Final answer:
The estimated population size of stickleback fish in the lake can be calculated using the mark and recapture method. In this case, 78 fish out of a total of 162 captured fish are marked. The estimated population size is 528.
Step-by-step explanation:
The estimated population size of stickleback fish in the lake can be calculated using the mark and recapture method. In this case, 78 fish out of a total of 162 captured fish are marked. We can use the formula N = (M*C)/R, where N is the estimated population size, M is the number of fish initially marked, C is the total number of fish captured in the second sample, and R is the number of marked fish recaptured in the second sample.
In this case, M = 255, C = 162, and R = 78. Plugging these values into the formula, we get N = (255*162)/78 = 528.46. Since the population size cannot be a fraction, we can round it to the nearest whole number. Therefore, the estimated population size of stickleback fish in the lake is 528.