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Cuarta SesiónDeriva Génica

Luis E. Eguiarte, Valeria Souza, et al.

La deriva génica y el tamaño efectivode las poblaciones.

¿Que es la deriva génica?

El tamaño efectivo de las poblaciones,definiciones y métodos para suestimación.

Efecto de fundador y cuellos de botella.

Deriva génica y selección natural.

Deriva Génica:Azar en la evoluciónCambios en las frecuencias alélicasfuerza dominante en poblacionespequeñas y en el cambio molecular.

Central en el estudio de laconservación!Su análisis es complicado y abstracto...Parámetro!: Tamaño efectivo de lapoblación: Ne

Deriva Génica:Dominante en poblaciones pequeñas(- de 100 individuos... pero...)depende del tamaño efectivo de la

población, Ne

1) Se pierde variación genética H2) Divergen las poblaciones

(aumenta la Fst).3) En total (“n –replicas”) se

mantiene la f. alélica q

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Ejemplo efectosDeriva Génica:Tristan da Cunha:Isla en medio delAtlántico, a 2900km de Sudáfrica:

poblaciónpequeña, Deriva +Endogamia...161 personas

Ejemplo efectos DerivaGénica:

Sólo genes de 7 fundadoras(mujeres), varias parientasentre ellas

a) linaje materno, X, 5 linajes,mitocondria hm=0.768

b) 7 apellidos (linajepaternos, Y), 9 linajes, hy =0.847

mitocondria, linajes maternos:5 y sólo 3 comunes, 1 raro... 9 linajes paternos, varios “colados”

un haplotipo Y, el cinco mucho más común...

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Efectos de la Deriva Génica

Errores de muestreo...similar en todos los lociUnos dejan más hijos que otrospor azar... mayor en poblaciones pequeñas

Efectos de la Deriva Génica

N= 20

promedio

Efectos de la Deriva GénicaN=9, fijacióndesde lageneración 4N= 50, no se hafijado ningunaen 20generaciones

1) Entre más pequeño el N, más violentos (rápido yabruptos) son los cambios (si N infinito no hay cambio,H.-W.!)2) Se va perdiendo variación (H) en el tiempo3) Se pierde toda la variación (se fija un alelo) en dospoblaciones, un q=1 en t= 20, en otra q= 0 en t= 284) Van divergiendo las poblaciones en el tiempo,o sea aumenta la varianza en la f. alélicas entre las poblaciones!5) La q se mantiene constante en promedio!

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4) Van divergiendo las poblaciones en el tiempo,o sea aumenta la varianza en la f. alélicas entre las poblaciones! N= 20 5) La q se

mantieneconstante enpromedio!

Probabilidadde fijación:igual que su f. alélicainicial! (u = 0.5)

pr. de fijación igual a la frec. alélica inicial:más fácil de fijarte si ya es común el alelo

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Experimento deBuri 19562 alelos neutros, bw75y bw, locusbrown, color de ojosen D. melanogaster

N = 16 por réplica.107 replicas, p=q=0.5iniciales19 generaciones.No se muestran laspoblaciones que sefijanal t= 19, 30 en bwy 28 en bw75.

Experimentode Buri 1956

tiempo

ExperimentodeBuri 1956

La media de q se mantiene

La varianza aumentasegún lo esperado(para una Ne de 9!)

Variación Genética:¿como se pierde la H por Deriva?

la probabilidad de tomar dos veces el alelo es:2N (total de alelos)x 1/2N x1/2N (la probabilidad de tomar unalelo dos veces) = 1/2N

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incrementodebido a quela pobl. es finita

la autocigosisanterior...

rearreglando y sumando 1 en los dos lados

como ya vimossustituyendo:

Si Ne es infinito, Ht+1= Ht, no hay cambios, estamos en H.-W.Si Ne es 1 (lo menos posible)la Ht+1 es la mitad de la HtEste es el máximo cambio posible por Deriva Génica

que esaproxima-damente:

Generalizando para t generaciones:

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¿en cuanto tiempose pierde un alelo?

x= Ht / Ho : que tanto quedade la variación genética inicial

Para que se pierda la mitad de lavar. genética, se necesita un tiempo delorden de magnitud del Ne(sólo es rápido si son apenas decenas deindividuos)

¿en cuanto tiempose pierde un alelo?

