Tracheal branching in ants is area-decreasing, violating a central assumption of network transport models

Abstract

The structure of tubular transport networks is thought to underlie much of biological regularity, from individuals to ecosystems. A core assumption of transport network models is either area-preserving or area-increasing branching, such that the summed cross-sectional area of all child branches is equal to or greater than the cross-sectional area of their respective parent branch. For insects, the most diverse group of animals, the assumption of area-preserving branching of tracheae is, however, based on measurements of a single individual and an assumption of gas exchange by diffusion. Here we show that ants exhibit neither area-preserving nor area-increasing branching in their abdominal tracheal systems. We find for 20 species of ants that the sum of child tracheal cross-sectional areas is typically less than that of the parent branch (area-decreasing). The radius, rather than the area, of the parent branch is conserved across the sum of child branches. Interpretation of the tracheal system as one optimized for the release of carbon dioxide, while readily catering to oxygen demand, explains the branching pattern. Our results, together with widespread demonstration that gas exchange in insects includes, and is often dominated by, convection, indicate that for generality, network transport models must include consideration of systems with different architectures.

X-ray micro-tomographic data of live larvae of the beetle Cacosceles newmannii

“…Future studies could explore possibilities to improve minimum resolution, for instance using machine learning algorithms that improve capacity to distinguish tracheal structures in fuzzy images (Yang et al, 2020). More generally, it would be important to study insect species across a wide range of body sizes to determine the distribution of tracheal size relationships (Aitkenhead et al, 2020;Kaiser et al, 2007) at different scanning resolutions (Iwan et al, 2015).…”

“…The smallest tracheae, with a diameter smaller than 2 µm, are called tracheoles and the major site of oxygen exchange (Schmitz and Perry, 1999;Wigglesworth, 1983). X-ray micro-tomography (µCT) is an emerging tool with which to study tracheal networks (Aitkenhead et al, 2020;Alba-Tercedor et al, 2019;Greenlee et al, 2009;Harrison et al, 2018a;Javal et al, 2019;Raś et al, 2018;Shaha et al, 2013;Wasserthal et al, 2018). Using µCT has the benefit of allowing reconstruction of the intact tracheal tree in its three-dimensional configuration.…”

What is the status of metabolic theory one century afterPütter invented the vonBertalanffy growth curve?

“…There is still great potential for empirical investigations into the different theoretical expectations of the two theories (Kearney & White, 2012). The theories may well be complementary in some respects (Maino et al ., 2014) and, although network limitations may not always exist or occur in the manner expected (Aitkenhead et al ., 2020), they may become limiting in certain situations such as low oxygen (Verberk & Bilton, 2011) and may be empirically tied to organismal shape changes (Hirst, Glazier, & Atkinson, 2014).…”

Universal rules of life: Metabolic rates, biological times and the equal fitness paradigm

“…The EFP raises questions about the nature of biological time. Our hypothesis (Box 4) that Kleiber’s m 3/4 scaling of metabolic rate reflects the m 1/4 scaling of biological time broadly and generation time in particular, is more general and widely applicable than existing models based on vascular and other systems that supply metabolites and remove wastes (e.g., West et al 1997; West et al 1999; Banavar et al 2002, 2010; Aitkenhead et al 2020). The 3/4-power scaling of respiration rate with body mass is pervasive across the animal kingdom, occurring in diverse taxonomic and functional groups that have distinctly different anatomies and physiologies for assimilating, transporting and excreting the substrates and wastes of respiratory metabolism (e.g., Peters 1983; Brown et al 2004).…”

“…When West et al (1997) purported to explain Kleiber’s law of m 3/4 scaling of “metabolic rate’’ in terms of the structure and function of the fractal-like vascular networks that distribute metabolic resources, it was followed a flurry of supporting and critical studies. Points of contention included: i) vascular networks that violate critical assumptions of the WBE model (e.g., Bannavar et al 2002, 2010; Chown et al 2007, White et al 2011; Seymour et al 2019; Aitkenhead et al 2020); ii) variation in the parameters of fitted regression equations (e.g., Darveau et al 2002; Kozłowski et al 2003; Kozlowski and Konarzewski 2004; Glazier 2005, 2010; Etienne et al 2006; Apol et al 2008; Dodds 2010); and iii) different statistical methods for analyzing data and evaluating hypotheses (e.g., Isaac and Carbone 2010; Kearney and White 2012; Uyeda et al 2019; White et al 2019). Many studies, and relevant theoretical and empirical issues, are addressed in Sibly et al (2012).…”