Appendix A. The model for calculating expected Daphnia fitness in the water column.
The vertical change of fitness of Daphnia galeata throughout the sampling period was modeled with respect to temperature and food in terms of the juvenile growth rate (g/d), which is based upon changes in mass. Juvenile growth rate was used as a measure of fitness as it is strongly correlated to the intrinsic rate of population increase (Lampert and Trubetskova 1996).
Daphnia growth rate from different food concentrations were obtained from two growth experiments conducted during the summer. In the laboratory, Daphnia were provided with lake seston from different water depth of the Oberer Arosasee. The experiments were carried out in flowthrough chambers with a constant flow rate and temperature (details are described in Winder et al. 2003). In addition, particulate organic carbon (POC) from lake seston was measured. These experiments provided juvenile growth rates at different POC concentrations. From these observed relations, expected growth rates of D. galeata were calculated from measured POC concentrations at different depths throughout the sampling period using the Monod equation:
gexp = gmax * (POCobs – POCmin) / (POChalf+ POCobs – 2 POCmin)
where gexp = expected growth rate, gmax = maximum growth rate observed, POCobs = observed POC concentration (mg/L), POCmin = minimum POC concentration necessary for Daphnia growth, and POChalf = POC concentration at 0.5 gmax. POCmin was set to 0.11 mg/L according to Boersma and Vijverberg(1995), POChalf to 0.60 mg/L, and gmax to 0.59 as measured in the experiment.
Because the experiment was carried out at constant temperature (18 ºC), the expected growth rates in the water column of the lake were corrected for the temperature measured in the specific depth layer of the lake. Therefore we used the relation between temperature and developmental time determined by Vijverberg (1980), under the assumption that somatic growth rates scale with temperature in a similar way. In addition, growth rates were corrected for ambient oxygen concentrations because oxygen declined considerable in the lake below 10-m depth during the summer, therefore making this depth layer less valuable for Daphnia. A critical level of 3.5 mg·oxygen·L-1 was taken into account (Hanazato 1992). Below this threshold expected growth rate was assumed to be linearly related to oxygen concentration. Depth of highest expected relative fitness was calculated by multiplying the expected growth rate per depth stratum by the average depth of the stratum. These values were summed and divided by the sum of growth rate of the water column. This estimated mean depth was expanded to a 2.5 m layer (Fig. 2) to account for the 2.5-m Daphnia sampling interval.
Boersma, M., and J. Vijverberg. 1995. Synergistic effects of different food species on life-history traits of Daphnia galeata. Hydrobiologia 307:109115.
Hanazato, T. 1992. Direct and indirect effects of low-oxygen layers on lake zooplankton communities. ArchivfürHydrobiologie, BeiheftErgebnissederLimnologie 35:8798.
Lampert, W., and I. Trubetskova. 1996. Juvenile growth rate as a measure of fitness in Daphnia. Functional Ecology 10:631635.
Vijverberg, J. 1980. Effect of temperature in laboratory studies on development and growth of Cladocera and Copepoda from Tjeukemeer, The Netherlands. Freshwater Biology 10:317340.
Winder, M., M. Boersma, and P. Spaak. 2003. On the cost of vertical migration: are feeding conditions really worse at deeper depth? Freshwater Biology 48:383393.