Question

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.

          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.

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

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