Duba tsatso na Yawan jama'a

{{databox}}
Matsakaici''N'' girman '''Yawan jama'a''' (Ne) shine girman yawan jama-a da aka tsara zai fuskanci irin wannan ƙarancin kwayar halitta ko karuwa a cikin inbreeding kamar yadda yake a cikin ainihin yawan jama'ar. Yawan jama'a masu kyau sun dogara ne akan tunanin da ba daidai ba amma ya dace ciki har da haɗuwa ta bazuwar, haihuwar lokaci guda na kowane sabon ƙarni, yawan jama'a na yau da kullun. Ga mafi yawa''N'' masu sha'awa da mafi yawa''N'' yawan jama'a na ainihi, Ne ya fi ƙarancin yawan jama'ar N na ainihin yawan jama'awa.<ref>{{Cite web |title=Effective population size |url=http://www.blackwellpublishing.com/ridley/a-z/Effective_population_size.asp |access-date=4 March 2018 |website=[[Blackwell Publishing]]}}</ref> Jama'a iri ɗaya na iya samun ƙididdigar ƙididdigatattun ƙididdigal don halaye daban-daban na sha'awa, gami da ƙwayoyin halitta da ƙwayoyi.

Yawa yawan jama'a da aka fi auna su dangane da lokacin coalescence. A cikin yawan jama'a masu ƙididdigar ƙididdiga ba tare da wani zaɓi a kowane wuri ba, tsammanin lokacin haɗuwa a cikin tsararraki daidai yake da sau biyu na yawan jama'ar. Ana auna girman yawan jama'a a matsayin Bambancin kwayoyin halitta na cikin jinsuna da aka raba da sau hudu na yawan maye gurbin 



μ 


{\displaystyle \mu } 

, saboda a cikin irin wannan yawan jama'a, heterozygosity daidai yake da 



4 N μ 


{\displaystyle 4N\mu } 

. A cikin yawan jama'a tare da zaɓaɓɓu a wurare da yawa da kuma haɗin haɗin haɗin kai mai yawa, ƙididdigar.

An gabatar da manufar tasirin yawan jama'a a fagen ƙwayoyin halittar jama'a cikin 1931 ta hanyar [[Masanin kwayar halitta]] na Amurka [[Sewall Wright]] . <ref>{{Cite journal |last=Wright S |year=1931 |title=Evolution in Mendelian populations |url=http://www.esp.org/foundations/genetics/classical/holdings/w/sw-31.pdf |journal=[[Genetics (journal)|Genetics]] |volume=16 |issue=2 |pages=97–159 |doi=10.1093/genetics/16.2.97 |pmc=1201091 |pmid=17246615}}</ref><ref>{{Cite journal |last=Wright S |year=1938 |title=Size of population and breeding structure in relation to evolution |journal=[[Science (journal)|Science]] |volume=87 |issue=2263 |pages=430–431 |doi=10.1126/science.87.2263.425-a}}</ref>

== Bayani: Nau'o'in yawan jama'a ==
Dangane da yawan sha'awa, ana iya bayyana yawan jama'a ta hanyoyi da yawa. Ronald Fisher da Sewall Wright da farko sun bayyana shi a matsayin "yawan mutanen da ke kiwo a cikin Yawan jama'a wanda zai nuna adadin warwatsewar allele a ƙarƙashin bazuwar kwayar halitta ko adadin inbreeding kamar yawan mutanen da ke ƙarƙashin la'akari". Gabaɗaya, ana iya bayyana girman yawan jama'a mai tasiri a matsayin yawan mutane a cikin yawan jama'ar da ke da darajar kowane yawan kwayar halitta da aka ba da shi wanda ya yi daidai da darajar wannan adadin a cikin yawan masu sha'awa. Yawan kwayoyin halitta guda biyu da Wright ya gano sune karuwar ƙarni ɗaya a cikin bambancin a tsakanin yawan jama'a masu yawa (yawan yawan jama'ar da suka dace) da kuma canjin ƙarni ɗaya cikin ƙimar ƙwayoyin cuta (ƙididdigar ƙwayoyin). Wadannan biyu suna da alaƙa sosai, kuma an samo su ne daga F-ƙididdiga, amma ba iri ɗaya ba ne.<ref>{{Cite journal |last=James F. Crow |author-link=James F. Crow |year=2010 |title=Wright and Fisher on Inbreeding and Random Drift |journal=Genetics |volume=184 |issue=3 |pages=609–611 |doi=10.1534/genetics.109.110023 |pmc=2845331 |pmid=20332416}}</ref>

