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C00002 00002	inhomo[w83,jmc]		Inhomgeneous environments stablize populating fluctuation
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inhomo[w83,jmc]		Inhomgeneous environments stablize populating fluctuation

	The examples I have seen of the Lotka-Volterra predator-prey
theory and related theories of population oscillation don't involve an
inhomogeneous environment.

	1. If two species compete for the same niche, there is a
high probability that one will exterminate the other.  However,
if within the common niche where the two species compete, there
is a small range where each is clearly dominant, then the
fluctuations in competition will sometimes drive one and sometimes
the other towards its sanctuary, but neither will be wiped out.
The difference between the sanctuaries and the general range
may not be large and may not be apparent to observers.
A tiny sanctuary for each species may suffice.
The required inhomogeneity can also be
supplied by a periodic change between times of the year favorable
to each species provided some age group of each species can survive
the unfavorable time.

	2. I started on the mathematics of a dual range predator-prey
system with migration between the two parts.  The object was to
show that the dual range can convert elliptic solutions into
limit cycles.  The mathematics got tedious, and I desisted.

	3. The speculations I have seen on punctuated evolution also don't
seem to take spacial inhomogeneity into account.  A species that shows up
suddenly in fossil strata may have evolved slowly somewhere else and may
have become preferred in that environment because of a parameter change,
e.g. water temperature.  The new species is like to have evolved where the
parameter change occurred first.

	The idea may be testable.  Suppose two new species come to
dominate in certain era, e.g. a species of clam and a species of
snail.  If the new snail radiated from one place and the new clam radiated
from another, we would find the new clam preceding the new snail in places
close to the source of clams and vice versa close to the source of snails.

	4. The edge of the range of a species presumably contains areas
where the species could not maintain itself except for migration from
central parts of the range.  A theory with sources and sinks may be
appropriate - or just sources.  It may be useful to classify parts of the
range of existing species.  Evolutionary changes in a species may
propagate from the sources.  They may originate at the edge of the range
where selection pressure is great and perhaps varied at different boundaries.
These places then become sources for the new variant.
How far from a source migration can sustain a
species will vary according to how unfavorable the immigration areas are
and how fast the animals travel.

	Another possibility for identifying the source of a variation is
the kind of genetic mapping used to make family trees.  We would expect
random variation to propagate preferentially downstream.

	5. It should be noted that the
favorable areas of a species may be isolated from each other.
Thus frogs live in frog ponds.  A favorable area may be wiped
out by a catastrophe such as a pond drying up or a disease or
conditions favorable to predators.  Such species will tend to
evolve strategies of emigration.

	For example, it might be favorable to frog survival that strong
frogs force their slightly weaker brothers and sisters to leave the home
pond and go hopping randomly across the countryside.  Almost all will die,
but if a new frog pond opens up somewhere within hopping distance, it will
be promptly occupied, reducing the probability that the line will be wiped
out by one pond drying up.  We could use this fact to account for
territoriality, and we can imagine seasonal migrations to be an
evolutionary outgrowth of emigration strategies.  It would be interesting
to know what fraction of salmon end up trying a different stream from the
one they hatched in.

	One would expect a species with localized range subject to
catastrophe evolve behavior that devotes a substantial fraction of its
resources to emigration especially when there is surplus population in a
locality.