Re: Reproductive Selection

leland.mcin...@xxxxxxxxx wrote:

What I really want here is a function of a continuous variable, since
it makes things easier. Critters are discrete, but are spaced through
time so we can use a function of time as a continuous approximation.
Approximating discrete systems with continuous ones is common enough
-- think of fluid mechanics, which approximates the discrete particles
of a fluid with a continuous idealised fluid.

The way to think of this is as a one dimensional curve twisting
through n-space, parameterised by time. We can think of the critters
as discrete points all along the continuous curve. Exactly how the
discrete critters are spaced along the curve is matter of how time
was parameterised (ie. if each unit time step is a year, then we might
have only a few critters over each unit of time, but if we are taking
each unit time step as 100 years then we will have many critters
packed into each unit of time). Since how time parameterises the curve
is arbitrary for us, we can essentially assume our discrete critter
points on the curve are as densely packed as we like (since if they
aren't, we can just reparameterise the curve to pack them more
densely).

Not to make too much of a peripheral point, but why use critters at
all? Why not show continuity of reproductive type with respect to time
directly? (It's fine as is.)

<snip>

Okay, good to know I have that much sorted. Now, my understanding is
that you are effectively claiming that reproductive selection, if it
is an active force, is going to prevent species evolving truly novel
or different reproductive types. That is, given a starting point (t=0
on our curve) there are going to be some points in our n-dimensional
reproductive type space that are "unreachable": we can't both satisfy
the reproductive selection constraint, and also be able to have our
curve pass through/get to these unreachable points. Is that a fair
representation of what you are claiming?

Yes, I think so.

The primitive complexity of the differences between species makes
things difficult. The continuity argument you made states what I
consider the official version quite well. I'm surprised I've never
seen it before. If the transition from one reproductive type to
another was that simple, the official version would be on a much
firmer theoretical footing. However, it is my opinion that the
primitive complexity separating the species (which prevents us from
writing transformation operations to convert between them on paper)
makes for a barrier that cannot be crossed though incremental changes
on one, or even most, of the constituent variables. Almost any change
to one or merely most of the constituent variables of the primitively
complex distinction between species (as if to transform one to the
other) is at best neutral to the fitness of the individual.

Sure, but neutral, or sufficiently small negative effect, will be
"good enough" if there are other factors that make the change
advantageous in other ways (long life, more offspring per breeding,
lower predation, more breeding cycles per lifetime, etc.); that is,
all we need is for the total offspring (on average) of carriers of the
mutation to be greater than those who don't carry it, despite the
(potentially only very slightly) lower number of possible mates
available to carriers. As long as that happens then, over time, the
percentage of the population that are carriers will increase, and soon
they will be more able to find more compatible mates than non-
carriers.

Naturally, yet what if reproductive type is dependent on emergent
characteristics composed of multiple independently nonadvantageous
traits? Perhaps it could be argued that each such trait made its own
contribution to fitness during some remote epoch, but that could prove
a difficult case to make for configurations requiring very large sets
of interoperating components in order to confer any advantage at all.
However, let's proceed and see how things develop in your
multidimensional vector space.

Well these things don't have to come together all at once. They can
come together bit by bit with each step completed and "fixed" before
the next step proceeeds, and each step along the way having its own
extra contributions to fitness that see it selected for. Add up enough
such increments and big changes can potentially be made.

That's a workable enough model, to be sure. How applicable it is to
real world conditions is, as always, another matter.

Still, I'm
keen to hear if I've actually managed to get a handle on what you are
arguing in my multidimensional space model. That will go a long way to
clearing up any lingering misunderstandings.

You've managed quite well in depicting the overall effect. (Whether
we're going to run into trouble with underlying dynamics remains to be
seen.)

.

Relevant Pages

  • Re: Reproductive Selection
    ... Critters are discrete, but are spaced through ... Approximating discrete systems with continuous ones is common enough ... as discrete points all along the continuous curve. ... Why not show continuity of reproductive type with respect to time ...
    (talk.origins)
  • Re: Reproductive Selection
    ... Approximating discrete systems with continuous ones is common enough ... as discrete points all along the continuous curve. ... Why not show continuity of reproductive type with respect to time ... most immediate is to simply claim that reproductive-type space is not ...
    (talk.origins)
  • Re: Ruler and Compass in Mathematics
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    ... Drawing a curve or line is useful. ... its discrete". ... I have argued that there is nothing in mathematics or out of mathematics that can quantify a continuity, ...
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