Incremento en la Varianza q:

la divergencia entre poblaciones, la Varianza en q,depende de la var. gen. inicial, de N y de t:mayor: entre más var. génica, más t y menor N

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Incremento en la Varianza q: entre mayor sea el Ne,menor es lavarianza entre laspoblaciones

Simulación de Deriva con 20 individuos, matriz 41 x 41

casi “plana”

0.08 fija 0.08 fija

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N=16Ne= ca. 9

n= 20

¿En cuanto tiempo se fija un alelo por Deriva Génica?

Obviamente, debe de depender de la Ney la frec. alélica inicial

se itera hasta que todas las poblaciones se fijan... aburrido

T. de fijación, aproximación de Kimura y Ohta (1971)

el t de fijación función lineal de Ne y decrece si la pinicial es mayorsi q= 0.2, t= 3.57 N, si q = 0.8, t= 1.61N; si q=.01, t=3.979

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tiempo de fijación(coalescencia) promedio deun nuevo alelo neutro,cuatro veces su Ne...

tpromedio =1.81N

tpromedio =3.57N q=0.2

en realidad el t a la fijaciónes una distribución de probabilidades

Experimento de Buritiempos de fijaciónobservados y esperados,matriz 2N=18

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El Tamaño efectivo de lapoblación Ne:

El tamaño de una población ideal queexperimenta los mismos efectos debidos a laDERIVA GENICA que la población real queestudiamos...

generalmente se sugiere que debe de sersimilar al número de adultos reproductivos,pero es más complejo...

Ne: el tamaño censal (real) se “convierte” al de una población ideal donde todolos progenitores tiene las mismasprobabilidad de reproducirse (dif. aleatorias)

Población ideal: 1) Diploide,2) Hermafrodita (monoico),autofertilización3) Varianza fecundidad al azar.

To estimate To estimate NNeeHow deviates from the ideal modelideal model? (Hartl and Clark, 1989):

1) Diploid organism2) Sexual reproduction3) Non-overlapping generations 4) Many independent subpopulation, each of constant size N5) Random mating within each subpopulation 6) No migration between subpopulations7) No selection

Fecundidad al azar: dist. de Poisson

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Cociente Ne/ N con diferentes fecundidades

Poisson fecundidad al azar: Ne/N = 1Exactamente dos hijos sin varianza: Ne/N=2Un sólo progenitor todos los hijos: Ne/N=1/N

siNf=NmNe=Nf+Nm(N total)

si un sexodominaNe sehacemínimo

a mayores diferencia aleatorias en la fecundidad, mayor deriva génica

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¿como son Ne/N en la naturaleza?entre 0.69 y 0.95 humanos... pero en bichos con mucha fedundidad,como moluscos, peces, árboles puede se MUY pequeño!

media armónica de Ne

variacióny cuellosde botellaen poblaciones humanas(Egipto)

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An example:An example:Astrocaryum mexicanumAstrocaryum mexicanum::

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

Effective population size Effective population size NNee

Astrocaryum mexicanumAstrocaryum mexicanumTo estimate To estimate NNeeHow deviates from the ideal modelideal model? (Hartl and Clark, 1989):

1) Diploid organism2) Sexual reproduction3) 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

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

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

Area that includes most (82 to 87%) of themost (82 to 87%) of theparentsparents of the individuals in the center of thearea.

Represents a more or less panmictic panmictic areaarea, andan approximation of the effective population sizewould be:

Neb = neighborhood area * effective density / m2

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

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

Outcrossing rates and Pollen dispersalestimates

t= outcrossing rateEstimated using 5 loci, Ritland and Jain’s (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.

