9780521861724htl 1..2

other extrinsic factors, but birth and death rates must match, and the rate

of production must offset the rate of mortality for a population to persist.

Population-turnover rate is another of those phenomena which is controlled

by metabolic rate and, consequently, shows characteristic 1/4-power scaling.

Metabolic rate determines the rate of population turnover, but what about

the abundances or steady-state densities of populations in the field? Based on

data for mammals, Damuth ( 1981 ) showed that population density scales as

M3/4. This is what would be expected if populations of a guild or trophic level

had equal rates of resource supply,R, because the steady-state population

density,N, should be proportional to the rate of resource supply divided

by the resource use or field metabolic rate per individual,P,soN/R/P/

M^0 /M3/4/M3/4. Recent compilations of data on population density as a func-

tion of mass generally support this prediction (Damuth, 1981 ; Belgranoet al.,

2002 ;Li, 2002 ; Allenet al., 2002 ;Brownet al., 2004 ). For example, Li (2002 ) showed

that the densities of morphospecies of phytoplankton in the North Atlantic

scaled asM0.78,whereMis cell carbon mass. An important community-level

consequence of population density or number of individuals per area, N,

y = –0.20x + 21.90

r^2 = 0.97

15

–30 –5 20

20

25

30

ln(body mass)

rmax

*e

E/kT

In(

)

algae

zooplankton

fish Figure 1.5The relationship between the

temperature-corrected maximum rate of

population growth (i.e. rmax), measured in

1/days, and the natural logarithm of body

mass, measured in grams, for various

aquatic organisms. Rmaxis temperature-

corrected using the Boltzmann factor,

eE/kT, following Eq. (1.2). Data and analyses

from Savageet al.(2004b).

y = –0.24x + 25.04

r^2 = 0.47

16

–5 7.5 20

22

28

ln(body mass)

In(mortality rate

*e

E/kT

)

Figure 1.6The relationship between the

temperature-corrected mortality rate of

marine fishes in the field, measured in

1/years, and the natural logarithm of body

mass, measured in grams. Mortality rate is

temperature-corrected using the Boltzmann

factor,eE/kT, following Eq. (1.2). Data and

analyses from Savageet al.(2004b).

8 J. H. BROWNETAL.