Modeling Reproductive Processes in Lake Trout

To model our observed reproductive processes from Firkus et al. (2022) (link) in our lake trout DEB, we added an egg module that allows reproductive hormone dynamics to dictate the conversion of energy in the reproductive buffer into eggs. Previous laboratory studies suggest that estradiol concentration modulates the effects of sea lamprey parasitism on lake trout reproduction (Smith et al., 2016 (link); Firkus et al., 2022 (link)), so it is necessary to account for estradiol's role in our model. A similar approach to incorporating hormone dynamics into a DEB model is outlined in Murphy et al. (2018) (link) and Muller et al. (2019) (link); however, we simplified this approach so that estradiol concentration was the only required input. This approach more explicitly describes the processes involved in egg development and allowed the model to account for differences in estradiol concentration in parasitized and unparasitized individuals. In the egg module, reproductive reserve (energy available for use towards reproduction) molecules are combined with estradiol to synthesize the egg yolk protein vitellogenin. Processes that take place in the blood plasma volume or liver are taken proportional to the structural mass. The energy flux for egg mass production is triggered by estradiol density of (i.e. the ratio of mass of estradiol in plasma and the structural mass, and follows the law of mass action with the reproductive reserve density ( ). Vitellogenin production occurs in the liver and is secreted into plasma and travels to the ovaries where it is absorbed by ovarian follicles; all processes involved are proportional to the structural mass of the fish . Thus, the rate of egg mass production is given by , where the parameters describing the conversion of reserve, estradiol and vitellogenin to egg mass are absorbed in the proportionality constant . The dynamics of the egg ovarian mass, , are given in Table 1.
Data for estradiol were obtained from laboratory studies of siscowet lake trout (Firkus et al., 2022 (link)) as ng/ml of plasma. These data were linked to the model variable that accounts for the mass of estradiol (in C-mol): , where is the estradiol concentration (ng/ml of plasma), is the molecular weight of estradiol (15.1 g/C-mol) and is the total volume of plasma in a lake trout in ml given by the following equation: , where is wet weight and is the proportionality constant (averaged value of 2.86% from Gingerich et al., 1987 (link) and Gingerich and Pityer, 1989 (link)). The total wet weight has contributions from structural mass, reserve mass and ripe ( and unripe ( r reproductive mass: , where and are the molecular weights and densities of structure and reserve, respectively (Table 3).