Seed dispersal estimates:Seed dispersal estimates:

Primary dispersal (seed fall under themother): using isolated palms

Secondary dispersal: attaching a nylonfilament to evaluate dispersal by mammals

Total Total neigborhood neigborhood =pollen dispersal + primary seeddispersal + secondary seed dispersal =2551 m2551 m22

This has to be multiplied by the effectivedensity.

We used three methods to estimate it:

Nei and Imaizumi (1966) Ne = Nr* LCrow and Kimura (1972) Ne = No *L *iHill (1972) Ne =(4No-2)L/(Var(f) +2)

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Effective population size inAstrocaryum mexicanumAstrocaryum mexicanum, directmethods:These methods gave the effective density by m2,and using it in the neigborhood:

Ne = 234 (Nei and Imaizumi); Ne /N= 0.177NNee = 560 (Hill); = 560 (Hill); NNee /N=0.434/N=0.434May be a gross subestimate, because, forinstance, long distance gene dispersal is verydifficult to estimate, but even if rare, it increasesNe dramatically.

Other direct attempts to measure Ne inplants:Using non-corrected neighborhood sizes (reviewedin Crawford, 1984; Eguiarte, 1990)Mean Neb herbs(20 studies) = 364 individuals364 individuals(range 2- 3844)Mean Neb trees (10 studies) = 292 individuals292 individuals(range 1- 3200)NNee = 560 (Hill); = 560 (Hill); NNee /N=0.434 in /N=0.434 in A. A. mexicanummexicanumLARGE!LARGE!NNee /N in /N in Papaver dubiumPapaver dubium = 0.07= 0.07 (Mackay, 1980;Crawford, 1994)[In humans range Ne /N 0.34 to 0.95, mean 0.60 ]

IndirectIndirect methods to estimate methods to estimate NmNm in in A.A.mexicanummexicanum::

FFstst: measure of genetic differentiation =: measure of genetic differentiation = (H (Htt - H - Hss)/ H)/ HttFFstst from 0 if there is no differences in allelic frequencies to 1 ifthe populations are fixed at different alleles.

S. Wright found that Fst = 1/ 4 Ne m +1,

and Crow and Aoki (1984) developed a more general modelincluding mutation:

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

A. A. mexicanummexicanum, indirect analyses:, indirect analyses:LocusLocus FFstst N Nee mm m m((NNee =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 0.005Lap-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 Las poblaciones poblaciones se se comportan como una grancomportan como una granpoblacipoblación panmícticaón panmíctica......

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Otra manera indirecta de estimar el Ne:

Infinite alleles model (Kimura)H= 4Neµ/(4Neµ+1)

if µµ (mutation rate) for allozymes is 10-6

in Zea spp. Doebly et al. (1984) reported a rangeH= 0.182-0.233Ne range 55,623-75,945

in 655 plant species, Hamrick et al. (1992) founda H=0.154Ne = 45,508

higher than direct and ecological methods.Vecindades genéticas, entre Ne 1 a 4000!

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

The differences among estimates:

a) may be due to the fact that the infinite alleles modelmay not describe their evolutionary process(Barbadilla et al. , 1996)

a) estan midiendo cosas diferentes: vecindades el Nelocal y ecológico, mientras que los alelos infinitos sonel resultado de la evolución histórica de toda unaespecie, formada por n poblaciones ligadas por flujogénico...

Vecindades el Ne local y ecológico.Alelos infinitos son el resultado de la evolución histórica

de toda una especie, formada por n poblacionesligadas por flujo génico...

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ESPECIE

poblaciones

Efecto de fundador y cuellos debotella.Una población puede descender de pocosindividuos por

a) la población fue iniciada por pocos: efecto defundador

b) porque solo sobrevivieron unos pocos encuellos de botella

Esto genera cambios al azar en las frecuenciaalelicas, disminuyendo la heterocigosis y dejandopoco alelos!

