Reproduction model following Illius & O’Connor (2000)
The formula is derived from the model by Illius & O’Connor (2000) [35]. Their variable names are used here:
B_annual: offspring count per year for one mature female
k: maximum annual offspring count of one female
F: current fat mass
F_max: maximum fat mass
b and c are parameters controlling the effect of body condition (F/F_max) on the reproductive rate and are set in Illius and O’Connor (2000) to b=15 and c=0.3 (unfortunately without explanation). c is called the midpoint, and b is called the growth rate a generalized logistic function.
50% of adults will breed when F/F_max=0.3
95% will breed when F/F_max=0.5
The annual rate is then converted to a daily rate over the breeding season length:
L: length of breeding season [days]
Note
This reproduction model principle also used by Pachzelt et al. (2013) [49] and Pachzelt et al. (2015) [50]