Influence of low and decreasing food levels on Daphnia-algal interactions: Numerical experiments with a new dynamic energy budget model

Based on numerical experiments with a new physiologically structured population model we demonstrate that predator physiology under low food and under starving conditions can have substantial implications for population dynamics in predator-prey interactions. We focused on Daphnia-algae interactions as model system and developed a new dynamic energy budget (DEB) model for individual daphnids. This model integrates the κ-rule approach common to net assimilation models into a net-production model, but uses a fixed allocation of net-productive energy in juveniles. The new DEB-model agrees well with the results of life history experiments with Daphnia. Compared to a pure κ-rule model the new allocation scheme leads to significant earlier maturation at low food levels and thus is in better agreement with the data. Incorporation of the new DEB-model into a physiologically structured population model using a box-car elevator technique revealed that the dynamics of Daphnia-algae interactions are highly sensitive to the assumptions on the energy allocation of juveniles under low food conditions. Additionally we show that also other energy allocation rules of our DEB-model concerning decreasing food levels and starving conditions at the individual level have strong implications for Daphnia-algae interactions at the population level. With increasing carrying capacity of algae a stable equilibrium with coexistence of Daphnia occurs and algae shifts to limit cycles. The amplitudes of the limit cycles increase with increasing percentage of sustainable weight loss. If a κ-rule energy allocation is applied to juveniles, the stable equilibrium occurs for a much narrower range of algal carrying capacities, the algal concentration at equilibrium is about 2 times larger, and the range of algae carrying capacities at which daphnids become extinct extends to higher carrying capacities than in the new DEB-model. Because predator-prey dynamics are very sensitive to predator physiology under low food and starving conditions, empirical constraints of predator physiology under these conditions are essential when comparing model results with observations in laboratory experiments or in the field.     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

A spatiotemporal individual-based fish model to investigate emergent properties at the organismal and the population level

A spatiotemporal individual-based model (IBM) of roach (Rutilus rutilus) including bioenergetic principles was used to study emergent properties at the individual and the population level which appeared as a result of resource allocation and time scheduling of activities related to maintenance, growth, and reproduction in a seasonally changing environment. The model was used as a virtual laboratory to consider the impact of various parameters on vital rates and spatial behaviour of roach, which is particularly difficult to study in the field. The parameterisation based on field studies performed at Lake Belau (Schleswig-Holstein, Germany) and laboratory measurements. This allowed us to explore the relationship between population structure and environmental heterogeneity on an integrated base. At the individual level emergent properties such as spatial behaviour, growth, and food consumption could be identified. Emergent properties at the population level resulted as phenotypic consequences of a trophic bottleneck, the influence of lake morphology on the phenotype as well as size-dependent winter mortality rates and post-reproductive mortality rates.     

Population energetics of the intertidal isopod Cirolana harfordi

Laboratory experiments and field measurements generated a population energy-budget estimate for the isopod Cirolana harfordi (Lockington). Assimilation of food energy averaged 88% on a diet of fish. About 35% of assimilated energy is allocated for growth and reproduction, while the bulk of the remainder is used for maintenance and activity (respiration). The high growth efficiency of C. harfordi is discussed with respect to ecological efficiency and energy transfer in marine systems.     

Animal community structure and energy budget calculations of a Daphnia magna (straus) population in relation to the rock pool environment