A yau, yawa yawan mutanen da ke da tasiri ana kimanta su ta hanyar kwarewa dangane da zama ko lokacin coalescence, wanda aka kiyasta a matsayin Bambancin kwayoyin halitta na cikin jinsin da aka raba ta hanyar maye gurbin, wanda ke samar da girman yawan jama'a mai tasiri.<ref name="Lynch 2003">{{Cite journal |last=Lynch, M. |last2=Conery, J.S. |year=2003 |title=The origins of genome complexity |journal=Science |volume=302 |issue=5649 |pages=1401–1404 |bibcode=2003Sci...302.1401L |citeseerx=10.1.1.135.974 |doi=10.1126/science.1089370 |pmid=14631042 |s2cid=11246091}}</ref> Wani muhimmin girman yawan jama'a mai tasiri shine zaɓin yawan jama'ar 1/scritical, inda scritical shine mahimmancin ƙimar zaɓe wanda zabin ya zama <sub>mai mahimmancimai mahimmanci</sub> halitta.<ref name="Neher 2011">{{Cite journal |last=R.A. Neher |last2=B.I. Shraiman |year=2011 |title=Genetic Draft and Quasi-Neutrality in Large Facultatively Sexual Populations |journal=Genetics |volume=188 |issue=4 |pages=975–996 |arxiv=1108.1635 |doi=10.1534/genetics.111.128876 |pmc=3176096 |pmid=21625002}}</ref>

=== Ma'auni na kwarewar ===
A cikin yawan jama'ar ''Drosophila'' na ƙidayar jama'a 16, an auna bambancin tasirin yawan jama'a daidai da 11.5. <ref>{{Cite journal |last=Buri |first=P |year=1956 |title=Gene frequency in small populations of mutant Drosophila |journal=Evolution |volume=10 |issue=4 |pages=367–402 |doi=10.2307/2406998 |jstor=2406998}}</ref> An sami wannan ma'auni ta hanyar nazarin canje-canje a cikin mitar tsaka-tsaki daga ƙarni ɗaya zuwa wani a cikin yawan jama'a sama da 100.

Do''N'' girma''N'' yawan jama'a mai tasiri, binciken wallafe-wallafen akan nau'ikan dabbobi da shuke-shuke 102 sun samar da nau'ikan Ne / N 192 . An yi amfani da hanyoyin kimantawa daban-daban guda bakwai a cikin binciken da aka bincika. Dangane da haka, rabon ya kasance daga 10<sup>''-6''</sup> ga oysters na Pacific zuwa 0.994 ga mutane, tare da matsakaicin 0.34 a fadin jinsunan da aka bincika. Dangane da waɗannan bayanan daga baya sun kiyasta ƙarin ƙididdigar ƙididdiga, lissafin canji a cikin yawan jama'a, bambancin girman iyali da rashin daidaito tsakanin jinsi. Wadannan rabo matsakaici zuwa 0.10-0.11 kawai.<ref name="Frankham 1995">{{Cite journal |last=R. Frankham |year=1995 |title=Effective population size/adult population size ratios in wildlife: a review |journal=Genetics Research |volume=66 |issue=2 |pages=95–107 |doi=10.1017/S0016672300034455 |doi-access=free}}</ref>

