84
L. B. SLOBODKIN
number of links in the food chain the lower the energy income per cm2
of earth surface per time of the organisms high in the chain. If foodchain efficiency is constant (say E ) , the energy income of any species
will be proportional to E' where i is the mean number of food-chain
links between that species and the autotrophs.
A species high in the food chain (j) might have an abundance equal t o
that of a species low in the food chain (i) if the ratio 2 is equal t o 2
or greater than E(j-') where E is the constant food-chain efficiency and
c is maintenance cost. Since a large part of the maintenance cost of any
species is respiration, and since there is no reason t o expect a hunter
t o do less work than its prey, we would not expect species high in the
food chain to be as abundant per unit area as those low in the food
chai.n. Should maintenance cost of species be constant, we would expect
the abundance of species at levels j and i t o be proportional to E@i).
The classical Eltonian pyramid depends on the fact that typically
there is a correlation between body size and trophic level. Reversal or
inverted Eltonian pyramids occasionally occur either as a temporary
distortion of the normal steady state (Evans and Lanham, 1960) or
as a consequence of extremely heavy predation and rapid growth in
the lower levels of the food chain (Odum and Odum, 1955).
The maximum number of possible links in the food chain is dependent
on relati/ve abundance as a function of food-chain position. Since X is
expressed as callarea, the food for an animal sufficiently high in the
food chain is so dilute as t o place it in the position of the sheep which
must run, not walk, between grass blades lest it starve t o death. The
questions raised by the Lindeman formulation are, therefore, intimately
interrelated.
There is, however, a serious logical error in Lindeman's study which
effectively invalidates all his estimates of productivity and efficiency.
This is not simply a matter of slight differences in definition or of high
variance in the initial estimates. Since his procedure has been followed
by other authors (Dineen, 1953) and his estimates have been quoted in
various contexts (Slobodkin, 1960; Patten, 1959; and others) it is of
importance t o prevent further reliance on these data.
As already indicated, the energy budget for a trophic level can be
written as
C.
C i
Ci
I =Respiration + Yield
Yield consists of all potential energy leaving the trophic level, including
that consumed by predators and decomposers.
Lindeman, however constructed the following energy budget
I =Respiration +Yield + (Turnover time x Stending crop)
L. B. SLOBODKIN
number of links in the food chain the lower the energy income per cm2
of earth surface per time of the organisms high in the chain. If foodchain efficiency is constant (say E ) , the energy income of any species
will be proportional to E' where i is the mean number of food-chain
links between that species and the autotrophs.
A species high in the food chain (j) might have an abundance equal t o
that of a species low in the food chain (i) if the ratio 2 is equal t o 2
or greater than E(j-') where E is the constant food-chain efficiency and
c is maintenance cost. Since a large part of the maintenance cost of any
species is respiration, and since there is no reason t o expect a hunter
t o do less work than its prey, we would not expect species high in the
food chain to be as abundant per unit area as those low in the food
chai.n. Should maintenance cost of species be constant, we would expect
the abundance of species at levels j and i t o be proportional to E@i).
The classical Eltonian pyramid depends on the fact that typically
there is a correlation between body size and trophic level. Reversal or
inverted Eltonian pyramids occasionally occur either as a temporary
distortion of the normal steady state (Evans and Lanham, 1960) or
as a consequence of extremely heavy predation and rapid growth in
the lower levels of the food chain (Odum and Odum, 1955).
The maximum number of possible links in the food chain is dependent
on relati/ve abundance as a function of food-chain position. Since X is
expressed as callarea, the food for an animal sufficiently high in the
food chain is so dilute as t o place it in the position of the sheep which
must run, not walk, between grass blades lest it starve t o death. The
questions raised by the Lindeman formulation are, therefore, intimately
interrelated.
There is, however, a serious logical error in Lindeman's study which
effectively invalidates all his estimates of productivity and efficiency.
This is not simply a matter of slight differences in definition or of high
variance in the initial estimates. Since his procedure has been followed
by other authors (Dineen, 1953) and his estimates have been quoted in
various contexts (Slobodkin, 1960; Patten, 1959; and others) it is of
importance t o prevent further reliance on these data.
As already indicated, the energy budget for a trophic level can be
written as
C.
C i
Ci
I =Respiration + Yield
Yield consists of all potential energy leaving the trophic level, including
that consumed by predators and decomposers.
Lindeman, however constructed the following energy budget
I =Respiration +Yield + (Turnover time x Stending crop)