[Popgenlunch] Robin Waples talk

Joe Felsenstein joe at gs.washington.edu
Mon Apr 5 12:23:25 PDT 2010

Folks --

We have no PopGenLunch seminar this week, but here's an interesting
population genetics seminar (in more or less the same time slot!)
by the ever-interesting Robin Waples of NOAA. Do forward to anyone
interested in population genetics. It is a quantitative seminar of
the School of Aquatic and Fisheries Sciences. Alas, I will be away that day,
but I hope some of you will attend.

Joe Felsenstein joe at gs.washington.edu
Department of Genome Sciences and Department of Biology,
University of Washington, Box 355065, Seattle, WA 98195-5065 USA

Join us this Friday!

Effective population size: two new twists on an old idea

Robin Waples, Northwest Fisheries Science Center
FISH 203 @ 12:30

The concept of effective population size (Ne) is based on an elegantly simple idea which, however, rapidly becomes very complex in most real world situations. Here I discuss two recent projects that reveal new twists in our understanding of effective size.

I. Inbreeding effective size and parentage analysis without parents
In a typical parentage analysis, multilocus genotypes are scored in both
parents and progeny, and these data are used to ‘assign’ progeny to parents.
This type of study has produced many novel insights, including the ability to
directly calculate the number of genes contributed to the next generation by
each parent (ki). From this information, and knowing the total number of
parents (N), one can use standard formulas to calculate Ne. But what if your
sample of parents is incomplete or missing entirely? In theory, it should be
possible to reconstruct parental genotypes based entirely on a sample of
progeny. This is not quite feasible yet but might be in the near future if
large enough numbers of SNPs become available. If the two parents for each
individual in a sample could be identified, it would be possible to construct
a vector of parental ki values, but this would provide information only about
parents that actually contributed offspring to your sample. What about the
‘null’ parents that produced no offspring in your sample, and how would they
affect an estimate of Ne? The surprising answer is that null parents have no
effect at all. I show the following:
1) It is possible to rewrite the standard formula for inbreeding effective
size so that it is only a function of ∑(ki) and ∑(ki2). That is, it is not
necessary to know N to calculate inbreeding Ne. This same relationship does
not hold for variance Ne.
2) It is easy to prove #1 assuming a complete sample of all progeny.
However, even if only a sample of progeny is taken, simulated data show that
the estimate of Ne using the simple formula that ignores null parents is
unbiased. This means that parentage analysis without parents can be used to
provide an unbiased, single-sample estimate of inbreeding Ne, provided
parental contributions to the offspring sample can be resolved.
3) It is not necessary to actually reconstruct parental genotypes; from a
matrix of pairwise relationships (as can be estimated by some current software
programs) it is possible to construct the vector of ki values and estimate
4) Accuracy and precision of the new method based on parentage analysis
without parents compares favorably with single-sample estimators of Ne
currently in use.

II. A hybrid Felsenstein-Hill method for calculating Ne in species with
overlapping generations
Like most population genetics theory, the concept of Ne was developed under
a discrete-generation model. During the Nixon administration, two papers
(Felsenstein 1971; Hill 1972) showed how to calculate Ne for age-structured
species. The two approaches produce the same answer under certain conditions
and have contrasting advantages and disadvantages. I describe a hybrid
approach that combines the best features of both. Like Felsenstein (1971),
the new method is based on age-specific survival and fertility rates and
therefore can be directly applied to any species for which life-table data are
available. However, like Hill (1972), the hybrid method is more general as it
relaxes Felsenstein’s assumption of Poisson variance in reproductive success
each time period. The basic principle underlying the new method is that age
structure stratifies a population into winners and losers in the game of life:
individuals that live longer have more opportunities to reproduce and
therefore have a higher mean lifetime reproductive success than do individuals
that die at a younger age. This creates different classes of individuals
within the population based on age at death. The new method has the following
* It uses demographic information of the type found in a life table;
* It can accommodate two sexes with unequal sex ratio and/or different
vital rates;
* It can accommodate overdispersed variance in reproductive success and
different ratios of variance to mean reproductive success in the two
* It can calculate effective size in species that change sex during their
* It can calculate Ne and Ne/N based on various ways of defining N;
* It can allow one to explore the relationship between the effective
number of breeders per year (Nb) and effective size per generation (Ne)
in age-structured species;
* It (will soon be) implemented in freely available software with a
flexible user interface.

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