Bottom-up derivation of discrete-time population models with the Allee effect

This paper presents a framework in which various single-species discrete-time population models exhibiting the Allee effect are derived from first principles. Here, the Allee effect means a reduction in individual fitness at low population sizes. The derivation is based on the distribution of female and male individuals among discrete resource sites, in addition to competitive and cooperative interaction among individuals. These derivations show how the derived population models depend on the type and the intensity of competition, and the degree of clustering of individuals. Along with these models exhibiting the Allee effect, this paper also presents first-principles derivation of population models without the Allee effect which include a parameter relating to the intensity of competition.     

Bottom-up derivation of population models for competition involving multiple resources

This paper provides first-principles derivations of population models for competition involving multiple resources with different competition types, based on resource partitioning between individuals. The following two cases are investigated. The first is the case in which the resource competed for and its competition type change depending on life stages from scramble to contest competition, or from contest to scramble competition. The second is the case in which individuals compete for two resources simultaneously with scramble and contest types, respectively. In both cases, population models are derived analytically, and in particular, the Hassell model is derived in the second case. The nature of reproduction curves and the stability properties of three population models derived are compared with each other. These models provide three representative models for competition involving both scramble and contest types.     

On the mechanistic underpinning of discrete-time population models with Allee effect

The Allee effect means reduction in individual fitness at low population densities. There are many discrete-time population models with an Allee effect in the literature, but most of them are phenomenological. Recently, Geritz and Kisdi [2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261-269] presented a mechanistic underpinning of various discrete-time population models without an Allee effect. Their work was based on a continuous-time resource-consumer model for the dynamics within a year, from which they derived a discrete-time model for the between-year dynamics. In this article, we obtain the Allee effect by adding different mate finding mechanisms to the within-year dynamics. Further, by adding cannibalism we obtain a higher variety of models. We thus present a generator of relatively realistic, discrete-time Allee effect models that also covers some currently used phenomenological models driven more by mathematical convenience.     

Contest versus scramble competition for mates: The composition and spatial structure of a population of gray mouse lemurs (Microcebus murinus) in North-west Madagascar

The modes of intrasexual competition interacting in many dispersed societies of nocturnal solitary foragers are still poorly understood. In this study we investigate the spatial structure within a free-living population of gray mouse lemurs (Microcebus murinus) in order to test for the first time the predictions from two contrasting models of male intrasexual competition on the population level. The contest competition model predicts an uneven distribution of the sexes in a population nucleus with a female biased sex ratio in the center and a male biased sex ratio in the periphery. In contrast the scramble competition model predicts males and females being distributed evenly throughout their habitat with a constant sex ratio. Nine capture/recapture periods within three consecutive mating seasons revealed a continuous male biased sex ratio in the adult population with even trapping rates for the sexes. The male biased sex ratio could either be explained with postnatal female biased mortality or with a male biased natal sex ratio. This male biased sex ratio was apparent in all parts of the study site, indicating that the population was not subdivided into a female biased core and a male biased periphery. Furthermore, the majority of adult males have been captured at the same site as or in vicinity to females. Consequently, a large proportion of males had spatial access to females during the mating season. No signs of monopolization of females by certain dominant males could be detected. These data support the predictions from the scramble competition model and the concept of a promiscuous mating system for this species.     

The social modes of men

Here we attempt to define a specifically human ecology within which male reproductive strategies are formulated. By treating the domestic and public spheres of social life as "ecological niches" that men have been forced to compete within or to avoid as best they can, we generate a typology of four "social modes" of human male behavior. We then attempt to explain the broad distribution of social modes within and between human groups based on the relative intensity of scramble and contest competition. This research was completed with the help of a Lowell M. Durham, Jr. Fellowship at the Tanner Humanities Center, University of Utah. Lars Rodseth (Ph.D., University of Michigan 1993) is Assistant Professor of Anthropology at the University of Utah. He has conducted fieldwork in Nepal and Micronesia and is the author of "Distributive Models of Culture: A Sapirian Alternative to Essentialism," American Anthropologist (1998) 100:55–69. Shannon A. Novak (Ph.D., University of Utah 1999) is Assistant Professor of Anthropology at Indiana State University. She has conducted fieldwork in Croatia and the United Kingdom and is the author of "Perimortem Processing of Human Remains among the Great Basin Fremont," International Journal of Osteoachaeology (2000) 10:65–75.     

