Fitness (biology)
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Fitness, in genetics and evolutionary biology, is the expected contribution of an individual or a genotype to the next generation.[1] The absolute fitness of a genotype, also called its Darwinian fitness, is the expected number of offspring of an individual of that genotype counted from birth. It is the product of viability, the probability of surviving to adulthood, with fertility, the mean number of offspring of a survivor.[2]
Relative fitness is absolute fitness divided by the fitness of a genotype taken as the standard, often the fittest.[1] Natural selection changes allele frequencies through relative fitness alone. A source of death or infertility that strikes every genotype alike changes the size of a population and leaves its genetic make-up unchanged.[3] The difference between two genotypes is usually written as a selection coefficient s, with relative fitnesses of 1 + s and 1 or of 1 and 1 − s.[4]
Fitness over a whole life is hard to measure. Most studies measure parts of it, called fitness components, such as survival, seed or fruit number or plant size used as a stand-in.[1][5] In Cannabis, a dioecious and wind-pollinated plant, the components measured include the amount of pollen a plant sheds and the share of its pollen that germinates, in male plants and in female plants made to bear male flowers.[6][7] Seed set and germination have been measured in female flowers that formed anthers in an all-female crop.[8]
Viability and fertility
The life of an individual can be divided into stages at which individuals differ: survival from zygote to adult, success in mating and the number of offspring produced. A difference at any stage makes individuals leave different numbers of progeny. Each stage is a fitness component. The components are not the same in every organism, since an asexual bacterium has no mating success. They can also be divided further at will, as when survival in an insect is split into its embryonic, larval, pupal and adult stages.[1]
Population-genetic models usually take two components. In a population of two asexual types A and a, an A individual survives to adulthood with probability vA. A survivor has on average fA offspring. A newborn A therefore leaves WA = vAfA offspring.[2] The mean of W over all newborns, the mean absolute fitness, is also the factor by which the population grows from one generation to the next.[3]
In a sexual diploid population the offspring of an AA parent may be AA or Aa. The number of offspring depends on both parents. The standard model of diploid selection takes the fertility of a mating as the product of the fertilities of the two parents, an assumption first pointed out by Walter Bodmer in 1965. The absolute fitness of AA is then half of vAAfAA, since each gamete a parent contributes is half an offspring. Under the product rule the newly formed zygotes are in Hardy–Weinberg proportions at the new allele frequency in every generation.[9]
A component measured alone can mislead. A genotype with high viability may still leave few offspring, or none, if it is partly or wholly sterile.[1]
Absolute and relative fitness
Fitness can be read as a property of an individual or of a genotype. Where selection acts on survival alone, an individual either survives or dies, so its fitness is 1 or 0. If a proportion P of zygotes survives, mean individual fitness is P. Among genetically identical individuals survival still differs by chance, but no evolution follows from it. A response to selection needs some of the differences in fitness to be genetic. The absolute fitness of a genotype is a mean over the individuals that carry it. The variance of fitness among genotypes is never larger than the variance of individual fitness, which also includes chance differences in the environment.[1]
The genetic make-up of a population depends on the ratios of fitnesses, not on their size. If A individuals leave 1.01 offspring each and a individuals leave 1, the ratio of A to a is multiplied by 1.01 every generation. If they leave 101 and 100, both types multiply fast, but the ratio of A to a again grows by 1.01 a generation.[3] Relative fitness, written w, is accordingly the measure evolutionary genetics nearly always uses. It is commonly set by dividing the absolute fitness of each genotype by that of the fittest, which then has a relative fitness of 1.[1]
| Genotype A | Genotype a | |
|---|---|---|
| Viability | 0.5 | 0.4 |
| Fertility at low density | 6 | 6 |
| Absolute fitness at low density | 3.0 | 2.4 |
| Fertility at high density | 2.2 | 2.2 |
| Absolute fitness at high density | 1.1 | 0.88 |
| Relative fitness at either density | 1.25 | 1 |
Population density shows why the distinction matters. In the example in the table, crowding cuts the fertility of both genotypes from six offspring to 2.2. Absolute fitness falls for both, while the relative fitnesses stay at 1.25 and 1, so the course of selection is the same at either density. Relative fitnesses stay constant whenever density multiplies the viabilities of all genotypes by one factor and their fertilities by another. They change if crowding instead takes a fixed number of offspring, say two, from each adult. Relative fitness then falls furthest in the genotypes that are already less fit. Density is less likely to multiply fertilities by a common factor than viabilities. Even for viability the factor may differ: the survivors of a less viable genotype may be weaker, so that crowding takes a greater toll of them.[3]
