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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.

Figure 2. Competition of three speciesClick to Enlarge Image

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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