Effective population size
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The effective population size (Ne) of a population is the number of individuals in an idealised population that would show the same amount of genetic drift or inbreeding as the population in question.[1][2] The idealised population keeps a constant size and mates at random. All its members have the same chance of leaving offspring.[3][1] Real populations depart from it, so their effective size is often smaller than their census size, the number of individuals counted.[1]
A population of effective size Ne loses about 1/(2Ne) of its heterozygosity in each generation.[4] Natural selection begins to outweigh drift when 4Nes exceeds about 1, where s is the selection coefficient.[5] Conservation uses the measure to judge whether populations can keep their variation: the share of populations within a species whose effective size exceeds 500 is a headline genetic indicator of the Kunming-Montreal Global Biodiversity Framework.[6]
Cannabis is dioecious, so the effective size of a cannabis population depends on how many male and how many female plants breed.[7] A genebank regrowing cannabis seed in the 1990s set the number of plants to grow for each accession by the share of its variation it aimed to keep.[8]
The idealised population
The concept comes from Sewall Wright's work on drift and inbreeding in 1931. Wright introduced the term "effective population number" in 1938.[7] An effective size is found by matching a real population against the idealised one. One comparison uses the rate at which the population becomes inbred. Another uses the rate at which the allele frequencies of replicate populations spread apart. They give an inbreeding effective size and a variance effective size, which sometimes differ. James Crow drew the distinction in 1954.[2]
The census size counts every individual, including those that do not breed. Where only some of them breed, it overstates their genetic contribution to the next generation. Skewed sex ratios, unequal reproductive success, overlapping generations and changes in population size all make the effective size smaller than the census size.[1] The effective size can also exceed the census size. If every individual contributed exactly two gametes to the next generation, the effective size of a population of N would be 2N − 1.[9] Where no genetic estimate is available, conservation assessments have taken the effective size to be a tenth of the adult census size. The ratio is a rule of thumb. Populations within a species are expected to depart from it.[6]
Effective size in a seed field
The effective size of a seed plot depends on how many of its plants breed, of which sex, how evenly they share the next generation and how the number changes from one generation to the next.[1]
Male and female plants
In a population with separate sexes the effective size is about 4NfNm / (Nf + Nm), where Nf and Nm are the numbers of females and males that breed. With equal numbers of each it is close to the total. As the sexes become unequal it falls towards four times the number of the scarcer sex. In a population of 100 it is about 100 with 50 of each sex, 37 with 10 females and 90 males, 20 with 5 females and 95 males and under 5 with a single female.[7] In a cannabis field from which most male plants have been removed before they shed pollen, the few remaining fathers set the effective size, as described under mass selection.
Unequal shares of seed
Plants that leave more offspring than others lower the effective size. For a population of N it is (4N − 2) / (Vn + 2), where Vn is the variance among parents in the number of gametes they pass to the next generation. Random sampling of parents, as in the idealised population, gives a variance close to 2 and an effective size equal to N. Equal contributions from every parent give a variance of 0 and the largest effective size, 2N − 1. Differences in fertility that are not inherited have the same effect: when the standard deviation of fitness is half its mean, the effective size is a fifth lower.[9]
Changes in size between generations
When the size of a population changes, its effective size over a run of generations is close to the harmonic mean of the sizes, which lies nearer the smallest values than the ordinary average does. Over 100 generations, each at a size of 10 or of 1,000, five generations at 10 bring the effective size down to about 165. An even split gives about 20, against an ordinary average of 505.[4] Overlapping generations usually lower the effective size too. Selection at nearby loci on a chromosome can lower it greatly, by carrying linked alleles to high frequency in what is called genetic hitchhiking.[10]
Estimating effective size
The effective size of a population can be estimated from demographic data or from genetic data. Demographic estimates need detailed observation of the population over time. Genetic estimates do not.[6] Drift creates associations between alleles at different loci, known as linkage disequilibrium, at a rate inversely proportional to the effective size. Linkage disequilibrium in a single sample therefore gives an estimate for the last few generations. Disequilibrium between closely linked loci reaches further into the past. Earlier temporal methods compare two samples taken at different times. The linkage disequilibrium method assumes that the population is isolated, which is rarely so. Gene flow, admixture, overlapping generations, bottlenecks and unequal reproductive success can bias them. Plants add difficulties of their own. They often have long lives with overlapping generations, mixed clonal and sexual reproduction or a mixture of selfing and outcrossing. Many grow across continuous ranges. In a test of genomic data from four plant species, populations of wild apricot needed samples of more than 30 individuals for consistent estimates.[6]
Over longer spans the effective size is read from the amount of sequence variation a population holds, which in models of drift and mutation depends on 4Neu, where u is the mutation rate.[11] Guangpeng Ren and colleagues used a coalescent method that infers past population sizes from the times to the most recent common ancestor of the two copies of the genome in one plant. They applied it to four groups of cannabis: a basal group of feral plants and landraces mostly from China, hemp, feral drug-type plants and drug-type cultivars. The four groups had similar histories. Their ancestral effective size peaked about a million years ago and then declined until the end of the last glacial maximum, about 20,000 years ago. The conversion to years assumed one generation a year and 2.5 × 10−9 mutations per nucleotide a year. Of 18 models of the crop's more recent history, the one that fitted best had a domestication in several steps, with changes in the size of every group and continuing gene flow from basal and feral plants into hemp and drug types.[12]
Effective size and the conservation of cannabis landraces
The effective size of a population determines how fast drift removes its variation. Populations with a low effective size run a higher risk of inbreeding depression. Conservation programmes aim to keep the effective size above critical thresholds.[13] Cannabis seed collections have to be regrown every few years. The collection of the Vavilov Institute in Russia, mostly of wild landraces and fibre hemp varieties, had to be grown again at least once every five years.[14] How variation is lost at those regrowings is described under genetic drift.
