Preferential entailment - Revision history

en>David Eppstein: source, ce

2014-10-28T19:55:03Z

source, ce

← Older revision		Revision as of 21:55, 28 October 2014
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	~~{{underlinked\|date=December 2012}}~~		Andrew Berryhill is what his wife enjoys to call him and he totally digs that name. It's not a common factor but what I like doing is to climb but I don't have the love psychic ([http://203.250.78.160/zbxe/?document_srl=1792908 http://203.250.78.160/zbxe/?document_srl=1792908]) time recently. For many years she's been living in Kentucky but her husband desires them to move. Invoicing is what I do for a residing but I've usually needed my personal company.<br><br>Here is my web-site :: online are psychics real ([http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ alles-herunterladen.de]) psychic readings ([http://srncomm.com/blog/2014/08/25/relieve-that-stress-find-a-new-hobby/ visit the following website page])

	~~'''Malecot~~'s ~~coancestry coefficient~~'~~'', '''<math>f</math>''', refers to an indirect [[measure]] of genetic [[similarity]] of two individuals which was initially devised by~~ the [~~[France\| French]] mathematician [[Gustave Malécot]]~~.

	~~<math>f</math> is defined as the probability that any two [[alleles]], [[sample (statistics)\|sampled]] at random (one from each individual), are identical copies of an ancestral allele~~. ~~In species with well-known lineages (such as domesticated crops), <math>f<~~/~~math> can be calculated by examining detailed pedigree records. Modernly, <math>f<~~/~~math> can be estimated using [[genetic marker]] data.~~

	~~== Evolution of inbreeding coefficient in finite size populations~~ ==
	~~In a finite size [[population]], after some generations, all individuals will have a [[common ancestor]]~~ : ~~<math>f \rightarrow 1 <~~/~~math>~~.
	~~Consider a non-sexual population of fixed size <math>N<~~/~~math>, and call <math>f_i<~~/~~math> the inbreeding coefficient of generation <math>i</math>~~. ~~Here, <math>f</math> means the probability that two individuals picked at random will have a common ancestor~~. ~~At each generation, each individual produces~~ a ~~large number <math>k \gg 1</math> of descendants, from the pool of which <math>N</math> individual will be chosen at random to form the new generation~~.

	~~At generation~~ <~~math~~>n<~~/math~~>~~, the probability that two individuals have a common ancestor~~ is ~~"they have a common parent" OR "they descend from two distinct individuals which have a common ancestor"~~ :

	:~~<math>f_n = \frac{k~~-~~1}{kN} + \frac{k(N~~-~~1)}{kN}f_{n~~-~~1}</math>~~
	~~:<math> \approx \frac{1}{N}+ (1~~-~~\frac{1}{N})f_{n~~-~~1}. </math>~~

	~~This is a [[recurrence relation]] easily solved. Considering~~ the ~~worst case where at generation zero, no two individuals have a common ancestor,~~
	~~:<math>f_0=0<~~/~~math>, we get~~

	~~:<math>f_n = 1~~ - ~~(1- \frac{1}{N}~~)~~^n.</math>~~

	~~The scale of the fixation time~~ (~~average number of generation it takes to homogenize the population) is therefore~~

	:~~<math> \bar{n}= -1~~/~~\log(1-1~~/~~N) \approx N~~. </~~math>~~

	~~This computation trivially extends to the inbreeding coefficients of alleles in~~ a ~~sexual population by changing <math>N<~~/~~math> to <math>2N</math> (~~the ~~number of [[gametes]~~]).

	~~== References ==~~
	*Malécot G. ''Les mathématiques de l'hérédité.'' Paris: Masson & Cie, 1948.

	~~[[Category:Classical genetics]]~~

en>Addbot: Bot: Removing Orphan Tag (Nolonger an Orphan) (Report Errors)

2013-01-09T16:46:44Z

Bot: Removing Orphan Tag (Nolonger an Orphan) (Report Errors)

← Older revision		Revision as of 18:46, 9 January 2013
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	~~The writer~~'s ~~title~~ is ~~Christy Brookins~~. ~~To climb is~~ some ~~thing I truly appreciate doing~~. ~~For years he's been living in Alaska~~ and ~~he doesn't strategy on altering it~~. ~~Invoicing is my profession~~.<br><br>~~Here~~ is ~~my site free tarot readings~~ ([~~http~~://1.~~234.36.240~~/~~fxac~~/~~m001_2~~/~~7330 Read Significantly more~~])		{{underlinked\|date=December 2012}}

			'''Malecot's coancestry coefficient''', '''<math>f</math>''', refers to an indirect [[measure]] of genetic [[similarity]] of two individuals which was initially devised by the [[France\| French]] mathematician [[Gustave Malécot]].

			<math>f</math> is defined as the probability that any two [[alleles]], [[sample (statistics)\|sampled]] at random (one from each individual), are identical copies of an ancestral allele. In species with well-known lineages (such as domesticated crops), <math>f</math> can be calculated by examining detailed pedigree records. Modernly, <math>f</math> can be estimated using [[genetic marker]] data.

			== Evolution of inbreeding coefficient in finite size populations ==
			In a finite size [[population]], after some generations, all individuals will have a [[common ancestor]] : <math>f \rightarrow 1 </math>.
			Consider a non-sexual population of fixed size <math>N</math>, and call <math>f_i</math> the inbreeding coefficient of generation <math>i</math>. Here, <math>f</math> means the probability that two individuals picked at random will have a common ancestor. At each generation, each individual produces a large number <math>k \gg 1</math> of descendants, from the pool of which <math>N</math> individual will be chosen at random to form the new generation.

			At generation <math>n</math>, the probability that two individuals have a common ancestor is "they have a common parent" OR "they descend from two distinct individuals which have a common ancestor" :

			:<math>f_n = \frac{k-1}{kN} + \frac{k(N-1)}{kN}f_{n-1}</math>
			:<math> \approx \frac{1}{N}+ (1-\frac{1}{N})f_{n-1}. </math>

			This is a [[recurrence relation]] easily solved. Considering the worst case where at generation zero, no two individuals have a common ancestor,
			:<math>f_0=0</math>, we get

			:<math>f_n = 1 - (1- \frac{1}{N})^n.</math>

			The scale of the fixation time (average number of generation it takes to homogenize the population) is therefore

			:<math> \bar{n}= -1/\log(1-1/N) \approx N. </math>

			This computation trivially extends to the inbreeding coefficients of alleles in a sexual population by changing <math>N</math> to <math>2N</math> (the number of [[gametes]]).

			== References ==
			*Malécot G. ''Les mathématiques de l'hérédité.'' Paris: Masson & Cie, 1948.

			[[Category:Classical genetics]]

en>Michael Hardy at 03:44, 2 November 2010

2010-11-02T03:44:42Z

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