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Efecto de fundador y cuellos de botella.Veamos los efectos de esta reducción en eltamaño en la var. genética:

donde Ht and Ht+1 son las heterocigosis en la población original y en el grupo fundador

despejando

Efecto de fundador y cuellos de botella.

si hay n generaciones con una N pequeña, como cuando hay cuellos de botella

donde la Hs es la heterocigosis antes del cuello de botella.si Ho = 0.7, Ht = 0.6, y t= 5, Ne = 16.4.ENTRE MAYOR o más larga sea LA REDUCCION EN LAH, MENOR Ne

BORREGO CIMARRON:

Bighorn sheep (Ovis canadensis) havegreatly declined in numbers and distributionin the past century because of disease,hunting,and other factors.

As a result, there have a number ofintroductions throughout western NorthAmerica in an effort to establish more viablepopulations.

BORREGO CIMARRON: isla Tiburón

For example, in early 1975, 20 desertbighorn sheep (4 males and 16 females)were captured in mainland Sonora,Mexico, and translocated to nearbyTiburon Island in the Sea of Cortez.The translocated population grew quickly, andby 1999, an estimated 650 sheep were on theisland, all descended from this small foundergroup.

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The number of alleles n and heterozygosity H (95%confidence intervals in parentheses) in theintroduced Tiburon Island population of bighornsheep and that for three populations of the samesubspecies for ten microsatellite loci and a MHClocus

MENOS VAR. GENÉTICA

Si comparamos la heterocigosis de los micros deArizona vs. la Isla Tiburón como Ht and Ht+t,respectivmente, nos da, Ne= 1.9, MUY BAJO!!!

= 0.57/(2(0.57-0.42))

The four males were ages 1 , I, 2, and 7 years,suggesting that the older ram may have madea greater initial contribution than the othermales.It is assumed that older ram was the onlybreeding male in the first cohortof males, then the effective size of the foundergeneration could have been,using expression 6.6a,Ne= 4(16)(1)/(16 + 1)= 3.8.

Ne= 4(16)(1)/(16 + 1)= 3.8.Although this does not explain all of theloss of heterozygosity, it may explainmuch of it.In addition, in the subsequent earlygenerations, there may have been moreloss of variation due to small numbers,particularly because of few effectivebreeding rams.

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EJEMPLO Elefante marino (ELEPHANT SEAL):

The northern elephant seal was thought to have beenhunted to extinction at the end of the 19th centurywhen the "last" 153 animals were killed by collectors in1884.Fortunately, some animals apparently survived on aremote beach on Isla Guadalupe, Mexico, and theirdescendants were rediscovered in 1892.

However, the ancestors of the present-day populationof approximately 200,000 stretching up to centralCalifornia may have numbered as few as 20 (Bonnelland Selander, I974).

EJEMPLO ELEPHANT SEAL:

Hoelzel et aI. (2002) found two mtDNAhaplotypes with estimated frequencies of 0.27and 0.73 in the contemporary northern elephantseal population, giving a haplotype diversityestimate of H= 0.40.

They also determined mtDNA haplotypes inpre-bottleneck museum and midden samplesand estimated the mtDNA diversity in thesesamples as H= 0.80.

To determine what bottleneck could result in this loss of variation,assume that the loss of mtDNA diversity can be described by the expression

where the original mtDNA diversity is Ho = 0.80, the observed contemporarydiversity is H1 = 0.40, and Nef.i is the effective female populationsize in generation .

Using the approach of Hedrick(1995b) and examiningvarious sizes and duration of thebottleneck, but allowing thepopulation to grow to known censuslevels in 1922 and 1960, a one-generation bottleneck of censussize 15 is consistent with thisobserved loss of mtDNA variation.

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PERDIDA DE ALELOS:En loci muy variables, se pierde másrápido los alelos que laheterocigosis... mejor medida decambio

Locus de microsatélites con 20 alelos enun cuello de botella de 5 individuos(2N=10) pierde cuando menos la mitad de losalelos, pero sólo se espera que pierda el10% de su heterocigosis

Selección en poblaciones finitas:Deriva sola: When there is no differentialselection at a locus, an allele may become fixed orlost as a result of genetic drift.The probability of fixation is equal to the initialfrequency of the allele so that when the allele is rarethe probability of fixation is quite low.

