**3. On population size and heterozygosity of brown trout**

#### **3.1. Heterozygote excess in small populations of brown trout**

In North America, the black-footed ferret (*Mustela nigripes*) has been present from pleistocen (> 11,700 years ago) when they immigrated from Asia over the Bering strait [26]. The species was extinct in the wild, after the close to extinction of its main prey the prairie dog (*Cynomys* sp), followed by plague, when a breeding program started in 1985, based on 18 individuals, of which seven reproduced in captivity [27]. The expected heterozygosity dropped to HE ≤ 0.11 in some populations after bottleneck events in the 1970s, but the populations now

The species described above, all with low genetic diversity in at least some populations, still seem viable, but a crucial question is whether the low diversity populations are sustainable. Can they meet environmental changes to come? The lower the diversity and population size N, the higher the risk of loss from genetic drift following bottleneck events, and after generations, fixation of the most frequent allele at a locus may be expected, when loss rate exceeds mutation rate. Experiments have demonstrated lower fitness of low diversity specimens of, for example an estuarine crustacean (*Americamysis bahia*) showed reduced fitness (fertility, survival) in populations with low genetic diversity compared to populations of high diversity, and this was most pronounced in stressful environments [28]. Closely related mates may lead to inbreeding depression with loss of low frequent alleles. Nevertheless, inbreeding in wild populations of moderate size is not necessarily harmful, as it may lead to exclusion of recessive harmful alleles, purging, and result in a population that is more adapted to its environment [29, 30]. The effect, or cost, of inbreeding in wild populations is difficult to observe, and unfit combinations may be excluded in all stages of life, from pre-zygotic to reproductive phase [31].

Salmonid fishes are commonly bred in fish farms for food production and for stocking in rivers and lakes to improve fishery. Major economic interests are involved, and considerable effort is spent on research. Lehnert et al. [32, 33] found that sperm competition and cryptic female choice (CFC) help to maintain allele richness in Chinook salmon (*Oncorhynchus tshawytscha*). An assessment of genetic variation within metapopulations of steelhead trout (*Oncorhynchus mykiss*) related to climate and landscape showed that climate variation induced genetic variation [34], and the genetics of river living salmonids is affected by dams as obstacles to migration [35]. Several studies have showed genetic differentiation between wild and hatchery stocks, though of common origin, indicating serious effects of breeding based on

Human interventions of different kinds affect populations and their genetic diversity and structure, and the effect within a given time span is impossible to predict. Nevertheless, the loss or exclusion of alleles from a population is in any circumstances worrisome when it is due to human action. Conservation of metapopulations, consisting of small and moderately sized (effective population size N<sup>e</sup> < 50) populations with some possibility of admixing, is one way to secure allele preservation. To explore this, natural metapopulations may be studied. Linløkken et al. [38] found in a study of brown trout (*Salmo trutta*) in nine tributaries to Lake Mjøsa in central Norway, that effective population size was positively related to habitat length (size). A bit unexpected, the heterozygosity based on MSs, was not correlated with

forced, artificial mating, avoiding natural sexual selection [36, 37].

seem to reproduce without noticeable effects of inbreeding.

**2.2. How to keep a small but diverse gene pool**

46 Genetic Diversity and Disease Susceptibility

A small tributary to the Lake Savalen in Central Norway serves as spawning area for brown trout of the lake. The number of breeders (effective population size of one cohort, N<sup>b</sup> ), based on linkage disequilibrium in 10 MS loci, was estimated to N<sup>b</sup> = 38 for young of the year (0+) in autumn, and Nb = 35 for 1-year (1+) old fish in June the subsequent year (i.e., of the same cohort) [41]. The observed heterozygosity based on the same MSs, was H<sup>O</sup> = 0.69 for 0+, and increased to HO = 0.78 for 1+, and both were significantly higher than the expected heterozygosity (H<sup>E</sup> = 0.67–0.72). This corresponded to H<sup>O</sup> = 0.333 for both 0+ and 1+ and H<sup>E</sup> = 0.323 and 0.325, respectively, based on SNPs. For both marker types, the deviation from Hardy– Weinberg equilibrium was significant, and this excess of heterozygotes is interesting. When comparing wild 0+ and 1+ and a group of hatchery brown trout, all of the same cohort, Linløkken et al. [41] found that allele frequencies were changed from October to June in the subsequent year and was even more differentiated in the hatchery group.

By analyzing biallelic markers, that is, with two possible homozygotes and one heterozygote, like in SNPs, this is simpler to explore than in cases of the poly-allelic microsatellites. Outlier FST analysis of 3871 SNP loci detected 421 (10.8%) loci as candidates of selection, and among those, 34 loci showed significant mean length differences between genotypes in the 1+ wild fish group. In 30 of these loci, the largest genotype was significantly more frequent in the 1+ than in the 0+ group, indicating positive selection of large specimens, and 19 (63%) of these large genotypes were heterozygotes. This indicated that the differentiation between fry and the yearlings was in part due to size selective mortality, disfavoring the smallest specimens of fry through increased autumn to spring mortality. At five loci, only one of the homozygotes was recorded in the 0+ group (**Figure 1**). The heterozygote was significantly more frequent in the 1+ than in the 0+ group (Fisher exact test, P < 0.05) and was larger than the homozygote, different from in the 0+ group (**Figure 2**) (t-test, P < 0.05).

