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Resources » Paper

Avery, Leon (2009) International Worm Meeting "Modeling behavioral strategies with stochastic calculus."

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    Publication type:
    Meeting_abstract
    WormBase ID:
    WBPaper00034129

    Avery, Leon (2009). Modeling behavioral strategies with stochastic calculus presented in International Worm Meeting. Unpublished information; cite only with author permission.

    Behavioral and developmental choices made by any animal represent a strategy for surviving and reproducing in its environment. The essence of strategy is making decisions on the basis of incomplete information, decisions whose costs and benefits can''t be accurately determined at the time they must be made. Worms make many such choices: the decision to leave low-quality food in search of higher quality, the decision to lay eggs or allow them to hatch internally, and the decision to become a dauer or remain a dauer are examples. Not coincidentally, most of these decisions involve food availability, perhaps the most important environmental variable to a worm. I am trying to quantitatively model such decisions, using mathematical tools developed for financial markets. The L2/L2d decision is particularly interesting, because it appears to be unnecessary. An L2d can become either an L3 or a dauer, while an L2 can only become an L3. Since the L2d can do everything the L2 can do and more, why does the L2 exist? A likely answer is suggested by the work of Golden and Riddle. They showed that L1 L2d L3 pathway takes a few hours more than L1 L2 L3. Under ideal conditions a worm population doubles in 10-11 hours. (This number is calculated from published life-history traits, and is in approximate accord with lab experience.) A delay of 7 hours, therefore, reduces fitness by a factor of 27/10.5 = 0.62. Thus a worm that becomes an L2d pays a price of about 40% of its fitness for the option of eventually becoming a dauer. A worm should become an L2d if it can confidently predict that conditions will be so bad in the future as to cause a decrease of fitness of this magnitude. Most of what we know about dauer formation concerns how the worm evaluates environmental conditions. However, the L2d should also be preferred in highly uncertain environments, since it postpones the dauer decision into the future, when more accurate information will be available. This effect can be modeled using the tools of stochastic calculus, used to price options in financial markets. They predict that the L2/L2d decision should be strongly influenced not only by how good the environment is, but also by how volatile it is.


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