Spider-web kleptoparasites as a model for studying producer-consumer interactions

In this study, we documented that the kleptoparasitic spidersArgyroes elvatus consume and assimilate web material from thehost spider Nephila clavipes. We also demonstrated quantitativelythat the amount of web material consumed by the kleptopa asiteis equivalent to the amount of insect material comsumed whenhost vigilance is low, as expected when foraging conditionsare very good. Argyrodes vary in their impact on their hosts,as they may steal large prey, small prey, or silk. This host-kieptoparasite interaction is therefore an ideal system for experimentallycramming a variable producer-consumer interaction. We compareour experimental results to published experiments showing thatthe impact of Arg on a Nephila host can be deleterious whenforaging conditions are poor.     

Stability in a metapopulation model with density-dependent dispersal

A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.     

Dynamic regimes in a model of single-locus density-dependent selection

A model of density-dependent selection in a Mendelian single-locus population was analyzed in the case where the fitnesses of genotypic forms are exponential functions of the population size. Analytical and numerical studies of the model were performed for a diallelic locus, and parametric regions were established for different dynamic behaviors of the model. The diallelic model of density-dependent selection was generalized to a multiallelic locus; the results of its analysis are described.     

A density-dependent Leslie matrix model

A density-dependent Leslie matrix model introduced in 1948 by Leslie is mathematically analyzed. It is shown that the behavior is similar to that of the constant Leslie matrix. In the primitive case, the density-dependent Leslie matrix model has an asymptotic distribution corresponding to the logistic equation. However, in the imprimitive case, the asymptotic distribution is periodic, with period depending on the imprimitivity index.     

On a density-dependent model of competition for one resource

We use the concept of steady-state characteristic of a population using a single limiting resource, in order to discuss the issue of the competition of many species for the same resource. The steady-state characteristic is a curve that is associated to each species, likely to be determined empirically. Once one knows the steady-state characteristics and the dynamic of the renewal of the resource, it is possible to predict to some extent the issue of the competition and to give sufficient conditions for coexistence.     

Testing for density-dependent effects in sequential censuses

Summary In response to Gaston and Lawton (1987), we evaluated the ability of four statistical procedures to detect density dependence. We used data from the same 16 populations as Gaston and Lawton (1987). In each population, density dependence had been previously established with techniques that use more extensive data. The major axis test (Slade 1977) was rarely (3 populations of 16) capable of detecting density dependence. The autocorrelation test (Bulmer 1975) detected density dependence in 5 of 16 species (14 of 59 tests overall). The randomization procedure (Pollard et al. 1987) detected density dependence in 7 of the 16 data sets (10 of 59 tests overall). The simulation procedure (Vickery and Nudds 1984) detected density dependence in 5 of the 16 data sets (11 of 59 tests overall). We suggest that not all annual census data taken from populations subject to density-dependent effects will actually show evidence of such effects. We conclude that Pollard et al. 's (1987) randomization procedure is the best test for detecting density dependence in sequential census data but it is not as powerful as more elaborate techniques (k-factor analysis, experimentation, etc.), nor is it meant to replace more extensive analyses.     

Spatial scaling in a benthic population model with density-dependent disturbance.

This work investigates approaches to simplifying individual-based models in which the rate of disturbance depends on local densities. To this purpose, an individual-based model for a benthic population is developed that is both spatial and stochastic. With this model, three possible ways of approximating the dynamics of mean numbers are examined: a mean-field approximation that ignores space completely, a second-order approximation that represents spatial variation in terms of variances and covariances, and a patch-based approximation that retains information about the age structure of the patch population. Results show that space is important and that a temporal model relying on mean disturbance rates provides a poor approximation to the dynamics of mean numbers. It is possible, however, to represent relevant spatial variation with second-order moments, particularly when recruitment rates are low and/or when disturbances are large and weak. Even better approximations are obtained by retaining patch age information.     

Dynamical analysis of density-dependent selection in a discrete one-island migration model

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in fitness are described. The birth of an unusual chaotic attractor is also illustrated. This attractor is produced when migration causes chaotic dynamics on a boundary of phase space to bifurcate into the interior of phase space, resulting in bistable genetic polymorphic behavior.     

Evolutionarily stable age at first reproduction in a density-dependent model.

We develop a new model of life history evolution to investigate the evolution of age at first reproduction. Density dependence is taken into account. For a given "species", age of maturity, offspring survival, immature survival, adult survival, fecundity, immature age-classes entering in competition with adults and immature competitive ability are traits adjustable by natural selection, and constitute a particular strategy. On the contrary, the type of intraspecific competition (scramble or contest), strength of competition and inherent net reproductive rate Ro(inh) are fixed (specific) characteristics. As a consequence of fixing Ro(inh), the evolution of any trait will affect trade-offs between others. Evolutionarily stable strategies are determined numerically by using the mathematical concept of Lyapunov exponents. Altogether, we consider 960 different hypothetical "species" (i.e. different combinations of fixed traits). Corresponding ESSs are analyzed with respect to their age at first reproduction, adult survival and immature competitive ability components. They appear to be gathered in three groups. One is intuitive and characterized by a reduction of immature competitive ability and a correlation of age of maturity with adult survival; populations reach mainly equilibria. The two other groups respectively include "species" with low age of maturity but high adult survival, and "species" close to semelparity with delayed maturity; immature competitive ability may not be minimized, and populations possibly exhibit complex dynamics. In conclusion, the hypothesis that the evolution of a demographic parameter modifies trade-offs between others turns out to have important consequences. We argue that life history theory cannot ignore the source and mode-of-operation of density dependence and must regard potential short-term instability as essential.     

