Competition in size-structured populations: mechanisms inducing cohort formation and population cycles

In this paper we investigate the consequences of size-dependent competition among the individuals of a consumer population by analyzing the dynamic properties of a physiologically structured population model. Only 2 size-classes of individuals are distinguished: juveniles and adults. Juveniles and adults both feed on one and the same resource and hence interact by means of exploitative competition. Juvenile individuals allocate all assimilated energy into development and mature on reaching a fixed developmental threshold. The combination of this fixed threshold and the resource-dependent developmental rate, implies that the juvenile delay between birth and the onset of reproduction may vary in time. Adult individuals allocate all assimilated energy to reproduction. Mortality of both juveniles and adults is assumed to be inversely proportional to the amount of energy assimilated. In this setting we study how the dynamics of the population are influenced by the relative foraging capabilities of juveniles and adults.In line with results that we previously obtained in size-structured consumer-resource models with pulsed reproduction, population cycles primarily occur when either juveniles or adults have a distinct competitive advantage. When adults have a larger per capita feeding rate and are hence competitively superior to juveniles, population oscillations occur that are primarily induced by the fact that the duration of the juvenile period changes with changing food conditions. These cycles do not occur when the juvenile delay is a fixed parameter. When juveniles are competitively superior, two different types of population fluctuations can occur: (1) rapid, low-amplitude fluctuations having a period of half the juvenile delay and (2) slow, large-amplitude fluctuations characterized by a period, which is roughly equal to the juvenile delay. The analysis of simplified versions of the structured model indicates that these two types of oscillations also occur if mortality and/or development is independent of food density, i.e. in a situation with a constant juvenile developmental delay and a constant, food-independent background mortality. Thus, the oscillations that occur when juveniles are more competitive are induced by the juvenile delay per se. When juveniles exert a larger foraging pressure on the shared resource, maturation implies an increase not only in adult density, but also in food density and consequently fecundity. Our analysis suggests that this correlation in time between adult density and fecundity is crucial for the occurrence of population cycles when juveniles are competitively superior.     

Simplifying a physiologically structured population model to a stage-structured biomass model

We formulate and analyze an archetypal consumer-resource model in terms of ordinary differential equations that consistently translates individual life history processes, in particular food-dependent growth in body size and stage-specific differences between juveniles and adults in resource use and mortality, to the population level. This stage-structured model is derived as an approximation to a physiologically structured population model, which accounts for a complete size-distribution of the consumer population and which is based on assumptions about the energy budget and size-dependent life history of individual consumers. The approximation ensures that under equilibrium conditions predictions of both models are completely identical. In addition we find that under non-equilibrium conditions the stage-structured model gives rise to dynamics that closely approximate the dynamics exhibited by the size-structured model, as long as adult consumers are superior foragers than juveniles with a higher mass-specific ingestion rate. When the mass-specific intake rate of juvenile consumers is higher, the size-structured model exhibits single-generation cycles, in which a single cohort of consumers dominates population dynamics throughout its life time and the population composition varies over time between a dominance by juveniles and adults, respectively. The stage-structured model does not capture these dynamics because it incorporates a distributed time delay between the birth and maturation of an individual organism in contrast to the size-structured model, in which maturation is a discrete event in individual life history. We investigate model dynamics with both semi-chemostat and logistic resource growth.     

Competitive exclusion in Cladocera through elevated mortality of adults

The population dynamics of two cladocerans, Ceriodaphnia pulchellaand Diaphanosoma brachyurum competing under laboratory conditionsin lake water was analysed using cross-correlations. Both mixedand isolated populations of the two cladocerans showed delayeddensity-dependence in the death rates of juveniles and adultsas well as in fecundity rate. The regressions for each of thethree rates on total density of competitors were compared betweenthe two species. There were no significant differences in theslopes of regressions for fecundity rates and the death ratesof juveniles. However, in the inferior competitor (Diaphanosoma)which went extinct in all treatments, the death rate of adultsincreased with total density much more quickly than in the superiorcompetitor (Ceriodaphnia). The intraspecific comparisons indicatedthat while Ceriodaphnia adults survived better than juvenilesunder conditions of crowding, in Diaphanosoma, juveniles werebetter survivors than adults. These data suggest that the contentionof higher vulnerability of cladoceran juveniles than adultsto starvation and crowding may prove to be not a universal phenomenon.     