Selection coefficients
With relative fitnesses of 1 + s for A and 1 for a, s is the selection coefficient in favour of A and can take any value from −1 upwards. Taking A as the standard and writing 1 and 1 − s makes s a coefficient against a, which can take any value up to 1. The two forms do not match: a coefficient of 0.01 in favour of A equals one of 0.0099 against a. The difference is slight while s is small.[4] Scaling fitnesses to the fittest genotype gives the second form, in which s measures how much less fit the other allele is.[1]
In a haploid population with relative fitnesses 1 and 1 − s and allele frequencies p and q, one generation of selection raises p by pqs/(1 − qs). The denominator, 1 − qs, is the mean relative fitness of the population, written w̄. The change depends only on the difference in relative fitness and on the starting frequency. Repeated over many generations, it carries a favoured allele from low to high frequency along an S-shaped curve.[1]
Overlapping generations
Where generations overlap and individuals breed throughout life, fitness becomes a rate. Each genotype has a birth rate b and a death rate d per unit of time. Its numbers grow at the rate r = b − d, sometimes called the Malthusian parameter. The frequency p of A then changes by (rA − ra)p(1 − p) per unit of time. In this model relative fitness is measured by differences between rates, where discrete generations use ratios. Growth rates of 2.7 and 2.5 become 0.2 and 0 when a is the standard. An effect of density that subtracts the same amount from both rates leaves the change in frequency unaltered.[10] This Malthusian fitness, m, is the logarithm of the fitness of discrete generations: m = log W. When two genotypes grow at constant rates for a time t, the ratio of their numbers is multiplied by e(m1 − m2)t, so the difference in their Malthusian fitnesses sets the outcome.[1]
Fitness that varies
Simple models treat fitnesses as constants, unaffected by time or by the make-up of the population.[2] The fitness of most alleles probably fluctuates from one generation to the next as the physical and biological environment changes. If the fitnesses of two haploid alleles vary at random over time, the allele that comes to predominate is the one with the higher geometric mean fitness, not the one with the higher arithmetic mean. For modest fluctuations the geometric mean is about W̄ − σ2/(2W̄), where σ2 is the variance in fitness over time. Of two alleles with the same arithmetic mean, the one whose fitness varies less therefore prevails. Selection over many generations multiplies fitnesses together. A poor generation lowers the product by more than an equally good one raises it.[1]
Fitness can also differ from place to place within one generation. Under soft selection each region sends a fixed share of adults into a common, randomly mating population, whatever the fitness of its residents. Variation at a locus is then kept if the harmonic mean fitness of the heterozygote across regions exceeds that of both homozygotes. Under hard selection each region contributes in proportion to the mean fitness of its residents. The arithmetic mean then decides instead.[1] Spatial differences in fitness that keep variation in this way are a form of balancing selection. Where the fitness of a genotype depends on its own frequency in the population, selection is frequency-dependent.[1]
Mean fitness
The mean absolute fitness of a population cannot rise without limit. Absolute fitness usually falls as density rises. When a population settles at a stable size, its mean absolute fitness is 1. Two kinds of progress remain possible: the population may settle at a higher density or come to consist of genotypes whose fitness relative to a standard genotype is higher.[11] In an asexual population, one generation of selection raises the mean relative fitness by the variance of fitness among genotypes divided by the mean, Var(w)/w̄. Since a variance cannot be negative, the mean never falls. Doubling every difference in fitness quadruples the variance, so the gain in mean fitness grows with the square of the selection coefficients.[12]
Ronald Fisher proposed in 1930 a fundamental theorem of natural selection: mean fitness increases at a rate set by the additive genetic variance in fitness, with a further term for deterioration of the environment. The model ran in continuous time and left some doubt about which measure of fitness was meant to increase.[12] Alan Robertson and George Price later showed, independently, that the change in any trait from one generation to the next equals its additive genetic covariance with relative fitness. For fitness itself that covariance is the additive genetic variance in relative fitness, so Fisher's theorem is a special case of the general result. H. Allen Orr regards the general result, known as the secondary theorem of natural selection, as the more fundamental of the two.[1] The approach applies to artificial and natural selection alike.[1]
