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.     

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.     

A model of physiologically structured population dynamics with a nonlinear individual growth rate

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497.     

Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development

The thymus provides a stable microenvironment for post-natal thymocyte development that is finely regulated by a complicated network of cytokines, chemokines, cell-cell contacts, etc., the dysregulations of which contribute to many immunologic diseases including malignant lymphomas. A physiologically structured model in the form of first order partial differential equation (PDE) was developed to simulate the whole process. The combined effects of the thymic microenvironment were conceptualized into two (proliferation and differentiation) fields to serve as kernels of the PDE. In this paper, a novel method is developed to estimate the maturity-time structures of the two fields based solely on cell population data that are experimentally viable. Numerical examples demonstrate the effectiveness of the present method in revealing the two-dimensional (maturity and time) landscapes of the thymic microenvironment.      

Determinants of polyphagy by a woolly bear caterpillar: a test of the physiological efficiency hypothesis

The physiological efficiency hypothesis argues that the physiological efficiency of food utilization determines feeding habits of herbivorous insects. Although relatively unsuccessful at explaining dietary specificity, it may explain the food-mixing habit of individually polyphagous herbivores because they may opportunistically increase physiological efficiency by optimizing nutrient balance or diluting toxins in the course of feeding on multiple host-plant species. This study tests two predictions of the physiological efficiency hypothesis with the woolly bear caterpillar, Grammia geneura (Strecker) (Lepidoptera: Arctiidae). Namely, both herbivore performance (survival, developmental rate, pupal mass) and growth efficiency should be better on mixed-plant diets than on single-plant diets. In a series of three laboratory experiments, I found that larval survival and developmental rate on mixed-plant diets were superior to performance on single-plant diets in only one of four cases. In all other cases, mixed-plant diets were either inferior (female pupal mass) to single-plant diets or not detectably different from them. Larval growth efficiency on mixed-plant diets was never superior to that on single-plant diets. In mixed-plant treatments, caterpillars often selected a diet that included plant species of relatively low suitability alone, thereby suffering reduced performance and growth efficiency. These results contradict predictions of the physiological efficiency hypothesis, indicating the limitations of the conventional focus on the physiological constraints on food utilization as an explanation for both individual polyphagy and dietary specificity in herbivorous insects.     

Sleep deprivation in a quantitative physiologically based model of the ascending arousal system

A physiologically based quantitative model of the human ascending arousal system is used to study sleep deprivation after being calibrated on a small set of experimentally based criteria. The model includes the sleep-wake switch of mutual inhibition between nuclei which use monoaminergic neuromodulators, and the ventrolateral preoptic area. The system is driven by the circadian rhythm and sleep homeostasis. We use a small number of experimentally derived criteria to calibrate the model for sleep deprivation, then investigate model predictions for other experiments, demonstrating the scope of application. Calibration gives an improved parameter set, in which the form of the homeostatic drive is better constrained, and its weighting relative to the circadian drive is increased. Within the newly constrained parameter ranges, the model predicts repayment of sleep debt consistent with experiment in both quantity and distribution, asymptoting to a maximum repayment for very long deprivations. Recovery is found to depend on circadian phase, and the model predicts that it is most efficient to recover during normal sleeping phases of the circadian cycle, in terms of the amount of recovery sleep required. The form of the homeostatic drive suggests that periods of wake during recovery from sleep deprivation are phases of relative recovery, in the sense that the homeostatic drive continues to converge toward baseline levels. This undermines the concept of sleep debt, and is in agreement with experimentally restricted recovery protocols. Finally, we compare our model to the two-process model, and demonstrate the power of physiologically based modeling by correctly predicting sleep latency times following deprivation from experimental data.     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

Evolution of genome size: A phylogenetic test of the DNA loss hypothesis

It has been recently suggested that the C-value paradox, the lack of an obvious association between organismal complexity and genome size, can result simply from biases in insertion and deletion rates—the DNA loss hypothesis. This hypothesis has been heavily criticized, particularly because its evidence, a negative relationship between genome size and DNA loss rate, is based on a highly selective use of the available data. In this study it is shown that the even the most favorable interpretation of the data favoring the DNA loss hypothesis is largely an artifact of phylogenetic nonindependence, supporting the assertion made by other authors that the mechanisms underlying genome size evolution might be more complex than envisioned by the DNA loss hypothesis. The text was submitted by the author in English.     

Evolution of genome size: a phylogenetic test of the DNA loss hypothesis

It has been recently suggested that the C-value paradox, the lack of an obvious association between organismal complexity and genome size, can result simply from biases in insertion and deletion rates--the DNA loss hypothesis. This hypothesis has been heavily criticized, particularly because its evidence, a negative relationship between genome size and DNA loss rate, is based on a highly selective use of the available data. In this study it is show that even the even the most favorable interpretation of the data favoring the DNA loss hypothesis is largely an artifact of phylogenetic nonindependence, supporting the assertion made by other authors that the mechanisms underlying genome size evolution might be more complex than envisioned by the DNA loss hypothesis.     

