Reply to Mike Zwick

Xuhua Xia xia at
Fri Apr 29 01:44:41 EST 1994

In <mezwick-280494120216 at> mezwick at (Mike Zwick) writes:

>In article <2poo23$9ji at>, xia at (Xuhua
>Xia) wrote:
>> This represents a  misconception of optimality models, i.e.
>> optimality models assume optimality without constraints. In fact, the
>> appropriate use of optimality models always depends on one's ability
>> to identify the constraints. What does Mike mean by "optimum phenotype"?
>> There is no optimum phenotype without specifying constraints. If you
>> have to define such an optimum phenotype, then it is one that can 
>> increase the fitness of its underlying genotype at an infinitely large
>> rate. Neither natural selection nor optimality models requires such
>> an optimum phenotype to work.

>I was not refering to constraints (linkage, developmental, genetic
>variation etc.), which can be included in a model(albet w/difficulty and
>often are not).  Rather I was refering to the underlying assumption of
>optimality models that the "optimum phenotype" can be reached prior to the
>optimum phenotype itself changing.  Clearly, in temporally and spatially
>varying selection scenaros, there may be optimum that are predicted
>(correctly) by the model, but the population never reaches the optimum
>because the environment is changing more rapidly (i.e. due to rapid change
>of parameter values).  It is not clear what use an optimality model may be
>in these situations.

You WERE and ARE refering to constraints. When there are no
constraints imposed by a fluctuating environment, we would have a
model of selection in a constant environment. Fisher's fundamental
theorem was derived on the basis of constant selection, and from
the theorem we expect the population to evolve towards increasing
fitness. When evolution is CONSTRAINED by temporally varying
selection, the optimum genotype is one with the largest geometric
mean fitness and the population will evolve towards the fixation of
this genotype. This is a result first obtained by Dempster (1953)
and elaborated by John Gillespie in 1970s.

I am not surprised that people from UC Davis, with John Gillespie
teaching there, should be very enthusiastic about selection in a
fluctuating environment. If Mike wants to make a contribution to
our understanding of selection in a fluctuating environment, it
would be a noble endeavour and should be encouraged. However, I
really do not enjoy answering questions that are irrelevant to the
central theme of my posting.

I suggest that Mike do two things:

First, if you want to pursue your question further in relation to
the phage replication, then think of some temporally varying
selection that favours "producing head and tail proteins first and
replicating phage DNA last" at one time, but favours "replicating
phage DNA first and producing head and tail proteins last" at
another time.

Secondly, if you want to press the issue of selection in a
fluctuating environment, it would be very helpful if you could
persuade Gillespie to post his lectures here. Or you can summarize
your understanding of his lectures and post it here.

Xuhua Xia
University of Manitoba
xia at

P.S. John Gillespie made the greatest contribution to our
understanding of selection in a fluctuating (temporally and
spatially varying) environment. He believes that most, perhaps all,
of those molecular data used to support the neutral theory of evolution 
by Kimura could be produced by, and in fact are expected from, selection 
in a fluctuating environment. For a single population, the neutral
models and the models of selection in a fluctuating environment
could have identical expectations, i.e., the two are not
I do not understand most of Gillespie's works. I went to University
of Washington partially because I wished to gain some understanding
of his works from Joe Felsenstein, but, seeing Joe very busy with
his family and research, I ended up without asking him to tutor me.

>mike zwick
>mezwick at
>Department of Ecology and Evolution
>Center for Population Biology
Xuhua Xia
University of Manitoba
xia at

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