Dynamic energy budget theory and population ecology: lessons from Daphnia

Dynamic energy budget (DEB) theory offers a perspective on population ecology whose starting point is energy utilization by, and homeostasis within, individual organisms. It is natural to ask what it adds to the existing large body of individual-based ecological theory. We approach this question pragmatically--through detailed study of the individual physiology and population dynamics of the zooplankter Daphnia and its algal food. Standard DEB theory uses several state variables to characterize the state of an individual organism, thereby making the transition to population dynamics technically challenging, while ecologists demand maximally simple models that can be used in multi-scale modelling. We demonstrate that simpler representations of individual bioenergetics with a single state variable (size), and two life stages (juveniles and adults), contain sufficient detail on mass and energy budgets to yield good fits to data on growth, maturation and reproduction of individual Daphnia in response to food availability. The same simple representations of bioenergetics describe some features of Daphnia mortality, including enhanced mortality at low food that is not explicitly incorporated in the standard DEB model. Size-structured, population models incorporating this additional mortality component resolve some long-standing questions on stability and population cycles in Daphnia. We conclude that a bioenergetic model serving solely as a 'regression' connecting organismal performance to the history of its environment can rest on simpler representations than those of standard DEB. But there are associated costs with such pragmatism, notably loss of connection to theory describing interspecific variation in physiological rates. The latter is an important issue, as the type of detailed study reported here can only be performed for a handful of species.     

Egg size evolution and energetic constraints on population dynamics.

We use population models that are based on dynamic energy budget models for individuals in order to study the evolution of offspring size and its relationship to the evolution of population dynamics. We show the existence of alternative evolutionarily stable strategies for offspring investment strategy resulting from a trade off between offspring number and time-to-maturity. The model predicts egg energy in Daphnia magna well, and suggests that the observed egg energy in D. magna is the result of selection for minimal egg investment constrained by minimum viable egg energy, combined with selection for a juvenile energy reserve. The selection for minimal egg size pushes populations toward chaotic dynamics. However, the minimum viable egg size combined with low efficiency of conversion of energy to new biomass is sufficient to keep population dynamics out of chaos.     

Predation-mediated coexistence of large- and small-bodied Daphnia at different food levels

Using an individual-based age-structured population model (a combination of O'Brien's apparent-prey-size approach, Eggers's reactive-field-volume model, and Holling's disk equation), we could predict that (1) a Daphnia population could be kept at low density by fish predation irrespective of food level, with greater recruitment at higher food being instantly compensated for by raised mortality reflecting increased predation, and (2) Daphnia density levels are species specific and inversely related to both body size at first reproduction and the reaction distance at which a foraging fish sees its Daphnia prey. These two hypotheses were experimentally tested in outdoor mesocosms with two Daphnia species of different body sizes grown in the absence or presence of fish that were allowed to feed for 2-3 h each evening. While each Daphnia quickly reached high density with reproduction halted by food limitation in the absence of fish, the populations stayed at much lower species-specific density levels, similar in low and high food concentrations, in the presence of fish. This suggests that our model offers a reasonable mechanistic explanation for the coexistence of large- and small-bodied zooplankton in proportions reflecting their body sizes throughout habitats comprising a wide productivity spectrum, with each species at a density level at which it becomes included in a predator's diet.     

Modeling Global Macroclimatic Constraints on Ectotherm Energy Budgets

We describe a mechanistic individual-based model of how globalmacroclimatic constraints affect the energy budgets of ectothermicanimals. The model uses macroclimatic and biophysical charactersof the habitat and organism and tenets of heat transfer theoryto calculate hourly temperature availabilities over a year.Data on the temperature dependence of activity rate, metabolism,food consumption and food processing capacity are used to estimatethe net rate of resource assimilation which is then integratedover time. We detail and explore the significance of assumptionsused in these calculations. We present a new test of this model in which we show that thepredicted energy budget sizes for 11 populations of the lizardSceloporus undulalus are in close agreement with observed resultsfrom previous field studies. This demonstrates that model testsare feasible and the results are reasonable. Further, sincethe model represents an upper bound to the size of the energybudget, observed residual deviations form explicit predictionsabout the effects of environmental constraints on the bioenergeticsof the study lizards within each site that may be tested byfuture field and laboratory studies. Three major new improvements to our modeling are discussed.We present a means to estimate microclimate thermal heterogeneitymore realistically and include its effects on field rates ofindividual activity and food consumption. Second, we describean improved model of digestive function involving batch processingof consumed food. Third, we show how optimality methods (specificallythe methods of stochastic dynamic programming) may be includedto model the fitness consequences of energy allocation decisionssubject to food consumption and processing constraints whichare predicted from the microclimate and physiological modeling Individual-based models that incorporate macroclimatic constraintson individual resource acquisition, assimilation and allocationcan provide insights into theoretical investigations about theevolution of life histories in variable environments as wellas provide explicit predictions about individual, populationand community level responses to global climate change.     

