is modeled as a nonsmooth function of their differences—specifically, if the competition kernel (differential response of species’ growth rates to changes in the density of other species along the trait axis) has a nondifferentiable sharp peak at zero trait difference. We will say that these kernels possess a “kink.” The difference in predicted behavior stems from the fact that smooth kernels do not change to a first-order approximation around their maxima, creating strong competitive interactions between similar species. “Kinked” kernels, on the other hand, decrease linearly even for small species differences, reducing interspecific competition compared with intraspecific competition for arbitrarily small species differences. We investigate what mechanisms would lead to kinked kernels in the first place. It turns out that discontinuities in resource utilization generate them. We argue that such sudden jumps in the utilization of resources are unrealistic, and therefore, one should expect kernels to be smooth in reality.     

Clutch-size behavior and coexistence in ephemeral-patch competition models

Systems of patchy, ephemeral resources often support surprisingly diverse assemblages of consumer insects. Aggregation of consumer individuals over the landscape of patches has been suggested as one mechanism that can stabilize competition among consumer species. One mechanism for larval aggregation is the laying of eggs in clutches by females traveling among patches to distribute their total fecundity. We use simulation models to explore the consequences, for coexistence of competitors, of larval aggregation that arises from clutch laying. Contrary to some previous treatments, we find that clutch laying can be strongly stabilizing and under certain conditions can be sufficient to allow competitors to coexist stably. We extend these models by considering clutch size as a variable that responds to the abundance of resource patches. Such a relationship might be expected because females should lay their eggs in fewer but larger clutches when the cost of travel among patches is high (because patches are rare). When females adjust clutch size in response to resource abundance, coexistence can be easiest when resource patches are scarce and most difficult when resources are abundant.     

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.     

Stability in Gilpin and Ayala's models of competition

Summary Simple and effective conditions for global stability in a class of models for m competing species are given. A numerical method is used to establish a large finite region of attraction for the feasible equilibrium in Gilpin and Ayala's model of two competing Drosophila populations.     

Density compensation in allopatric populations of the pygmy shrewSorex minutus on Gotland and the outer hebrides: evidence for the effect of interspecific competition

Pygmy shrewsSorex minutus occur allopatrically in Ireland, the Outer Hebrides and Gotland in Sweden, and sympatrically with common shrewsS. minutus on the European mainland and in England. Competition theory redicts higher population density in allopatric populations as a consequence of relaxed competition. Here this prediction is tested by comparing allopatric populations of pygmy shrews in the Outer Hebrides and in Gotland with sympatric populations on the Swedish mainland. Population densities were higher in allopatry than in sympatry. Lower summed densities in allopatry, which is predicted by niche theory, was found on the Outer Hebrides, but not on Gotland. Size distributions of carabids, which are important food items, could not explain the differences in population densities. Since both avian predators and snakes are present in all areas, population density of pygmy shrews during autumn in concluded to be regulated primarly by competition with common shrews in areas of sympatry.     

Latitudinal and voltinism compensation shape thermal reaction norms for growth rate

Latitudinal variation in thermal reaction norms of key fitness traits may inform about the response of populations to climate warming, yet their adaptive nature and evolutionary potential are poorly known. We assessed the contribution of quantitative genetic, neutral genetic and environmental effects to thermal reaction norms of growth rate for populations of the damselfly Ischnura elegans. Among populations, reaction norms differed primarily in elevation, suggesting that time constraints associated with shorter growth seasons in univoltine, high-latitude as well as multivoltine, low-latitude populations selected for faster growth rates. Phenotypic divergence among populations is consistent with selection rather than drift as Q(ST) was greater than F(ST) in all cases. Q(ST) estimates increased with experimental temperature and were influenced by genotype by environment interactions. Substantial additive genetic variation for growth rate in all populations suggests that evolution of trait means in different environments is not constrained. Heritability of growth rates was higher at high temperature, driven by increased genetic rather than environmental variance. While environment-specific nonadditive effects also may contribute to heritability differences among temperatures, maternal effects did not play a significant role (where these could be accounted for). Genotype by environment interactions strongly influenced the adaptive potential of populations, and our results suggest the potential for microevolution of thermal reaction norms in each of the studied populations. In summary, the observed latitudinal pattern in growth rates is adaptive and results from a combination of latitudinal and voltinism compensation. Combined with the evolutionary potential of thermal reaction norms, this may affect populations' ability to respond to future climate warming.     