Effect of parental care and aggregation on population dynamics

Behavioral changes of animal species can influence the consequence of population dynamics. One of the most remarkable behaviors of animal species is the aggregation by which species can reduce predation risk as a consequence of dilution or the other effects by forming a group. Empirical studies have demonstrated that an incompatibility exists in aggregation since resource competition might become severe at the cost of reducing predation pressure from predatory species. Parental care by supplying the food consumed by adults to their juveniles would reduce the mortality of juvenile due to starvation, but it would reduce the reproduction rate at the same time. In this paper, we study a class of stage-structured resource-consumer models to investigate the effect of behavioral changes on population dynamics. It is shown that under the presence of trade-off in parental care, moderate degrees of parental care will be favored as maximizing the equilibrium density of consumers. For consumer species having a long maturation period, consumer species might get benefit from dilution effects as a result of aggregation despite the elevated resource competition. Aggregation gives rise to two different outcomes in consumer extinction. Resource exhaustion as a consequence of over-exploitation can induce extinction of consumers due to Allee effects if aggregation strongly mediates juvenile survival.     

Demographic response of plant populations to habitat fragmentation and temporal environmental variability

Many plant species currently exist in fragmented populations of different sizes, while they also experience unpredictable climatic fluctuation over time. However, we still understand little about how plant demography responds to such spatial and temporal environmental variability. We studied population dynamics of an understory perennial herb Trillium camschatcense in the Tokachi plain of Hokkaido, Japan, where a significant effect of forest fragmentation on seedling recruitment was previously reported. Four populations across a range of fragment sizes were studied for 6 years, and the data were analyzed using matrix population models. Per capita fecundity (the number of recruits per plant) varied greatly among populations, but the variation in population growth rates (λ) was mainly driven by the variation in stasis and growth rates, suggesting that the general trend of reduced fecundity in fragmented populations may not be readily translated into subsequent dynamics. Temporal variation in λ among years was more than 2 times larger than spatial variation among populations, and this result was likely attributable to the contrasting response of correlation structures among demographic rates. The among-population variation in λ was dampened by negative covariation between matrix elements possibly due to density-dependent regulation as well as an inherent constraint that some elements are not independent, whereas positive covariation between matrix elements resulted in large temporal variation in λ. Our results show that population dynamics responded differently to habitat fragmentation and temporal variability of the environment, emphasizing the need to discriminate these spatial and temporal variations in demographic models. Although no populations were projected to be declining in stochastic simulations, correlation between current habitat size and plant density implies historical λ is positively related to habitat size.     

Intra-specific competition and density dependent juvenile growth

A difference equation model for the dynamics of a semelparous size-structured species consisting of juvenile and adult individuals is derived and studied. The adult population consists of two size classes, a smaller class and a larger more fertile class. Negative feedback occurs through slowed juvenile growth due to increased total population levels during the developmental period and consequently a smaller adult size at maturation. Intra-specific competition coefficients are size dependent and measure the strength of intra-specific competition between juveniles and adults. It is shown that equilibrium states in which adults and juveniles occur together at all times are in general destabilized by significantly increased juvenilevs adults competition with the result that stable periodic cycles appear, in which the generations alternate in time and hence avoid competition. This result supports the tenet that intra-specific competition between juveniles and adults is destabilizing. Exceptions to this destabilization principle are found, however, in which populations exhibiting non-equilibrium, aperiodic dynamics can be equilibrated by increase competition between juveniles and adults. This occurs, for example, when adult fertility and competition coefficients are significantly size class dependent. The author gratefully acknowledges the support of the Applied Mathematics Division and the Population Biology/Ecology Division of the National Science Foundation under NSF grant No. DMS-8902508. Research supported by the Department of Energy under contracts W-7405-ENG-36 and KC-07-01-01.     

