Assuming logistic growth, if I told you there are currently 100 quail on campus, with r=0.1, but that they have greatly exceeded their carrying capacity = K = 50. How many quail will be in the population next generation

I don't remember how K factors in

In logistic growth, the carrying capacity (K) represents the maximum number of individuals an environment can sustainably support. When a population exceeds its carrying capacity, it will face resource limitations, competition, and other factors that may cause the growth rate (r) to decline.

To calculate the population size of quail in the next generation, we can use the logistic growth equation:

N1 = N0 + (r * N0 * (1 - N0/K))

Where:
N1 = population size in the next generation
N0 = initial population size
r = growth rate
K = carrying capacity

In this case, we are given:
N0 = 100 (initial population size)
r = 0.1 (growth rate)
K = 50 (carrying capacity)

Substituting these values into the equation, we can calculate N1:

N1 = 100 + (0.1 * 100 * (1 - 100/50))
N1 = 100 + (0.1 * 100 * (1 - 2))
N1 = 100 + (0.1 * 100 * (-1))
N1 = 100 - (0.1 * 100)
N1 = 100 - 10
N1 = 90

Therefore, the estimated population size of quail in the next generation would be approximately 90.