#### **3.2. Simulating the fate of a low frequency allele at biallelic loci**

The low allele frequency of **Figure 1** (p = approximately 0.10) was used to simulate allele exclusion by means of the Allele Simulator software (available on the web: http://popgensimulator.pitt.edu/graphs/allele), choosing population size N = 25, 50, and 100, and performing 50 replicates of 50 simulations over 50 generations (corresponding to 150–250 years with maturation at 3–5 years of age). To explore the effect of allele frequency on exclusion rate, 50 simulations with N = 25 and allele frequency p = 0.01, 0.05, 0.10, 0.25, and 0.50 were conducted. Fitness was set to 1.00 for all genotypes, and the proportion of exclusion showed a curved decrease by increasing p and resulted in 97% exclusion with p = 0.01, being reduced to 90% with p = 0.05, further to 78% with p = 0.10 and to 23% with p = 0.50 (**Figure 3**). This suggests that with N = 25, the probability of retaining a p = 0.01 allele in 50 generations, without any heterozygote superiority, is close to null.

The initial allele frequency was then set to p = 0.10, and 50 simulations were run with fitness = 1.00 of all genotypes and N = 25, 50, 100, 200, and 400. The proportion of exclusion decreased exponentially by increasing N, and less than 50% of the simulations ended in exclusion when N > 77, and 62% of the simulations ended with exclusion with N = 50 (calculated from the regression, **Figure 4**). With N = 400, only 4% of the simulations resulted in exclusion.

**Figure 3.** The proportion of 50 simulations that led to extinction during 50 generations in a population of N = 25 as a

function of the initial frequency of the allele.

**Figure 2.** Mean lengths of young of the year (+) and 1-year-old brown trout (□) of different genotypes at loci at which mean length of heterozygotes were larger than that of homozygotes, and heterozygotes were more frequent in the 1-year-old group (W.1+) than in the young of the year group (W.0+) (**Figure 1**). Vertical lines show 95% confidence limits.

Genetic Diversity in Small Populations http://dx.doi.org/10.5772/intechopen.76923 49

**Figure 1.** The distribution of genotypes of five SNP loci (numbers refer to Linløkken et al. [36]) in young of the year (W.0+, N = 48) and 1-year-old (W.1+, N = 47) brown trout of the same cohort and population. P denotes the observed frequency of the low frequency allele at the five loci.

the 1+ than in the 0+ group (Fisher exact test, P < 0.05) and was larger than the homozygote,

The low allele frequency of **Figure 1** (p = approximately 0.10) was used to simulate allele exclusion by means of the Allele Simulator software (available on the web: http://popgensimulator.pitt.edu/graphs/allele), choosing population size N = 25, 50, and 100, and performing 50 replicates of 50 simulations over 50 generations (corresponding to 150–250 years with maturation at 3–5 years of age). To explore the effect of allele frequency on exclusion rate, 50 simulations with N = 25 and allele frequency p = 0.01, 0.05, 0.10, 0.25, and 0.50 were conducted. Fitness was set to 1.00 for all genotypes, and the proportion of exclusion showed a curved decrease by increasing p and resulted in 97% exclusion with p = 0.01, being reduced to 90% with p = 0.05, further to 78% with p = 0.10 and to 23% with p = 0.50 (**Figure 3**). This suggests that with N = 25, the probability of retaining a p = 0.01 allele in 50 generations, without

**Figure 1.** The distribution of genotypes of five SNP loci (numbers refer to Linløkken et al. [36]) in young of the year (W.0+, N = 48) and 1-year-old (W.1+, N = 47) brown trout of the same cohort and population. P denotes the observed

different from in the 0+ group (**Figure 2**) (t-test, P < 0.05).

48 Genetic Diversity and Disease Susceptibility

any heterozygote superiority, is close to null.

frequency of the low frequency allele at the five loci.

**3.2. Simulating the fate of a low frequency allele at biallelic loci**

**Figure 2.** Mean lengths of young of the year (+) and 1-year-old brown trout (□) of different genotypes at loci at which mean length of heterozygotes were larger than that of homozygotes, and heterozygotes were more frequent in the 1-year-old group (W.1+) than in the young of the year group (W.0+) (**Figure 1**). Vertical lines show 95% confidence limits.

The initial allele frequency was then set to p = 0.10, and 50 simulations were run with fitness = 1.00 of all genotypes and N = 25, 50, 100, 200, and 400. The proportion of exclusion decreased exponentially by increasing N, and less than 50% of the simulations ended in exclusion when N > 77, and 62% of the simulations ended with exclusion with N = 50 (calculated from the regression, **Figure 4**). With N = 400, only 4% of the simulations resulted in exclusion.

**Figure 3.** The proportion of 50 simulations that led to extinction during 50 generations in a population of N = 25 as a function of the initial frequency of the allele.