ESS analysis of mechanistic models for territoriality: the value of scent marks in spatial resource partitioning

In this paper elements of game theory are used to analyse a spatially explicit home range model for interacting wolf packs. The model consists of a system of nonlinear partial differential equations whose parameters reflect the movement behavior of individuals within each pack and whose solutions describe the patterns of space-use by each pack. By modifying the behavioral parameters, packs adjust their patterns of movement so as to maximize their reproductive output. This involves a tradeoff between maximizing prey intake and minimizing conflict with neighbors. Evolutionarily stable choices of the behavioral parameters yields territories that are immune to invasion by groups with alternate behaviors.     

On the mechanistic underpinning of discrete-time population models with complex dynamics

We present a mechanistic underpinning for various discrete-time population models that can produce limit cycles and chaotic dynamics. Specific examples include the discrete-time logistic model and the Hassell model, which for a long time eluded convincing mechanistic interpretations, and also the Ricker- and Beverton-Holt models. We first formulate a continuous-time resource consumption model for the dynamics within a year, and from that we derive a discrete-time model for the between-year dynamics. Without influx of resources from the outside into the system, the resulting between-year dynamics is always overcompensating and hence may produce complex dynamics as well as extinction in finite time. We recover a connection between various standard types of continuous-time models for the resource dynamics within a year on the one hand and various standard types of discrete-time models for the population dynamics between years on the other. The model readily generalizes to several resource and consumer species as well as to more than two trophic levels for the within-year dynamics.     

The relative importance of spatial aggregation and resource partitioning on the coexistence of mycophagous insects

The relative importance of spatial aggregation and resource partitioning on coexistence was investigated for mycophagous insects in central Japan. The effects of spatial aggregation and resource partitioning were separated by a randomization procedure. From 124 patches of macrosporophores belonging to 37 species, 3275 individuals belonging to 14 families of Diptera and 11 individuals to Lepidoptera emerged. Since the level of identification varied among insect taxa, the analysis was made in three ways; 1) for all taxa to assess the stability of the whole community, 2) for drosophilid species to assess their persistence in the community, and 3) for species of Drosophila and Mycodrosophila to assess their persistence against congeneric and heterogeneric species. Both spatial aggregation and resource partitioning functioned for the stability of whole mycophagous insect community, and spatial aggregation played a more important role than resource partitioning. On the other hand, only spatial aggregation functioned for the persistence of drosophilid species in the community. According to the analysis on species of Drosophila and Mycodrosophila against congeneric and heterogeneric species, the relative importance of resource partitioning was smaller for the coexistence of within-genus species pairs than for that of between-genus species pairs. These results suggest that the relative importance of these two mechanisms depends on the phylogenetic and guild diversity of community.     

Predicting attenuant and resonant 2-cycles in periodically forced discrete-time two-species population models

Periodic environments may either enhance or suppress a population via resonant or attenuant cycles. We derive signature functions for predicting the responses of two competing populations to 2-periodic oscillations in six model parameters. Two of these parameters provide a non-trivial equilibrium and two provide the carrying capacities of each species in the absence of the other, but the remaining two are arbitrary and could be intrinsic growth rates. Each signature function is the sign of a weighted sum of the relative strengths of the oscillations of the perturbed parameters. Periodic environments are favourable for populations when the signature function is positive and are deleterious if the signature function is negative. We compute the signature functions of four classical, discrete-time two-species populations and determine regions in parameter space which are either favourable or detrimental to the populations. The six-parameter models include the Logistic, Ricker, Beverton–Holt, and Hassell models.     

Models of optimal foraging and resource partitioning: deep corollas for long tongues

We model the optimal foraging strategies for 2 nectarivore species,differing in the length of their proboscis, that exploit thenectar provided by 2 types of flowers, differing in the depthsof their corollas. When like flowers appear in clumps, nectarivoresmust decide whether to forage at a patch of deep or shallowflowers. If nectarivores forage optimally, at least one flowertype will be used by a single nectarivore species. Long-tonguedforagers will normally visit deep flowers and short-tonguedforagers shallow flowers, although extreme asymmetries in metaboliccosts may lead to the opposite arrangement. When deep and shallowflowers are randomly interspersed, nectarivores must decide,on encounter with a flower, whether to collect its nectar orcontinue searching. At low nectarivore densities, the optimalstrategy involves exploiting every encountered flower; however,as nectarivore densities increase and resources become scarce,long-tongued individuals should start concentrating on deepflowers and short-tongued individuals on shallow flowers. Therefore,regardless of the spatial distribution of flowers, corolla depthcan determine which nectarivore species exploit the nectar fromeach flower type in a given community. It follows that corollaelongation can evolve as a means to keep nectar thieves at bayif short-tongued visitors are less efficient pollinators thanlong-tongued visitors.     

