Choose an ecology solve, logistic or exponential growth calculation, or D&D 2014 carrying task. Time units are converted consistently; years mean 365 days and months one-twelfth year. Game weight uses pounds or kilograms with actual conversion.

Instantaneous logistic model.

Use this basis consistently for N, K and population change; counts and densities are not converted.

0.5 means a decimal rate of 0.5 per selected time unit. Year = 365 days; month = one-twelfth year.

Carrying Capacity Formula

The logistic population growth model is:

(dN) / (dt) = rN(1 - (N) / (K))

If you know the current population size N, the intrinsic growth rate r (per time), and the instantaneous population change rate (CP = dN/dt), you can rearrange to estimate carrying capacity K:

K = (N) / (1 - (CP) / (rN))
  • Where K is the carrying capacity (individuals)
  • r is the intrinsic growth rate (as a decimal per unit time; e.g., 50% per year = 0.50/year)
  • N is the current population size (individuals)
  • CP is the instantaneous change in population per unit time (dN/dt, in individuals per unit time). A time-average ฮ”N/ฮ”t is an approximation only over a suitable short interval

To estimate the carrying capacity, convert r from percent to a decimal, compute the fraction CP/(rN), then calculate K = N / (1 โˆ’ CP/(rN)). The time unit used for r and CP must match (for example, both โ€œper yearโ€).

Carrying Capacity Definition

Carrying capacity (often written as K) is the maximum population size of a species that an environment can sustainably support given available resources and other constraints. In simple models it is treated as constant, but in real ecosystems it can change over time as conditions change.

Carrying Capacity Example

How to calculate a carrying capacity?

First, determine the intrinsic growth rate r over a specific time unit. In this example, r = 50% per year, so r = 0.50/year.

Next, determine the current population size. For this example, N = 5000 individuals.

Next, estimate the instantaneous population change using the same time unit. In this example, CP = 100 individuals per year (dN/dt = 100/year).

Finally, calculate the carrying capacity using the formula above:

K = N / (1 โˆ’ CP/(rN))

K = 5000 / (1 โˆ’ 100/(0.50ยท5000))

K = 5000 / (1 โˆ’ 0.04) = 5000 / 0.96 = 5208.33

Estimated carrying capacity: K โ‰ˆ 5208 individuals

FAQ

What is carrying capacity?

Carrying capacity (K) is the maximum population size an environment can sustainably support. It is a key parameter in the logistic population growth model.