ENERGY I N ANIMAL ECOLOQY
83
representing any organism from the points representing all other
organisms from which it has at any time received a high-energy molecule. The resultant network of arrows is a food chain. Since objective
taxonomic criteria of specific discreteness exist, it is possible t o superimpose all points representing organisms of the same species, which
considerably simplifies the diagram. The concept of trophic level is
based on the assumption that in any food-chain (or food-web) diagram
there exist classes of points, each class being defined by a constant
number of arrows intervening between any point in the class and some
initial point characterized by the absence of arrows directed towards
it (i.e. an autotroph). This also carries the implication that there is
always a fixed number of arrows, or food-chain links, in the passage
from an autotroph to any particular species, regardless of the route
chosen. If this assumption is met, then all points characterized by a
constant number of arrows (i) between them and an autotroph can be
collapsed into a single point. The mean standing crop of all species
represented by this single point is called Ai+l since autotrophs are
A l . All arrows leading to this point can be collapsed into a single arrow
and the total energy flow represented by this arrow (in cal/time) is
referred to as hi.
Several questions are raised by this formulation and the attempt
to answer these questions empirically and theoretically has occupied
most of the workers in the field of ecological energetics ever since
Lindeman’s paper appeared.
1. Is there any maximum number of possible links in a food chain?
In a stronger form, we could ask, is there any characteristic number of
links in a food chain.
2. Is there any characteristic ratio between standing crops of species
at different locations in a food chain? In the terminology of trophic
levels does knowledge of the indices i and j of two trophic levels predict
in any sense the ratio Ai : Aj.
3. Are there any constsncies in the ratios of the productivities of a
species and the predators feeding on it? That is, is *a constant? This
A ,
- . I
ratio has been called either food-chain efficiency or ecological efficiency
by other authors (Slobodkin, 1959, 1960; Englemann, 1961).
4. Are all or any of these questions interdependent? For example,
could the existence of a characteristic number of links in a food chain
permit prediction of the answer t o the other questions.
These questions are independent of the simplifying assumptions
made by Lindeman and a.lso independent of the criticism of Lindeman’s
work which will be stated below.
Since food-chain efficiency is clearly less than one, the greeter the
83
representing any organism from the points representing all other
organisms from which it has at any time received a high-energy molecule. The resultant network of arrows is a food chain. Since objective
taxonomic criteria of specific discreteness exist, it is possible t o superimpose all points representing organisms of the same species, which
considerably simplifies the diagram. The concept of trophic level is
based on the assumption that in any food-chain (or food-web) diagram
there exist classes of points, each class being defined by a constant
number of arrows intervening between any point in the class and some
initial point characterized by the absence of arrows directed towards
it (i.e. an autotroph). This also carries the implication that there is
always a fixed number of arrows, or food-chain links, in the passage
from an autotroph to any particular species, regardless of the route
chosen. If this assumption is met, then all points characterized by a
constant number of arrows (i) between them and an autotroph can be
collapsed into a single point. The mean standing crop of all species
represented by this single point is called Ai+l since autotrophs are
A l . All arrows leading to this point can be collapsed into a single arrow
and the total energy flow represented by this arrow (in cal/time) is
referred to as hi.
Several questions are raised by this formulation and the attempt
to answer these questions empirically and theoretically has occupied
most of the workers in the field of ecological energetics ever since
Lindeman’s paper appeared.
1. Is there any maximum number of possible links in a food chain?
In a stronger form, we could ask, is there any characteristic number of
links in a food chain.
2. Is there any characteristic ratio between standing crops of species
at different locations in a food chain? In the terminology of trophic
levels does knowledge of the indices i and j of two trophic levels predict
in any sense the ratio Ai : Aj.
3. Are there any constsncies in the ratios of the productivities of a
species and the predators feeding on it? That is, is *a constant? This
A ,
- . I
ratio has been called either food-chain efficiency or ecological efficiency
by other authors (Slobodkin, 1959, 1960; Englemann, 1961).
4. Are all or any of these questions interdependent? For example,
could the existence of a characteristic number of links in a food chain
permit prediction of the answer t o the other questions.
These questions are independent of the simplifying assumptions
made by Lindeman and a.lso independent of the criticism of Lindeman’s
work which will be stated below.
Since food-chain efficiency is clearly less than one, the greeter the