Question

Male beetles are of two phenotypes: horned and hornless. Horned males mate with twice as many females compared with hornless males. But females mated to hornless males produce one-third more offspring. The reproductive success of a male (number of offspring fathered) is the number of females he mates with multiplied by the number of offspring each female produces. The reproductive success of horned males is \(\underline{\hspace{1cm}}\) times that of hornless males. (Round off to one decimal place.)

Hint:

The reproductive success ratio can be found by comparing the number of females mated and the number of offspring produced by both phenotypes.

Answer 1

Correct Answer: 1.4

Let the reproductive success of a hornless male be \( R_h \) and the reproductive success of a horned male be \( R_t \).

Step 1: Reproductive success of hornless males.
The hornless male mates with \( F \) females, and each female produces \( O_h \) offspring. Thus, the reproductive success of a hornless male is: \[ R_h = F \times O_h. \]

Step 2: Reproductive success of horned males.
The horned male mates with \( 2F \) females (twice as many), and each female produces \( O_h + \frac{O_h}{3} = \frac{4O_h}{3} \) offspring. Thus, the reproductive success of a horned male is: \[ R_t = 2F \times \frac{4O_h}{3} = \frac{8F O_h}{3}. \]

Step 3: Ratio of reproductive success.
The ratio of the reproductive success of horned males to hornless males is: \[ \text{Ratio} = \frac{R_t}{R_h} = \frac{\frac{8F O_h}{3}}{F O_h} = \frac{8}{3} = 2.7. \] Thus, the reproductive success of horned males is \( \boxed{2.7} \) times that of hornless males.