JAHAYES@MIAMIU.BITNET (Josh Hayes) (10/15/90)
In a related question, I am planning to embark on a study that the net might be able to discourage or encourage. Here's a brief description: The marine gastropod Coralliophila abbreviata feeds on stony corals in the Western Atlantic. It's a sequential hermaphrodite (protandrous), and produces planktonic larvae after brooding them briefly in the mantle cavity. It's a simple matter to develop a model to predict the adaptive size/age at which an individual should switch from male to female (I can supply references if anyone's interested -- heck, even a manuscript rejected from American Naturalist!), within the constraints of local size/age structure and known fecundity/size relationships. My snails don't do it right; at four out of five sites they're way off the predicted sex ratio. I hope to get some rough idea of gene flow in the critters by using allozyme analysis a la Nei's stats (pace Hillis, 1984). The question is, is this a reasonable way to look for gene flow? Obviously, there are possible results that would vitiate the study, but is this at least a reasonable approach? Planktonic larvae are a real bear to work with, for the simple reason that they're planktonic. Once produced, they pretty much vanish. Then when they recruit to some substrate, there's no way of knowing whether they were PRODUCED there (and thus ought to exihibit locally adaptive phenotypes) or elsewhere (and so might not be adaptive for these local conditions). We're having trouble getting resolution on the gels so far, but I would appreciate any comments or questions about the study. Thanks! Josh Hayes, Zoology Department, Miami University, Oxford OH 45056 voice: 513-529-1679 fax: 513-529-6900 jahayes@miamiu.bitnet, or jahayes@miamiu.acs.muohio.edu I'm back, I'm back! I've been to ancient Greece -- I have proof, look at this grape!
blot@URZ.UNIBAS.CH (Michel Blot) (10/16/90)
As you mentioned, planktonic larvae are a real bear to work with, especially with allozyme methods, not only because the small size do not allow individual analysis with a satisfactory resolution but also because we donot have any idea of the fitness of genotypes at the time of recruitment. There is a meanto measure gene flow with allozyme data with a statistical model by Slatkin (1985) based on the rare allozyme distribution among demes. However, one condition is that the genotypes are equally fitted, which has been shown not to be the case in a number of studies with marine mollusks (see Koehn & Hil lbish 1987 for a review). There is an alternative with the use of another tool Reatriction Fragment Length Polymorphism of mitochondrial DNA which evolves fas t enough to be a non-adaptive tagger of populations. Slatkin(1989) made a model to analyse gene flow with the distribution of mtDNA patterns. The method works fine in marine mollusks (Skibinski 1985, Reeb and Avise 1990, Blot et al. 1990) and is on the way to be used for estimating precisely gene flow. Slatkin 1985 Evolutio 39:53-65 Koehn & Hillbish 1987 Amer.Scient. 75:134-141 Slatkin & Madison 1989 Genetics 123:603-613 Skibinski 1985 J.Exp.Mar.Biol.Ecol.92:251-258 Reeb & Avise 1990 Genetics 124:397-406 Blot et al 1990 J.Exp.Mar.Biol.Ecol.141:-- Yours Sincerely, Michel Blot Dept Microbiology, Biozentrum CH-Basel
joe@GENETICS.WASHINGTON.EDU (Joe Felsenstein) (10/17/90)
Josh Hayes proposes to use allozymes to look for gene flow in his planktonic critters. The main difficulty is that if the amount of gene flow is above a critical minimum the allozymes will be essentially randomized. This means he will have difficulty telling medium from high amounts of gene flow. (He should look into Slatkin's rare allele methods, but the problem remains with that as well). At the same time, the genes for the sex ratio he is looking at could remain differentiated geographically, as they are (putatively) under selection. The allozymes are neutral or nearly so, and would be randomized much more easily than selected loci. This makes it hard to conclude from "medium-to-high" gene flow as judged from allozymes whether the gene flow level is high enough to explain why sex ratios appear to be wrong for local conditions. ----- Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle, WA 98195 Internet/ARPANet: joe@genetics.washington.edu (IP No. 128.208.128.1) Bitnet/EARN: felsenst@uwalocke UUCP: ... uw-beaver!evolution.genetics!joe