Binciken asalin masu farauta da masu tarawa (Eskimo) sun ƙayyade tasirin yawan jama'a don haploid (mitochondrial DNA, Y chromosomal DNA), da diploid (autosomal DNA) daban: an kiyasta rabo na tasiri ga girman yawan jama'ar a matsayin 0.6-0.7 don autosomal da X-chromosomal DNA, 0.7-0.9 don mitochondrial ADN da 0.5 don Y-chromosomaal DNA.<ref name="Matsumura 2008">{{Cite journal |last=S. Matsumura |last2=P. Forster |year=2008 |title=Generation time and effective population size in Polar Eskimos. |journal=Proc Biol Sci |volume=275 |issue=1642 |pages=1501–1508 |doi=10.1098/rspb.2007.1724 |pmc=2602656 |pmid=18364314}}</ref>

== Bambancin girman tasiri ==
A cikin tsarin yawan jama'a na Wright-Fisher, bambancin yanayi mitar allele 




p ′ 



{\<math>p'</math>https://wikimedia.org/api/rest_v1/media/math/render/svg/40e623e3163571a220ed60ecb31aa78c24104b85<nowiki/>'} 

, an ba da mitar allele 



p 


{\displaystyle p} 

a cikin ƙarni da ya gabata, shine

: <math>\operatorname{var}(p' \mid p)= {p(1-p) \over 2N}.</math>

Bari mu bar 






ya kasance mai suna 



(Abin da ya fi dacewa da shi)  

p ′ 

Sanya p)  


{\displaystyle {\widehat {\operatorname {var} }} (p'\mid p) } 

nuna iri ɗaya, yawanci mafi girma, bambancin a cikin ainihin yawan mutanen da ake la'akari da su. Bambancin tasirin yawan jama'a 




N 

da kuma 


(v)  




{\displaystyle N_{e}^{ (v) }} 

an bayyana shi azaman girman yawan jama'a masu kyau tare da bambancin iri ɗaya. Ana samun wannan ta hanyar maye gurbin 






ya kasance mai suna 



(Abin da ya fi dacewa da shi)  

p ′ 

Sanya p)  


{\<math>N</math>\widehat {\operatorname {var} }} (p'\mid p) } 

don 



An yi amfani da shi a matsayin 

p ′ 

Sanya p)  


{\displaystyle \operatorname {var} (p'\mid p) } 

da kuma warwarewa 



N 


{\displaystyle N} 

wanda ke ba da

: <math>N_e^{(v)} = {p(1-p) \over 2 \widehat{\operatorname{var}}(p)}.</math>

=== Misalan ka'idoji ===
A cikin misalai masu zuwa, ɗaya ko fiye daga cikin zato na yawan jama'a masu tsananin gaske suna shakatawa, yayin da wasu zato ke riƙewa. Bambancin tasirin yawan jama'a na tsarin yawan jama'ar da ya fi kwanciyar hankali ana lissafa shi dangane da tsarin tsananin.

==== Bambance-bambance a cikin yawan jama'a ====
Yawan jama'a ya bambanta a tsawon lokaci. A ce akwai ''t'' t da ba su da alaƙa, to ana ba da girman yawan jama'a ta hanyar ma'auni na girman yawan jamaʼa: <ref>{{Cite journal |last=Karlin |first=Samuel |date=1968-09-01 |title=Rates of Approach to Homozygosity for Finite Stochastic Models with Variable Population Size |journal=The American Naturalist |volume=102 |issue=927 |pages=443–455 |doi=10.1086/282557 |issn=0003-0147 |s2cid=83824294}}</ref>

: <math>{1 \over N_e} = {1 \over t} \sum_{i=1}^t {1 \over N_i}</math>

Misali, a ce yawa''N'' jama'a ya kasance N = 10, 100, 50, 80, 20, 500 na ''t'' shida (t = 6). Sa'an nan kuma girman yawan jama'a mai tasiri shine [[Harmoniya ma'ana|ma'anar jituwa]] na waɗannan, yana ba da:

Lura wannan ƙasa da matsakaicin lissafi na yawan jama'a, wanda a cikin wannan misali shine 126.7. Matsakaicin jituwa yana mamayewa ta hanyar mafi ƙanƙanta da yawan jama'a ke wucewa.

