| dbo:description
|
- procés estocàstic utilitzat en biologia per descriure poblacions finites (ca)
- proceso estocástico usado en biología (es)
- stochastic process used in biology to describe finite populations (en)
|
| dbo:wikiPageExternalLink
| |
| dbo:wikiPageWikiLink
| |
| dbp:content
|
- For the expected value the calculation runs as follows
:
For the variance the calculation runs as follows, using the variance of a single step
:
---- (en)
- The mean time spent in state j when starting in state i which is given by
:
Here denotes the Kroenecker delta. This recursive equation can be solved using a new variable so that and thus and rewritten
:
The variable is used and the equation becomes
:
Knowing that and
:
we can calculate :
:
Therefore
:
with . Now , the total time until fixation starting from state i, can be calculated
:
---- (en)
- Also in this case, fixation probabilities can be computed, but the transition probabilities are not symmetric. The notation and is used. The fixation probability can be defined recursively and a new variable is introduced.
:
Now two properties from the definition of the variable can be used to find a closed form solution for the fixation probabilities:
:
Combining and :
:
which implies:
:
This in turn gives us:
:
---- (en)
- For the expected value the calculation runs as follows. Writing
:
Writing and , and applying the law of total expectation, Applying the argument repeatedly gives or
For the variance the calculation runs as follows. Writing we have
:
For all , and are identically distributed, so their variances are equal. Writing as before and , and applying the law of total variance,
:
If , we obtain
:
Rewriting this equation as
:
yields
:
as desired.
---- (en)
|
| dbp:contentstyle
|
- border:1px #C4C3D0 solid; (en)
|
| dbp:header
|
- For a mathematical derivation of the equation above, click on "show" to reveal (en)
|
| dbp:titlestyle
|
- background-color:#f2dfce; color:black; (en)
- background-color: #f2dfce; color:black; (en)
|
| dbp:wikiPageUsesTemplate
| |
| dct:subject
| |
| gold:hypernym
| |
| rdfs:label
|
- Moran process (en)
- Proceso de Moran (es)
- Processo de Moran (pt)
|
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:wikiPageRedirects
of | |
| is dbo:wikiPageWikiLink
of | |
| is foaf:primaryTopic
of | |
