Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks

Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to capillaries and uses scaling exponents to quantify these changes. Prominent scaling theories predict that combinations of these exponents explain how metabolic, growth, and other biological rates vary with body size. Nevertheless, direct measurements of individual vessel segments have been limited because existing techniques for measuring vasculature are invasive, time consuming, and technically difficult. We developed software that extracts the length, radius, and connectivity of in vivo vessels from contrast-enhanced 3D Magnetic Resonance Angiography. Using data from 20 human subjects, we calculated scaling exponents by four methods--two derived from local properties of branching junctions and two from whole-network properties. Although these methods are often used interchangeably in the literature, we do not find general agreement between these methods, particularly for vessel lengths. Measurements for length of vessels also diverge from theoretical values, but those for radius show stronger agreement. Our results demonstrate that vascular network models cannot ignore certain complexities of real vascular systems and indicate the need to discover new principles regarding vessel lengths

The scaling of carbon dioxide release and respiratory water loss in flying fruit flies (Drosophila spp.)

By simultaneously measuring carbon dioxide release, water loss and flight force in several species of fruit flies in the genus Drosophila, we have investigated respiration and respiratory transpiration during elevated locomotor activity. We presented tethered flying flies with moving visual stimuli in a virtual flight arena, which induced them to vary both flight force and energetic output. In response to the visual motion, the flies altered their energetic output as measured by changes in carbon dioxide release and concomitant changes in respiratory water loss. We examined the effect of absolute body size on respiration and transpiration by studying four different-sized species of fruit flies. In resting flies, body-mass-specific CO(2) release and water loss tend to decrease more rapidly with size than predicted according to simple allometric relationships. During flight, the mass-specific metabolic rate decreases with increasing body size with an allometric exponent of -0.22, which is slightly lower than the scaling exponents found in other flying insects. In contrast, the mass-specific rate of water loss appears to be proportionately greater in small animals than can be explained by a simple allometric model for spiracular transpiration. Because fractional water content does not change significantly with increasing body size, the smallest species face not only larger mass-specific energetic expenditures during flight but also a higher risk of desiccation than their larger relatives. Fruit flies lower their desiccation risk by replenishing up to 75 % of the lost bulk water by metabolic water production, which significantly lowers the risk of desiccation for animals flying under xeric environmental conditions

Subsistence: A Bio-economic Foundation of the Malthusian Equilibrium

This paper develops a bio-economic Malthusian growth model. By integrating recent research on allometric scaling, energy consumption, and ontogenetic growth we provide a model where subsistence consumption is endogenously linked to body mass and fertility. The theory admits a two-dimensional Malthusian equilibrium characterized by population density and body mass (metabolic rate) of the representative adult. As a result, the analysis allows us to examine the link between, in particular, human biology and long run income, body mass and population size. Off the steady-state we investigate the possibility of cyclical behavior of the size of a population and the size of its representative member. We also demonstrate that a take-off into sustained growth should be associated with increasing income, population size, and body mass. The increase in the latter is, however, bounded and can be viewed as convergence to a biologically determined upper limit. --Subsistence,Nutrition,Metabolism,Population Growth,Ontogenetic Growth,Malthus

Plant height and hydraulic vulnerability to drought and cold

Understanding how plants survive drought and cold is increasingly important as plants worldwide experience dieback with drought in moist places and grow taller with warming in cold ones. Crucial in plant climate adaptation are the diameters of water-transporting conduits. Sampling 537 species across climate zones dominated by angiosperms, we find that plant size is unambiguously the main driver of conduit diameter variation. And because taller plants have wider conduits, and wider conduits within species are more vulnerable to conduction-blocking embolisms, taller conspecifics should be more vulnerable than shorter ones, a prediction we confirm with a plantation experiment. As a result, maximum plant size should be short under drought and cold, which cause embolism, or increase if these pressures relax. That conduit diameter and embolism vulnerability are inseparably related to plant size helps explain why factors that interact with conduit diameter, such as drought or warming, are altering plant heights worldwide

Soft bounds on diffusion produce skewed distributions and Gompertz growth

Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound". At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.Comment: 9 pages, 6 color figure