Ontogeny and Phylogeny II

Xuhua Xia xia at cc.umanitoba.ca
Mon Apr 11 18:12:11 EST 1994


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"He who sees things from their beginnings will have the most advantageous
view of them." ------Aristotle
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                    Ontogeny and Phylogeny II:
     The Length of the Ontogenic Chain and its Evolutionary Implications

In a previous posting I have sketched ontogeny in the following figure:

Egg with
Maternal --------Group 1----Group 2...Group n...Group N---death
Gene Product      genes      genes      genes    genes

I will refer to this chain of gene expression as an ontogenic chain, with
Group 1-terminal at the beginning and Group N-terminal at the end.

I have also argued that mutations occurring at the the Group N-terminal
should disrupt normal development less than mutations occurring at the
Group 1-terminal. This is because mutations at the Group N-terminal 
affect few genes that are to express in the future, whereas mutations at
the Group 1-termianl will affect many genes that are to be expressed in the
future.

Now by a little jump of faith, we can express the magnitude of deleterious
effect (s) of a mutation as a function of number of genes whose expression
pattern will be altered by the mutation:

           s = f(N - n)                      (1)

where n is the location of the mutated gene on the ontogenic chain.

I do not know how s would change with (N-n), so Equation (1) only states
that s is a function of (N-n). But from our biological common sense, we
know that s should be an increasing function of (N-n). When a mutation
occurs at Group N so that n = N, apparently there will be little effect 
because the individual is dying already. But s will increase as n
becomes small, i.e., when mutations occur at the Group 1-terminal. This
is the result obtained by population geneticists many years ago.

Let us further make an oversimplification by assuming that the relationship
is linear so that:

              s = a * (N - n)                    (2)

where a is the slope (a constant).

(I can assure you that the relationship is not linear, for good biological
reasons. But for the time being, let us not be overburdened by unnecessary
complications.)

ONTOGENIC RULE 1: The deleterious effect of a mutation increases with N-n.

Now I will use Equation (2) in an unusually way so that some
genuine insights can be derived.

Let's have one more look at the ontogenic chain,

Egg with
Maternal --------Group 1----Group 2...Group n...Group N---death
Gene Product      genes      genes      genes    genes

and ask how the Creator would modified the chain to produce more
complicated organisms. You can even picture yourself as the creator and
see what you would come up with.

The most straightforward way of increasing complexity would be to keep 
adding genes at the Group N-terminal. This is in fact what Ernst
Haeckel envisioned. So you are in good company if you come up with the
same.

But this would have to be wrong. For simplicity, let's start with
an organism with only 3 groups of genes expressed sequentially, with Group
3 gene being the death gene (N = 3). Let's further assume that each group
has just a single gene. For this organism, a mutation has no effect when
occuring at the Group 3 gene, a deleterious effect of "a" when occurring at
Group 2 genes, and a deleterious effect of "2*a" when occurring at Group 1
genes, according to Equation (2). The average deleterious effect of a
mutation is then

                           0 + a + 2*a
                          ------------- = a
                                3

Now if the Creator add, say 7 more group of genes (again 1 gene per group),
at the 3 end so that now we have N = 10. The deleterious effect of a
mutation on each of this 10 genes is tabulated below:

==============================
Group     Deleterious effect
1         9 * a
2         8 * a
3         7 * a
4         6 * a
5         5 * a
6         4 * a
7         3 * a
8         2 * a
9         1 * a
10        0 * a
==============================

Now the average deleterious effect of a mutation is 

      a + 2*a + 3*a + ... + 9*a
     --------------------------- = 4.5*a
                 10

You see that with increasing length of the ontogenic chain, the deleterious
effect of a mutation increases rapidly. Haeckel's terminal addition is
therefore an unlikely mechanism for increasing complexity of organic
structure.

But what about adding side chains to the ontogenic chain?

(to be continued)

Xuhua Xia



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