Question

15. Young rainbow trout were sampled along a river to study the population and determine if recreational fishing or other factors might be affecting the size of the population. A. In the first year of the study, researchers estimated the size of the population. They performed the first stage of their analysis after breeding season had ended. The first week, 92 trout were captured and marked. In a second round of capture one week later, 108 trout were captured; of these, 12 were marked. Estimate the size of the population based on these data. Round your anwer to the nearest whole number. 15B. In the second year of the study, researchers estimated the per capita population growth rate at -0.15. Based on this value, what is the size of the population in the second year of the study? Round your answer to the nearest whole number. 15C. Identify two factors that could have caused the population to change in this way, and briefly explain how each factor could result in this change in 1-2 sentences (each).

Answer 1

A) we can estimate size of population using following formula

(marked recaptures)/ (total in second sample)=(marked initially)/(total population size)

, 12/108 = 92/ total population size

Total population size = (92x 108)/12 = 828

B) we can calculate population size based on growth rate using following equation

dN/dt = rN which represent an exponential growth equation or

dN/dt = r(K-N)N/K which represent a logistic growth equation

here, dnN/dt represents the change in population size,

r represents the growth rate

N represent population size and K represent carrying capacity,

your problem have not provided any value regarding carrying capacity. Therefore, we will proceed with exponential growth equation

if we solve exponential growth equation for the population we will get

ln(N/N_o) = r(t - t_o)

where N = population size at time t

N_o = initial population size

now we found of in 5a that the size of the population was 828

at the second year, (t - t_o) =1

so, ln(N/828) = -0.15 x 1

N= 828 x e^-0.15 = 712.66 = 713(approx)

C) two factors that could have caused a decrease in population of trout, could be depletion of aliment from water body and predation.

Depletion of nourishment from water could have cause to starve many trout, Therefore, result in increased death rate over survival rate.

over predation can also affect overall survival rate of species.