==== Rashin hankali ====
Idan yawan jama'a ne dioecious, watau babu wani man fetur to

: <math>N_e = N + \begin{matrix} \frac{1}{2} \end{matrix}</math>

ko kuma gabaɗaya,

: <math>N_e = N + \begin{matrix} \frac{D}{2} \end{matrix}</math>

in''D'' D ke wakiltar dioeciousness kuma yana iya ɗaukar darajar 0 (don ba dioecious ba) ko 1 don dioecious.

Lokaci''N'' da ''N'' ya fi girma, ''N'' kusan daidai yake da N, don haka wannan yawanci ba shi da mahimmanci kuma sau da yawa an yi watsi da shi:

: <math>N_e = N + \begin{matrix} \frac{1}{2} \approx N \end{matrix}</math>

==== Bambanci a cikin nasarar haihuwa ====
Idan yawan jama'a ya kasance daidai, kowane mutum dole ne ya ba da gudummawa a matsakaita ga gametes biyu ga ƙarni na gaba. Yawan jama'a mai ''k'' yana zaton cewa wannan ya biyo bayan rarrabawar Poisson don haka bambancin yawan gametes da aka ba da gudummawa, k daidai yake da matsakaicin adadin da aka ba, watau 2:

: <math>\operatorname{var}(k) = \bar{k} = 2.</math>

Koyaya, a cikin yawan jama'a bambancin sau da yawa ya fi wannan girma. Yawancin mutane bazai da 'ya'ya, kuma ƙarni na gaba ya samo asali ne kawai daga ƙananan mutane, don haka

: <math>\operatorname{var}(k) > 2.</math>

Yawan jama'a mai tasiri ya fi karami, kuma an ba shi ta:

: <math>N_e^{(v)} = {4 N - 2D \over 2 + \operatorname{var}(k)}</math>

Lura cewa ida''N'' bamba''V''">''N'' ''<sub>k</sub>'' bai kai 2, ''N'' ya fi N girma. A cikin matsanancin yanayin yawan jama'a da ba su da bambanci a cikin girman iyali, a cikin yawan dakin gwaje-gwaje wanda ake sarrafa yawan 'ya'ya ta wucin gadi, Vk = 0 da Ne = 2N.

Lokacin da rabo na jima'i na yawan jama'a ya bambanta daga rabo na Fisherian 1: 1, ana ba da girman yawan jama'ar ta hanyar:

: <math>N_e^{(v)} = N_e^{(F)} = {4 N_m N_f \over N_m + N_f}</math>

I''''m''">''N'''' Nm shine yawan maza kuma N<sub>''f''</sub> yawan mata. Misali, tare da maza 80 da mata 20 (cikakken yawan jama'a na 100):

== Girman inganci na shayarwa ==
A madadi''N'' haka, ana iya bayyana girman yawan jama'a mai tasiri ta hanyar lura da yadda matsakaicin ƙwayoyin cuta ya canza daga ƙarni ɗaya zuwa na gaba, sannan kuma ya bayyana Ne a matsayin girman yawan mutanen da aka tsara waɗanda ke da irin wannan canji a cikin matsakaicin cuta kamar yadda yawan mutanen da ake la'akari da su. Gabatarwar ta biyo bayan Kempthorne (1957). 

