Deriva_2.pdf

7/30/2019 Deriva_2.pdf

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An example:An example: Astrocaryum mexicanum Astrocaryum mexicanum ::

A tropical rain forest palm,palm, Los Tuxtlas Veracruz, monoecious,pollinated by beetles

Effective population size NEffective population size N ee


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Astrocaryum mexicanum Astrocaryum mexicanum To estimate N To estimate N e e How deviates from the ideal modelideal model ? (Hartl and Clark, 1989):

1) Diploid organism2) Sexual reproduction

3) Non-overlapping generations *4) Many independent subpopulation, each of constant size N5) Random mating within each subpopulation *6) No migration between subpopulations7) No selection* = violated by A. mexicanum


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Effective populationEffective population

We estimated its effective population sizeusing direct and indirect methods.

Direct methods:Analyzing how violates the ideal model:

Non- random mating in the population:Neighborhood analysis

Overlapping generations:Different methods


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Direct methods:Direct methods:Neighborhood area (Wright 1946):

Area that includes most (82 to 87%) of the parentsmost (82 to 87%) of the parents ofthe individuals in the center of the area.

Represents a more or less panmictic areapanmictic area , and anapproximation of the effective population size wouldbe:

Neb

= neighborhood area * effective density / m 2


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Neighborhood area Neighborhood area =( [AFp * 1/2Vp *t]+ [AFsp *Vsp * (1+t) /2] +[AFss *Vss * (1+t) /2])

p= pollen

sp= seeds, primary dispersionss= seed, secondary dispersion = 3.1416AF = Area correction factor for pollen, = 4 ifnormalV= Axial variance in dispersal distancest= outcrossing rate (0 to 1)


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Outcrossing rates and Pollen dispersalOutcrossing rates and Pollen dispersalestimatesestimates

t= outcrossing ratet= outcrossing rateEstimated using 5 loci, Ritland and Jains (1981) method,several sites (6) and 3 years:

Is not different from 1.

Pollen dispersal:Pollen dispersal: Estimated using 3 methods:

a) Dispersal of fluorescent dyes in two different years.b) Minimum distance between an active female and maleinflorescence.c) Paternity analysis based upon progeny with a rare

allele (LAP 3) and 4 other loci.


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Seed dispersal estimates:Seed dispersal estimates:Primary dispersal (seed fall under the mother):using isolated palms

Secondary dispersal: attaching a nylon filamentto evaluate dispersal by mammals


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Total neigborhoodTotal neigborhood = pollen dispersal + primary seed dispersal +

pollen dispersal= 2551 m2551 m22

This has to be multiplied by the effective density.

We used three methods to estimate it:

Nei and Imaizumi (1966) Ne = Nr* LCrow and Kimura (1972) N

e= No *L *i

Hill (1972) Ne =(4No-2)L/(Var(f) +2)


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Effective population size inAstrocaryum mexicanum Astrocaryum mexicanum , direct

methods: These methods gave the effective density by m 2,and using it in the neigborhood:

Ne = 234 (Nei and Imaizumi); N e /N= 0.177NNee = 560 (Hill); N= 560 (Hill); N ee /N=0.434/N=0.434

May be a gross subestimate, because, for instance,

long distance gene dispersal is very difficult to estimate,but even if rare, it increases N e dramatically.


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IndirectIndirect methods to estimate Nm inmethods to estimate Nm in A.A.mexicanum mexicanum ::

FF stst : measure of genetic differentiation =: measure of genetic differentiation = (H(H tt - H- H ss )/ H)/ H tt FF stst from 0 if there is no differences in allelic frequencies to1 if the populations are fixed to different alleles.

S. Wright found that F st = 1/ 4 N e m +1,

and Crow and Aoki (1984) developed a more generalmodel including mutation:

F st = (1/ (4 N e ma +1)), where a= [n/n-1] 2(if the number of populations is large, both estimatesconverge).