Mean fitness does not always increase under selection. It can fall where the fitness of a genotype depends on its frequency. In sexual species it can also fall under some forms of epistasis.[1] With several loci, selection and recombination together can lower it.[12]
Adaptive landscapes
Sewall Wright pictured mean fitness in the early 1930s as a surface over the allele frequencies at two or more loci. High points on this adaptive landscape are populations of high mean fitness and valleys populations of low mean fitness. Where selection raises mean fitness it moves a population uphill, to the top of the nearest peak, where it stops even if a higher peak exists elsewhere. Wright proposed in his shifting balance theory that genetic drift, together with selection among local populations, allows populations to reach the highest peaks. Orr describes the theory as extremely controversial.[1]
Later landscapes are built over DNA or protein sequences instead of allele frequencies. Each sequence has a fitness. Selection moves a gene one mutational step at a time to a fitter neighbouring sequence. On a rugged landscape, with many local peaks, a population is easily stranded. Hybrid sterility and inviability show that real landscapes are rugged to some degree, while the many mutations of small or no effect suggest they fall short of the most rugged possible. These models generally assume a landscape that stays fixed for long stretches of time. They can mislead if fitnesses change at least as fast as evolution proceeds.[1]
Measuring fitness
Studies of fitness take one of three routes: measuring differences in fitness among genotypes present in a population now, inferring past gains in fitness from DNA sequences or watching fitness change in experimental populations. The second route finds where favoured mutations have spread from the patterns they leave in sequence variation, as in a selective sweep. The third uses microbes, whose growth rate serves as a stand-in for total fitness. In such experiments fitness typically rises fast at first and then levels off as the population nears a new optimum.[1]
Fitness differences among living genotypes are hard to measure. Differences in viability can be estimated by comparing genotype frequencies in zygotes or seedlings with those in adults. Under strict conditions adults can stay in Hardy–Weinberg proportions despite large differences in fitness among genotypes, so a test against those proportions can miss strong selection. If selection over the life cycle is not complete at the stage at which genotypes are counted, the change in genotype frequencies between generations can give the wrong fitnesses. Even a complete history of allele frequencies over many generations does not fix the fitnesses uniquely. A further difficulty is scale: selection can act on an advantage as small as the reciprocal of the population size, while experiments usually detect only large differences.[1]
Plants
Plants raise further problems. Most are hermaphroditic, so their success as seed parents and as pollen parents must both be counted. Several sires may fertilise the seeds of one fruit. Pollen and seed may travel far from the parent. Some plants also reproduce asexually, while perennials reproduce over many years. Brett Younginger and colleagues examined 170 studies of plant fitness, drawn at random from 8,548 articles published from 1935 to 2016. Seed counts were the commonest measure, used in 58 per cent of the studies; biomass, size or performance appeared in 42 per cent, flowers in 39 per cent and fruits in 33 per cent. Only 20 studies (12 per cent) followed the offspring that parents recruited into the population. Six (4 per cent) traced those offspring with molecular markers. Of the 71 studies that used size, 33 found it positively correlated with fecundity and 17 found no clear relation. None found a negative correlation. The other 21 measured no fecundity. The authors judge biomass a fair estimate of fitness only between plants of the same species and the same age. Female fitness is usually measured by seed set and male fitness by pollen export. In wind-pollinated plants, theory suggests that a larger size may favour male fitness more than female, since taller plants may export pollen more readily while seed not carried by animals stays near the parent.[5]
Jon Ågren and colleagues measured fitness directly in Arabidopsis thaliana: the number of fruits produced per seedling planted. The measure combines survival with the fruit production of the survivors. Over three years they planted 398 recombinant inbred lines and their two parents at the parents' home sites in Italy and Sweden. In all they grew 43,964 plants and counted 565,070 fruits. Differences between lines accounted for 18.1, 9.9 and 14.7 per cent of the variance in fitness among individual plants in Italy in the three years and for 9.5, 1.4 and 5.8 per cent in Sweden.[13]
Fitness components in cannabis