Ga yawan mutanen da aka tsara, ƙididdigar ƙwayoyin suna bin ma'aunin maimaitawa

: <math>F_t = \frac{1}{N}\left(\frac{1+F_{t-2}}{2}\right)+\left(1-\frac{1}{N}\right)F_{t-1}.</math>

Yin am''F'' da Panmictic Index (1 − F) maimakon inbreeding coefficient, muna samun kimanin daidaitattun maimaitawa&nbsp;&nbsp;

: <math>1-F_t = P_t = P_0\left(1-\frac{1}{2N}\right)^t. </math>

Bambanci a kowace tsara shine

: <math>\frac{P_{t+1}}{P_t} = 1-\frac{1}{2N}. </math>

Za'a iya samun girman ingancin shuka ta hanyar warwarewa

: <math>\frac{P_{t+1}}{P_t} = 1-\frac{1}{2N_e^{(F)}}. </math>

: <math>N_e^{(F)} = \frac{1}{2\left(1-\frac{P_{t+1}}{P_t}\right)} </math>

kodayake masu bincike ba sa amfani da wannan daidaitattun kai tsaye.

=== Misali na ka'ida: tsararraki masu haɗuwa da yawan mutanen da aka tsara shekaru ===
Lokacin da kwayoyin halitta suka rayu fiye da lokacin haifuwa guda, yawan jama'a masu tasiri dole ne su yi la'akari da teburin rayuwa ga jinsin.

==== Haploid ====
Ka yi la'akari da yawan jama'a tare da tsarin shekaru masu rarrabe. Misali na iya zama kwayar halitta wacce za ta iya tsira da lokutan haifuwa da yawa. Bugu da ƙari, bayyana halaye masu zuwa na tsarin shekaru:

: v    i     =     {\displaystyle v_{i}=}    Darajar haihuwar Fisher don shekaru      i     {\<math>i</math>    ,

: l    i     =     {\displaystyle \ell _{i}=}    Da damar da mutum zai tsira har zuwa tsufa      i     {\<math>i</math>    , da kuma

: N    0     =     {\displaystyle N_{0}=}    Adadin jarirai a kowane lokacin haifuwa.

Ana lissafin lokacin ƙarni kamar yadda

: T =    Sanya    i = 0     ∞      l    i      v    i     =     {\displaystyle T=\sum _{i=0}^{\infty }\ell _{i}v_{i}=}    matsakaicin shekarun haifuwa

Sa'an nan kuma, yawan mutanen da ke da tasiri shine <ref>{{Cite journal |last=Felsenstein J |year=1971 |title=Inbreeding and variance effective numbers in populations with overlapping generations |journal=[[Genetics (journal)|Genetics]] |volume=68 |issue=4 |pages=581–597 |doi=10.1093/genetics/68.4.581 |pmc=1212678 |pmid=5166069}}</ref>

: <math>N_e^{(F)} = \frac{N_0T}{1 + \sum_i\ell_{i+1}^2v_{i+1}^2(\frac{1}{\ell_{i+1}}-\frac{1}{\ell_i})}.</math>

==== Diploid ====
Hakazalika, ana iya lissafin adadin ingantattun mutane don yawan jama'a masu tsayi tare da tsarin shekaru masu rarrabe. Johnson ne ya fara bayar da wannan, <ref>{{Cite journal |last=Johnson DL |year=1977 |title=Inbreeding in populations with overlapping generations |journal=[[Genetics (journal)|Genetics]] |volume=87 |issue=3 |pages=581–591 |doi=10.1093/genetics/87.3.581 |pmc=1213763 |pmid=17248780}}</ref> amma bayanin ya fi kama da Emigh da Pollak. <ref>{{Cite journal |vauthors=Emigh TH, Pollak E |year=1979 |title=Fixation probabilities and effective population numbers in diploid populations with overlapping generations |journal=Theoretical Population Biology |volume=15 |issue=1 |pages=86–107 |bibcode=1979TPBio..15...86E |doi=10.1016/0040-5809(79)90028-5}}</ref>

Ka yi la'akari da <sup>''m''</sup>'au''0">''N'''' iri ɗaya na teburin rayuwa kamar yadda aka ba shi don yanayin haploid, amma rarrabe tsakanin namiji da mace, kamar N<sub>0</sub><sup>''''ƒ''''</sup> da N0m don yawan jarirai mata da maza, bi da bi (lura ƙaramin shari'ar ƒ ga mata, idan aka kwatanta da ma''F'' girma F don inbreeding).

