BioSystems 90 (2007) 224–233
The linear allometric relationship between total metabolic
energy per life span and body mass of mammals
Atanas Todorov Atanasov
∗
Department of Physics and Biophysics, Medical Faculty, Thracian University-Stara Zagora, 6000 Stara Zagora,
11 Armeiska Str., Bulgaria
Received 31 July 2006; accepted 17 August 2006
Abstract
The aim of this study is to establish and calculate the exact allometric relationship between the total metabolic energy per life
span and the body mass in a wide range of mammals with about six orders of magnitude variation of the body mass of animals. The
study shows that it exists a linear relationship between the total metabolic energy per life span PT
ls
(kJ) and the body mass M (kg)
of 95 mammals (3 monotremes, Subclass Prototheria, 16 marsupialis (Subclass Theria, Infraclass Metatheria) and 76 placentals
(Subclass Theria, Infraclass Eutheria)) from type: PT
ls
= A
ls
+
M
1.0511
, where P (kJ/day) is the basal rate of metabolism and T
ls
(days)
is the mean life span of animals. The linear coefficient A
ls
+
= 7.158 × 10
5
kJ/kg is the total metabolic energy, exhausted during the
life span per 1 kg body mass of the animals. The mean values of the total metabolic energy per life span, per unit body mass (A
ls
)
for orders from Subclass Prototheria and Theria (Infraclass Metatheria) and orders Xenarthra, Pholidota, Soricomorpha, Rodentia
(Infraclass Eutheria) varied negligible in interval (4.656–5.80) × 10
5
kJ/kg. The coefficient A
ls
grows from (7.68–8.36) × 10
5
kJ/kg
in Lagomorpha and Artiodactyla (Eutheria) to (10.58–12.64) × 10
5
kJ/kg in orders Carnivora, Pinnipeda and Chiroptera (Eutheria).
A
ls
grows maximum to 18.5 × 10
5
kJ/kg in Primates. Thus, the values of coefficient A
ls
differ maximum four-fold in all orders.
Across the all species the values of A
ls
are changes about one order of magnitude. Consequently, our survey shows that the changes
of the body mass, basal metabolic rate and the life span of animals are three mutually related parameters, so that the product
A
ls
=(PT
ls
)/M remains relatively constant in comparison to 1 million fold difference in body mass and total metabolic energy per
life span between mammals.
© 2006 Elsevier Ireland Ltd. All rights reserved.
Keywords: Mammals; Basal metabolic rate; Life span; Total metabolic energy
1. Introduction
The patterns existing between the other fundamental
characters of living organisms and her body mass are
generally described as a power function. The bioener-
getic studies on animals (Hemmingsen, 1960; Kleiber,
1961; Schmidt-Nielsen, 1984; McNab, 1988; Speakman,
2005; Nagy, 2005) have shown that the rate of oxy-
∗
Fax: +359 42 600705.
E-mail address: atanastod@abv.bg.
gen consumption P (kJ/day) is related to the body mass
M (kg) as expressed by the equation of type P = aM
k
,
where a and k are allometric parameters. The study of
this fundamental equation continues on theoretical and
experimental level, concerning the effects of physical
and physiological factors on metabolic rate: tempera-
ture (Gillooly et al., 2001), an allometric cascade that
links the cellular and the whole animal metabolism
(Darveau et al., 2002), changes of the power coeffi-
cient in equations P = aM
k
in evolutionary process of
animals (Atanasov and Dimitrov, 2002), membranes
and the setting of energy demand (Hulbert and Else,
0303-2647/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights reserved.
doi:10.1016/j.biosystems.2006.08.006