HOLSINGE%UCONNVM@PUCC.PRINCETON.EDU ("Kent E. Holsinger") (10/18/90)
Joe Felsenstein pointed out one difficulty with the estimation of gene flow from allozyme data. There is another one that he did not mention. It applies equally to Slatkin's private allele method and to Fst methods. In both cases the assumption is made that similarities between populations reflect an equilibrium between gene flow and drift. The problem is that the distribution of genetic variation among populations is often influenced by historical factors, e.g. the re-colonization of north temperate latitudes after the last glacial maximum. If the pattern of genetic differentiation is primarily, or largely, a result of the history of population establishment, allele frequencies will contain no information about the extent of between population gene flow. I don't recall whether Slatkin's 1989 method based on the coalescent is subject to the same limitations. Perhaps Joe will. Kent E. Holsinger
joe@GENETICS.WASHINGTON.EDU (Joe Felsenstein) (10/19/90)
I agree with Kent Holsinger's comment about the possible confounding of gene flow with historical effects. Maddison and Slatkin's measure of gene flow using coalescents should be subject to much the same dilemma, that we cannot easily tell history from geography, even though some information seems present to do it. In 1982 in Journal of Theoretical Biology I agonized about this for the case of polymporhic markers. But little has been done to try to solve the problem and really find out to what extent we can tell one from the other. ----- Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle, WA 98195 Internet/ARPANet: joe@genetics.washington.edu (IP No. 128.208.128.1) Bitnet/EARN: felsenst@uwalocke UUCP: ... uw-beaver!evolution.genetics!joe
rogers@ARSUN.ANTHRO.UTAH.EDU (Alan R. Rogers) (10/19/90)
Kent Holsinger and Joe Felsenstein have commented on the difficulty of
estimating gene flow from genetic data when equilibrium assumptions are not
satisfied. Here is a suggestion that may work if you are willing to buy
the assumptions. Let x denote a vector containing the frequencies of some
allele among newborns (or larvae, or whatever) in a variety of places, and
let y denote the corresponding vector for adults. Even when the system is
far from equilibrium, we can write
y = M x + e
where M is an unknown migration matrix, and e a vector of random displacements
due to genetic drift. This formulation implies that population
regulation occurs after migration, i.e. that there is initially a large
number of juveniles who then migrate and whose number is then reduced to Ni
in group i. If population regulation is mainly prior to migration, a
different formulation is needed. Anyway, writing Ci for the covariance
matrix of vector i, and using "'" to denote matrix transpose, we have
Cy = M Cx M' + Ce (1)
where Ce is approximately diag[p(1-p)(1-Fst)/2Ni], p is the mean juvenile
allele frequency, and Fst is Var(juvenile allele freq)/p(1 - p). If you know
the effective population sizes, Ni, then Cy, Cx, and Ce can all be estimated.
What we don't know, but would like to know, is the contents of M.
Unfortunately, as it stands, the system of equations that (1) represents has
more unknowns than equations. If there are K groups, then there are K(K +
1)/2 equations (since the covariance matrices are symmetric) in K(K - 1)
unknowns (since the rows of M must sum to 1), so there are K(K - 1)/2 more
unknowns than equations. You have to assume something about M to make any
progress. But in some cases, perhaps that will be possible. If you assume,
for example, that migration is symmetric, the number migrating from i to j
being the same as the number migrating from j to i, then (1) is no longer
underdetermined, and could presumably be solved. Even better, if some
variant of a gravity model makes sense, or if you can build in information
about ocean currents, you may end up with a few extra degrees of freedom.
Thus, I see no reason why migration could not be estimated from genetic data
even where no equilibrium assumption is warranted.
Alan Rogers
INTERNET: rogers@anthro.utah.edu
USMAIL : Dept. of Anthropology, Univ. of Utah, S.L.C., UT 84112
PHONE : (801) 581-5529