Relationships between heterotrophic nanoflagellates and the demographic response of Daphnia longispina in a eutrophic lake with poor food quality conditions

1. Based on both field data and laboratory studies, the summer population of Daphnia longispina living in a stratified eutrophic lake was examined in relation to the abundance of algae, nanoflagellates and picocyanobacteria.
2. In early July, the Daphnia population replaced Bosmina and remained the dominant zooplankter during summer 1994. Its development in July was concomitant with an increase of edible algae but, despite the apparent abundance in available food, the Daphnia population decreased throughout August suggesting poor food conditions.
3. From mid-August to the beginning of September, the biomass of inedible phytoplankton was greater than that of the smaller, edible fraction. Consequently the average rate of increase, birth rates and fecundity of Daphnia remained low. Although the biomass of heterotrophic nanoflagellates was consistently low, the demographic parameters of Daphnia were correlated throughout this period with these protozoans.
4. Life table experiments run in the laboratory showed that epilimnetic food supported both the growth in length of individual Daphnia and an increase in fecundity, but metalimnetic food supported only individual growth. D. longispina probably failed to reproduce because of the abundance of detritus mixed with the heterotrophic nanoflagellates in the metalimnetic water at that period of the year. The vertical migration of Daphnia into these deeper layers could be caused by a predator avoidance mechanism.     

Evidence of phosphorus-limited individual and population growth of Daphnia in a Canadian Shield lake

We performed bag experiments in a Canadian Shield lake with generally high seston (suspended food particles mainly composed of algae) carbon (C):phosphorus (P) ratios, and investigated the responses of individual and population growth of herbivorous Daphnia dentifera on their abundance with (+P) and without (−P) a phosphorus enrichment to lake water. In both treatments, increased abundance of D. dentifera reduced seston C concentration and was accompanied by decreases in population and individual growth rates. However, P-enrichment increased seston P concentration and then reduced seston C:P ratio from 400–700 to ca 100 (by atoms). As a result, both individual and population growth rates were significantly higher in the +P treatment at all animal abundances even though seston C concentrations were similar between the treatments. The magnitude of the growth enhancement by the P-enrichment was independent of animal abundance. Stepwise regression analyses revealed that 71 and 90% of the variance in the population and individual growth rates, respectively, were explained by seston C and P concentrations, and that the contribution of the seston P concentration was roughly the same as that of seston C. Such joint effects of seston C and P indicate that food quality (P content) as well as food quantity (C concentration) can influence Daphnia not only at the level of individual growth but also at the level of population dynamics in P-limited lakes. Our results thus strongly corroborate the hypothesis that the population development of a key herbivore Daphnia in P-limited Canadian Shield lakes is inhibited by the direct effects of P-limited food on individual growth, which weaken the strength of trophic cascading interactions starting from piscivorous fish through planktivorous fish and zooplankton to algae.     

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.     

Winter energy requirements of soricine shrews

The energy requirements of shrews under snow cover have not been determined. This is an expository paper attempting to ascertain the daily energy budget of a soricine in subnivean conditions. By means of extrapolation from past work (Morrison, Ryser & Dawe, 1959; Gebczynski, 1965, 1971), a winter individual of Sorex cinereus (mean weight of 2–6 g) in southern Manitoba has a rather high energy budget at 2^oC of about 38-6 kj or 9-2kcal per day. It is assumed that winter prey include invertebrates and small mammals, and their biomass and energy content are estimated. Compensatory factors reducing energy needs are considered, i.e. Dehnel's Phenomenon, extended periods in the nest, low population densities and adequate snow cover. We can probably reduce the above figure for a daily energy budget when considering all the above factors, so that about 30 kj are required daily at the mean subnivean temperature of – 4–5^oC.     

