78
L. B. S L O B O D K I N
or, if he also takes yields of the sortsj, L, 1 . . .
Yi
I = P'c + c -
EDi
where E,, (population efficiency) is given by
Equation (8) represents a particularly interesting energy-budget
equation for a single species since it combines certain properties of all
three energy-budget equations. Since yield is consumed within a
community, Eq. (8) reduces t o Eq. (2'), for complete communities.
I n summary, the various equations that have been utilized for
energy studies in ecology can be intertranslated in a straightforward
manner. They differ primarily in the kind of data used and in emphasis.
111. ENTROPY A N D INFORMATION IN ECOLOQY
A review of energy relations in ecology can be written with suitable
incorporation of all relevant data, without ever mentioning either
entropy or information in their rigorous meanings. Several recent
authors have, nevertheless, felt it of value t o discuss ecological energetics in terms of entropy and information. Since the theory of information has been developed, specifically, t o deal with communication
problems, such as determining which of a particular set of messages
was actually transmitted through a communications channel which
was not perfect, it is immediately adaptable to situations in which the
investigator's concern is with the distribution, organization, number
or arrangement of entities in an imperfectly understood situation about
which he has some partial knowledge.
Margalef (1958), Hairston (1959), MacArthur (1960), and MacArthur
and MacArthur (1961) have used communication theory in this way
t o great profit. The significance of their work has been discussed at
some length by Hutchinson (1959) and Slobodkin (1961a,b).
Occasionally, information theory has been used as an analogy t o
suggest models that might be of ecological interest (MacArthur, 1955).
There exists a certain formal correspondence between the rigorously
defined concept of information and the rigorously defined concept of
entropy.
I n particular
n
H = C P i l o g p i
0
represents the information H in a set of n independent messages, each
with a probability Pi of being transmitted.
L. B. S L O B O D K I N
or, if he also takes yields of the sortsj, L, 1 . . .
Yi
I = P'c + c -
EDi
where E,, (population efficiency) is given by
Equation (8) represents a particularly interesting energy-budget
equation for a single species since it combines certain properties of all
three energy-budget equations. Since yield is consumed within a
community, Eq. (8) reduces t o Eq. (2'), for complete communities.
I n summary, the various equations that have been utilized for
energy studies in ecology can be intertranslated in a straightforward
manner. They differ primarily in the kind of data used and in emphasis.
111. ENTROPY A N D INFORMATION IN ECOLOQY
A review of energy relations in ecology can be written with suitable
incorporation of all relevant data, without ever mentioning either
entropy or information in their rigorous meanings. Several recent
authors have, nevertheless, felt it of value t o discuss ecological energetics in terms of entropy and information. Since the theory of information has been developed, specifically, t o deal with communication
problems, such as determining which of a particular set of messages
was actually transmitted through a communications channel which
was not perfect, it is immediately adaptable to situations in which the
investigator's concern is with the distribution, organization, number
or arrangement of entities in an imperfectly understood situation about
which he has some partial knowledge.
Margalef (1958), Hairston (1959), MacArthur (1960), and MacArthur
and MacArthur (1961) have used communication theory in this way
t o great profit. The significance of their work has been discussed at
some length by Hutchinson (1959) and Slobodkin (1961a,b).
Occasionally, information theory has been used as an analogy t o
suggest models that might be of ecological interest (MacArthur, 1955).
There exists a certain formal correspondence between the rigorously
defined concept of information and the rigorously defined concept of
entropy.
I n particular
n
H = C P i l o g p i
0
represents the information H in a set of n independent messages, each
with a probability Pi of being transmitted.