The dietary basis for temporal partitioning: food habits of coexisting Acomys species

Two rodent species of the genus Acomys coexist on rocky terrain in the southern deserts of Israel. The common spiny mouse (A. cahirinus) is nocturnally active whereas the golden spiny mouse (A. russatus) is diurnally active. An early removal study suggested that competition accounts for this pattern of temporal partitioning: the golden spiny mouse is forced into diurnal activity by its congener. Theoretically, temporal segregation should facilitate coexistence if the shared limiting resources differ at different times (primarily among predators whose prey populations have activity rhythms), or if they are renewed within the period of the temporal segregation. We studied food preferences of the two Acomys species in a controlled cafeteria experiment in order to assess resource overlap and the potential for competition for food between the two species. We found no significant difference in food preferences between species. The dietary items preferred by both were arthropods. We also carried out a seasonal study of the percentage and identity of arthropods taken in the field by individuals of the two species. Individuals of both species took on annual average a high percentage of arthropods in their diets. Seasonal diet shifts reflect seasonal abundance of arthropods at Ein Gedi during day and night. Diurnal activity may also reduce interspecific interference competition between A. russatus and A. cahirinus. However, the strong interspecific dietary overlap in food preference, the heavy reliance on arthropods in spiny mouse diets, and the seasonal and circadian differences in arthropod consumption suggest that prey partitioning may be a viable mechanism of coexistence in this system. Received: 6 July 1998 / Accepted: 10 May 1999     

The role of male contest competition over mates in speciation

Research on the role of sexual selection in the speciation process largely focuses on the diversifying role of mate choice.In particular,much attention has been drawn to the fact that population divergence in mate choice and in the male traits subject to choice directly can lead to assortative mating.However,male contest competition over mates also constitutes an important mechanism of sexual selection.We review recent empirical studies and argue that sexual selection through male contest competition can affect speciation in ways other than mate choice.For example,biases in aggression towards similar competitors can lead to disruptive and negative frequency-dependent selection on the traits used in contest competition in a similar way as competition for other types of limited resources.Moreover,male contest abilities often trade-off against other abilities such as parasite resistance,protection against predators and general stress tolerance.Populations experiencing different ecological conditions should therefore quickly diverge non-randomly in a number of traits including male contest abilities.In resource based breeding systems,a feedback loop between competitive ability and habitat use may lead to further population divergence.We discuss how population divergence in traits used in male contest competition can lead to the build up of reproductive isolation through a number of different pathways.Our main conclusion is that the role of male contest competition in speciation remains largely scientifically unexplored.     

Diel variation in feeding and vertical distribution of ten co-occurring fish species: consequences for resource partitioning

The diel variations in feeding behaviour and vertical distribution were determined for ten species of a tropical fish community in a shallow SE Sri Lankan reservoir. The fish community consisted of two introduced exotic tilapias and eight indigenous riverine species including five cyprinids, one clarid, one hemiramphid and one gobid. Multi-mesh gillnets dividing the water column in six depth strata were set with a six-hour interval throughout four 24-hour periods. The study of the diel variation in feeding behaviour was based on analysis of catch data, gut contents and gut fullness per setting time. The diel variation in vertical distribution was determined per species for each of the six depth-strata. Feeding behaviour and vertical distribution differed significantly among species and for most species throughout the 24-hour period. Feeding behaviour and vertical distribution were correlated. The status of whether or not a fish is feeding determines if the trophic and spatial resource dimensions are interrelated. Resource partitioning along the spatial dimension may reduce exploitative competition at the time of feeding, whereas it may limit interference competition or predation during non-feeding periods. This revised version was published online in July 2006 with corrections to the Cover Date.     