Stoichiometric food quality and herbivore dynamics

Herbivores may grow with nutrient or energy limitation, depending on food abundance and the chemical composition of their food. We present a model that describes herbivore growth as a continuous function of two limiting factors. This function uses the synthesizing unit concept, has the hyperbolic Monod model as a limiting case, and has the same number of parameters as the Monod model coupled to Liebig's discontinuous minimum rule. We use the model to explore nutrient-limited herbivore growth in a closed system with algae, Daphnia and phosphorus as the limiting nutrient. Phosphorus in algae may substantially influence Daphnia growth. This influence changes over time and is most pronounced when algae and Daphnia populations fluctuate strongly. Relative to classic models that only consider food quantity as a determinant of Daphnia growth, our model shows richer dynamical behaviour. In addition to the standard positive equilibrium, which may be stable or unstable depending on nutrient availability, a new positive equilibrium may arise in our model when mortality rates are relatively high. This equilibrium is unstable and reduces the likelihood of long-term persistence of Daphnia in the system.     

Field Studies Concerning the Fecundity of Daphnia galeata,its Causes and Consequences

Field studies on a Daphnia galeata population in the mesotrophic man-made lake Saidenbach show that the fecundity of the animals depends on individual size, water temperature and the food supply (absolute quantity, specific food supply, food quality). These different factors are subsumed in the ingestion rate (rate of individual food intake per unit time), which is of an integrative character. The fecundity plotted versus ingestion rate yields a graph with the shape of a saturation curve. Attention is drawn to the consequences in terms of variation in population size.     

Complex dynamic behaviour of autonomous microbial food chains

 The dynamic behaviour of food chains under chemostat conditions is studied. The microbial food chain consists of substrate (non-growing resources), bacteria (prey), ciliates (predator) and carnivore (top predator). The governing equations are formulated at the population level. Yet these equations are derived from a dynamic energy budget model formulated at the individual level. The resulting model is an autonomous system of four first-order ordinary differential equations. These food chains resemble those occuring in ecosystems. Then the prey is generally assumed to grow logistically. Therefore the model of these systems is formed by three first-order ordinary differential equations. As with these ecosystems, there is chaotic behaviour of the autonomous microbial food chain under chemostat conditions with biologically relevant parameter values. It appears that the trajectories on the attractors consists of two superimposed oscillatory behaviours, a slow one for predator–top predator and a fast one for the prey–predator on one branch at which the top predator increases slowly. In some regions of the parameter space there are multiple attractors. Received 8 November 1995; received in revised form 7 January 1997     

Influence of food density on the effects of a Chaoborus-released chemical on Daphnia ambigua

SUMMARY 1. Daphnia ambigua was reared individually at four different food levels in water conditioned by a predator, Chaoborus flavicans. Daphnia ambigua developed spike-like helmets during the first four instars in each treatment with the Chaoborus-conditioned water, but only during the first instar in untreated water. The helmet development at instars 2–4 was probably induced by a chemical released from the Chaoborus .
2. The helmets decreased in size with decreasing food levels, but never ceased to form, even at a very low food concentration.
3. Daphnids cultured in the Chaoboras -conditioned water exhibited reduced growth, reproduction and survival rates at low food levels. These results might be induced by the energy loss associated with producing the helmets.
4. It is suggested that the predator releases a chemical, which reduces the tolerance of the cyclomorphic Daphnia to food deficiency, thus accentuating the summer decline in the Daphnia population caused by food shortage.     

From inducible defences to population dynamics: modelling refuge use and life history changes in Daphnia