The evolution of density-dependent dispersal in a noisy spatial population model

It is well-known that dispersal is advantageous in many different ecological situations, e.g. to survive local catastrophes where populations live in spatially and temporally heterogeneous habitats. However, the key question, what kind of dispersal strategy is optimal in a particular situation, has remained unanswered. We studied the evolution of density-dependent dispersal in a coupled map lattice model, where the population dynamics are perturbed by external environmental noise. We used a very flexible dispersal function to enable evolution to select from practically all possible types of monotonous density-dependent dispersal functions. We treated the parameters of the dispersal function as continuously changing phenotypic traits. The evolutionary stable dispersal strategies were investigated by numerical simulations. We pointed out that irrespective of the cost of dispersal and the strength of environmental noise, this strategy leads to a very weak dispersal below a threshold density, and dispersal rate increases in an accelerating manner above this threshold. Decreasing the cost of dispersal increases the skewness of the population density distribution, while increasing the environmental noise causes more pronounced bimodality in this distribution. In case of positive temporal autocorrelation of the environmental noise, there is no dispersal below the threshold, and only low dispersal below it, on the other hand with negative autocorrelation practically all individual disperses above the threshold. We found our results to be in good concordance with empirical observations.     

Quasi-equilibrium reduction in a general class of stoichiometric producer-consumer models

This article compares a general closed nutrient, stoichiometric producer-consumer model to a two-dimensional 'quasi-equilibrium' approximation. We demonstrate that the quasi-equilibrium system can be rigorously analysed, resulting in nullcline-based criteria for the local stability of system equilibria and for the non-existence of periodic orbits. These results are applied to a study of the dependence of the reduced system on nutrient and energy enrichment. When energy and nutrient enrichment are considered together, the associated bifurcation structures of the two models are seen to share the same essential qualitative characteristics. However, numerical simulations of the three-dimensional parent model show highly complex domains of the persistence and extinction that by Poincare-Bendixson theory are not possible for the two-dimensional reduction. This complexity demonstrates a major difference between the two models, and suggests potential challenges in the use of either model for predicting the long-term behaviour of real-world systems at specific nutrient and energy levels.     

Dispersion movements in ants: spatial structuring and density-dependent effects

This paper examines whether the characteristics of individual dispersion movements in ants are changed when workers are moving solitarily or in a group. We analyzed the trajectories of workers of the species Messor sancta moving solitarily or in groups of different size (5, 10, 15 individuals), tested for density-dependent effects on their trajectory characteristics and investigated through resampling techniques whether ants are able to spatially structure their movements through direct (e.g. contact) or indirect (pheromone deposited on the ground) interactions. In addition to group size, the effects of the nutritional state of the colony and of the state of the area on which ants were dispersing were also examined. Solitary ants moved faster and had more sinuous trajectories than ants moving in a group. We found however no significant differences in trajectory characteristics between groups of different size. Whatever the group size, ants from starved colonies moved more slowly and had more direct trajectories than their counterpart coming from fed colonies. On the other hand, the state of the area on which ants were moving had no direct significant effect on dispersion movement. Ants dispersing in a group moved independently and did not coordinate their movements through direct or indirect interactions. However, the geometry of their path was changed not only through the effect of random encounters with other workers but also through an active modification of their movement when they perceived directly or indirectly the presence of nearby workers.     

Effects of density-dependent migrations on stability of a two-patch predator-prey model

We consider a predator-prey model in a two-patch environment and assume that migration between patches is faster than prey growth, predator mortality and predator-prey interactions. Prey (resp. predator) migration rates are considered to be predator (resp. prey) density-dependent. Prey leave a patch at a migration rate proportional to the local predator density. Predators leave a patch at a migration rate inversely proportional to local prey population density. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. First, we show that for a large class of density-dependent migration rules for predators and prey there exists a unique and stable equilibrium for migration. Second, a numerical bifurcation analysis is presented. We show that bifurcation diagrams obtained from the complete and aggregated models are consistent with each other for reasonable values of the ratio between the two time scales, fast for migration and slow for local demography. Our results show that, under some particular conditions, the density dependence of migrations can generate a limit cycle. Also a co-dim two Bautin bifurcation point is observed in some range of migration parameters and this implies that bistability of an equilibrium and limit cycle is possible.     

