The rate of inbreeding in a saved seed stock is 1 divided by twice the effective population size per generation, so 50 effective plants give 1% a generation and 100 give 0.5%. Taking an equal amount of seed from every plant raises the effective size to almost twice the number of plants, which is why 50 plants with equal seed can match 100 plants with unequal seed.
Part of Community Seed Bank Management
Effective population size is the size of an idealised random-mating population that would lose genetic variation at the same rate as the actual one.
Inbreeding Per Generation Falls As One Over Twice The Effective Size
For an ideal randomly mating population of effective size Ne, the inbreeding coefficient rises each generation by
ΔF = 1 ÷ (2 × Ne)
and after t generations F = 1 − (1 − ΔF)^t (Wright 1931; Falconer and Mackay, Introduction to Quantitative Genetics, 4th edition, 1996). F is the probability that two copies of a gene in one plant are identical by descent. As F rises, harmful recessive variants are more often paired and the crop loses vigour, yield and resistance. The table applies the formula; every entry is computed from it.
| Ne | ΔF per generation | F after 5 | after 10 | after 20 generations |
|---|---|---|---|---|
| 12 | 4.2% | 19.2% | 34.7% | 57.3% |
| 25 | 2.0% | 9.6% | 18.3% | 33.2% |
| 50 | 1.0% | 4.9% | 9.6% | 18.2% |
| 100 | 0.5% | 2.5% | 4.9% | 9.5% |
| 200 | 0.25% | 1.2% | 2.5% | 4.9% |
| 500 | 0.1% | 0.5% | 1.0% | 2.0% |
Worked example for Ne = 50: ΔF = 1 ÷ 100 = 0.01. After 10 generations, F = 1 − 0.99^10 = 1 − 0.904 = 0.096, or 9.6%.
Franklin (1980) proposed a rule of thumb from this arithmetic: keep Ne at 50 or above to hold short-term inbreeding to about 1% per generation, and 500 or above to keep variation over the long term. Later work argued the 500 should be higher. Treat both numbers as heuristics, not thresholds.
Counting Plants Is Not The Same As Counting Ne
The formula applies to effective size, which is at most the number of plants that actually contribute seed and often less.
- Unequal seed. If plants differ in how many offspring they leave, the effective size falls. With constant population size, Ne = (4N − 2) ÷ (Vk + 2), where N is the number of plants and Vk is the variance in number of offspring per plant (Falconer and Mackay 1996). For random contribution, Vk is about 2 and Ne is about N − 0.5.
- Equal seed per plant. If every plant gives the same number of offspring, Vk = 0 and Ne = 2N − 1. Taking the same weight or the same number of seeds from each plant nearly doubles Ne.
- Limited mating. If plants only pollinate their near neighbours, the effective size is smaller than the count of plants. This effect is not computed here.
- Plants that die. Count only plants that reach seed.
Worked comparison. 100 plants contributing at random: Ne ≈ 100 − 0.5 = 99.5, ΔF = 1 ÷ 199 = 0.50%. 50 plants contributing equally: Ne = 2 × 50 − 1 = 99, ΔF = 1 ÷ 198 = 0.51%. The two are nearly the same.
What This Says About The Corpus’s Numbers
The corn minimums in this corpus are 100 plants (the seed bank carrier) and 50 plants (the Genetic Diversity guide, Genetic Diversity). The arithmetic shows how both can be right: 50 plants give 1% a generation if their contributions are random and 0.5% if equalised, and 100 give 0.5% to 0.25%. The numbers the sources do not state are the assumptions: random mating, no selection, even pollination. Equalise the seed and the 50-plant minimum is close to the 100-plant one.
Self-Pollinating Crops Are Different
A fully self-pollinating variety is already near homozygous, so inbreeding depression is not the concern; harmful variants have mostly been purged. The effective size with selfing is about N ÷ 2 (Ne = N ÷ (1 + F), with F near 1). Six to twelve plants are then Ne of 3 to 6, and variation within a mixed or landrace population will drift quickly:
- Ne = 3: ΔF = 1 ÷ 6 = 16.7% per generation
- Ne = 6: ΔF = 1 ÷ 12 = 8.3% per generation
For a pure line the loss is harmless because there is little variation to lose. For a mixed landrace or a population you are trying to keep diverse, use many more plants than the minimum.
Method
- Decide the rate you accept: 1% a generation (Ne 50) for a short-term working stock, 0.25% (Ne 200) or lower for a stock meant to last.
- Add the plants lost before seed. If 85% reach seed and you need 100 contributing plants, sow 100 ÷ 0.85 = 118 (illustrative survival figure; use your own).
- At harvest, take the same weight of seed from every plant and mix. Do not take extra from the largest plants.
- Record the number of contributing plants with the lot (Seed Inventory and Catalog System).
- Every few generations, cross in unrelated seed of the same variety from another grower.
Limits
The model assumes random mating, constant size, no selection and non-overlapping generations. Strong selection shrinks Ne further; deliberate selection of the best 10% of plants gives an Ne far below the count of plants in the field (Selecting for Adaptation vs Uniformity).
What’s Next
- Learn next: Selecting for Adaptation vs Uniformity — selection costs effective size
- Combine with: Isolation Distances by Crop Family — population size and purity are decided together