Figure 3

The horn length allometry of the male offspring produced by females from different experimental groups. These groups differed in the population density experienced by females during their pre-mating (PM) period. Offspring produced by females from the low-density experimental group are indicated by open circles and a continuous curve, whereas offspring produced by females from the high-density experimental group are indicated by crosses, and a broken curve. Again, both axes were transformed using natural logarithms, and the curves were fitted with a Richards’ growth function, but this time (A) only parameter μ (Model 4), (B) or parameter λ (Model 5) were allowed to vary between the experimental groups, whereas parameters A and v were always common across experimental groups (see Table 4). A. According to the model that allows only parameter μ to vary between experimental groups (Model 4, Table 4), the vertical dotted line depicts a value of body size for which the model predicts a horn length 8.4% greater for offspring of females that experienced high population density in their pre-mating period (upper dotted horizontal line) than for offspring of females that experienced low population density during their pre-mating period (lower dotted horizontal line). This line was chosen to depict the biggest possible difference in the horns of offspring produced by females of the two experimental groups described above.