4. Consider two species, species X and species Y, with linear selection functions based on the
trait variable t, the average amount of body fat as a percentage of lean body mass (as mature
adults). These selection functions are given as
$w_x(t) = -0.4t + 0.8$
$w_y(t) = 0.25t + 0.25$
for species X and species Y respectively, where $t > 0$.
(You may find it advantageous to change decimals to fractions for this problem.)
(a) (3 points) What is the relevant domain of $w_x(t)$ (in interval notation)?
(b) (2 points) Suppose the relative fitness of species Y is 0.4. What is the trait value $t$ which
gives this fitness level?
(c) (3 points) At what trait level $t$ do the two species have the same relative fitness?
(d) (2 points) Are the two linear functions $w_x$ and $w_y$ parallel, perpendicular, or neither?
Explain how you know mathematically.