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A. mexicanum A. mexicanum , indirect analyses:, indirect analyses:LocusLocus FFstst NNee mm mm(N(Nee =560)=560)Mdh-1 0.0318 4.3 0.0086Pgd-1 0.0563 2.4 0.004Pgi-1 0.0141 9.8 0.018Adh-1 0.0537 2.5 0.005

Lap-2 0.0422 3.2 0.005

Low or little differentiation among sitesAverage NNee mm 4.44:

NNee m larger than 1.m larger than 1.Las poblaciones se comportan como una granLas poblaciones se comportan como una granpoblacipoblaci n panmctica...n panmctica...


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Otra manera indirecta de estimar el N e :Infinite alleles model (Kimura)

H= 4NH= 4Nee /(4N/(4Nee +1)+1)if (mutation rate) for allozymes is 10-6in Zea spp. Doebly et al. (1984) reported a range H=

0.182-0.233Ne range 55,623-75,945

in 655 plant species, Hamrick et al. (1992) found aH=0.154

Ne = 45,508higher than direct and ecological methods.Vecindades genticas, entre Ne 1 a 4000!


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Otra manera indirecta de estimar el N e :Infinite alleles model (Kimura)

H= 4NH= 4Nee /(4N/(4Nee +1)+1)Ne = 45,508 -75,945Vecindades genticas, entre Ne 1 a 4000!

The differences among estimates: may be due to the fact that the infinite alleles model

may not describe their evolutionary process(Barbadilla et al. , 1996)

estan midiendo cosas diferentes: vecindades el Ne local y ecolgico, mientras que los alelos infinitos sonel resultado de la evolucin histrica de toda unaespecie, formada por n poblaciones ligadas por flujo

gnico...


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Efecto de fundador y cuellos de botella.

A population may descend from only a small number of

individuals either because the population is initiated from asmall number of individuals, causing a founder effect ,

or because a small number of individuals survivedin a particular generation or consecutive generations, resultingin a population bottleneck .

These situations can lead to chance changes ingenetic variation so that allele frequencies are different from

those in the ancestral population, resulting in lowerheterozygosity and fewer alleles.


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Efecto de fundador y cuellos de botella .Veamos los efectos de esta reduccin en eltamao en la var. gentica:

where Ht and Ht+1 are the heterozygositiesin the original population and the founding group.

despejando


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Efecto de fundador y cuellos de botella.Assuming that there are t generations of small numbersas in a bottleneck with size Ne,

where Hs is the heterozygosity before the bottleneck. Forexample, if Ho = 0.7, Ht = 0.6, and t= 5, then Ne = 16.4.

ENTRE MAYOR LA REDUCCION EN LA H, MENOR Ne


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Efecto en la distancias gentica:In an effect related to the reduction in heterozygosity, afounder event(or a bottleneck) can also quickly generate geneticdistance between the ancestral population and the newlyfounded or bottlenecked population.

This can be understood intuitively if we assume that there are10 alleles in the ancestral population , and the founder (orbottleneck) generation consists of one fertilized female(2N= 4) (suponiendo un slo padre), as a result, at least sixalleles must be lost in the bottleneck , resulting insignificant changes in allele frequencies in the descendantpopulation and genetic distance from the ancestral populationin one generation.


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Distancias de Nei, 1972:

I= identidad genticaI= Jxy/ (Jx Jy) 1/2 dondeJx = sum pix *piyJx= sum pix 2 Jy= sum piy 2 pobl. x y y

0= no se comprten alelos1= idnticos en las f. allica slas 2 pobl.

D= -ln (I)D= 0, identicos en las f.allicasD = infinito, si no comparten alelos...


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D, LA DISTANCIA ESPERADA, COMO FUNCIN DE:

a partir deel cambio enH

como cambia la D a partirde una H original en el t

Efecto en la distancias genticas:


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Efecto en la distancias genticas:

Ne infinitoNe chico y/o mucho tiempo


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Ne infinitoNe chico y/o mucho tiempoWhen there is high initial heterozygosity , such as found for microsatelliteloci, the effect can be quite large.A one-generation bottleneck of two individuals (0.75 on the horizontal axis), thenfor Ho of 0.7 and 0.9 , the genetic distances are 0.230 and 0.589 , respectively

Incrementoen la Den unageneracinNe=2Ho=0.7y 0.9


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BORREGO CIMARRON: isla TiburnBighorn sheep ( Ovis canadensis ) have greatly declined innumbers and distribution in the past century because of

disease, hunting ,and other factors.