The fauna and environmental conditions in a freshwater rock pool ecosystem were followed by a weekly quantitative sampling program from April to August, 1974. The rock pool, situated on a small island in the northern Baltic Sea, was heavily eutrophicated by droppings from the surrounding colony of sea birds. The intermittent flushing of the pool with rainwater and the input of bird droppings, as well as the biological activity, contributed to the large seasonal variations in nutrients and organic matter that were observed. A dense algal bloom of flagellates occurred in April but vanished when the animal population started to increase in the middle of May. During the rest of the summer, most of the photosynthetic pigments were found in the bottom sediment, mostly as degraded phaeo-pigments due to intensive grazing by the animals in the pool. Very few animal taxa were found and the phyllopod Daphnia magna (Straus) dominated throughout the whole sampling period. D. magna contributed to more than 50% of the total biomass, except in late July when chironomid larvae were most abundant. The total biomass in the pool increased from about 15 mg (dry weight) l^?1 in May to a maximum of about 60 mg l^?1 at the end of June. There were few carnivores in the system, except during the spring when the water bug Deronectes griseostriatus (de Geer) was common.Analyses of size, age and sex structure and calculations of birth and death rates of the D. magna population showed large seasonal variations, correlated with the volume fluctuations and flushings of the pool which stimulated both the algal production and the growth and reproduction of Daphnia. Data from the extensive literature that exists on D. magna and other species of the same genus were used, together with field and experimental data from the rock pool population, in a numerical model describing the energy budget of this species. The model describes variations in weight-specific growth, reproduction, moulting, feeding and respiration rates in relation to temperatures and food concentrations. Energy budget relationships that maximise the chances for survival and utilisation of the available energy for a population exposed to varying food concentrations are predicted by the model. The energy budget model was also used to estimate the secondary production of the rock pool population of D. magna. The total production between April and August was 203 mg (dry weight) l^?1 and the average production per biomass ratio was 0.094 day^?1. The average net production efficiency was 42%, very close to other values reported for D. magna from other biotopes. The relative importance of different factors controlling the production was also analysed with the model. Production per biomass ratio was calculated, assuming a constant temperature and/or food concentration for the whole sampling period. The varying food concentrations in the rock pool had the most pronounced influence, greater than that of temperature and size structure variations in the population.     

Effects of water temperature and mixed layer depth on zooplankton body size

Ecological consequences of global warming include shifts of species ranges toward higher altitudes and latitudes as well as temporal shifts in phenology and life-cycle events. Evidence is accumulating that increasing temperature is also linked to reduced body size of ectotherms. While temperature can act directly on body size, it may also act indirectly by affecting the timing of life-cycle events and the resulting population age and size structure, especially in seasonal environments. Population structure may, in turn, be influenced by temperature-driven changes in resource availability. In a field mesocosm experiment, we investigated how water temperature and mixed surface layer depth (a temperature-dependent determinant of light availability to phytoplankton) affected population dynamics, population age and size structure, and individual size at stage (size at first reproduction) of Daphnia hyalina during and after a phytoplankton spring bloom. Mixed layer depth was inversely related to the magnitudes of the phytoplankton spring bloom and the subsequent Daphnia peak, but had no effect on the body size of Daphnia. Conversely, temperature had no effects on abundance peaks but strongly affected the timing of these events. This resulted in at times positive, at other times negative, transient effects of temperature on mean body size, caused by asynchronous changes in population size structure in cold versus warm treatments. In contrast to mean body size, individual size at stage consistently decreased with increasing temperature. We suggest that size at stage could be used as an unbiased response parameter to temperature that is unaffected by transient, demographically driven changes in population size structure.     

Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia

In population modeling, a considerable level of complexity is often required to provide trustworthy results, comparable with field observations. By assuring sufficient detail at the individual level while preserving the potential to explore the consequences at higher levels, individual-based modeling may thus provide a useful tool to investigate dynamics at different levels of organization. Still, population dynamics resulting from such models are often at odds with observations from the field. This may be partly caused by a lack of focus on the individual dynamics under conditions of food stress and starvation. I developed a physiologically structured, individual-based simulation model to investigate life history of Daphnia and its effect on population dynamics in response to the productivity of the system. In verifying model behavior with available literature data on life history and physiology, I paid special attention to the dynamics of food intake and the verification of individual level results under conditions of food limitation and starvation. I show that the maximum filtering rates under low food levels used in the current model are much closer to measured filtering rates than the ones used in other models. Being consistent with results on physiology and life history from experiments at a wide range of food availability (including starvation), the model generates low amplitude or high amplitude population density cycles depending on the productivity of the system, as observed in field and experimental populations of Daphnia and with the minimum population densities being one to two orders of magnitude lower in the high amplitude than in the low amplitude cycles. To generate results which are not only qualitatively but also quantitatively comparable to experimental and field observations, however, a crowding effect on the filtering response has to be incorporated in the model.     

