Random genetic drift Genetic drift and mutation balance Population - - PowerPoint PPT Presentation

Population size is an important number

A random-mating population of diploid individuals looses by chance alleles, it looses at a rate of 1/(2N) where N is the number of diploid individuals: Small populations loose alleles faster than large populations, If the population is infinitely large then the frequency of different alleles stays the same.

Random genetic drift Genetic drift and mutation balance

With mutations a random mating population of diploids can acquire 2N new alleles every generation. We can calculate how many alleles are on average in a population assuming mutation rate and loss are equal. We can turn around and find out how big the population is when we use genetic data (number of alleles in the populations) to infer the population size N. Historical humpback whale population size

using the data by Joe Roman and Stephen R. Palumbi (Science 2003 301: 508-510) Θ =2 N~µ 0.01529 Population size of the North Atlantic population, estimated using migrate N~ = Θ

2µ

31,854 with µ = 2.0×10−8bp−1year−1 and a generation time of 12 years Ne = N~ + N| 63,708 Sex ratio is 1:1 NB = 2Ne 127,417 ratio NT/Ne assumed, using other data NT = NB

Njuveniles+Nadults Nadults

203,867 from catch and survey data (used a ratio of 1.6)

Real populations often do not follow the Wright-Fisher population model, but one can often correct for such differences when we know demographic parameters: for example length of a generation, mating mechanism, age structure, etc. When we use real populations and calculate population sizes using these theoretical approaches, we talk of effective population size, which means if the data would come from a Wright-Fisher population we would get that number. The effective population size is almost always much smaller than the actual census population size because of the deviation from the Wright-Fisher population model.

Effective population size Complications

Fluctuating population size Cycles Bottleneck Unequal sex ratios Uneven distribution of progeny (family size) Overlapping generations Age structure (non-random mating)

Population size changes through time

Cycles: Snowshoe hare and Lynx

Bottleneck

2 4 6 8 10 12 250 500 750 1000 1250 1500 1750 2000

A population undergoes a bottleneck when it experiences a time with a very small size the longer the bottlenecks takes the more serious is the loss of variability the effect of very small sizes (<50) is serious

Ne 800 Ne 300

Northern Elephant Seal

Population Bottlenecks Harmonic mean

Ne = 1

1 t ( 1 N1 + 1 N2 + 1 N3 + 1 N4 + ... + 1 Nt )

Cyclic

20 40 60 80 100 500 1000 1500 2000

Ne = 20

Bottleneck

2 4 6 8 10 12 250 500 750 1000 1250 1500 1750 2000

Ne = 812

Unequal sex ratio

1:1 1:100 100:1

Nm Nf

effective size of females effective size of males

Ne = 4NmNf Nm + Nf

sex ratio Ne

100 199 1 100 133 2 100 100 5 100 57 10 100 33

Uneven distribution of progeny

σ2

variance of family size

Nc

census size

σ2 Nc Ne

Ne = 4Nc − 2 σ2 + 2

σ2

random mating = 2(1 − 1/Nc)

Uneven distribution of progeny

Red Drum (redfish)

Family Sciaenidae, DRUMS Sciaenops ocellatus Description: chin without barbels; copper bronze body, lighter shade in clear waters; one to many spots at base of tail (rarely no spots); mouth horizontal and openng downward; scales large. Similar Fish: black drum, Pogonias cromis. Where found: juveniles are an INSHORE fish, migrating out of the estuaries at about 30 inches (4 years) and joining the spawning population OFFSHORE. Size: one of 27 inches weighs about 8 pounds. *Florida Record: 51 lbs., 8 ozs. Remarks: red drum are an INSHORE species until they attain roughly 30 inches (4 years), then they migrate to join the NEARSHORE population; spawning occurs from 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

• r more.

Turner, T. F., J.P. Wares, and J.R. Gold. 2002. Genetic Effective Size is Three Orders of Magnitude lower than Adult Census Size in an Abundant, Estuarine Dependent Marine Fish (Sciaenops ocellatus). Genetics

Ne = 1854 Nc = 3, 400, 000

Genetic drift and mutation balance

With mutations a random mating population of diploids has the chance to acquire 2N new alleles every generation. A population looses variability at a rate of

1 2Ne ∆H = µ − 1 2Ne mutation rate loss rate ∆H = µ − 1 2Ne

Small population loose alleles faster than they arrive in by mutation Small population are not at mutation-drift equilibrium. Heterozygosity H will decrease over time

Small populations

→

Relationship between Heterozygosity and Population size

Red-cockaded woodpecker

Founder effect

Locality Heterozygosity Expected Heterozygosity 8 Selçuk 0.114 0.132 13 Samos 0.097 0.119 14 Ikaria 0.042 0.050

13

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.

Reduction of population size

Genetic drift (loss of alleles is larger than gain of alleles) Founder effects Bottlenecks Inbreeding

Inbreeding

Breeding with close relatives

Inbreeding depression

Breeding with close relatives

Reduced heterozygosity and increased mortality of offspring caused by mating of close relatives

Disease susceptibility in California sea lion

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 parents5.

Experiment showing inbreeding in a cricket

Causes of inbreeding depression

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

Measuring inbreeding

F = HExpected − Hobserved HExpected

for population we use the heterozygosity as a proxy

HExpected = 2pq using Hardy-Weinberg proportions and two alleles

F measures the deviation from a random mating population

Measuring inbreeding

F = He − Ho He

if Hois zero, F is maximal and 1 if Ho is equal to He, F is 0