: <math>
\begin{align}
\frac{1}{N_e^{(F)}} = \frac{1}{4T}\left\{\frac{1}{N_0^f}+\frac{1}{N_0^m} + \sum_i\left(\ell_{i+1}^f\right)^2\left(v_{i+1}^f\right)^2\left(\frac{1}{\ell_{i+1}^f}-\frac{1}{\ell_i^f}\right)\right. \,\,\,\,\,\,\,\, & \\
 \left. {} + \sum_i\left(\ell_{i+1}^m\right)^2\left(v_{i+1}^m\right)^2\left(\frac{1}{\ell_{i+1}^m}-\frac{1}{\ell_i^m}\right) \right\}. &
\end{align}
</math>

== Girman dake da tasiri ==
Dangane da ka'idar tsaka-tsaki na juyin halitta, wani tsaka-tsakin allele ya kasance a cikin yawan jama'a don Ne tsararraki, inda Ne shine girman yawan jama'ar da ya dace. Yawan jama'a na diploid da aka tsara zai sami Bambancin nucleotide guda biyu daidai da 4 



μ 


{\displaystyle \mu } 

Babu, inda 



μ 


{\displaystyle \mu } 

shine yawan maye gurbin. Saboda haka ana iya kimanta yawan jama'a ta hanyar rarraba bambancin nucleotide ta hanyar maye gurbin.<ref name="Lynch 2003">{{Cite journal |last=Lynch, M. |last2=Conery, J.S. |year=2003 |title=The origins of genome complexity |journal=Science |volume=302 |issue=5649 |pages=1401–1404 |bibcode=2003Sci...302.1401L |citeseerx=10.1.1.135.974 |doi=10.1126/science.1089370 |pmid=14631042 |s2cid=11246091}}</ref>

Girman tasirin coalescent na iya samun ƙarancin dangantaka da yawan mutanen da ke cikin jiki a cikin yawan jama'a.<ref>
{{Cite journal |last=Gillespie, JH |year=2001 |title=Is the population size of a species relevant to its evolution? |journal=Evolution |volume=55 |issue=11 |pages=2161–2169 |doi=10.1111/j.0014-3820.2001.tb00732.x |pmid=11794777 |doi-access=free}}
</ref> Auna girman yawan jama'a masu tasiri sun bambanta tsakanin kwayoyin halitta a cikin wannan yawan jama'ar, kasancewa ƙasa a cikin yankunan kwayar halitta na ƙananan haɗuwa da kuma sama a cikin yankuna na kwayar halitta mai girma.<ref>{{Cite journal |last=Hahn, Matthew W. |year=2008 |title=Toward a selection theory of molecular evolution |journal=Evolution |volume=62 |issue=2 |pages=255–265 |doi=10.1111/j.1558-5646.2007.00308.x |pmid=18302709 |doi-access=free}}</ref><ref>{{Cite journal |last=Masel, Joanna |author-link=Joanna Masel |year=2012 |title=Rethinking Hardy–Weinberg and genetic drift in undergraduate biology |journal=BioEssays |volume=34 |issue=8 |pages=701–10 |doi=10.1002/bies.201100178 |pmid=22576789 |s2cid=28513167}}</ref> Lokaci na cin abinci daidai yake da N a cikin ka'idar tsaka-tsaki, amma ga alamomi a ƙarƙashin zaɓi, lokutan zama daidai ne da rajista (N). Jirgin motsa jiki na kwayoyin halitta na iya haifar da maye gurbi mai tsaka-tsaki don samun lokutan zama daidai da log (N): wannan na iya bayyana alaƙar da ke tsakanin girman yawan jama'a da ƙimar sake haɗuwa ta gida.  {{Ana bukatan hujja|date=April 2021}}<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">&#x5B;''<nowiki><span title="This claim needs references to reliable sources. (April 2021)">citation needed</span></nowiki>''&#x5D;</sup>

