Re: poly: Re: ESS for HPLD

At 12:31 PM 12/5/97 -0800, you wrote:
>Trying to reproduce/understand Robin's algebra:

Sorry to have been too terse.

>This should be N1/exp(X/A), right?

Yeah. I missed typing a minus sign in N1*exp(-X/A).

>> The maximum possible speed is where on average only one spore survives to
>> grow in a new oasis per each previous colonized oasis. So assume N1 = N2.
>
>I don't really follow this. Are you saying that it is wasteful to have
>two spores hit one oasis? ...
>I'm not sure what it means to assume that N1=N2.

No. If on average fewer new spores hit oases than what you started with,
the process dies away. If on average more new spores hit oases than you
started with, the number of spores grows exponentially. At the sustainability
boundary point you just get out as many as you put in on average. This is
the maximal possible speed boundary; any more growth could have been traded
for traveling just a little farther each generation.

The original question, as I understood it, was what are the implications if
evolution pushes for maximum speed of expansion. Not clear that it would,
but it is a clear question we can study.

>So you have W = exp(T/G) where T is the growth time (capped by Wmax). ...
>> A little algebra shows X = A*ln(WS/C) and T = D + g*ln(W) + X/V .
>
>There must be some equations leading up to this. What is T? Is it the
>time between generations, emission of spore to emission of daughter spore?

Sorry - I used "T" for two different things, didn't I. The first T above
was the time spend at an oasis. The second T is the time between generations.

>Instead of "g", you mean "G", right?

Right. I think you have the rest of it right as well.

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614
Received on Fri Dec 5 13:00:57 1997