Reproductive effort in viscous populations

Abstract.— Here I study a kin selection model of reproductive effort, the allocation of resources to fecundity versus survival, in a patch-structured population. Breeding females remain in the same patch for life. Offspring have costly, partial long-distance dispersal and compete for breeding sites, which become vacant upon the death of previous occupants. The main result is that the evolutionarily stable reproductive effort decreases as offspring dispersal rate increases. The result can be understood as follows: In a well-mixed population with global competition, neither adults nor juveniles compete with relatives, but in a patch-structured population with dispersal restricted to the juvenile phase, juveniles experience relatively less competition with relatives than adults, thus making juveniles relatively more valuable. Because this asymmetry between adults and juveniles decreases with the dispersal rate, so does the evolutionarily stable level of allocation to fecundity.     

A stage structured predator-prey model and its dependence on maturation delay and death rate

Many of the existing models on stage structured populations are single species models or models which assume a constant resource supply. In reality, growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predator-prey model with stage structure with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (through-stage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory dynamics.Work is partially supported by NSF grant DMS-0077790.Mathamatics Subject Classification (2000):92D25, 35R10Revised version: 26 February 2004     

Biodiversity,habitat area,resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.     

Persistent directional selection on body size and a resolution to the paradox of stasis

Directional selection on size is common but often fails to result in microevolution in the wild. Similarly, macroevolutionary rates in size are low relative to the observed strength of selection in nature. We show that many estimates of selection on size have been measured on juveniles, not adults. Further, parents influence juvenile size by adjusting investment per offspring. In light of these observations, we help resolve this paradox by suggesting that the observed upward selection on size is balanced by selection against investment per offspring, resulting in little or no net selection gradient on size. We find that trade‐offs between fecundity and juvenile size are common, consistent with the notion of selection against investment per offspring. We also find that median directional selection on size is positive for juveniles but no net directional selection exists for adult size. This is expected because parent–offspring conflict exists over size, and juvenile size is more strongly affected by investment per offspring than adult size. These findings provide qualitative support for the hypothesis that upward selection on size is balanced by selection against investment per offspring, where parent–offspring conflict over size is embodied in the opposing signs of the two selection gradients.     

Recruitment pulses induce cannibalistic giants in Arctic char

1. Recent theoretical studies on the population dynamic consequences of cannibalism have focused on mechanisms behind the emergence of large cannibals (giants) in size-structured populations. Theoretically, giants emerge when a strong recruiting cohort imposes competition induced mortality on stunted adults, but also provides a profitable resource for a few adults that accelerate in growth and reach giant sizes. 2. Here the effects of a recruitment pulse on the individual and population level in an allopatric Arctic char population have been studied over a 5-year period and these results were contrasted with theoretical model predictions for the conditions necessary for the emergence of cannibalistic giants. 3. The recruitment pulse had negative effects on invertebrate resource abundance, and the decrease in body condition and increase in mortality of adult char suggested that strong intercohort competition took place. 4. The frequency of cannibalism increased and a few char accelerated in growth and reached 'giant' sizes. 5. The main discrepancy between model predictions and field data was the apparently small effect the recruited cohort had on resources and adult char performance during their first summer. Instead, the effects became pronounced when the cohort was 1 year old. This mismatch between model predictions and field observations was suggested to be due to the low per capita fecundity in char and the restricted nearshore habitat use in young-of-the-year (YOY) char. 6. This study provides empirical evidence that the emergence of giants is associated with the breakthrough of a strong recruiting cohort and also suggests that the claimed stable char populations with large cannibals may instead be populations with dynamic size structure that results in intermittent breakthroughs of recruitment pulses, providing the conditions necessary for char to enter the cannibalistic niche. 7. The data suggest that increased recruit survival through restricted habitat use may destabilize dynamics and cause the emergence of giants. However, they also suggest that this does not necessarily develop into populations with bi-modal size structure in populations with low per capita fecundity and size- and density-dependent habitat use of recruiting cohorts.     