As a result, there have a number of introductionsthroughout western North America in an effort to establishmore viable populations.

For example, in early 1975, 20 desert bighorn sheep (4males and 16 females) were captured in mainland Sonora,Mexico, and translocated to nearby Tiburon Island in theSea of Cortez.

The translocated population grew quickly, and by 1999, anestimated 650 sheep were on the island, all descended from

this small founder group.


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Nmero de alelos y probabilidad de polimorfismo

When there are Hardy-Weinberg proportions in the parentalpopulation,the probability of polymorphism R in a foundergroup of size N is

which is one minus the probability of monomorphism.


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R as a function of founder size for several allele frequencies when there are only two alleles.If the alleles are equal in frequenc y, then the founder size does not need to be very large for a highprobability of inclusion of both alleles.The founder population need be only 3 individuals (2N=6) or larger for there to be a greater than 95%chance of including both alleles when they are equal in frequency.If the frequencies in the parental population of the two alleles are far from equal (e.g., 0.95 and 0.05), thenthe founder number needs to be 30 or larger for there to be a 95% chance of including both alleles (inreality, of including the rarer allele).

PERDIDA DE ALELOS:


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PERDIDA DE ALELOS:For highly variable loci in particular, theloss of allelesoccurs more rapidly than the loss ofheterozygosity.

For example, a microsatellite locus with 20alleles in a bottleneck of 5 (2N= 10) wouldlose at least half of its alleles , but only 10% of

its heterozygosity would be expected to belost.


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EJEMPLO ELEPHANT SEAL:

Hoelzel et aI. (2002) found two mtDNA haplotypes with estimated frequencies of 0.27 and 0.73 in thecontemporary northern elephant seal population,giving a haplotype diversity estimate of H= 0.40.

They also determined mtDNA haplotypes in pre-bottleneck museum and midden samples and

estimated the mtDNA diversity in these samples as H= 0.80.

Seleccin en poblaciones finitas:


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Seleccin en poblaciones finitas:Deriva sola: When there is no differential selection

at a locus, an allele may become fixed or lost as aresult of genetic drift.The probability of fixation is equal to the initialfrequency of the allele so that when the allele israre the probability of fixation is quite low.Seleccin sola: In contrast, in an infinitepopulation, which by definition has no geneticdrift, a favorable allele always increases andasymptotically approaches fixation.

Seleccin + Deriva:


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Seleccin + Deriva:

In a finite population, however, afavorable allele may not always be fixed because it may be lost because of the chanceeffects of genetic drift.

The probability of fixation of a favorable allele in afinite population, u(p), is a function of theinitial

frequency of the allele, the amount of selection favoring the allele, and the finite population size.


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Seleccin direccional, generaciones continuasIf it is assumed that the relative fitnesses of the three genotypes

A1A1,=1 +s,A1A2 = 1 + hsA2A2 =1,the general diffusion equation(Kimura, 1962, Kimura y Otha, 1971) becomes

The probability of fixation


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The probability of fixation is calculated for three levels ofdominance and different initial allelefrequencies for Ns= 2.0.A Ns value of 2.0 can result, for example,from a combination of .N= 1000 and s =0.002 or N= 100 and s = 0.02.The initial allele frequency has alarge effect on the probability offixation, withu(p) increasing quicklyas p increases from a low value. The difference in u(p) for differentlevels of dominance is alsosubstantial at low allele frequencies.Ifp=0.1, the probabilities of fixation forh= 0.0, 0.5, and 1.0 are 0.223, 0.335, and0.461 respectively. In general, anincreasing level of dominancesignificantly increases u(p) unless u(p)is already near 1.0.

p de fijacin muchos ms alta que


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azar (Ne= inf.)

al azar si hay sel. dir.

l


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When Ns 1, then the change inallele frequency is primarily determinedby selection and u(p) >> p.SI LA SEL. ES INTENSA O Ne GRANDE, SOLOOPERA LA SELECCIN...