The heart-brain connection: mechanistic insights and models

While both cardiac dysfunction and progressive loss of cognitive function are prominent features of an ageing population, surprisingly few studies have addressed the link between the function of the heart and brain. Recent literature indicates that autoregulation of cerebral flow is not able to protect the brain from hypoperfusion when cardiac output is reduced or atherosclerosis is prominent. This suggests a close link between cardiac function and large vessel atherosclerosis on the one hand and brain perfusion and cognitive functioning on the other. Mechanistically, the presence of vascular pathology leads to chronic cerebral hypoperfusion, blood brain barrier breakdown and inflammation that most likely precede neuronal death and neurodegeneration. Animal models to study the effects of chronic cerebral hypoperfusion are available, but they have not yet been combined with cardiovascular models.     

How spatial resource distribution and memory impact foraging success: A hybrid model and mechanistic index

Understanding how animals forage has always been a fundamental issue in Ethology and has become critical more recently in Environmental Conservation. Since the formalization of optimal foraging theory, theoretical models intended to depict the behavior of a generic forager have served as the main tools to analyze and ultimately comprehend the mechanisms of foraging. Due to complexity and technical constraints, these models have traditionally focused on single aspects of foraging, leaving out other concurrent processes that may also interplay. The recent inclusion of several facets inside united models has given rise to interesting results on the importance of interacting factors such as memory and resource heterogeneity.In this paper, we present a hybrid model integrating metabolism, foraging decisions, memory, as well as spatially explicit movement and resource distribution. We use it to examine the effects of spatial resource distribution – an aspect often neglected in favor of probabilistic resource heterogeneity – on the viability of a generic random-walking forager, and rely on the model to devise an ecological metric that can explain and render the relative profitability of given spatial distributions. Furthermore, we assess the significance of memory properties relatively to the profitability of resource distributions. Most notably, we reveal contrasted effects of memory depending on the aspect of resource varied in space (i.e. prey abundance, or prey body mass).On the whole, a general comparison of our findings with results obtained with spatially implicit models leads us to stress the complex interaction between memory and spatial resource distribution as well as the criticality of spatial representation in the modeling of foraging. Accordingly, we conclude with a discussion on the ecological implications of these results, as well as the advantages of hybrid modeling for the accurate simulation of foraging.     

Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning

Can a difference in the heights at which plants place their leaves, a pattern we call canopy partitioning, make it possible for two competing plant species to coexist? To find out, we examine a model of clonal plants living in a nonseasonal environment that relates the dynamical behavior and competitive abilities of plant populations to the structural and functional features of the plants that form them. This examination emphasizes whole plant performance in the vertical light gradient caused by self-shading. This first of three related papers formulates a prototype single species Canopy Structure Model from biological first principles and shows how all plant properties work together to determine population persistence and equilibrium abundance. Population persistence is favored, and equilibrium abundance is increased, by high irradiance, high maximum photosynthesis rate, rapid saturation of the photosynthetic response to increased irradiance, low tissue respiration rate, small amounts of stem and root tissue necessary to support the needs of leaves, and low density of leaf, stem, and root tissues. In particular, equilibrium abundance decreases as mean leaf height increases because of the increased cost of manufacturing and maintaining stem tissue. All conclusions arise from this formulation by straightforward analysis. The argument concludes by stating this formulation's straightforward extension, called a Canopy Partitioning Model, to two competing species.     

Biases in the estimation of spatial egg aggregation and association based on emergence data

Spatial aggregation and association of conspecific and allospecific eggs over resource patches have often been estimated based on emergence data. However, intra-specific competition reduces the number of emergents of conspecifics, and inter-specific competition reduces the number of emergents of allospecifics, causing biases in the estimation of spatial distribution of eggs using emergence data. The present study investigated, by laboratory experiments using drosophilids and simulation models, how the use of emergence data causes such biases. In the laboratory experiments, females were allowed to oviposit over resource patches, and spatial aggregation and association of eggs were examined. The number of emergents from each resource patch was then estimated from the density-survival relationship, and spatial aggregation and association of emerging adults thus estimated were compared with those of eggs. In the simulation models, the spatial distributions of adults emerging from eggs that varied in their degree of spatial aggregation were evaluated under different intensities of intra- and/or inter-specific competition. Both laboratory experiments and simulations indicate that the use of emergence data always causes an underestimation of spatial aggregation and association of eggs. Relaxation of intra- and inter-specific competition by addition of extra resources would improve the estimation of spatial egg distribution based on emergence data.