The virtual moth genome
(Bond & Kamil 2002)
incorporated many features of the developmental genetics of the wing patterns of moths
and butterflies (Robinson 1971; Nijhout 1991; Carroll et al. 1994;
Brakefield et al. 1996), including loci that code for individual patches of
pattern elements, loci that produce global changes in wing brightness or contrast
without modifying pattern elements, and linkage mechanisms that protect favorable
genetic combinations from being lost during recombination. As in real moths,
phenotypic characters were polygenic. The intensity of each of the 75 unique pixels
in the phenotype was affected by multiple overlapping patches that interacted additively,
providing redundancy and maintaining genetic variance in spite of the absence of
The unique pixels of the moth phenotype are here outlined
in yellow. The right wing is a mirror image of the
117-byte genome consisted of nine cistrons, or linkage
cistron was a string of 13 eight-bit genes, comprising two
gene patch loci and a block of three regulator
The five genes in each
patch locus, taken together, defined an elliptical pixel patch of
specified location, size, shape, and brightness. Each regulatory locus
included genes for global brightness, global contrast, and the
probability of recombination between cistrons. Values of the brightness
and contrast regulators were summed over the genome, and their aggregate
value determined adjustments in absolute or relative brightness that were
applied to the entire wing. Mutations in just a few of these regulatory
locations could rapidly produce very bright or dark
Recombination in this system helped
to insure that deleterious patterns were rapidly removed from the population.
To preserve integrated pattern features from being broken up by recombination,
crossing-over only took place between linkage groups, and the probability
of a cross-over was determined by the combined values of the recombination
probability regulators above and below the exchange point. Similar recombination
restraints are common in the developmental
genetics of real lepidoptera (Nijhout 1991).
Our moth population
was maintained at a constant density of 200 individuals, but each day the
gene pool was reassorted, producing a novel generation of
prey. At the
start of the session, phenotypes were developed from the current
population of genotypes and exposed to jay predation. For each moth, the
program recorded whether that individual was correctly detected and, if
so, how long the bird took to find it. After all moths had been
presented to jays, the fitness of each individual in the population was
evaluated, based on its success at avoiding detection. A genetic
algorithm provided the interface between the birds' detection
performance and its selective effects on the moths. Moths that were
overlooked had 2.5 times the probability of being chosen to breed as
the average detected individual. Within the group of detected moths,
individuals were ranked in inverse order of the time the bird took to
detect them, and the highest-ranked individual had a 25% higher
probability of being chosen than the lowest-ranked.
Pairs of moths were
chosen at random from the pool, in accordance with their fitness values,
and their two genomes were recombined to produce a single progeny chromosome.
The parents were subsequently returned to the pool and could be chosen
again in a subsequent random draw. Once each progeny genome was
obtained, it was passed through a mutation step. Mutation was accomplished in
bitwise fashion, considering the 117-byte genome as a string of 936
binary digits. The mutation algorithm searched down the string and,
with a fixed probability of 0.003, randomly selected digits to be toggled.
To regulate the magnitude of the effects of single mutations, we used
Gray code, which minimizes the difference in number of bits between
adjacent integers, for interpreting individual gene values (Bäck
1996; Mars, Chen & Namibar 1996).
Production of a new
generation entailed iterated selection, recombination, and mutation steps
until 200 progeny individuals had been obtained. For the following
day's session, the parental population was discarded and replaced with
the progeny. There was no generational overlap.
References from Other Sources
Bäck, T. (1996). Evolutionary Algorithms in Theory and Practice. New York:
Oxford U. Press.
Brakefield, P.M., Gates, J., Keyes, D., et al. (1996). Development, plasticity and evolution of
butterfly eyespot patterns. Nature 384: 236-242.
Carroll, S.B., Gates, J., Keyes, D.N., et al. (1994). Pattern formation and eyespot
determination in butterfly wings. Science 265: 109-114.
Mars, P., Chen, J.R., & Nambiar, R. (1996). Learning Algorithms: Theory
and Applications in Signal Processing, Control, and Communications. Boca Raton,
FL: CRC Press.
Nijhout, H.F. (1991). The Development and Evolution of Butterfly Wing Patterns.
Washington, D.C.: Smithsonian Institution.
Robinson, R. (1971). Lepidopteran Genetics. Oxford: Pergamon.