# Intrinsic rate of increase (r_m)

> The per-day rate at which an unchecked pest population multiplies under set conditions, from a life table; N(t) = N0 x e^(r_m x t).

- Canonical: https://genetixbay.com/knowledge/glossary/intrinsic-rate-of-increase.html
- Also written: r_m, rm, intrinsic rate of natural increase, per-capita growth rate
- Glossary category: Pests and diseases · Evidence: Established
- Status: Draft: awaiting expert review · Updated: 2026-10-31
- Licence: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/), attribute "GenetixBay cannabis glossary"

The intrinsic rate of increase, written r_m, is the exponential growth rate a population reaches when food is unlimited and nothing eats it, at one temperature and host. Birch set out the modern method in 1948: combine age-specific survival and egg-laying from a [life table](https://genetixbay.com/knowledge/glossary/life-table.md) and solve for r. It is the best single number for comparing how fast pests explode.

## In practice

An r_m of 0.25 per day means the population grows by e^0.25, about 28%, every day and doubles in ln 2 / 0.25 = 2.8 days. Ten [mites](https://genetixbay.com/knowledge/glossary/two-spotted-spider-mite.md) become 10 x e^(0.25 x 21), about 1,900, in three weeks. Values come from lab leaf discs or single host plants, so treat them as an upper bound for a cannabis room with predators, crowding and plant defences. Temperature changes r_m more than anything else a grower controls.

## Don't confuse with

- **Net reproductive rate (R0)**: offspring per female per generation, not per day.
- **Finite rate of increase (lambda)**: e^r_m, the daily multiplication factor.
- **Fecundity**: [eggs per female](https://genetixbay.com/knowledge/glossary/fecundity.md), one input to r_m.

## Related terms

[Life table](https://genetixbay.com/knowledge/glossary/life-table.md), [Net reproductive rate (R0)](https://genetixbay.com/knowledge/glossary/net-reproductive-rate.md), [Generation time](https://genetixbay.com/knowledge/glossary/generation-time.md), [Doubling time](https://genetixbay.com/knowledge/glossary/doubling-time.md), [Fecundity](https://genetixbay.com/knowledge/glossary/fecundity.md)

## Read more

- [Temperature, humidity and pest population growth in cannabis: every major pest compared](https://genetixbay.com/knowledge/pests/temperature-humidity-and-pest-population-growth.md)
- [Spider mites on cannabis: life tables, ID and IPM](https://genetixbay.com/knowledge/pests/spider-mites.md)
- [Aphids on cannabis: species, life tables, population growth and IPM](https://genetixbay.com/knowledge/pests/aphids.md)

## Sources

1. Birch, L.C., 1948. The intrinsic rate of natural increase of an insect population. Journal of Animal Ecology 17:15-26. https://doi.org/10.2307/1605
2. UC IPM. Pest Notes: Spider Mites (Publication 7405). University of California ANR. https://ipm.ucanr.edu/PMG/PESTNOTES/pn7405.html