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To illustrate the effect of the size of Ns on u(p), the figure gives theprobability of fixation for several initial allele frequencies for various levelsof Ns when there is additivity (h = 0.5) . As Ns increases, the probability offixation also increases quite dramatically so that even if p is only 0.1,the probability of fixation when Ns= 5 is already 0.631.


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SELECCION

DERIVA

Seleccin direccional generaciones discretas:


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Seleccin direccional generaciones discretas:When time is discontinuous, the transition matrix approach can be usedto calculate the probability of fixation of a favorable allele and to follow

the change in allele frequency distribution over time. In such a situation,the elements in the matrix must be modified to reflect selection as well asgenetic drift. This can be done by assuming that selection changes allelefrequency before sampling so that


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N= 20, s =0.1, h= 0.5, and the initial frequency of A1 in all the populations was 0.5. The probability offixationfor these parameter values, from expression 6.23b, is 0.78. The distribution of the frequency ofthe favorable allele reflects the effect of directional selection even after five generations. After 20generations, 20.6% of the populations are fixed for the favorable allele and only 3.1% for the unfavorableallele.

N=20


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con sels ca.10%

sin sel.n=20

In an infinite population a detrimental allele always


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In an infinite population, a detrimental allele alwaysdecreases in frequency and asymptotically approachesloss.

In contrast, in a finite population , an unfavorableallele , particularly if its detrimental effects are not large,may increase in frequency by chance and may

potentially become fixed.This effect, in which adetrimentalallele behaves much like aneutral allele in a smallpopulation was pointed out byWright (1931).

ESPECIES AMENAZADAS:


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Important concerns for many endangered species are that

the existing population generally is small , the species hasgone through a bottleneck in recent generations or thecaptive or extant population descends from only a fewfounder individuals.

AII of these factors may cause extensive genetic drift witha potential loss of genetic variation for future adaptiveselective change. In addition, small effective populationsizes may result in chance increases in the frequency ofdetrimental alleles because the absolute value ofNs is so low.



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For example, the captive population of Scandinavianwolves , initiated from 4 founders , had a high frequency ofhereditary blindness (Laikre et al.,1993).

The captive California condor population, initiated from 14founders , had a high frequency of a lethal form ofdwarfism (Ralls et al.,2000).Although a management strategy of selecting againstcarriers may reduce the frequency of these detrimental

alleles , it may also result ina reduction in variation at other genes.!!!!


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Ejemplos de la Deriva Gnicay Estimacin del TamaoEfectivo .

Deriva gnica y cuello de


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Deriva gnica y cuello debotella en Mirounga

angustirostrus.

Sobree plotacin


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Sobreexplotacin...

...prcticamente extinta, laextincin qued a cargo debilogos

Pero...


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Tamao efectivo y explotacin


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y pde Eschrichtius robustus.

Explotacin histrica de las


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Explotacin histrica de laspoblaciones.

Principalmente en el Pacfico.

La poblacin deOeste an en veda...

...la poblacin delEste lista paraexplotarse.

Usando censos , estimaron un


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Usando censos , estimaron untamao poblacional previo a la cacera deentre 19,480 y 35,430 individuos.

Los censos recientes estiman unatamao de entre 18,000 y 29,000individuos.


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El tamao seha recuperado,vamos acazar!!!!!

Adems...Adems...

Oigan pero hay otra evidencias


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Oigan, pero hay otra evidenciasque demuestran lo contrario!!!


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Estimaron 96,400 individuos , ms de 3veces el tamao actual reportado.

Los resultados preceden a la cacera (milesde generaciones).


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Deriva Gnica:


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FIN!!!

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