ЖУРНАЛ ОБЩЕЙ БИОЛОГИИ, 2008, том 69, № 5, с. 355-363
УДК 591.134
SPECIFIC METABOLIC RATE, LONGEVITY AND "RUBNER CONSTANT" FOR BIRDS © 2008 A. F. Alimov, T. I. Kazantseva
Zoological Institute, Russian Academy of Sciences 199034 St. Petersburg, Universitetskaya Emb, 1, Russia e-mail: model@zin.ru
An assumption was made that age constituent axe of mortality of individuals in a population in Weibull equation mx = m0 + axe (Ricklefs, 2000) reflects change of specific metabolic rate of one individual with age. Based upon that hypothesis a formula was proposed for relationship of specific metabolic rate of an adult individual after cessation of growth, when mass W is attained, and age t : q(t) = q0(1 - юв + xte) where q0 = aW— is value q(t) at the moment of growth cessation and ю = а1/(в + 1) is "ageing rate", determined and estimated by R. Rick-
(1 - qcrit/q0 )1/в
lefs. Maximum longevity of an individual was determined as tmax =-1 + B-, where qcrit is specific met-
ю + в
abolic rate at the age tmax. Parameter в and relationships ra(W) and (qcrit/q0)(W) were approximated for birds from data of Ricklefs. Statistical comparison of results of calculations of tmax was carried out on the basis of the above formula and other known formulas for groups of Passeriformes and non-Passeriformes. Rubner constant
Ru = fmax q (t)dt was calculated assuming that body mass of an adult individual (W) is attained in the first year
J'A
of life (tA = 0). Average values of 602.4 ± 2.5 kcal g-1 (n = 83) for non-Passeriformes and 963 ± 6.3 kcal g-1 (n = 41) for Passeriformes were obtained.
Total specific metabolic rate during lifetime can be used as a measure of internal (physiological) age of an organism (Reiss, 1989; Alimov, Kazantseva, 2007). There is a hypothesis that this value calculated for the maximum life duration is a constant for a species or at least for animals that are on the same evolutionary level (Bauer, 1935; Zotin, Zotin, 1999). However up to now this hypothesis has not been corroborated for animals of different organization levels. In 1908, M. Rubner estimated for several mammal species the value, the so-called Rubner constant (Ru):
tmax
Ru = J q (t) dt (1)
tA
where tA is age when the animal stops growing attaining permanent body mass, tmax is maximum possible life duration, q(t) is specific oxygen consumption rate. Rubner made a conclusion that "...1 kg Lebendgewicht der Tiere nach dem Wachstum verbraucht während der Lebenszeit annähernd die gleichen Energiemengen, der Mensch übertrifft in dieser Hinsicht alle anderen untersuchten Säugetiere"* (Rubner, 1908, p. 204, cited after Bauer, 1931). G. Winberg and A. Shcherbakov (1937)
* "1 kg of living mass of animals after cessation of growth utilizes during lifetime approximately equal amounts of energy, man in that respect surpasses all other mammals".
studied metabolic intensity and life duration in three species of Drosophila. With 2-2.5-fold differences in results they came to a conclusion that "Rubner value" may have similar values for these species, mean life duration depending to a large extent on conditions, intensity of respiration being relatively stable. Our estimates of specific metabolism per maximum life duration for some fish species from different water-bodies (Alimov, Kazantseva, 2007) allow neither accepting nor rejecting the idea of "Rubner constant".
Apparently, both growing during the entire lifetime and ceasing their growth after reaching a certain developmental stage, specific metabolism, total for the life time, is not a species characteristic for animals. This may be accounted for by the absence of such characteristic as species specific life duration, i.e. a limit of life duration inherent to individuals of a particular species (Gavrilov, Gavrilova, 1991). Maximum life duration of separate individuals is a random variable; therefore it would be erroneous to speak of exact value of potential life duration for any species. G. Caughley (1977) wrote that the concept of potential life duration should be replaced by probability assertion: the reason why animals do not live infinitely long is not that they physically cannot surpass a certain threshold age, but because probability of surpassing it even with a permanent risk of death becomes vanishingly small. Thus, the estimates of maximum lon-
355
3*
gevity and total specific metabolism of individuals of certain species should be stochastic values.
To test the hypothesis proposed by Bauer (1931) for growing total specific metabolism of organisms in the evolution, it is necessary to calculate this value for animals of different organization levels. This study is an attempt to determine physiologically important maximum life duration of birds through the function of change of specific oxygen consumption rate of an adult organism with age and calculation of Rubner constant for birds.
