The scaling of postcranial muscles in cats (Felidae) I: forelimb, cervical, and thoracic muscles

The body masses of cats (Mammalia, Carnivora, Felidae) span a ~300‐fold range from the smallest to largest species. Despite this range, felid musculoskeletal anatomy remains remarkably conservative, including the maintenance of a crouched limb posture at unusually large sizes. The forelimbs in felids are important for body support and other aspects of locomotion, as well as climbing and prey capture, with the assistance of the vertebral (and hindlimb) muscles. Here, we examine the scaling of the anterior postcranial musculature across felids to assess scaling patterns between different species spanning the range of felid body sizes. The muscle architecture (lengths and masses of the muscle‐tendon unit components) for the forelimb, cervical and thoracic muscles was quantified to analyse how the muscles scale with body mass. Our results demonstrate that physiological cross‐sectional areas of the forelimb muscles scale positively with increasing body mass (i.e. becoming relatively larger). Many significantly allometric variables pertain to shoulder support, whereas the rest of the limb muscles become relatively weaker in larger felid species. However, when phylogenetic relationships were corrected for, most of these significant relationships disappeared, leaving no significantly allometric muscle metrics. The majority of cervical and thoracic muscle metrics are not significantly allometric, despite there being many allometric skeletal elements in these regions. When forelimb muscle data were considered in isolation or in combination with those of the vertebral muscles in principal components analyses and MANOVAs, there was no significant discrimination among species by either size or locomotory mode. Our results support the inference that larger felid species have relatively weaker anterior postcranial musculature compared with smaller species, due to an absence of significant positive allometry of forelimb or vertebral muscle architecture. This difference in strength is consistent with behavioural changes in larger felids, such as a reduction of maximal speed and other aspects of locomotor abilities

A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf's law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached to 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.Comment: 28 pages, 10 figures, 5 table

Hierarchicality of Trade Flow Networks Reveals Complexity of Products

With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be regarded as a value chain. The problem is weather we can discriminate between these products based on their unique flow network structure. This paper applies the flow analysis method developed in ecology to 638 trading flow networks of different products. We claim that the allometric scaling exponent $\eta$ can be used to characterize the degree of hierarchicality of a flow network, i.e., whether the trading products flow on long hierarchical chains. Then, the flow networks of products with higher added values and complexity, such as machinery&transport equipment with larger exponents, are highlighted. These higher values indicate that their trade flow networks are more hierarchical. As a result, without extra data such as global input-output table, we can identify the product categories with higher complexity and the relative importance of a country in the global value chain solely by the trading network.Comment: 14 pages,7 figure

Observation of Mammalian Similarity Through Allometric Scaling Laws

We discuss the problem of observation of natural similarity in skeletal evolution of terrestrial mammals. Analysis is given by means of testing of the power scaling laws established in long bone allometry, which describe development of bones (of length $L$ and diameter $D$) with body mass in terms of the growth exponents, \QTR{it}{e.g.} $\lambda =d\log L/d\log D$. The bone-size evolution scenario given three decades ago by McMahon was quiet explicit on the geometrical-shape and mechanical-force constraints that predicted $\lambda =2/3$. This remains too far from the mammalian allometric exponent $\lambda ^{(\exp)}=0.80\pm 0.2$, recently revised by Christiansen, that is a chief puzzle in long bone allometry. We give therefore new insights into McMahon's constraints and report on the first observation of the critical-elastic-force, bending-deformation, muscle-induced mechanism that underlies the allometric law with estimated $\lambda =0.80\pm 0.3$. This mechanism governs the bone-size evolution with avoiding skeletal fracture caused by muscle-induced peak stresses and is expected to be unique for small and large mammals.Comment: Keywords: allometric scaling, long bones, muscles, mammals 21 pages, 1 Table, 2 Figure

