How do you calculate the intrinsic rate of increase (r) from population data?

Calculating r depends on the type of data you have available. When you know births and deaths over a specific period, use: r = (births - deaths) / (population size × time period). This gives you the per capita growth rate.

When you have population counts at two time points, use the exponential growth formula: r = ln(final population / initial population) / time elapsed. For example, if marine algae increase from 100,000 cells to 500,000 cells in 10 days, r = ln(500,000/100,000) / 10 = ln(5) / 10 = 1.609 / 10 = approximately 0.161 per day. This means each individual contributes to a 16.1% daily population increase.

The natural logarithm (ln) is essential here because it accounts for continuous, compound growth—reflecting how populations actually reproduce. Always ensure your time units are consistent and clearly defined, as r values change dramatically depending on whether you're measuring growth per day, month, or year.