Soil organisms shape the competition between grassland plant species

Decomposers and arbuscular mycorrhizal fungi (AMF) both determine plant nutrition; however, little is known about their interactive effects on plant communities. We set up a greenhouse experiment to study effects of plant competition (one- and two-species treatments), Collembola (Heteromurus nitidus and Protaphorura armata), and AMF (Glomus intraradices) on the performance (above- and belowground productivity and nutrient uptake) of three grassland plant species (Lolium perenne, Trifolium pratense, and Plantago lanceolata) belonging to three dominant plant functional groups (grasses, legumes, and herbs). Generally, L. perenne benefited from being released from intraspecific competition in the presence of T. pratense and P. lanceolata. However, the presence of AMF increased the competitive strength of P. lanceolata and T. pratense against L. perenne and also modified the effects of Collembola on plant productivity. The colonization of roots by AMF was reduced in treatments with two plant species suggesting that plant infection by AMF was modified by interspecific plant interactions. Collembola did not affect total colonization of roots by AMF, but increased the number of mycorrhizal vesicles in P. lanceolata. AMF and Collembola both enhanced the amount of N and P in plant shoot tissue, but impacts of Collembola were less pronounced in the presence of AMF. Overall, the results suggest that, by differentially affecting the nutrient acquisition and performance of plant species, AMF and Collembola interactively modify plant competition and shape the composition of grassland plant communities. The results suggest that mechanisms shaping plant community composition can only be understood when complex belowground interactions are considered.     

Cellular automaton models for competition in patchy environments: Facilitation, inhibition, and tolerance

We have developed cellular automaton models for two species competing in a patchy environment. We have modeled three common types of competition: facilitation (in which the winning species can colonize only after the losing species has arrived) inhibition (in which either species is able to prevent the other from colonizing) and tolerance (in which the species most tolerant of reduced resource levels wins). The state of a patch is defined by the presence or absence of each species. State transition probabilities are determined by rates of disturbance, competitive exclusion, and colonization. Colonization is restricted to neighboring patches. In all three models, disturbance permits regional persistence of species that are excluded by competition locally. Persistence, and hence diversity, is maximized at intermediate disturbance frequencies. If disturbance and dispersal rates are sufficiently high, the inferior competitor need not have a dispersal advantage to persist. Using a new method for measuring the spatial patterns of nominal data, we show that none of these competition models generates patchiness at equilibrium. In the inhibition model, however, transient patchiness decays very slowly. We compare the cellular automaton models to the corresponding mean-field patch-occupancy models, in which colonization is not restricted to neighboring patches and depends on spatially averaged species frequencies. The patch-occupancy model does an excellent job of predicting the equilibrium frequencies of the species and the conditions required for coexistence, but not of predicting transient behavior.     

Two models for competition between age classes

We consider two lumped age-structured models of juvenile against adult competition, one of which is a compartmental ordinary differential equation (ODE) model and one of which is a system of ODEs with delay derived from the McKendrick partial differential equation (PDE) model. Existence and stability of positive equilibria and existence of oscillatory solutions of both models are studied. Using a competition parameter, which measures the intra-specific competition, we investigate the effects of the competitive interactions between juveniles and adults on the dynamics of the population for both models. We find that these effects are different for the two models and discuss the differences from the modeling perspective. The discussion reveals an interesting relation between the length of the maturation period and the vital rates' dependence on the competition parameter.     

Coexistence in competition models with density-dependent mortality

We consider a two-competitor/one-prey model in which both competitors exhibit a general functional response and one of the competitors exhibits a density-dependent mortality rate. It is shown that the two competitors can coexist upon the single prey. As an example, we consider a two-competitor/one-prey model with a Holling II functional response. Our results demonstrate that density-dependent mortality in one of the competitors can prevent competitive exclusion. Moreover, by constructing a Liapunov function, the system has a globally stable positive equilibrium.