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Background: According to the classical model of Macevicz and Oster, annual eusocial insects should show a clear dichotomous "bang-bang" strategy of resource allocation; colony fitness is maximised when a period of pure colony growth (exclusive production of workers) is followed by a single reproductive period characterised by the exclusive production of sexuals. However, in several species graded investment strategies with a simultaneous production of workers and sexuals have been observed. Such deviations from the "bang-bang" strategy are usually interpreted as an adaptive (bet-hedging) response to environmental fluctuations such as variation in season length or food availability. To generate predictions about the optimal investment pattern of insect colonies in fluctuating environments, we slightly modified Macevicz and Oster's classical model of annual colony dynamics and used a dynamic programming approach nested into a recurrence procedure for the solution of the stochastic optimal control problem. Results: 1) The optimal switching time between pure colony growth and the exclusive production of sexuals decreases with increasing environmental variance. 2) Yet, for reasonable levels of environmental fluctuations no deviation from the typical bang-bang strategy is predicted. 3) Model calculations for the halictid bee Lasioglossum malachurum reveal that bet-hedging is not likely to be the reason for the graded allocation into sexuals versus workers observed in this species. 4) When environmental variance reaches a critical level our model predicts an abrupt change from dichotomous behaviour to graded allocation strategies, but the transition between colony growth and production of sexuals is not necessarily monotonic. Both, the critical level of environmental variance as well as the characteristic pattern of resource allocation strongly depend on the type of function used to describe environmental fluctuations. Conclusion: Up to now bet-hedging as an evolutionary response to variation in season length has been the main argument to explain field observations of graded resource allocation in annual eusocial insect species. However, our model shows that the effect of moderate fluctuations of environmental conditions does not select for deviation from the classical bang-bang strategy and that the evolution of graded allocation strategies can be triggered only by extreme fluctuations. Detailed quantitative observations on resource allocation in eusocial insects are needed to analyse the relevance of alternative explanations, e.g. logistic colony growth or reproductive conflict between queen and workers, for the evolution of graded allocation strategies.
In a nice assay published in Nature in 1993 the physicist Richard God III started from a human observer and made a number of witty conclusions about our future prospects giving estimates for the existence of the Berlin Wall, the human race and all the rest of the universe. In the same spirit, we derive implications for "the meaning of life, the universe and all the rest" from few principles. Adams´ absurd answer "42" tells the lesson "garbage in / garbage out" - or suggests that the question is non calculable. We show that experience of "meaning" and to decide fundamental questions which can not be decided by formal systems imply central properties of life: Ever higher levels of internal representation of the world and an escalating tendency to become more complex. An observer, "collecting observations" and three measures for complexity are examined. A theory on living systems is derived focussing on their internal representation of information. Living systems are more complex than Kolmogorov complexity ("life is NOT simple") and overcome decision limits (Gödel theorem) for formal systems as illustrated for cell cycle. Only a world with very fine tuned environments allows life. Such a world is itself rather complex and hence excessive large in its space of different states – a living observer has thus a high probability to reside in a complex and fine tuned universe.