COMPUTING SCIENCE
Experimental Lamarckism
Brian Hayes
Modeling Melanism
The main actors in a StarLogo program are mobile, animal-like
objects. For historical reasons they are known as turtles, but they
can just as well represent moths. Each moth has its own internal
state, which includes a genome, a camouflage color and a level of
energy reserves. The moths move over a background of
"patches," which represent the color of the environment.
Melanism is often a polygenic trait, producing a more-or-less
continuous range of hues. For simplicity I encode the camouflage
color in a single gene with a continuous range of alleles; color can
take on any value from 0 (darkest) to 1,000 (lightest). Separate
variables represent the color genotype and the color phenotype; at
birth the two variables have identical values, but in animals that
learn they can later diverge. Lamarckian inheritance is implemented
as feedback from the color phenotype of the parent to the color
genotype of the offspring. In the extreme case of perfect
Lamarckism, the color gene of the offspring is set equal to the
parent's color phenotype; lesser degrees of Lamarckism interpolate
between the original genotype and the acquired phenotype.
The moths have three other genes, which also range in value between
0 and 1,000. Following the custom of geneticists, I give the genes
names: kudzu, harvard and vanderbilt.
Kudzu is a growth gene: It determines the rate at which the
moth absorbs resources, gains weight and grows toward reproductive
maturity. Other things being equal, natural selection would drive
this gene toward its maximum value, and that's what happens in the
purely Darwinian case. For learning and Lamarckian moths, however,
kudzu is linked to the harvard gene, which governs
the rate of learning, and the vanderbilt gene, which
controls the inheritance of acquisitions. The linkage is negative,
so that faster learning or more complete inheritance of acquired
traits entails a more severe penalty in growth rate. The constants
that determine the degree of linkage—the tuition charged for
learning and the inheritance tax imposed on Lamarckism—are the
main parameters under investigation in the model.
A simulation begins with randomly assigned genotypes. Each moth
grows at a rate determined by the value of the kudzu gene.
On reaching a threshold weight (which takes 100 days at the highest
possible growth rate), the moth produces two offspring and
immediately dies. Meanwhile, each day a fraction of the moths are
killed by predators. The probability of being killed increases in
proportion to the difference between the moth's color and the
background color. The overall death rate is adjusted to match the
birth rate, keeping the population constant.
In those moths that learn, the color phenotype is adjusted every
day, bringing it into closer correspondence with the background
color at a rate determined by the value of the harvard
gene. In the same way, Lamarckian inheritance adjusts the color
genotype of the offspring toward the parental phenotype by an amount
proportional to the value of the vanderbilt gene. All of
the genes are also subject to random mutation and natural selection.
(Even in Lamarckian moths, only the camouflage gene evolves by
Lamarckian methods; all the other genes are purely Darwinian.)
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