Population viability analysis of Lower Missouri River shovelnose sturgeon with initial application to the pallid sturgeon

Demographic models for the shovelnose (Scaphirhynchus platorynchus) and pallid (S. albus) sturgeons in the Lower Missouri River were developed to conduct sensitivity analyses for both populations. Potential effects of increased fishing mortality on the shovelnose sturgeon were also evaluated. Populations of shovelnose and pallid sturgeon were most sensitive to age‐0 mortality rates as well as mortality rates of juveniles and young adults. Overall, fecundity was a less sensitive parameter. However, increased fecundity effectively balanced higher mortality among sensitive age classes in both populations. Management that increases population‐level fecundity and improves survival of age‐0, juveniles, and young adults should most effectively benefit both populations. Evaluation of reproductive values indicated that populations of pallid sturgeon dominated by ages ≥35 could rapidly lose their potential for growth, particularly if recruitment remains low. Under the initial parameter values portraying current conditions the population of shovelnose sturgeon was predicted to decline by 1.65% annually, causing the commercial yield to also decline. Modeling indicated that the commercial yield could increase substantially if exploitation of females in ages ≤12 was highly restricted.     

Floral resources impact longevity and oviposition rate of a parasitoid in the field

1. The use of floral resource subsidies to improve herbivore suppression by parasitoids requires certain trophic interactions and physiological changes to occur. While the longevity and fecundity of parasitoids are positively affected by nectar subsidies in laboratory studies, the impacts of floral subsidies on the fecundity and longevity of freely foraging parasitoids have not been studied. 2. We studied the longevity and per capita fecundity of naturally occurring Diadegma insulare foraging in cabbage plots with and without borders of flowering buckwheat, Fagopyrum esculentum, as well as relationships between longevity, fecundity, sugar feeding and parasitism rates on larvae of the diamondback moth, Plutella xylostella. 3. Relative longevity was estimated by counting broken setae on the fringe of the forewing. Floral borders increased the longevity of males and females in adjacent cabbage plots. 4. The egg maturation rate of D. insulare was estimated by comparing egg loads of females collected early in the day with egg loads of females held without hosts in field cages throughout the day. Females in buckwheat cages matured 2.7 eggs per hour while females in control cages resorbed 0.27 eggs over the same time period. 5. The fecundity of females collected in the afternoon was estimated by comparing their actual egg load to the estimated egg load in the absence of oviposition for females in a given plot. Females foraging in buckwheat plots had marginally fewer eggs remaining in their ovaries, and laid marginally more eggs than females in control plots. Females from both treatments carried 30-60 eggs by the afternoon and therefore were time-limited rather than egg-limited. 6. Plots where a greater proportion of females had fed on sugar had longer-lived females. This suggests that feeding enhanced longevity of D. insulare. However, plots with longer-lived and more fecund females did not exhibit higher parasitism rates, although the power of these tests were low.     

Effects of experimental manipulations on the life history pattern of Lymnaea stagnalis appressa say (pulmonata: lymnaeidae)

Field sampling of an Iowa population of Lymnaea stagnalis appressa Say indicated an annual generation pattern, with survivorship to maturity of i percent or less. Estimates of adult fecundity ranged from about 300 to 800 eggs.Density and food manipulations were performed to determine whether density dependent limitation of growth rates, maturation, or fecundity occurs in this fresh water pulmonate snail. Addition of a high quality food resource, spinach, accelerated growth rates, but did not drastically accelerate maturity, nor increase fecundity. Density increments lowered growth rates, delayed maturity, and lowered fecundity, and the addition of spinach did not counteract high densities. Adult densities are fairly low in the field population, and adults are randomly dispersed, indicating little density dependent regulation of fecundity in this population. However, the low survivorship to maturity, response in growth rates with food addition, and increasing survivorship with age and size indicate that juvenile mortality may play an important role in structuring life history patterns in this population.     

The ontogenetic stoichiometric bottleneck stabilizes herbivore–autotroph dynamics

In the ecological stoichiometry theory of population dynamics, ontogenetic changes in nutrient demand have been ignored. Here, I studied a stage-structured Daphnia–algae herbivore–autotroph model, in which the juveniles of the herbivore had a higher nutrient (phosphorous) demand for maturation than the adults for reproduction. The model predicted that while an increase in the juvenile nutrient demand (i.e., ontogenetic stoichiometric bottleneck) affects stage-specific performances in complex ways through nutrient dynamics and resource quality, in general it has stabilizing effects on the population dynamics.     

How does adaptive consumer movement affect population dynamics in consumer-resource metacommunities with homogeneous patches?

