Figure 1.
Schematic representation of the DEB model.
Given parameters are involved in different resource-related and crowding-related hypotheses respectively (see Table 1). For modelling adaption of food ingestion and change in energy allocation, we applied an adaptive plasticity function F (upper right panel) to the respective parameter, where the level of plasticity increases with decreasing scaled reserve density e (or rather increasing 1-e) beyond a threshold (dashed line). Similarly, we used a stress function s (lower right panel) for modelling crowding effects at increasing population density d. More detailed explanations are given in the main text.
Table 1.
Hypotheses for resource-related adaptive plasticity and crowding-related mechanisms.
Figure 2.
Somatic growth and reproduction under different food conditions (mg carbon) in flow-through systems.
Somatic growth was measured as increase in body length (excluding spine) during the course of time whereas cumulative reproduction is given as mean offspring number produced per daphnid during a certain period of time (data from [48]). A and B: total data, model fit based on hypothesis H3; C: low food for different values of filtration adaptive plasticity factor ({fa}, hypothesis H1); D: low food for different values for κ (hypothesis H2); solid lines represent modelled growth and reproduction considering resource-related adaptive plasticity; dashed lines in C and D represent model without plasticity (hypothesis H0).
Figure 3.
A: Filtration rate as a function of daphnid body length, measurements excluding spine, B: ingestion rate as function of algal resource density and c) assimilation rate per unit of Daphnia dry weight as function of resource density; data in A and B from [48], data in C extracted from [49].
Table 2.
Performance of different hypotheses.
Table 3.
Parameter estimates and confidence intervals (CI) for the individual-based model.
Figure 4.
Somatic growth in terms of body size and cumulative reproduction (mean offspring number per female) for different crowding conditions (daphnids per mL).
Model fit (lines) is based on the assumption of reduced filtration rate and increased costs for reproduction (hypothesis H6); data (circles) from [31]; note that in B the data for highest density (white circles) relate to lowest predicted cumulative reproduction; high density reproduction data (at 0.8 mL−1) were not included in model parameterisation.
Table 4.
Parameter estimation for crowding mechanisms.
Figure 5.
Survival and D. magna body sizes based on hypothesis H3.
A: Fraction of survivors as function of time of medium- (2.9±0.2 mm) and large- (4.1±0.1 mm) bodied daphnids in the absence of food, B: survivorship for daphnids that were supplied with two different (high) amounts of algal food, C: dry weight as function of physical body length for daphnids that were kept under culture conditions (black dots) or that were starved until death (white dots); dots and lines represent empirical data and model fit respectively; data in A and C this study and data in B published in [14].
Figure 6.
Population level test of hypotheses.
Population-level consequences of different hypotheses (see Table 1) are shown for high (1.3 mgC per day and population) and low food (0.5 mgC per day and population) conditions respectively; empirical data (dots) and model predictions (lines) are given for total abundances (population size in total numbers) and abundances (numbers) within three size classes: small <1.25 mm; medium 1.25–2.10 mm, large ≥2.10 mm; for reasons of clarity, not all hypotheses and combinations are shown; but see summary statistics in Table 2; data from [50].