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'''Evolutionary graph theory''' is an area of research lying at the intersection of [[graph theory]], [[probability theory]], and [[mathematical biology]]. Evolutionary graph theory is an approach to studying how [[topology]] affects [[evolution]] of a [[population]]. That the underlying topology can substantially affect the results of the evolutionary process is seen most clearly in a paper by [[Erez Lieberman]], Christoph Hauert and [[Martin Nowak]].<ref>{{cite doi|10.1038/nature03204}}</ref>
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In evolutionary graph theory, individuals occupy [[vertex (graph theory)|vertices]] of a weighted [[directed graph]] and the weight w<sub>i j</sub> of an [[Edge (graph theory)|edge]] from vertex ''i'' to vertex ''j'' denotes the probability of ''i'' replacing ''j''. The weight corresponds to the biological notion of [[Fitness (biology)|fitness]] where fitter types propagate more readily.
One property studied on graphs with two types of individuals is the ''fixation probability'', which is defined as the probability that a single, randomly placed mutant of type A will replace a population of type B. According to the ''isothermal theorem'', a graph has the same fixation probability as the corresponding [[Moran process]] if and only if it is isothermal, thus the sum of all weights that lead into a vertex is the same for all vertices. This probability is
: <math> \begin{align}
\rho_M = \frac{1-r^{-1}} { 1-r^{-N} }
\end{align}</math>
where ''r'' is the relative fitness of the invading type. Thus, a [[complete graph]] with equal weights describes a Moran process.
 
Graphs can be classified into amplifiers of selection and suppressors of selection. If the fixation probability of a single advantageous mutation <math> \rho_G </math> is higher than the fixation probability of the corresponding [[Moran process]] <math> \rho_M </math> then the graph is an amplifier, otherwise a suppressor of selection. One example of the suppressor of selection is a linear process where only vertex ''i-1'' can replace vertex ''i'' (but not the other way around). In this case the fixation probability is <math> \rho_G = 1/N </math> (where ''N'' is the number of vertices) since this is the probability that the mutation arises in the first vertex which will eventually replace all the other ones. Since <math> \rho_G < \rho_M </math> for all ''r'' greater than 1, this graph is by definition a suppressor of selection.
 
Evolutionary graph theory may also be studied in a dual formulation, as a [[coalescing random walk]].
 
Also [[Evolutionary game theory|evolutionary games]] can be studied on graphs where again an edge between ''i'' and ''j'' means that these two individuals will play a game against each other.
 
Closely related stochastic processes include the [[voter model]], which was introduced by Clifford and Sudbury (1973) and independently by Holley and Liggett (1975), and which has been studied extensively.
 
==Bibliography==
* {{cite jstor|2959329}}
* {{cite book |author=Liggett, Thomas M. |title=Stochastic interacting systems: contact, voter, and exclusion processes |publisher=Springer |location=Berlin |year=1999 |pages= |isbn=3-540-65995-1 |oclc= |doi= |accessdate=}}
* {{cite doi|10.1093/biomet/60.3.581}}
* {{cite book |author=Martin A. Nowak |title=Evolutionary dynamics: exploring the equations of life |publisher=Belknap Press of Harvard University Press |location=Cambridge |year=2006 |pages= |isbn=0-674-02338-2 |oclc= |doi= |accessdate=}}
 
==External links==
A virtual laboratory for studying evolution on graphs:[http://www.univie.ac.at/virtuallabs/Moran/]
 
==References==
{{reflist}}
 
[[Category:Evolution]]
[[Category:Graph theory]]
[[Category:Evolutionary dynamics]]

Latest revision as of 17:43, 26 December 2014

Based on property sale singapore analyst, the Urban Redevelopement Authority has revealed the brand new draft Master Plan 2013 for property launch which supplies detailed information on the development of Singapore when it comes to the next few years. The master plan has been extremely anticipated as it is the first plan to be released after a severe of property cooling measures by the Republic.

Go to the City Redevelopment Authority website to examine the newest printed figures on ‘Rentals of Private Residential Properties'. Find a comparable unit in a close-by project that's comparatively new. Test the vary of month-to-month rent to see whether the numbers given are too optimistic. The blame has been placed on a number of elements, most notably the World Cup (why??) and perhaps the Authorities Land Sales Programme, which implies that we've got a wider (and perhaps better) selection so there is no hurry to commit to purchasing a non-public home so quickly. Sunnyvale Residences is a freehold apartment alongside Lorong Ok Telok Kurau, situated at the prime of District 15. Sunnyvale Residences comprising 30 unit Learn Extra Govt Director (Strategic Planning & Communications)

The Panorama, positioned alongside Ang Mo Kio Ave 2, will be the next upcoming new launch with strolling distance to approaching new MRT Station, Mayflower, and also surrounded with Schooling Institution with just a stone throw away Latest improvement by Hong Leong Holdings Pte Ltd location at Flora Drive. 8-storey condominium growth comprising 1BR, 2BR, 2+Examine, 3BR, 4BR, 4BR Twin Key & 3BR Roof Terrace Apartments. Units are nicely-designed & practical layout totally-equipped with free oven, fridge, washer/ dryer (Microwave oven for selected units) Respond to the rental listings of latest tasks in the same district to check the recognition of properties for rent there. Feb Sales Plunge – Has the Storm Arrived? (at Propwise.sg) District 18, 999 year LH house

The knowledge contained herein is subject to change and cannot kind a part of a suggestion or contract. Whereas every cheap care has been taken in providing this data, bestnewlaunches.com or its agent cannot be held liable for any inaccuracies. Challenge data, costs, opinions, images, artist impressions, plans, measurements and colour representations on this website are presented as an indicative guide solely and subject to vary at any time.

Whereas every effort has been made to make sure that all info displayed herein are correct and full, the data are indicative rather than definitive. Thus its accuracy, whether or not specific or implicit, will not be guaranteed and to the fullest extent permitted by applicable legal guidelines. The Writer/Developer/Huttons Actual Estate Group doesn't settle for responsibility for any errors, inaccuracies, omissions or for any loss which could outcome directly or indirectly from reliance on the content herein. The Writer also reserves the suitable to correct or update the content at any time without prior notification. Users are advised to contact the advertiser for any clarifications or newest updates.

Try our Featured Launches in this website, or just find the very the highest left undertaking from the homepage of www.singaporepropertylisting.com ! That's the newest new launch undertaking, and usually VIP Preview can be held inside 3 weeks from the time the venture surface on the highest left homepage. District 19, Freehold condominium District 15, Freehold Cluster landed house Before one can fault the company big for opening a restaurant in a historical landmark, it should first be famous that this mansion - identified by locals as the Denton House - was abandoned and on the snapping point earlier than McDonald's bought the property within the 1980s Continuereading "Trilive at Kovan Preview Launch Soon" Simply TOP City Resort Condominium Are We There But? (at Propwise.sg)

For leisure, East Coast Park is well accessible by way of park connectors.City Vista can also be a mere 2 MRT stops away from Changi Airport , and 1 MRT cease away from Changi Enterprise Park and Singapore Expo. According a submit on The Real Singapore (TRS) by a reader referred to as Esther, the contest, organised by SingTel and SCORCHING FM 91.three, came about at The Cathay over the weekend of 8 and 9 February. With a client-oriented staff of recent apartment and property launch specialists, in depth trade data, strong real property analytic system and a willpower to reliably present the very best service within the enterprise, at AtasLaunch.com we now have created a company that puts you, the consumer - first. The Tembusu @ Kovan (Freehold) New Apartment in 2013 July

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