Fisher's reproductive value
Encyclopedia
Fisher's reproductive value was defined by R. A. Fisher
in his 1930 book The Genetical Theory of Natural Selection
as the expected
reproduction of an individual from their current age onward, given
that they have survived to their current age. It is used in describing populations with age structure.
with survival and reproductive parameters given by
and 
, where
and
Depending on whether the breeding is discrete or continuous, Fisher's reproductive value is calculated as
where
the net reproductive rate of the population.
The average age of a reproducing adult is the generation time and is
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
in his 1930 book The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection
The Genetical Theory of Natural Selection is a book by R.A. Fisher first published in 1930 by Clarendon. It is one of the most important books of the modern evolutionary synthesis and is commonly cited in biology books.-Editions:...
as the expected
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
reproduction of an individual from their current age onward, given
Conditional probability
In probability theory, the "conditional probability of A given B" is the probability of A if B is known to occur. It is commonly notated P, and sometimes P_B. P can be visualised as the probability of event A when the sample space is restricted to event B...
that they have survived to their current age. It is used in describing populations with age structure.
Definition
Consider a species with a life history tableLife table
In actuarial science, a life table is a table which shows, for each age, what the probability is that a person of that age will die before his or her next birthday...
with survival and reproductive parameters given by
and , where-
= probability of surviving from age 0 to age 
and
-
= average number of offspring produced by an individual of age 
Depending on whether the breeding is discrete or continuous, Fisher's reproductive value is calculated as
where
the net reproductive rate of the population.
The average age of a reproducing adult is the generation time and is
