Form, function, and evolution of living organisms

Abstract

Despite the vast diversity of sizes and shapes of living organisms, life's organization across scales exhibits remarkable commonalities, most notably through the approximate validity of Kleiber's law, the power law scaling of metabolic rates with the mass of an organism. Here, we present a derivation of Kleiber's law that is independent of the specificity of the myriads of organism species. Specifically, we account for the distinct geometries of trees and mammals as well as deviations from the pure power law behavior of Kleiber's law, and predict the possibility of life forms with geometries intermediate between trees and mammals. We also make several predictions in excellent accord with empirical data. Our theory relates the separate evolutionary histories of plants and animals through the fundamental physics underlying their distinct overall forms and physiologies.allometric scaling | biological scaling | tree geometry | fractal U nderstanding the origin and evolution of the geometries of living forms is a formidable challenge (1, 2). The geometry of an object can be characterized by its surface−volume relationship-the surface area S of an object of volume V can scale at most as S ∼ V and at least as S ∼ V 2=3 (3). These geometries have been used by nature in space-filling trees and animals, respectively. Here, our principal goal is to explore how it is that both geometries of life coexist on Earth, whether intermediate geometries are possible, and what all this implies for evolution of life on Earth.Living organisms span an impressive range of body mass, shapes, and scales. They are inherently complex, they have been shaped by history through evolution and natural section, and they continually extract, transform, and use energy from their environment. The most prevalent large multicellular organisms on Earth, namely plants and animals, exhibit distinct shapes, as determined by the distribution of mass over the volume. Animals are able to move and are approximately homogeneous in their mass distribution-yet they have beautiful fractal transportation networks. Plants are rooted organisms with a heterogeneous selfsimilar (fractal) geometry-the mass of the tree is more concentrated in the stem and branches than in the leaves.The approximate power law dependence of the metabolic rate, the rate at which an organism burns energy, on organism mass has been carefully studied for nearly two centuries and is known as allometric scaling (4-32). From the power law behavior, with an exponent around 3/4, one can deduce the scaling of characteristic quantities with mass and, through dimensional analysis, obtain wide-ranging predictions often in accord with empirical data. However, what underlies this ubiquitous quarter-power scaling, and with a dominant exponent of 3/4?In an influential series of papers, West and coworkers (11, 12, 14-16) suggested that fractality was at the heart of allometric scaling. Inspired by these papers, a contrasting view was presented (13), which argued that, although fractal circulatory networks m...

Effects of Contingency versus Constraints on the Body-Mass Scaling of Metabolic Rate

“…RTN models are clearly inadequate. These models either ignore the possibility of temperature effects [33][34][35][36][37], or assume that body size and temperature act independently on metabolic rate [49,60]. According to the metabolic theory of ecology (MTE) [8,49], which includes the RTN model of [33], temperature should affect the elevation, but not the slope (exponent) of metabolic scaling relationships.…”

Rediscovering and Reviving Old Observations and Explanations of Metabolic Scaling in Living Systems

“…According to this model and others like it ( [80,84,[159][160][161][162]; and other references cited in [19,20]), as body size increases, the average travel distance and energetic/structural costs for resource distribution to metabolizing cells increases, which reduces the rate at which cells receive oxygen and nutrients, thus decreasing mass-specific metabolic rate. However, these resource-transport network (RTN) models are not entirely novel, but represent partial rediscoveries and reformulations of explanations already proposed as early as the 1800s [108,163].…”

“…These include models or hypotheses invoking the effects of four-dimensional geometry, sometimes including biological time as the fourth dimension [17,[77][78][79][80][81][82][83][84], the relative effects of resource supply versus demand (e.g., [19,20,46,70,[85][86][87][88][89][90]), the biological regulation of metabolic rate (e.g., [20,87,[90][91][92][93][94][95][96][97][98]), and various adaptive effects resulting from interactions with ecological factors (e.g., [19,20,46,[99][100][101][102][103][104][105][106][107]). Here I focus on four major, much-discussed theoretical approaches encompassed by the 'contextual multimodal theory' (CMT) of metabolic scaling ( Figure 1) recently proposed in this journal [20].…”

“…Hemmingsen (1960) later reported metabolic scaling exponents near 3/4 in not only endothermic animals, but also ectothermic animals, and even unicellular organisms [70]. As a result, the 3/4-power (Kleiber's) law was canonized as the predominant (if not universal) pattern of metabolic scaling [17,51,[63][64][65][66]70,80,84,92,[113][114][115][116]. Many investigators (but surprisingly not Kleiber himself, a founder of the 3/4-power law) rejected the thermoregulatory surface-area model of metabolic scaling, because it seemed incapable of explaining 3/4-power scaling, especially in ectothermic organisms that do not actively maintain constant body temperatures (see also [20]).…”

“…New RTN-based models (e.g., [84,[173][174][175][176]) or applications (e.g., [22,172,177]) continue to appear that have not sufficiently heeded the history of accumulating negative evidence against the assumptions, logic and predictions of previous RTN models.…”