RE: Terminology and Quantification (revised "fitness"

Aaron Lynch (
Fri, 23 Jul 1999 13:55:46 -0500

Message-Id: <>
Date: Fri, 23 Jul 1999 13:55:46 -0500
From: Aaron Lynch <>
Subject: RE: Terminology and Quantification (revised "fitness"
In-Reply-To: <>

At 08:13 PM 7/22/99 -0500, Aaron Lynch wrote:
>At 09:22 AM 7/20/99 +0200, Paul Marsden wrote:
>>David asked a simple, but critical question in Science that deserves a
>>straight and clear answer.
>>How do you define memetic fitness? Answers please.
>A more considered definition (given in replacement to my previous one) is
>as follows [switching to N1'(t) = dN1(t)/dt and N2'(t) = dN2(t)/dt notation]:
>Fitness(meme1) = 1 + N1'(t)/N1(t)
>Fitness(meme2) = 1 + N2'(t)/N2(t)

A still further considered definition is as follows:

Fitness(meme1) = exp[N1'(t)/N1(t)]

Fitness(meme2) = exp[N2'(t)/N2(t)]

This is approximately equal to the preceding definition for small values of
N1'(t)/N1(t) and N2'(t)/N2(t), but works for all values more analogously to
Darwinian fitnesses used in population genetics. Again, it is not a
normalized or relative fitness.

Although this definition gives a population-genetics like fitness scalar,
the equations for N1(a, t) and N2(a, t) are not isomorphic to ones from
population genetics, epidemiology, predator-prey ecology, plasmid
transmission, etc. For instance, the delay in parent to child meme
transmission causes mathematical differences from the plasmid transmission
problem and epidemiology. Horizontal transmission differs from diploid
population genetics, etc.

>These are not normalized or relative fitnesses. But David Sloan Wilson did
>not specify absolute, relative, or normalized fitness, or ones based on
>discrete or continuous models. Besides, it is not at all important in
>determining non-tautology. Giving equations for meme prevalence as a
>function of time and propagation parameters is sufficient to avoid
>"tautology" whether the word "fitness" is used or not. Merely giving
>definitions of fitnesses as above without providing equations to solve for
>N1'(t), N1(t), N2'(t) and N2(t) is not sufficient to avoid potential
>"tautology" charges.
>To avoid confusion, and minimize offense to geneticists (based on
>traditions), I will probably refrain from calling my ideas of matrices and
>vector functions "fitnesses." Instead, I will most likely label them
>otherwise, perhaps as "propagative profile vectors" or "propagative profile
>matrices." Note that all of my listserver discussion of the use of such
>terminology was and currently remains tentative. As my paper did not depend
>upon having any quantity defined as "fitness" in modeling meme prevalence,
>I am only now considering how to define the term "fitness" in relation to
>my mathematical model. I do try to pay attention to the effectiveness in
>communication when considering terminology.

--Aaron Lynch

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