**Figure 4.** The proportion of 50 simulations that led to extinction during 50 generations of an allele with initial frequency p = 0.10 as a function of population size N = 25, 50, 100, 200, and 400.

To explore the effects of relative heterozygote fitness, the fitness of the heterozygote was set to 1.0, whereas the fitness of the two homozygotes was set equal, varying from 0.75 to 1.0, that is, the heterozygote fitness was similar or higher than that of the homozygotes. The simulations (**Figure 5**) showed that when fitness was equal for all genotypes, exclusion of the p = 0.10 allele decreased from 78% with N = 25 to 65% of the simulations with N = 50 and further to 40% with N = 100 (**Figure 6**). With fitness 0.90 of the homozygotes, less than 50% of the simulations ended with exclusion with N = 25, corresponding to less than 20% with N = 50, and less than 5% ended in exclusion with N = 100. Less than 10% of the simulations led to exclusion with homozygote fitness = 0.75 and N = 25, less than 1% led to exclusion with N = 50, and null

**Figure 6.** Proportion of 50 simulations of the frequency of an allele with initial frequency p = 1.0 that led to extinction within 50 generation with fitness = 1 of the heterozygote and fitness 0.75–1.0 of the two homozygotes and population

Genetic Diversity in Small Populations http://dx.doi.org/10.5772/intechopen.76923 51

Many animal species, among them representatives of advanced groups like birds and mammals, thrive well despite low genetic diversity, that is, apparently with a limited toolbox for evolutionary adaptation to new environments. Nevertheless, when genetic diversity is low, it is important to retain the alleles that still exist to avoid fixation at all loci. In small populations, like N = 25, the exclusion rate is quite high for alleles of frequency p = 0.10, and it increased inversely with the allele frequency and population size, according to the simulation experiments. This will, to some extent, be compensated for by mutations and introgression from migrants. The exclusion rate was reduced when heterozygote fitness exceeded that of the homozygotes, as was expected, and the increased heterozygote fitness helps effectively to retard the exclusion rate of alleles. As an example, young of the year and 1-year-old brown trout suggested positive selection of heterozygotes during the first winter, possibly due to faster growth and increased survival of large specimens.

simulations ended with exclusion with N = 100.

**4. Conclusion**

size N = 25, 50, and 100.

**Figure 5.** Proportion of 50 simulations of the frequency of an allele with initially p = 0.10 during 50 generations, population size N = 50 with fitness = 1 for all genotypes (upper panel), and with fitness = 1.0 of the heterozygote and fitness = 0.80 for both the homozygote (lower panel).

**Figure 6.** Proportion of 50 simulations of the frequency of an allele with initial frequency p = 1.0 that led to extinction within 50 generation with fitness = 1 of the heterozygote and fitness 0.75–1.0 of the two homozygotes and population size N = 25, 50, and 100.

To explore the effects of relative heterozygote fitness, the fitness of the heterozygote was set to 1.0, whereas the fitness of the two homozygotes was set equal, varying from 0.75 to 1.0, that is, the heterozygote fitness was similar or higher than that of the homozygotes. The simulations (**Figure 5**) showed that when fitness was equal for all genotypes, exclusion of the p = 0.10 allele decreased from 78% with N = 25 to 65% of the simulations with N = 50 and further to 40% with N = 100 (**Figure 6**). With fitness 0.90 of the homozygotes, less than 50% of the simulations ended with exclusion with N = 25, corresponding to less than 20% with N = 50, and less than 5% ended in exclusion with N = 100. Less than 10% of the simulations led to exclusion with homozygote fitness = 0.75 and N = 25, less than 1% led to exclusion with N = 50, and null simulations ended with exclusion with N = 100.

#### **4. Conclusion**

**Figure 5.** Proportion of 50 simulations of the frequency of an allele with initially p = 0.10 during 50 generations, population size N = 50 with fitness = 1 for all genotypes (upper panel), and with fitness = 1.0 of the heterozygote and

**Figure 4.** The proportion of 50 simulations that led to extinction during 50 generations of an allele with initial frequency

p = 0.10 as a function of population size N = 25, 50, 100, 200, and 400.

50 Genetic Diversity and Disease Susceptibility

fitness = 0.80 for both the homozygote (lower panel).

Many animal species, among them representatives of advanced groups like birds and mammals, thrive well despite low genetic diversity, that is, apparently with a limited toolbox for evolutionary adaptation to new environments. Nevertheless, when genetic diversity is low, it is important to retain the alleles that still exist to avoid fixation at all loci. In small populations, like N = 25, the exclusion rate is quite high for alleles of frequency p = 0.10, and it increased inversely with the allele frequency and population size, according to the simulation experiments. This will, to some extent, be compensated for by mutations and introgression from migrants. The exclusion rate was reduced when heterozygote fitness exceeded that of the homozygotes, as was expected, and the increased heterozygote fitness helps effectively to retard the exclusion rate of alleles. As an example, young of the year and 1-year-old brown trout suggested positive selection of heterozygotes during the first winter, possibly due to faster growth and increased survival of large specimens.