We investigated the relative importance of a behavioural defence (refuge use through diel vertical migration) and a life history change (a reduced size at first reproduction) that are used by daphnids to decrease the risk of predation by visually hunting fish. We used an individual based model of a Daphnia population in a stratified lake to quantify the effects of these inducible defences on Daphnia predation-mortality and the resulting Daphnia population dynamics. Our analysis shows that diel vertical migration (DVM) confers a much stronger protection against fish predation than a reduced size at first reproduction (SFR). DVM allows daphnids to withstand a higher predation pressure in the epilimnion and it decelerates a Daphnia population decline more strongly than a reduced SFR. DVM effectively reduces the (P/B) flow of carbon from daphnids to fish.
Many theoretical studies have only considered the fitness benefits of DVM above 'staying up' in the epilimnion of a lake. Our results suggest that 'staying down' in the hypolimnion would confer an even stronger fitness benefit to Daphnia than DVM at times of peak predation risk. Daphnids that remain in the hypolimnion avoid the predation suffered by migrating daphnids around dusk and dawn. Staying down could prevent a Daphnia population decline, while DVM and a reduced SFR can only decelerate the decrease of Daphnia population densities under heavy fish predation. Staying down at high concentrations of fish infochemicals has in fact been observed within a variety of Daphnia clones and species, both in the laboratory and in stratified lakes.     

A community model of ciliateTetrahymena and bacteriaE. coli: Part I. Individual-based models ofTetrahymena andE. coli populations

The dynamics of a microbial community consisting of a eucaryotic ciliateTetrahymena pyriformis and procaryoticEscherichia coli in a batch culture is explored by employing an individual-based approach. In this portion of the article, Part I, population models are presented. Because both models are individual-based, models of individual organisms are developed prior to construction of the population models. The individual models use an energy budget method in which growth depends on energy gain from feeding and energy sinks such as maintenance and reproduction. These models are not limited by simplifying assumptions about constant yield, constant energy sinks and Monod growth kinetics as are traditional models of microbal organisms. Population models are generated from individual models by creating distinct individual types and assigning to each type the number of real individuals they represent. A population is a compilation of individual types that vary in a phase of cell cycle and physiological parameters such as filtering rate for ciliates and maximum anabolic rate for bacteria. An advantage of the developed models is that they realistically describe the growth of the individual cells feeding on resource which varies in density and composition. Part II, the core of the project, integrates models into a dynamic microbial community and provides model analysis based upon available data.     

Temperature-dependent energy budget of an Arctic Cladoceran, Daphnia middendorffiana

1. Global change models predict the greatest impact in climate to occur in the northern polar region. Change in temperature will alter individual metabolism and has the potential to change community structure to an unknown degree.
2. The temperature-dependent energy budget of Arctic Daphnia middendorffiana was investigated by measuring respiration rates, ingestion rates and assimilation rates. The scope for growth and reproduction was determined and compared with data from the literature for a clone of Daphnia pulicaria collected in the temperate zone.
3. A difference was observed between the Arctic species and the temperate zone clone in both temperature tolerance, and the energy available for growth and reproduction at various temperatures. A low availability of energy for growth and reproduction indicated that life history patterns as well as physiological mechanisms are important in allowing D. middendorffiana to exist successfully in Arctic environments.
4. The lower available energy for growth compared to Daphnia clones from temperate zones may be detrimental to D. middendorffiana , which might have to compete with species expanding their range under the predicted temperature increase for Arctic regions.     

Continuous Structured Population Models for <Emphasis Type="Italic">Daphnia magna</Emphasis>

We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.     

Food quantity and quality regulation of trophic transfer between primary producers and a keystone grazer (Daphnia) in pelagic freshwater food webs

The transfer of energy and nutrients from plants to animals is a key process in all ecosystems. In lakes, inefficient transfer of primary producer derived energy can result in low animal growth rates, accumulation of nuisance phytoplankton blooms and dissipation of energy from the ecosystem. Most research on carbon transfer efficiency in pelagic food webs has focused on either food quantity or food quality, with the latter considered separately as either elemental stoichiometry or biochemical composition. The natural occurrence and magnitude of these types of growth limitations and their combined effects on Daphnia , a keystone grazer in pelagic freshwater ecosystems, are largely unknown. Our empirical models predict that the strength and nature of food quantity and quality limitation varies greatly with lake trophic state (total phosphorus, TP) and that Daphnia growth rates and thus energy and nutrient transfer efficiency are highest in lakes with intermediate trophic status (TP 10–25 μg l⁻¹). We predict that food availability place the greatest constraint on Daphnia growth in nutrient poor lakes (TP≤4 μg l⁻¹). Phosphorus limitation of Daphnia growth increased with decreasing TP, but the overall effect was never predicted to be the dominant constraining factor. Eicosapentaenoic acid (EPA, 20:5ω3) limitation was predicted to occur in both nutrient poor and nutrient rich lakes and placed the primary constraint on food quality in the most productive lakes. Two contrasting EPA-models gave different results on the magnitude of EPA-limitation, implying that additional food quality factors decrease Daphnia growth at high TP. In conclusion, the model predicts that Daphnia growth should peak in mesotrophic lakes, food quantity will place the greatest constraint on growth in oligotrophic lakes and EPA will primarily limit growth in eutrophic lakes.     