== Zaɓin girman tasiri ==
A cikin samfurin Wright-Fisher, ƙaddamar da allele, wanda ya fara a matsakaiciyar mitar, an ƙaddara shi da yawa ta hanyar zaɓe idan ma'aunin zaɓe s ≫ 1/N, kuma an ƙaddara ta hanyar tsaka-tsaki na kwayoyin halitta idan s ≪ 1/N. A cikin al'ummomi na ainihi, ƙimar yankewa na s na iya dogara da ƙimar sake haɗuwa ta gida.<ref name="Neher 2011">{{Cite journal |last=R.A. Neher |last2=B.I. Shraiman |year=2011 |title=Genetic Draft and Quasi-Neutrality in Large Facultatively Sexual Populations |journal=Genetics |volume=188 |issue=4 |pages=975–996 |arxiv=1108.1635 |doi=10.1534/genetics.111.128876 |pmc=3176096 |pmid=21625002}}</ref><ref>{{Cite journal |last=Daniel B. Weissman |last2=Nicholas H. Barton |year=2012 |title=Limits to the Rate of Adaptive Substitution in Sexual Populations |journal=PLOS Genetics |volume=8 |issue=6 |pages=e1002740 |doi=10.1371/journal.pgen.1002740 |pmc=3369949 |pmid=22685419 |doi-access=free}}</ref> Wannan iyaka ga zabin a cikin ainihin yawan jama'a za a iya kama shi a cikin wasan kwaikwayo na Wright-Fisher ta hanyar zaɓin da ya dace na Ne. Yawan jama'a tare da zaɓin zaɓin tasiri masu tasiri ana hasashen su canza tsarin gine-gine daban-daban.<ref>{{Cite journal |last=Rajon, E. |last2=Masel, J. |author-link2=Joanna Masel |year=2011 |title=Evolution of molecular error rates and the consequences for evolvability |journal=PNAS |volume=108 |issue=3 |pages=1082–1087 |bibcode=2011PNAS..108.1082R |doi=10.1073/pnas.1012918108 |pmc=3024668 |pmid=21199946 |doi-access=free}}</ref>

== Dubi kuma ==

* Ƙananan yawan jama'a
* Ƙananan yawan jama'a

== Manazarta ==
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== Haɗin waje ==

* {{Cite web |last=Holsinger |first=Kent |date=2008-08-26 |title=Effective Population Size |url=http://darwin.eeb.uconn.edu/eeb348/lecture-notes/drift/node7.html |url-status=dead |archive-url=https://web.archive.org/web/20050524233613/http://darwin.eeb.uconn.edu/eeb348/lecture-notes/drift/node7.html |archive-date=2005-05-24 |publisher=University of Connecticut}}
* {{Cite web |last=Whitlock |first=Michael |year=2008 |title=The Effective Population Size |url=http://www.zoology.ubc.ca/~whitlock/bio434/LectureNotes/05.EffectiveSize/EffectiveSize.html |url-status=dead |archive-url=https://web.archive.org/web/20090723072549/http://www.zoology.ubc.ca/~whitlock/bio434/LectureNotes/05.EffectiveSize/EffectiveSize.html |archive-date=2009-07-23 |access-date=2005-02-25 |website=Biology 434: Population Genetics |publisher=The University of British Columbia}}
* https://web.archive.org/web/20050524144622/http://www.kursus.kvl.dk/shares/vetgen/_Popgen/genetics/3/6.htm &#x2D; a kan Københavns Universitet.
{{qg}}{{Population genetics}}{{modelling ecosystems|expanded=none}}
[[Rukuni:Al'umma]]
[[Rukuni:Yawan al'umma]]
[[Rukuni:Shafuka masu fassarorin da ba'a duba ba]]