Comparative study of the carbon cycle in Venus verrucosa fed on bacteria and phytoplankton

The aim of this, the third part of our study, was to compare the quantities of food consumed and assimilated by Venus verrucosa L. fed on two different living suspensions: the bacterium Lactobacillus sp. and the alga Pavlova lutheri. The experimental results have been presented in parts I and II of our study. The present paper describes a model constructed for each series of experiments with bacteria and with phytoplankton. An analog-computer model was succesfully applied and revealed that bacterial food was more easily consumed and assimilated than algal food, the dissolved form more easily assimilated than the living particulate form.     

Stage-specific biomass overcompensation by juveniles in response to increased adult mortality in a wild fish population

Recently developed theoretical models of stage-structured consumer-resource systems have shown that stage-specific biomass overcompensation can arise in response to increased mortality rates. We parameterized a stage-structured population model to simulate the effects of increased adult mortality caused by a pathogen outbreak in the perch (Perca fluviatilis) population of Windermere (UK) in 1976. The model predicts biomass overcompensation by juveniles in response to increased adult mortality due to a shift in food-dependent growth and reproduction rates. Considering cannibalism between life stages in the model reinforces this compensatory response due to the release from predation on juveniles at high mortality rates. These model predictions are matched by our analysis of a 60-year time series of scientific monitoring of Windermere perch, which shows that the pathogen outbreak induced a strong decrease in adult biomass and a corresponding increase in juvenile biomass. Age-specific adult fecundity and size at age were higher after than before the disease outbreak, suggesting that the pathogen-induced mortality released adult perch from competition, thereby increasing somatic and reproductive growth. Higher juvenile survival after the pathogen outbreak due to a release from cannibalism likely contributed to the observed biomass overcompensation. Our findings have general implications for predicting population- and community-level responses to increased size-selective mortality caused by exploitation or disease outbreaks.     

Convexity in projection matrices: Projection to a calibration problem

Convexity, as a fundamental property of sets and functions defined on convex sets, plays an important role in many mathematical and applied disciplines, including extremal and optimal-control problems. We prove the set of all feasible projection matrices in a general class of matrix models for stage-structured population dynamics to be convex and the dominant eigenvalue (λ₁) of any projection 2 × 2 matrix to be either a convex, or a concave function on a simplex of the matrix first-row entries (i.e., stage-specific reproduction rates). The latter is also conjectured for the general n × n case. Though looking far from practical needs of matrix population models, this mathematical result has appeared to be quite useful in solving a practical problem to calibrate the projection matrix, i.e., to estimate all the stage-specific vital rates, from empirical data. The data from monitoring of individual life histories of marked plants on permanent sample plots during successive years enable direct calculation of the stage-specific survival and ontogenetic transition rates, but the rates of reproduction do remain uncertain as far as the parent plants can hardly be determined for the (not yet marked!) recruitment.     

Data-directed modelling of Daphnia dynamics in a long-term micro-ecosystem experiment

The micro-ecosystem under consideration consists of three compartments forming a closed chain in which water circulates. Three trophic levels are represented in different compartments: autotrophs (algae, mainly Chlorella vulgaris), herbivores (Daphnia magna) and microbial decomposers. From a 20 years experiment with this system, data has been selected for this study. The dynamics of algae and Daphnia magna in only one of the compartments were modeled by different systems of differential and difference equations. We describe the successive steps in the process of model development, and the fitting of parameters using a Nelder-Mead simplex calibration method. Identification problems were overcome by taking values for physiological parameters in agreement with the literature. It turned out that a logistic type of model gives the best result for the structured Daphnia population because of the set up of the experiment: algae grow and reproduce in the upstream compartment. For this reason well-known plant–herbivore models did not comply with the data. The results of the parameter estimation procedure are discussed. The estimated grazing rate by Daphnia was smaller than expected. Possibly the Daphnia fed also on detritus and decomposing algae which were not measured.     

