They argue that symmorphosis is not an inevitable outcome because environmental unpredictability means that evolutionary selective forces vary too much in space and time to produce a structure that is functionally optimal ( Dudley and Gans, 1991). However, symmorphosis has also evoked criticism, especially from evolutionary biologists, who argue that natural selection leads to adequate or sufficient design but not optimal or symmorphic design ( Dudley and Gans, 1991 Garland, 1998 Garland and Huey, 1987 Smith, 1978). Where these simple economy-based expectations break down, an opportunity arises to analyse the reasons for such a breakdown ( Diamond, 1992). Since its conception, symmorphosis has received the support of a number of workers who view the optimal design idea as a useful null hypothesis of biological design on which to base analytical studies ( Diamond, 1992 Suarez, 1996). In contrast, the pulmonary anatomical diffusing capacity of birds appears to be symmorphic, both phylogenetically and ontogenetically ( Canals et al., 2011 Runciman et al., 2005 Seymour et al., 2004 Seymour et al., 2008). It was suggested that larger mammals may have a lower alveolar pressure head for diffusion and, therefore, require a greater pulmonary diffusing capacity to transfer oxygen from the lungs to the blood at the same rate as smaller mammals ( Gehr et al., 1981). Interestingly, the anatomical diffusing capacity of the lung was found to scale with an exponent, b=0.99, significantly steeper than that derived for maximum oxygen consumption rate, which means that larger mammals appear to possess excess lung structure ( Gehr et al., 1981). It was also established that total capillary length in selected muscles scales roughly parallel with aerobic capacity, b=0.86 to 0.91, but because of scatter in the data it was not possible to determine whether the slopes were statistically similar ( Hoppeler et al., 1981b Weibel et al., 1981a). They found that maximum oxygen consumption rate scales with body mass with an exponent of 0.80 ( Taylor et al., 1981), and that this is congruent with the allometric scaling of mitochondrial volume in the diaphragm and locomotory muscles, b=0.80 to 0.82 ( Mathieu et al., 1981). Taylor and Weibel predicted that if their theory of symmorphosis holds for the mammalian respiratory system, then maximum oxygen uptake should scale with an exponent ( b) that is statistically indistinguishable from the exponents derived for each of the structural variables ( Taylor and Weibel, 1981). The effect of body mass on the maximum oxygen consumption rate of mammals and the amount of respiratory structure they possess was expressed as an allometric equation, y= aM b b, where y is the variable of interest, a is the coefficient, M b is body mass and b is the scaling exponent. Next, a number of structural variables crucial in the delivery and consumption of oxygen during exercise were morphometrically quantified ( Gehr et al., 1981 Hoppeler et al., 1981a Hoppeler et al., 1981b Mathieu et al., 1981 Weibel et al., 1981b). First, the functional capacity of the respiratory system was determined by measuring the maximum oxygen consumption rate of mammals during exercise of progressive increasing intensity ( Seeherman et al., 1981).
CYCLOID SHAPE TEST LINES VERTICAL PLANE STEREOLOGY SERIES
In a seminal series of papers, Taylor and Weibel tested their theory on the respiratory system of mammals. Therefore, the principles of symmorphosis are upheld at each step of the oxygen cascade in the respiratory system of the migratory locust. Likewise, at the oxygen supply end of the insect respiratory system, there is congruence between the aerobic capacity of the hopping muscle and the total volume of tracheoles in the hopping muscle, M b 0.99☐.16, the total inner surface area of the tracheoles, M b 0.99☐.16, and the anatomical radial diffusing capacity of the tracheoles, M b 0.99☐.18. The maximum oxygen consumption rate of the hopping muscle during jumping exercise scales as M b 1.02☐.02, which parallels the scaling of mitochondrial volume in the hopping muscle, M b 1.02☐.08, and the total surface area of inner mitochondrial membrane, M b 0.99☐.10. We tested this hypothesis in the respiratory system of the migratory locust, Locusta migratoria, by comparing the aerobic capacity of the jumping muscles with the morphology of the oxygen cascade in the hopping legs using an intraspecific allometric analysis of different body mass ( M b) at selected juvenile life stages. Taylor and Weibel's theory of symmorphosis predicts that structures of the respiratory system are matched to maximum functional requirements with minimal excess capacity.
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