Article,
Maximum-likelihood estimation of evolutionary trees from continuous characters
Am J Hum Genet, 25 (5): 471-492 (September 1973)
Abstract
When we try to reconstruct the evolutionary tree of a group of organisms by
examining a series of characters, we are not applying strict logical deduction but
are making a guess in the presence of uncertainty. It is therefore appropriate to
think of the problem in terms of statistical inference. This approach was first sug-
gested by Edwards and Cavalli-Sforza 1-4. The data collected by systematists
and by students of molecular evolution are mostly for discrete characters, such as
the presence or absence of a morphological structure or the amino acid sequence
of a protein. But much data are also collected for quantitative characters, such as
gene frequencies and measurements on morphological traits. In this paper, I will
confine my attention to quantitative characters. This is the case originally con-
sidered by Edwards and Cavalli-Sforza. They proposed that the estimation of
evolutionary trees be carried out by the method of maximum likelihood. However,
they found troublesome singularities in what they believed to be the likelihood
surface 3, 4. They were forced to fall back on ad hoc approaches which did not
have an explicit statistical justification (their "method of minimum evolution" and
ädditive tree model"; see also 5). Malyutov et al. 6 have described another
ad hoc approach.
In this paper, I will use the basic model proposed by Edwards and Cavalli-Sforza.
I will show that if we are less ambitious than they were, and redefine the problem
so as not to attempt to estimate as many quantities, we can construct a likelihood
function which does not have any such singularities. It is then possible to construct
computer programs which obtain maximum-likelihood estimates of the evolutionary
tree when the data are in the form of quantitative measurements.