Trade-offs in the vertical distribution of zooplankton: ideal free distribution with costs?

Zooplankton vertical migratory patterns are a classic example of optimal habitat choice. We hypothesize that zooplankton distribute themselves vertically in the water column according to an ideal free distribution (IFD) with costs such as to optimize their fitness. In lakes with a deep-water chlorophyll maximum, zooplankton are faced with a trade-off, either experiencing high food (high reproductive potential) but low temperature (slow development) in the hypolimnion or high temperature and low food in the epilimnion. Thus, in the absence of fish predation (e.g. at night) they should allocate the time spent in the different habitats according to fitness gain dependent on the temperature gradient and distribution of food. We tested this hypothesis with a Daphnia hyalina x galeata clone in large indoor columns (Plön Plankton Towers) and with a dynamic energy budget model. In the tower experiments, we simulated a deep-water algal maximum below the thermocline with epilimnetic/hypolimnetic temperature differences of 2, 5 and 10 degrees C. Experimental data supported the model. We found a significantly larger proportion of daphniids in the hypolimnion when the temperature difference was smaller. Our results are consistent with the concept of IFD with costs originally developed for stream fishes. This concept can be applied to predict the vertical distribution of zooplankton in habitats where fish predation is of minor importance.     

An Individual-Based Model of Zebrafish Population Dynamics Accounting for Energy Dynamics

Developing population dynamics models for zebrafish is crucial in order to extrapolate from toxicity data measured at the organism level to biological levels relevant to support and enhance ecological risk assessment. To achieve this, a dynamic energy budget for individual zebrafish (DEB model) was coupled to an individual based model of zebrafish population dynamics (IBM model). Next, we fitted the DEB model to new experimental data on zebrafish growth and reproduction thus improving existing models. We further analysed the DEB-model and DEB-IBM using a sensitivity analysis. Finally, the predictions of the DEB-IBM were compared to existing observations on natural zebrafish populations and the predicted population dynamics are realistic. While our zebrafish DEB-IBM model can still be improved by acquiring new experimental data on the most uncertain processes (e.g. survival or feeding), it can already serve to predict the impact of compounds at the population level.     

Temperature is the key factor explaining interannual variability of Daphnia development in spring: a modelling study

Plankton succession during spring/early summer in temperate lakes is characterised by a highly predictable pattern: a phytoplankton bloom is grazed down by zooplankton (Daphnia) inducing a clear-water phase. This sequence of events is commonly understood as a cycle of consumer-resource dynamics, i.e. zooplankton growth is driven by food availability. Here we suggest, using a modelling study based on a size-structured Daphnia population model, that temperature and not food is the dominant factor driving interannual variability of Daphnia population dynamics during spring. Simply forcing this model with a seasonal temperature regime typical for temperate lakes is sufficient for generating the distinctive seasonal trajectory of Daphnia abundances observed in meso-eutrophic temperate lakes. According to a scenario analysis, a forward shift of the vernal temperature increase by 60 days will advance the timing of the Daphnia maximum on average by 54 days, while a forward shift in the start of the spring bloom by 60 days will advance the Daphnia maximum only by less than a third (17 days). Hence, the timing of temperature increase was more important for the timing of Daphnia development than the timing of the onset of algal growth. The effect of temperature is also large compared to the effect of applying different Daphnia mortality rates (0.055 or 0.1 day(-1), 38 days), an almost tenfold variation in phytoplankton carrying capacity (25 days) and a tenfold variation in Daphnia overwintering abundance (3 days). However, the standing stock of Daphnia at its peak was almost exclusively controlled by the phytoplankton carrying capacity of the habitat and seems to be essentially independent of temperature. Hence, whereas food availability determines the standing stock of Daphnia at its spring maximum, temperature appears to be the most important factor driving the timing of the Daphnia maximum and the clear-water phase in spring.