This article uses simple models to explore the impact of adaptive movement by consumers on the population dynamics of a consumer-resource metacommunity consisting of two identical patches. Consumer-resource interactions within a patch are described by the Rosenzweig-MacArthur predator-prey model, and these dynamics are assumed to be cyclic in the absence of movement. The per capita movement rate from one patch to the other is an increasing function of the difference between the per capita birth minus death rate in the destination patch and that in the currently occupied patch. Several variations on this model are considered. Results show that adaptive movement frequently creates anti-phase cycles in the two patches; these suppress the predator-prey cycle and lead to low temporal variation of the total population sizes of both species. Paradoxically, even when movement is very sensitive to the fitness difference between patches, perfect synchrony of patches is often much less likely than in comparable systems with random movement. Under these circumstances adaptive movement of consumers often generates differences in the average properties of the two patches. In addition, mean global densities and responses to global perturbations often differ greatly from similar systems with no movement or random movement.     

Harvesting and predation of a sex- and age-structured population

We study a discrete-time system of equations for a structured ungulate population exploited by human harvesting or a dynamic predator. The population is divided into juveniles, and female and male adults. Harvesting is concentrated on adults (trophy hunting of males or population control measures on females), whereas predation occurs in juveniles. Though the model consists of four nonlinear equations, we find explicit expressions for the steady states. We use these explicit expressions to investigate harvesting rates that allow population persistence, rates that ensure population control, and optimal harvesting efforts. Several reductions of complexity allow for a detailed analysis of the dynamics of the model. Most notably, we find that even compensatory density dependence can lead to a period doubling bifurcation, that the model does not support consumer–resource cycles, and that an Allee effect can emerge from the interplay of stage-specific predation and density-dependent prey reproduction.     

Note on the effects of maternal selection in biological populations

The dynamics of the genetic structure of populations under various selection factors are considered. The effect of selection by way of the maternal genotype through fecundity, favorable placement of eggs and such factors as are dependent on the character of the maternal parent is emphasized. This factor can lead to a stable equilibrium with genotype frequencies which would appear to be unstable. A similar result can be obtained as a result of differences in mating probabilities which may arise due to differences in maturation rates. A number of cases are treated to illustrate the dynamics as well as conditions for stable equilibrium.     

Effects of larval density on a natural population of Culex restuans (Diptera: Culicidae): no evidence of compensatory mortality

1. This study investigated the effects of strong density dependence on larval growth, development, and survival of the mosquito Culex restuans (Theobald). It also tested the hypothesis that density reduction early in larval development could result in as many or more individuals surviving to adulthood (compensation or over‐compensation, respectively), or increased reproductive performance via rapid development and greater adult size. 2. In a field study of a natural population of C. restuans, the effects of a 75% lower density on percentage survivorship to adulthood, number of adults, development time, adult size, adult longevity, and size dependent fecundity were tested. 3. No evidence was found of compensation or over‐compensation in adult production, or of effects of lower density on percentage survivorship. Low density yielded significant increases in adult size, adult longevity, and size‐dependent fecundity, and a decrease in development time. 4. Estimated per‐capita population growth rate was significantly greater in the low‐density treatment than in the high‐density treatment. It is inferred that this difference was due to greater per‐capita resources, which increased female size and fecundity, and reduced development time. Greater per‐capita population growth could therefore result from early mortality of larvae, meaning that the hydra effect, which predicts greater equilibrium population with, as opposed to without, extrinsic mortality, may be possible for these mosquitoes.     

How effective are maternal effects at having effects?

The well studied trade-off between offspring size and offspring number assumes that offspring fitness increases with increasing per-offspring investment. Where mothers differ genetically or exhibit plastic variation in reproductive effort, there can be variation in per capita investment in offspring, and via this trade-off, variation in fecundity. Variation in per capita investment will affect juvenile performance directly--a classical maternal effect--while variation in fecundity will also affect offspring performance by altering the offsprings' competitive environment. The importance of this trade-off, while a focus of evolutionary research, is not often considered in discussions about population dynamics. Here, we use a factorial experiment to determine what proportion of variation in offspring performance can be ascribed to maternal effects and what proportion to the competitive environment linked to the size-number trade-off. Our results suggest that classical maternal effects are significant, but that in our system, the competitive environment, which is linked to maternal environments by fecundity, can be a far more substantial influence.