Random genetic drift Genetic drift and mutation balance Population size is an important number With mutations a random mating population of diploids can acquire 2N � new alleles every generation. A random-mating population of diploid individuals looses by chance alleles, it looses at a rate of 1/(2N) where N is the We can calculate how many alleles are on average in a number of diploid individuals: population assuming mutation rate and loss are equal. Small populations loose alleles faster than large populations, We can turn around and find out how big the population is when we use genetic data (number of alleles in the If the population is infinitely large then the frequency of populations) to infer the population size N. different alleles stays the same. Effective population size Complications Real populations often do not follow the Wright-Fisher Historical humpback whale population size population model, but one can often correct for such Fluctuating population size differences when we know demographic parameters: using the data by Joe Roman and Stephen R. Palumbi (Science 2003 301: Cycles for example length of a generation, mating mechanism, age 508-510) structure, etc. Bottleneck Θ =2 N ~ µ 0.01529 Population size of the North Atlantic population, estimated using migrate When we use real populations and calculate population sizes Unequal sex ratios with µ = 2 . 0 × 10 − 8 bp − 1 year − 1 and using these theoretical approaches, we talk of effective N ~ = Θ 31,854 2 µ Uneven distribution of progeny (family size) population size, which means if the data would come from a a generation time of 12 years Wright-Fisher population we would get that number. Overlapping generations N e = N ~ + N | 63,708 Sex ratio is 1:1 The effective population size is almost always much smaller Age structure (non-random mating) N B = 2 N e 127,417 ratio N T /N e assumed, using other than the actual census population size because of the data deviation from the Wright-Fisher population model. N juveniles + N adults N T = N B 203,867 from catch and survey data (used a N adults ratio of 1.6)
Population Bottlenecks Bottleneck Population size changes through time 2000 1750 1500 1250 1000 A population undergoes a bottleneck 750 500 when it experiences a time with a 250 Northern Elephant Seal very small size 2 4 6 8 10 12 N e � 800 the longer the bottlenecks takes the more serious is the loss of variability the effect of very small sizes (<50) is serious Cycles: Snowshoe hare and Lynx N e � 300 Uneven distribution of progeny Harmonic mean Unequal sex ratio 1 N e = 4 N c − 2 N e = 4 N m N f N e = σ 2 N c N e 1 t ( 1 1 1 1 1 N 1 + N 2 + N 3 + N 4 + ... + N t ) σ 2 + 2 N m + N f 0 100 199 Cyclic Bottleneck Ne N f effective size of females σ 2 1 100 133 variance of family size N m effective size of males 2000 2000 1750 1500 1500 2 100 100 1250 1000 1000 750 N c census size 500 500 250 5 100 57 1:100 1:1 100:1 20 40 60 80 100 2 4 6 8 10 12 sex ratio 10 100 33 N e = 20 N e = 812 σ 2 random mating = 2(1 − 1 /N c )
Uneven distribution of progeny Genetic drift and mutation balance Small populations Red Drum (redfish) 1 With mutations a random mating population of diploids has ∆ H = µ − the chance to acquire 2N � new alleles every generation. 2 N e 1 A population looses variability at a rate of Small population loose alleles faster than they arrive in by Family Sciaenidae, DRUMS Sciaenops ocellatus 2 N e mutation Small population are not at mutation-drift → Description: chin without barbels; copper bronze body, lighter shade in clear waters; one N e = 1854 to many spots at base of tail (rarely no spots); mouth horizontal and openng downward; equilibrium. scales large. N c = 3 , 400 , 000 Similar Fish: black drum, Pogonias cromis . Where found: juveniles are an INSHORE fish, migrating out of the estuaries at about 30 Heterozygosity H will decrease over time inches (4 years) and joining the spawning population OFFSHORE. 1 Size: one of 27 inches weighs about 8 pounds. ∆ H = µ − *Florida Record: 51 lbs., 8 ozs. Turner, T. F. , J.P. Wares, and J.R. Gold. 2002. Genetic 2 N e Remarks: red drum are an INSHORE species until they attain roughly 30 inches (4 Effective Size is Three Orders of Magnitude lower than years), then they migrate to join the NEARSHORE population; spawning occurs from Adult Census Size in an Abundant, Estuarine Dependent August to November in NEARSHORE waters; sudden cold snaps may kill red drum in shallow, INSHORE waters; feeds on crustaceans, fish and mollusks; longevity to 20 years Marine Fish (Sciaenops ocellatus). Genetics or more. mutation rate loss rate Relationship between Founder effect Reduction of population size Heterozygosity and Population size When only few individuals from a large population colonize an island (or other isolated habitat), only a small number of alleles will be present in the new population. Genetic drift (loss of alleles is larger than gain of alleles) Expected Locality Heterozygosity Heterozygosity Founder effects 8 Selçuk 0.114 0.132 Bottlenecks 13 Samos 0.097 0.119 13 Inbreeding Red-cockaded woodpecker 14 Ikaria 0.042 0.050
Disease susceptibility in California sea lion Inbreeding Inbreeding depression Breeding with close relatives Breeding with close relatives Reduced heterozygosity and increased mortality of offspring caused by mating of close relatives Causes of inbreeding depression Experiment showing inbreeding in a cricket Reduced heterozygosity Increased exposure of recessive deleterious alleles in homozygotes Recessive deleterious alleles are common in large populations. These alleles are at low frequencies and typically occur mainly in heterozygotes and are therefore not purged from the populations because there is no associated penalty for the heterozygotes. In small populations, just by chance, they might get fixed Figure 2 Internal relatedness in sea lions and the incidence of different disease classes. Carcinoma, n = 13; helminth infection, n = 72; nonspecific, n = 51; bacterial infection, n = 98; algal toxin, n = 101; trauma (control), n = 36. Values are means s.e. The mean internal relatedness value of trauma animals (-0.004) is indistinguishable from zero, as would be expected for individuals born to randomly mated parents 5 .
Measuring inbreeding Measuring inbreeding for population we use the heterozygosity as a proxy F = H Expected − H observed F = H e − H o H Expected H e F measures the deviation from a random mating population if Hois zero, F is maximal and 1 if Ho is equal to He, F is 0 using Hardy-Weinberg proportions and H Expected = 2 pq two alleles
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