In dioecious cannabis, female and male flowers grow on separate plants.[8] A female plant passes on its genes through seed and a male plant through pollen. Female fitness is usually measured by seed set and male fitness by pollen export.[5] Commercial drug-type crops are grown from genetically female plants alone. Male plants are removed, since seed lowers the quality of the harvested flowers.[8] Facilities growing plants for high cannabinoid yields often produce sinsemilla, unpollinated female flowers.[6]
Pollen
Sydney Wizenberg, Michelle Dang and Lesley Campbell measured two properties of pollen in the hemp cultivar CFX-2, which they describe as proxies of male fitness. The non-abortion rate is the share of pollen grains with an intact nucleus, shown by a stain. Viability is the share of grains that germinate in a liquid medium. On the day the anthers opened, 93.35 per cent of grains were non-aborted on average and 38.69 per cent germinated. Kept at room temperature (22 °C), pollen no longer germinated two weeks after the anthers opened. Pollen kept at −4 °C did not germinate at all. The non-abortion rate fell slowly: it averaged 68.8 per cent after 12 weeks at room temperature and 63.1 per cent after 96 weeks in the freezer. The two measures were not correlated, so neither can be predicted from the other. The authors conclude that male fitness cannot be inferred from one measure alone. They add that germination in a medium may not reflect fertility outside the laboratory.[6]
The same group compared male plants of CFX-2 with female plants that formed male flowers, which they call cosexual. Seven did so under mild drought; twelve were sprayed daily for 14 days with colloidal silver at 20 ppm. Pollen from such genetically female plants is used to produce feminised seeds. The male plants began flowering 5.4 days earlier than the drought-induced cosexual plants and flowered 6.6 days longer. They produced 223 per cent more pollen per plant than the cosexual plants, while pollen per flower did not differ. Pollen viability was 200 per cent higher in the male plants and the drought-induced cosexual plants than in the silver-treated plants. Non-abortion rates did not differ significantly. The authors attribute the lower pollen output of cosexual plants to their division of resources between male and female function. They suggest that the silver may account for the low germination of the treated plants' pollen. The study used one cultivar in one growing environment, with few drought-induced plants.[7]
Seed
Zamir Punja and Janesse Holmes examined about 1,000 plants of three drug-type strains grown indoors under commercial conditions. Hermaphroditic flowers, female flowers that also formed anthers, appeared spontaneously on 5 to 10 per cent of the plants. Seed set began within these flowers. Three seed-bearing inflorescences gave 34, 48 and 22 seeds. In moist potting medium 90 to 95 per cent of the seeds germinated within 10 to 14 days. Since male plants are excluded from indoor production, the authors expect most seed formed there to come from self-fertilisation. Outdoors, with several pollen sources, seed is more likely to come from both selfing and cross-fertilisation.[8]
See also
References
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 Orr, H.A. (2009). "Fitness and its role in evolutionary genetics". Nature Reviews Genetics. 10 (8): 531–539. doi:10.1038/nrg2603. PMC 2753274.
- ↑ 2.0 2.1 2.2 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 51–52.
- ↑ 3.0 3.1 3.2 3.3 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 53–57.
- ↑ 4.0 4.1 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 57–58.
- ↑ 5.0 5.1 5.2 Younginger, B.S.; Sirová, D.; Cruzan, M.B.; Ballhorn, D.J. (2017). "Is biomass a reliable estimate of plant fitness?". Applications in Plant Sciences. 5 (2) 1600094. doi:10.3732/apps.1600094. PMC 5315378.
- ↑ 6.0 6.1 6.2 Wizenberg, S.B.; Dang, M.; Campbell, L.G. (2022). "Methods for characterizing pollen fitness in Cannabis sativa L." PLOS ONE. 17 (7) e0270799. doi:10.1371/journal.pone.0270799. PMC 9262209.
- ↑ 7.0 7.1 Wizenberg, S.B.; Muir-Guarnaccia, J.; Campbell, L.G. (2023). "Cosexuality reduces pollen production and fitness in Cannabis sativa L." Plants. 12 (21) 3731. doi:10.3390/plants12213731. PMC 10648298.
- ↑ 8.0 8.1 8.2 8.3 Punja, Z.K.; Holmes, J.E. (2020). "Hermaphroditism in marijuana (Cannabis sativa L.) inflorescences – impact on floral morphology, seed formation, progeny sex ratios, and genetic variation". Frontiers in Plant Science. 11 718. doi:10.3389/fpls.2020.00718.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 61–63.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 59–61.
- ↑ Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 92–93.
- ↑ 12.0 12.1 12.2 Felsenstein, J. (December 2019). Theoretical evolutionary genetics. Seattle: Department of Genome Sciences, University of Washington. pp. 93–94.
- ↑ Ågren, J.; Oakley, C.G.; McKay, J.K.; Lovell, J.T.; Schemske, D.W. (2013). "Genetic mapping of adaptation reveals fitness tradeoffs in Arabidopsis thaliana". Proceedings of the National Academy of Sciences. 110 (52): 21077–21082. doi:10.1073/pnas.1316773110. PMC 3876199.