A survival-analysis-based simulation model for Russian wheat aphid population dynamics

A simulation model for Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), populations is built by integrating survival-analysis-based development and survivor functions and the same-shape reproduction distribution model in the framework of Leslie [Leslie, P.H., 1945. On the use of matrices in certain population mathematics. Biometrika 33, 183–212] matrix structure. Survival analysis is utilized to model both the development and survival of RWA populations, and the Cox (1972) proportional hazards model is fitted with the data sets from our laboratory observation of 1800 RWA individuals under 25 factorial combinations of five temperature regimes and five barley plant-growth stages. Rather than using simple age-specific survivor rates as in the traditional Leslie matrix, the survivor functions based on survival analysis describe age-specific, temperature and plant stage-dependent RWA survival probabilities. Similarly, a probability model from survival analysis to estimate the probability that an individual will reach mature adult stage is utilized to describe the development process; this makes the transition from nymphal stage to mature adult stage dependent on RWA age as well as temperature and plant-growth stage.Inspired by the same-shape distribution and rate-summation approach for modeling insect development, a similar approach for modeling insect reproduction under variable temperature is developed. This new same-shape reproduction distribution model incorporates individual variation in reproduction capability, as well as the effects of RWA age, temperature and plant-growth stage. Consequently, the same-shape reproduction distribution model replaces the simple age-specific fecundities in Leslie matrix model. To the best of our knowledge, this work is the first to introduce survival analysis to simulation modeling in entomology and ecology and also the first to integrate our newly developed same-shape reproduction distribution model into application.     

Density-dependent effects control the reproductive strategy and population growth of <Emphasis Type="Italic">Aurelia</Emphasis><Emphasis Type="Italic">aurita</Emphasis> s.l. scyphistomae

Aureliaaurita s.l. scyphistomae are capable of developing different asexual modes for propagation and thus present a multi-mode reproductive strategy. The reproduction rates and the reproductive strategy they adopt depend on a combination of various environmental parameters. We investigated the A.aurita s.l. polyp-to-polyp reproduction strategy and population growth in relation to polyp density. Our results confirmed that density-dependent factors control population growth of A. aurita s.l. scyphistomae in three different ways: (1) decreasing the polyp reproduction rate, (2) triggering the production of motile bud-like tissue particles and (3) inducing the detachment of developed scyphistomae. Whereas the decrease in the reproduction rate reduces the number of recruits, the motile particles and the detachment of scyphistomae contribute to minimizing density-dependent effects by allowing reproductive products and scyphistomae to drift away. Thus, not only are the negative effects of intraspecific competition for space and food diminished but also the potential colonization of new substrates, and further increase in scyphistoma density is favoured on larger spatial scales. The potential capability to switch its polyp-to-polyp reproduction strategy in response to environmental clues and population density may give Aurelia high adaptability in the temperate coastal waters where they commonly live and where they may be exposed to wide-ranging and fluctuating environmental variables that affect their survival and longevity. Considering these features, as well as the wide tolerance of Aurelia scyphistomae (and medusae) to environmental parameters, it is not surprising that the species/lineages of Aurelia are cosmopolitan and exhibit the most frequent bloom events worldwide.     

A finite element method to solve a population dynamics stage-structured model of intertidal barnacles

Many marine organisms are fixed or highly sedentary as adults but the adult population may be strongly dependent on the oceanic transport of planktonic larvae. In order to assess interactions between oceanographic and biological processes that determine the population dynamics of marine organisms with a sessile adult phase restricted to the coastline and a planktonic larval phase, we present a stage-structured finite element model for the barnacle Balanus glandula that inhabits the rocky intertidal zone of central California, USA.     

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature.     

Temperature-dependent ranges of coexistence in a model of a two-prey-one-predator microbial food web

The objective of our study was to analyze the effects of temperature on the population dynamics of a three-species food web consisting of two prey bacteria (Pedobacter sp. and Acinetobacter johnsonii) and a protozoan predator (Tetrahymena pyriformis) as model organisms. We assessed the effects of temperature on the growth rates of all three species with the objective of developing a model with four differential equations based on the experimental data. The following hypotheses were tested at a theoretical level: Firstly, temperature changes can affect the dynamic behavior of a system by temperature-dependent parameters and interactions and secondly, food web response to temperature cannot be derived from the single species temperature response. The main outcome of the study is that temperature changes affect the parameter range where coexistence is possible within all three species. This has significant consequences on our ideas regarding the evaluation of effects of global warming.     