THE MAIN HYPOTHESES
Growth of fledgling since the moment of hatching until reaching size of an adult bird continues for several weeks or months and takes a small part of the total life duration. Further, the individuals live several years until the end of life, only breeding. At that time, active mass (participating in metabolic processes) of animal gradually declines. However, it is practically impossible to assess directly the mass and its change with age. It has been shown by numerous studies that intensity of basic metabolism, i.e. energy expenditures per unit mass per unit time in resting state, declines with age in growing animals (Brody, 1945; Zotin, Vladimirova, 2001; Zotin, Ozernyuk, 2004). Data about decline of specific rate of metabolism with age in animals (man included) that stop growing after reaching maximum body mass are rather fragmentary and insufficient to argue for reliable patterns (Frolkis, 1969; Zotin, 1974).
Energy expenditures of an adult bird for annual performance of different stages of life cycle depending on its body mass, which is regarded to be permanent, are assessed relatively precisely (Dolnik, 2006). Evidently during a year, bird's expenditures of energy are quite uneven, in certain periods intensive expenditures of energy from organisms supplies occur, in resting periods these reserves are replenished. Special studies (Anorova, 1979; Artemyev, 1998) show that although age of partners forming a parental pair affects the number and mass of eggs laid to a certain extent, in natural conditions the impact of environmental factors on the main indices of reproductive cycle appears to be stronger than impact of age factor. Therefore we accepted that average annual expenditure of energy of an adult bird is determined by its active mass only.
Relationships of rate of basal metabolism (Q) to total body mass of adult bird (W) have been established experimentally (Lasiewski, Dawson, 1967):
for Passeriformes Q = 3.63W0724,
for non-Passeriformes Q = 2.22W0723,
where W is measured in grams, Q - in kjoule d-1. Specific metabolic rate q = Q/W, expressed in kcal g -1 d-1 (1kjoule = 0.24 kcal), is equal respectively,
for Passeriformes q = 0.8712W-0 276,
Our task was to include time parameter into relationship (2), i.e. to determine the function of change of specific metabolic rate of a bird having body mass alteration with age. To resolve this task we used the idea and data of R. Ricklefs (2000).
Ricklefs studied relationship of bird mortality and age. He used Weibull function mx = m0 + axP (Gavrilov, Gavrilova, 1991) as a basis, where mortality mx of an individual of age x is a sum of two components: mortality m0 of young birds that have reached body mass of an adult individual and age constituent axP. Whereas m0 reflects the impact of external factors on the population, axP is determined by internal factors, related to individuals age. Coefficient P is non-dimensional, a has dimension [time-® + X)]. Of parameters a and P Ricklefs formed a new parameter o> = a1/(P + X), having dimension [time-1], and interpreted it as ageing rate.
Thus, he related age constituent of mortality and factor of physiological changes occurring in an animal organism with age. Values a and P were calculated from survival curves (based on observation data) for a number of populations of different bird species living in captivity and in nature. From these estimates value o> was calculated for each species. We assumed that growth of "internal" constituent of mortality with age is determined to a large extent by a decline of specific metabolic rate of an individual q, and therefore, these changes can be described by one and the same law. We set relationship q(t) by function
q(t) = qo( 1 - a,
(3)
where q0, calculated from formulas (2), is specific metabolic rate at the moment of attaining of adult individual body mass (W), a and P, are parameters of Weibull function. If it is assumed that P is known and parameter o> = = a1/(P + 1) is included into formula (3), this formula acquires appearance
q ( t) = qo( 1- œ
в +
11в).
(4)
According to our hypothesis specific metabolic rate q(t) during life time declines according to law (4) reaching at the end of life at t = tmax its critical value
- 11 в +1 f в
qcrit - q0( 1 - œ tma
) -
By means of simple transformation we obtain formula:
^max
( 1 - qcrit/qo)
1/в
œ
1 + 1/в
(5)
for non-Passeriformes q = 0.5328W-
0.277
(2)
Thus, maximum (physiologically possible) longevity is expressed through parameters P = const, o> and qcrit/q0. If ffl and qcrit/q0 is related to mass W, estimate tmax = f(W) based on metabolic process is obtained.
3
0
-0,5 -1 -1,5 -2 -2,5 -3 -3,5 ln(œ)
ln(W) 9 10
Fig. 1. Relationship between body mass of an adult bird (W, g) and "rate of aging" (o> , year-1), n = 29.
qcrit/q0
1.0 г
0.8 -
0.6 - ▼
----
0.4 ♦
0.2 ♦ ♦ ♦
0 1 1
10 ln W
gether within the range of mass 12-8663 g. Average value of p was equal to 2.600 ± 0.182**.
For approximation of relationship o>(W) 29 values of ffl calculated by Ricklefs and res
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