Enrichment in a general class of stoichiometric producer-consumer population growth models

This paper presents the derivation and partial analysis of a general producer-consumer model. The model is stoichiometric in that it includes the growth constraints imposed by species-specific biomass carbon to nutrient ratios. The model unifies the approaches of other studies in recent years, and is calibrated from an extensive review of the algae-Daphnia literature. Numerical simulations and bifurcation analysis are used to examine the impact of energy enrichment under nutrient and stoichiometric constraints. Our results suggest that the variety of system responses previously cited for related models can be attributed to the size of the total system nutrient pool, which is here assumed fixed. New, more complicated bifurcation sequences, such as multiple homoclinic bifurcations, are demonstrated as well. The mechanistic basis of the model permits us to show the robustness of the system’s dynamics subject to alternate approaches to modeling producer and consumer biomass production.     

Convergence to constant equilibrium for a density-dependent selection model with diffusion

We consider the classical single locus two alleles selection model with diffusion where the fitnesses of the genotypes are density dependent. Using a theorem of Peter Brown, we show that in a bounded domain with homogeneous Neumann boundary conditions, the allele frequency and population density converge to a constant equilibrium lying on the zero population mean fitness curve. The results agree with the case without diffusion obtained by Selgrade and Namkoong. Frequency and density dependent selection is also considered.Research partially supported by NSF grant DMS-8601585     

Context- and density-dependent effects of introduced oysters on biodiversity

Pacific oysters, Crassostrea gigas, have been introduced throughout much of the world, become invasive in many locations and can alter native assemblage structure, biodiversity and the distribution and abundance of other species. It is not known, however, to what extent their effects on biodiversity change as their cover increases, and how these effects may differ depending on the environmental context. Experimental plots with increasing cover of oysters were established within two estuaries in two different habitats commonly inhabited by C. gigas, (mussel-beds and mud-flats) and were sampled after 4 and 15 months. Within mud-flat habitats, macroscopic species living on or in the substratum increased in richness, Shannon–Wiener diversity and number of individuals with oyster cover. In mussel-bed habitats, however, these indices were unaffected by the cover of oysters except at one estuary after 15 months when species richness was significantly lower in plots with the greatest cover of oysters. Assemblage structure differed with oyster cover in mud-flats but not in mussel-beds, except at 100 % cover in one location and at one time. Within mud-flats at one location and time (of four total tests), assemblages became more homogenous with increasing cover of oysters leading to a significant decrease in β-diversity. These responses were primarily underpinned by the facilitation of several taxa including a grazing gastropod (Littorina littorea), an invasive barnacle (Austrominius modestus) and a primary producer (Fucus vesiculosus) with increasing cover of oysters. Although there were consistent positive effects of C. gigas on mud-flat biodiversity, effects were weak or negative at higher cover on mussel-beds. This highlights the need for the impacts of invasive species to be investigated at a range of invader abundances within different environmental contexts.     

Transgenerational effects modulate density-dependent prophylactic resistance to viral infection in a lepidopteran pest

There is an increasing appreciation of the importance of transgenerational effects on offspring fitness, including in relation to immune function and disease resistance. Here, we assess the impact of parental rearing density on offspring resistance to viral challenge in an insect species expressing density-dependent prophylaxis (DDP); i.e. the adaptive increase in resistance or tolerance to pathogen infection in response to crowding. We quantified survival rates in larvae of the cotton leafworm (Spodoptera littoralis) from either gregarious- or solitary-reared parents following challenge with the baculovirus S. littoralis nucleopolyhedrovirus. Larvae from both the parental and offspring generations exhibited DDP, with gregarious-reared larvae having higher survival rates post-challenge than solitary-reared larvae. Within each of these categories, however, survival following infection was lower in those larvae from gregarious-reared parents than those from solitary-reared, consistent with a transgenerational cost of DDP immune upregulation. This observation demonstrates that crowding influences lepidopteran disease resistance over multiple generations, with potential implications for the dynamics of host–pathogen interactions.     

Non-linear density-dependent effects of an intertidal ecosystem engineer

Ecosystem engineering is an important process in a variety of ecosystems. However, the relationship between engineer density and engineering impact remains poorly understood. We used experiments and a mathematical model to examine the role of engineer density in a rocky intertidal community in northern California. In this system, the whelk Nucella ostrina preys on barnacles (Balanus glandula and Chthamalus dalli), leaving empty barnacle tests as a resource (favorable microhabitat) for other species. Field experiments demonstrated that N. ostrina predation increased the availability of empty tests of both barnacle species, reduced the density of the competitively dominant B. glandula, and indirectly increased the density of the competitively inferior C. dalli. Empty barnacle tests altered microhabitat humidity, but not temperature, and presumably provided a refuge from wave action. The herbivorous snail Littorina plena was positively associated with empty test availability in both observational comparisons and experimental manipulations of empty test availability, and L. plena density was elevated in areas with foraging N. ostrina. To explore the effects of variation in N. ostrina predation, we constructed a demographic matrix model for barnacles in which we varied predation intensity. The model predicted that number of available empty tests increases with predation intensity to a point, but declines when predation pressure was strong enough to severely reduce adult barnacle densities. The modeled number of available empty tests therefore peaked at an intermediate level of N. ostrina predation. Non-linear relationships between engineer density and engineer impact may be a generally important attribute of systems in which engineers influence the population dynamics of the species that they manipulate.