A New General Allometric Biomass Model

To implement monitoring and assessment of national forest biomass, it is becoming the trend to develop generalized single-tree biomass models suitable for large scale forest biomass estimation. Considering that the theoretical biomass allometric model developed by West et al. [1,2] was statistically different from the empirical one, the two parameters in the most commonly used biomass equation M=aDb were analyzed in this paper. Firstly, based on the knowledge of geometry, the theoretical value of parameter b was deduced, i.e., b=7/3(~2.33), and the comparison with many empirical studies conducted throughout the globe indicated that the theoretical parameter could describe soundly the average allometric relationship between aboveground biomass M and D (diameter on breast height). Secondly, using five datasets of aboveground biomass which consisted of 1441 M-D pairs of sample trees, the new general biomass allometric model was validated. Finally, the relationship between parameter a and wood density p was analyzed, and the linear regression was developed. The new model, which is not only simple but also species-specific, offers a feasible approach on establishment of generalized biomass models for regional and national forest biomass estimation

Validation and refinement of allometric equations for roots of northern hardwoods

The allometric equations developed by Whittaker et al. (1974. Ecol. Monogr. 44: 233–252), at the Hubbard Brook Experimental Forest have been used to estimate biomass and productivity in northern hardwood forest systems for over three decades. Few other species-specific allometric estimates of belowground biomass are available because of the difficulty in collecting the data, and such equations are rarely validated. Using previously unpublished data from Whittaker’s sampling effort, we extended the equations to predict the root crown and lateral root components for the three dominant species of the northern hardwood forest: American beech (Fagus grandifolia Ehrh.), yellow birch (Betula alleghaniensis Britt), and sugar maple (Acer saccharum Marsh.). We also refined the allometric models by eliminating the use of very small trees for which the original data were unreliable. We validated these new models of the relationship of tree diameter to the mass of root crowns and lateral roots using root mass data collected from 12 northern hardwood stands of varying age in central New Hampshire. These models provide accurate estimates of lateral roots (diameter) in northern hardwood stands \u3e20 years old (mean error 24%–32%). For the younger stands that we studied, allometric equations substantially underestimated observed root biomass (mean error \u3e60%), presumably due to remnant mature root systems from harvested trees supporting young root-sprouted trees

An allometric smoothing function to describe the relation between otolith and somatic growth over the lifespan of walleye pollock (Theragra chalcogramma)

We propose a new equation to describe the relation between otolith length (OL) and somatic length (fork length [FL]) of fish for the entire lifespan of the fish. The equation was developed by applying a mathematical smoothing method based on an allometric equation with a constant term for walleye pollock (Theragra chalcogramma) —a species that shows an extended longevity (>20 years). The most appropriate equation for defining the relation between OL and FL was a four-phase allometric smoothing function with three inflection points. The inflection points correspond to the timing of settlement of walleye pollock, changes in sexual maturity, and direction of otolith growth. Allometric smoothing functions describing the relation between short otolith radius and FL, long otolith radius and FL, and FL and body weight were also developed. The proposed allometric smoothing functions cover the entire lifespan of walleye pollock. We term these equations “allometric smoothing functions for otolith and somatic growth over the lifespan of walleye pollock.

Quantitative assessment of the effects of space allowance, group size and floor characteristics on the lying behaviour of growing-finishing pigs

To obtain quantitative information that can be later used in animal welfare modelling, the relationship between the lying behaviour of growing-finishing pigs (initial body weight (BW) between 19 and 87 kg) and different factors related to the housing conditions, with a potential negative effect on their welfare, was studied by means of a meta-analytical approach. Data from 22 experiments reported in 21 scientific publications were collected. The space allowance, expressed on an allometric basis by means of a k-value (m2/BW0.667), the group size (n) and the floor characteristics (fully and partly slatted v. non-slatted floor), as well as their significant two-way interactions were used as fixed effects, and the experiment was used as a random factor to take into account the interexperiment effect. Further regression analyses were performed on the predicted values of observations in order to improve the adjustment of data. A significant quadratic relationship was established between space allowance (k-value, P <0.05; squared k-value, P <0.01) and the percentage of time spent lying. A significant interaction between the k-value and the floor type was also found (P <0.05), showing that the relationship between space allowance and lying behaviour is affected by the presence or absence of slats. Threshold k-values were obtained using broken-line analyses, being about 0.039 for slatted floors and almost double for non-slatted floors. Compared to other studies, these values suggest that the ability to rest as space availability decreases may be compromised before a reduced performance becomes apparent. Group size did not show a significant effect. Additional information should be added to the model, as further data become available, to adjust the proposed parameters as well as to try to include the effect of other important aspects such as that of ambient temperature