The seed regeneration programme that the Vavilov Institute and the International Hemp Association ran from 1993 set a minimum of 1,000 plants for each regrowing of an accession, to keep nearly all the alleles of its gene pool in the new seed. The project expected 1,000 plants to keep 99 per cent of the gene pool of a monoecious variety but only 95 per cent of a dioecious one. It gave 2,000 plants as the number a dioecious accession needs to keep 99 per cent, citing a 1993 study by Crossa and colleagues. Plots were isolated by at least 2 km. Sowing early- and late-ripening varieties alternately in effect doubled the distance. In 1993 and 1994 only 11 of the 172 accessions sown met both the 1,000-plant standard and the 200 g standard for seed. Of the accessions, 77 held too little viable seed to grow 1,000 plants at all.[8]
Pollen-proof indoor facilities, a standard alternative to isolated fields, limit by their size the number of plants that can be crossed at each regrowing.[15] The hemp collection of the National Plant Germplasm System of the United States at Geneva, New York, held 581 accessions in 2024 and regrew them indoors over four to five months, with the aim of keeping the allelic diversity of each population. Its curator, Zachary Stansell, described growing as many plants as possible at each regrowing, because seed often arrives with no information on whether it comes from an inbred line or from a variable population. Because hemp is wind-pollinated and usually dioecious, the collection could not be regrown outdoors. It was adding growth chambers and building "hemp huts", outdoor structures that keep out pollen.[16]
See also
References
- ↑ 1.0 1.1 1.2 1.3 1.4 Davinack, D. (2024). Molecular Ecology & Evolution: An Introduction. Norton, Massachusetts: Wheaton College. pp. 110–112.
- ↑ 2.0 2.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. p. 263.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 251–252.
- ↑ 4.0 4.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 269–270.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 326–328.
- ↑ 6.0 6.1 6.2 6.3 Gargiulo, R.; Decroocq, V.; González-Martínez, S.C.; Paz-Vinas, I.; Aury, J.-M.; et al. (2024). "Estimation of contemporary effective population size in plant populations: limitations of genomic datasets". Evolutionary Applications. 17 (5) e13691. doi:10.1111/eva.13691.
- ↑ 7.0 7.1 7.2 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 266–268.
- ↑ 8.0 8.1 Lemeshev, N.; Rumyantseva, L.; Clarke, R.C. (1995). "Report on the maintenance of hemp (Cannabis sativa L.) germplasm accessioned in the Vavilov Research Institute Gene Bank – 1994". Journal of the International Hemp Association. 2 (1): 10–13.
- ↑ 9.0 9.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 271–273.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 273–275.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 289–290.
- ↑ Ren, G.; Zhang, X.; Li, Y.; Ridout, K.; Serrano-Serrano, M.L.; Yang, Y.; Liu, A.; Ravikanth, G.; Nawaz, M.A.; Mumtaz, A.S.; Salamin, N.; Fumagalli, L. (2021). "Large-scale whole-genome resequencing unravels the domestication history of Cannabis sativa". Science Advances. 7 (29) eabg2286. doi:10.1126/sciadv.abg2286.
- ↑ Davinack, D. (2024). Molecular Ecology & Evolution: An Introduction. Norton, Massachusetts: Wheaton College. pp. 165–166.
- ↑ Lemeshev, N.; Rumyantseva, L.; Clarke, R.C. (1994). "Maintenance of Cannabis germplasm in the Vavilov Research Institute Gene Bank – 1993". Journal of the International Hemp Association. 1 (1): 3–5.
- ↑ Welling, M.T.; Shapter, T.; Rose, T.J.; Liu, L.; Stanger, R.; King, G.J. (2016). "A belated green revolution for Cannabis: virtual genetic resources to fast-track cultivar development". Frontiers in Plant Science. 7 1113. doi:10.3389/fpls.2016.01113.
- ↑ Cramer, C. (January 2024). "The USDA-ARS hemp germplasm repository". Cornell Hemp. Cornell University. Retrieved 1 November 2026.