Estimation of axial dispersion in horizontal rotating tubular bioreactor by means of a structured model

A horizontal rotating tubular bioreactor (HRTB) is designed as the combination of a "thin layer bioreactor" and a "biodisc" reactor. The investigation of mixing in HRTB was done by the temperature step method in a wide range of process conditions [residence time (t_z=360036000 s) and bioreactor rotation speed (n=0.0830.917 s^у)]. In all experiments heat losses were detected. A mathematical model based on "tank in series" concept was developed to describe the mixing in HRTB - a "spiral flow" model (SFM) which has incorporated heat losses. However, the simulations of SFM could be used for calculation of temperature response curves for the case when there is no heat losses. These corrected curves were used then to estimate Bodenstein number as a parameter of standard dispersion model (SDM). The obtained Bodenstein numbers were in the range 10-17. The simulations showed that SFM was more capable to describe the mixing in HRTB giving better fitting with experimental measurements than SDM, indicating that mixing pattern in HRTB is too complex to be described with this relatively simple, one-parameter model.     

Hormaphis hamamelidis and gall size: a test of the plant vigor hypothesis

We tested the Plant Vigor Hypothesis by determining the distribution of galls formed on leaves of witch hazel, Hamamelis virginiana , by the aphid Hormaphis hamamelidis , and by determining various factors that affect the fecundity of the gall-forming fundatrices. We also studied the role of the fundatrix in host plant manipulation. While the mean number of galls per leaf was low, galls had an aggregated distribution among leaves. Among trees, the average number of galls per leaf was not related to the mean leaf size, contrary to the preference prediction of the Plant Vigor Hypothesis. While fundatrices preferred the distal leaves of buds, which grew more than the proximal leaves, being on distal leaves conferred no increase in fecundity for fundatrices, contrary to predictions of the Plant Vigor Hypothesis. Gall size was the factor that explained the largest proportion of variation in fundatrix fecundity; fundatrix size explained somewhat less of the variation. Also, gall position on the leaf, number of aphid galls on the leaf, and on which leaf of the bud the gall was located all played small, statistically significant roles in explaining fundatrix fecundity, but their effects were variable between experiments. Removal of fundatrices shortly after galls had enclosed them limited the growth of galls, indicating the role of the fundatrices in gall growth. We compare and contrast this system versus other gall-forming insects, as well as discuss the adaptive significance of the aphid manipulation of the host plant. Much of the data contradict predictions of the Plant Vigor Hypothesis, and we discuss how gall size, as a measure of plant growth caused by insect manipulation, explains the observed patterns.     

Lessons from the size efficiency hypothesis II. The mire of complexity

Over the years, models and concepts developed to explain the behaviour of lake plankton have been generalized and extended to most parts of the limnetic community. This development has now fused with parallel research programs into stream and marine benthos and fish, to yield an imposing literature dealing with complex interactions in aquatic communities. Although the size of this literature has grown, its basic elements, i.e. the allometries of organismal capacity and environmental opportunity, remain those associated with the seminal size efficiency hypothesis. Unfortunately, the difficulties that eventually buried that hypothesis in a welter of detail and special cases were not resolved, so the newer, broader concepts associated with complex interactions remain difficult or impossible to test. Those concepts are so subjective, poorly defined, and variably interpreted that they are more effective in explaining our observations after the fact than in predicting them before-hand. Despite predictive failure, such explanatory models have achieved wide acceptance. Once accepted as substitutes for predictive theory, they mire the advance of science by hiding its deficiencies. One solution to this cloying complexity is insistence that the theories of ecology specify simple, observable response variables so that theories may be evaluated by their predictive power. Components of a general refuge concept illustrate the point. This policy has implications for environmental science well beyond the confines of plankton ecology.Dedicated to Dr Karl Banse, School of Oceanography, University of Washington on his 60th Birthday.     

Egg size variability in trematodes: test of the bet-hedging hypothesis

The hypothesis according to which egg size variability in hermaphroditic parasites results from bet-hedging was investigated in a comparative analysis using trematodes as a model. We hypothesized that the species reproducing mainly by self-fertilization should produce smaller eggs than those species that regularly practice cross-fertilization. Indeed, because self-fertilization is usually associated with inbreeding depression, selection should favor individuals spreading the risk of genetically disturbed development across more but smaller eggs, instead of producing fewer eggs, each possessing a large resource supply, of which many may fail to develop because of genetic deficiencies. On the basis of earlier theoretical and empirical studies, we assumed that the ratio length of testis-length of ovary positively correlates with the mating group size and, hence, with opportunities for cross-fertilization. In accordance with the bet-hedging hypothesis, we found, across trematode species, a positive relationship between this ratio and the mean egg volume produced by adults. This result was, however, observed only for the trematodes infecting birds and not for the species infecting fishes and mammals. In addition, once the influence of trematode phylogeny was taken into account, there was no significant trend, suggesting that phylogenetic legacies played a large role in generating the previous signal. Experimental tests of the bet-hedging hypothesis will be necessary to clarify the matter.     