Selección sola: In contrast, in an infinitepopulation, which by definition has no geneticdrift, a favorable allele always increases andasymptotically approaches fixation.

Selección + Deriva:In a finite population, however,a favorable allele may not always befixed because it may be lost because ofthe chance effects of genetic drift.

The probability of fixation of a favorable allelein a finite population, u(p), is a function of theinitial frequency of the allele, the amount ofselection favoring the allele, and the finitepopulation size.

Selección 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

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azar (deriva)

p de fijación muchos más alta que al azar si hay sel. dir.

The probability of fixationis calculated for three levels ofdominance and different initialallele frequencies for Ns= 2.0.A Ns value of 2.0 can result, forexample, 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, with u(p) increasingquickly as p increases from alow value. The difference in u(p)for different levels of dominanceis also substantial at low allelefrequencies.If p=0.1, the probabilities of fixationfor h = 0.0, 0.5, and 1.0 are 0.223,0.335, and 0.461 respectively. Ingeneral, an increasing level ofdominance significantly increasesu(p) unless u(p) is already near 1.0.

When Ns<< l that is, s << 1/N, the change inallele frequency is primarily determined bygenetic drift:SI HAY POCA SELECIÓN Y/ONe ES PEQUEÑO, LA EVOLUCION ES PORAZAR

On the other hand if Ns>> 1, then the changein allele frequency is primarily determinedby selection and u(p) >> p.SI LA SEL. ES INTENSA O Ne GRANDE,SOLO OPERA LA SELECCIÓN...

SELECCION

DERIVA

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

Selección 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 followthe 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

N= 20, s =0.1, h= 0.5, and the initial frequency of A1 in all the populations was 0.5. Theprobability of fixation for these parameter values, from expression 6.23b, is 0.78. Thedistribution of the frequency of the favorable allele reflects the effect of directional selection evenafter five generations. After 20 generations, 20.6% of the populations are fixed for the favorableallele and only 3.1% for the unfavorable allele.

N=20 N=20s=0.1

con sels =0.1

sin sel.Ne=20

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In an infinite population, a detrimental allelealways decreases in frequency and asymptoticallyapproaches loss.

In contrast, in a finite population, anunfavorable allele, particularly if its detrimentaleffects are not large, may increase in frequency bychance and may potentially become fixed.

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

Finite population:an unfavorable allele, particularly if itsdetrimental effects are not large, mayincrease in frequency by chance and maypotentially become fixed.

Ohta (1973) discussed thisphenomenon in terms of molecularevolution and described it as thenearly neutral model.

Ohta (1973) nearly neutral model.

She suggested that the relative impactof genetic drift and selection varies withthe population size sothat detrimental variants may beeffectively neutral in a small population,whereas in large populations, theybecome selected against.

POBLACIONES CHICAS,ACUMULAN VAR. GEN.DELETEREA!!!

ESPECIES AMENAZADAS:Important concerns for many endangered speciesare that the existing population generally is small,the species has gone through a bottleneck in recentgenerations or the captive or extant populationdescends from only a few founder individuals.AII of these factors may cause extensive genetic driftwith a potential loss of genetic variation for futureadaptive selective change. In addition, smalleffective population sizes may result in chanceincreases in the frequency of detrimental allelesbecause the absolute value of Ns is so low.

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ESPECIES AMENAZADAS:

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

The captive California condor population, initiatedfrom 14 founders, had a high frequency of a lethalform of dwarfism (Ralls et al.,2000).Although a management strategy of selectingagainst carriers may reduce the frequency of thesedetrimental alleles, it may also result ina reduction in variation at other genes.!!!!

Deriva Génica:

¡¡¡FIN!!!