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(small 9) and a slow increase of fertility with age (small b). If two related species live under conditions of unequal mortality, everything else being equal, the one living under the highest mortality regime should have the shortest juvenile period. In the numerical example of Fig. 5.1, a — 7 and the net reproductive rate of the optimal life history is 30.8.

This simple example shows how mathematical models can help to draw inferences on the optimality of life-history traits if some basic attributes of the species and its environment are given. Whereas age at maturity, body size, and clutch size are important traits for animals, for plants traits such as germination fraction, shoot-root allocation, flowering time, and number of seeds are considered. Much more complicated elaborations of the basic demographic principles are discussed in Roff (2002), including fluctuating and predictably changing environments. A crucial role in many models is played by trade-offs; in the present case it was assumed that the organism could increase its fertility by postponing maturity and growing larger first, and that there was a linear relationship between the two. Such a mechanism is often considered a consequence of energy allocation: what is spent on one side cannot be spent on the other side. The idea of trade-offs due to energy allocation is very old and can be traced back to the 'loi de balancement' proposed by Geoffroy Saint Hilaire in 1818 (Leroi 2001). Darwin (1859) noted that artificial selection of domestic animals and plants showed many examples of correlated reponses or 'compensation of growth'. He referred to both Geoffroy and Goethe in stating 'if nourishment flows to one part or organ in excess, it rarely flows, at least in excess, to another part; thus it is difficult to get a cow to give much milk and to fatten readily'.

The principle of energy acquisition and allocation was developed by Kooijman (2000) into a systematic physiology-based framework of growth, reproduction, and aging, the dynamic energy budget model (DEB model). In this model, food uptake is assumed to be proportional to body surface and assimilated energy is converted into reserves. The reserve pool is in dynamic equilibrium with a mobile pool available to all organs of the body. A fixed proportion (k) of the circulating pool is spent on growth plus maintenance, and the remaining portion, 1-k on development plus reproduction. This aspect of the model is designated as the k rule for allocation. Energy taken up by somatic tissues is first used for maintenance, and the remainder is used for growth. In this way growth competes directly with maintenance, but reproduction competes with growth only through the k rule. This model can explain why many animals continue to grow after the onset of reproduction. Their growth slows down due to the increasing maintenance costs of a larger body, not directly through competition with reproduction. In the model, the onset of reproduction, which is due to the 1-k flux being redirected from development to reproduction, does not create the discontinuities and inconsistencies that are present in other allocation models. The great variety of examples discussed in Kooijman's (2000) book illustrates that the DEB model is a powerful instrument for analysing energetic relationships since it argues from first principles rooted in thermodynamics and emphasizes the similarities across organisms as different as yeast, waterfleas, parasites, fish, and birds.

Despite the importance of allocations and trade-offs in life-history theory, reliable empirical measurements are difficult. This is especially annoying because often the outcome of an optimization procedure depends critically on the shape of a trade-off function, for example a convex relationship between reproduction and survival predicts iteroparity (repeated ongoing reproduction), whereas a concave relationship predicts semelparity (a single, large reproductive output followed by death). Empirical studies are hardly able to distinguish between these two forms of trade-off. In addition, trade-offs may be masked by fluctuation in the resource that is the subject of allocation. For example, if the total energy available for growth and reproduction increases due to increasing food intake, the allocation between them becomes invisible, and the correlation between growth and reproduction at the phenotypic level may turn from negative to positive (Van Noordwijk and De Jong 1986). There has been a tendency to measure trade-offs in terms of negative genetic correlations between life-history traits, either by pedigree analysis or by selection, using the formalism of quantitative genetics; however, such estimates have not produced satisfactory results because very large sample sizes are needed to resolve the presence of genetic correlations (Roff 2002).

In addition to energy allocation, two other classes of mechanism can cause negative associations between life-history traits: negative (antagonistic) pleiotropy and hormonal signals (Zera and Harshman 2001; Leroi et al. 2005). Geneticists define pleiotropy as the phenomenon that one gene affects two or more phenotypic traits. Negative pleiotropy arises when expression of a single gene affects one trait in a positive way and another trait in a negative way. This can also be true for hormonal control: the same hormone may affect one process in a positive direction, and another in a negative direction. Negative pleiotropy may be a more common mechanism for negative association between life-history traits than energy allocation. Leroi et al. (2005) examined several classes of genes involved with the regulation of longevity and concluded that many of them have antagonistic effects on life-history traits. Additional evidence for the importance of negative pleiotropy comes from the literature on tolerance to pesticides (Van Straalen and Hoffmann 2000). Many pesticide tolerances are associated with apparent 'costs' to vitality or reproductive capacity, but these costs are more often due to metabolic side effects of a gene mutation that confers tolerance, than to an energy drain towards detoxification of the pesticide.

A new framework for addressing questions about life-history patterns may come from genome-wide gene-expression studies. Stearns and Magwene (2003) suggested that trade-offs can be seen as conflicts over gene expression. This argument is illustrated in Fig. 5.2. If two functions in an organism—for example, reproduction and longevity—are regulated by two sets of genes, a trade-off between the functions may arise if the two sets overlap and if, for example, one function calls for upregulation and the other for down-regulation. Such a trade-off can also arise from

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