Clutch size variation in the Nazca booby: a test of the egg quality hypothesis

In obligately siblicidal bird species, aggressive behavior bya dominant chick results in a fixed brood size of one, yetthese species usually show clutch size variation between individuals.Simmons proposed that variation in clutch size in obligatelysiblicidal species is related to a trade-off between egg qualityand egg quantity: some individuals produce a single highly hatchable egg, while others produce two small, lower qualityeggs. We tested the egg quality hypothesis as an explanationfor observed clutch size variation in the Nazca booby (Sulagranti), an obligately siblicidal seabird. We tested the assumptionthat egg volume is positively correlated with hatchabilityand the prediction that eggs from one-egg clutches are largerthan eggs from two-egg clutches. We did not find a positive relationship between egg volume and hatchability in this species.Eggs from two-egg clutches were either equivalent in volumeor larger than eggs from one-egg clutches. Thus, the egg qualityhypothesis was rejected as an explanation for clutch size variationin the Nazca booby. Instead, two-egg clutches appear to befavored because of the insurance value of the second-laid egg,while one-egg clutches result from food limitation.     

Evolution of genome size in fishes: a phylogenetic test of the Hinegardner and Rosen hypothesis

Despite remarkable advances in genomic studies over the past few decades, surprisingly little is known about the processes governing genome evolution at macroevolutionary timescales. In a seminal paper, Hinegardner and Rosen (Am Nat 106:621–644, 1972) suggested that taxa characterized by larger genomes should also display disproportionately stronger fluctuations in genome size. Therefore, according to the Hinegardner and Rosen (HR) hypothesis, there should be a negative correlation between average within-family genome size and its corresponding coefficient of variation (CV), a prediction that was supported by their analysis of the genomes of 275 species of fish. In this study we reevaluate the HR hypothesis using an expanded dataset (2050 genome size records). Moreover, in addition to the use of standard linear regression techniques, we also conducted modern comparative analyses that take into account phylogenetic non-independence. Our analyses failed to confirm the negative relationship detected in the original study, suggesting that the evolution of genome size in fishes might be more complex than envisioned by the HR hypothesis. Interestingly, the frequency distribution of fish genome sizes was strongly skewed, even on a logarithmic scale, suggesting that the dynamics underlying genome size evolution are driven by multiplicative phenomena, which might include chromosomal rearrangements and the expansion of transposable elements.     

Predator foraging success and habitat complexity: quantitative test of the threshold hypothesis

Summary Numerous studies have demonstrated a negative relationship between increasing habitat complexity and predator foraging success. Results from many of these studies suggest a non-linear relationship, and it has been hypothesised that some threshold level of complexity is required before foraging success is reduced significantly. We examined this hypothesis using largemouth bass (Micropterus salmoides) foraging on juvenile bluegill sunfish (Lepomis macrochirus) in various densities of artificial vegetation. Largemouth foraging success differed significantly among the densities of vegetation tested. Regression analysis revealed a non-linear relationship between increasing plant stem density and predator foraging success. Logistic analysis demonstrated a significant fit of our data to a logistic model, from which was calculated the threshold level of plant stem desity necessary to reduce predator foraging success. Studies with various prey species have shown selection by prey for more complex habitats as a refuge from predation. In this stydy, we also examined the effects of increasing habitat complexity (i.e. plant stem density) on choice of habitat by juvenile bluegills while avoiding predation. Plant stem density significantly effected choice of habitat as a refuge. The relationship between increasing habitat complexity and prey choice of habitat was found to be positive and non-linear. As with predator foraging success, logistic analysis demonstrated a significant fit of our data to a logistic model. Using this model we calculated the threshold level of habitat complexity required before prey select a habitat as a refuge. This density of vegetation proved to be considerably higher than that necessary to significantly reduce predator foraging success, indicating that bluegill select habitats safe from predation.Implications of these results and various factors which may affect the relationships described are discussed.     

Clutch size and the rejection of parasitic eggs: a comparative test of the maternal investment hypothesis

Evolutionary Ecology - Obligate brood parasitic birds lay their eggs in the nests of other species, reducing the host’s own reproductive output. To circumvent these fitness costs,...