Ecotoxicology and population dynamics: Using DEBtox models in a Leslie modeling approach

Although the ecological risks of toxic chemicals are usually assessed on the basis of individual responses, such as survival, reproduction or growth, ecotoxicologists are now attempting to assess the impact of environmental pollution on the dynamics of naturally exposed populations. The main issue is how to infer the likely impact on the population of the toxic effects observed at the individual level. Dynamic energy budget in toxicology (DEBtox) is the most user-friendly software currently available to analyze the experimental data obtained in toxicity tests performed on individuals. Because toxic effects are diverse and because the sensitivity of individuals varies considerably depending on life-cycle stage, Leslie models offer a convenient way of predicting toxicant effects on population dynamics.In the present study, we first show how parameter inputs, estimated from individual data using DEBtox, can be coupled using a Leslie matrix population model. Then, using experimental data obtained with Chironomus riparius, we show how the effects of a pesticide (methiocarb) on the population growth rate of a laboratory population can be estimated. Lastly, we perform a complex sensitivity analysis to pinpoint critical age classes within the population for the purposes of the field management of populations.     

A stage-structured, Aedes albopictus population model

Aedes albopictus has been the fastest spreading invasive animal species in the world from the mid-1980s until the mid-2000s. In areas it infests, it disrupts native mosquito ecology and can potentially vector up to 21 viruses. To better understand the population dynamics of this species, we created a temperature dependent population model. A stage-structured model was chosen to allow each life-stage to have different temperature dependent mortality and development rates, and each stage was modeled with an ordinary differential equation. Model parameters and distributions were based upon literature values. Initially, a basic model was constructed. This model then had parameters that were forced based upon daily average temperatures. Several criteria were used to evaluate the model, including a comparison to field data from Lubbock, TX. In a stochastic version of the model, a 95% confidence limit contained 70.7% of the field data points. Based upon these results, we feel reasonably confident that we have captured the role of temperature in driving the population dynamics of Ae. albopictus.     

Recruitment and attrition of associated plants under a shading crop canopy: Model selection and calibration

Associated plant and animal diversity provides ecosystem services within crop production systems. The importance of the maintenance or restoration of diversity is therefore increasingly acknowledged. Here we study the population dynamics of associated annual plants (‘weeds’) during the growth of a crop in a season and introduce a minimal model to characterize the recruitment and attrition of the associated plants under the influence of shading by the crop. A mechanistically based, logistic, light interception model was parameterized with light interception measurements in two single crops (barley and rye) and in mixtures of these cereals with peas. Population dynamics data were collected for the annuals Papaver rhoeas, Centaurea cyanus, Chrysanthemum segetum, and Misopates orontium. A minimal population dynamics model was identified for each annual plant species, using system identification techniques as model selection and calibration.     

Effects of El Niño-Southern oscillation on the population dynamics of the tropical bivalve Donax dentifer from Málaga bay, Colombian Pacific

The population dynamics of a Donax dentifer (Hanley, 1843) population from Málaga bay, Colombia, was studied during two periods (August 1997–July 1998 and November 1999–February 2002) in order to investigate the effects of El Niño (EN) 1997/1998 and La Niña (LN) 1998/2000. The EN–LN cycle was strongly associated to an interannual precipitation and salinity variability in Málaga bay. Additionally, these factors were highly correlated with the reproductive cycle. Results indicate that EN had negative effects on the reproductive cycle, leading to weak, abnormal spawning events. In contrast, good spawning events were recorded during LN and post-LN. Based on these findings, an opportunistic reproductive strategy is proposed for this species. Overall growth performance (P) was higher during LN (P=4.41) than during EN and post-LN (P=4.20, P=4.28, respectively). These results indicate that D. dentifer has a higher overall growth performance compared to several tropical species reported in the literature. Total mortality rate of small individuals was higher during LN whereas that of large individuals was higher during EN. These results are best explained by recruitment variability and spatial differences between recruits and adults. Individual production and productivity were higher during LN, although annual biomass was relatively low. This, together with the results regarding growth and reproduction, suggests that food availability was higher during LN, thus positive effects under LN may be concluded. In contrast, EN seems to have negative effects on growth, reproduction and somatic production for this surf clam.