202
SYUNRO
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Ecology, Vol. 36, No. 2
UTIDA
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FLUCTUATIONS IN THE INTERACTING POPULATIONS OF HOST
AND PARASITE IN RELATION TO THE BIOTIC POTENTIAL
OF THE HOST'
SYUNRO UTIDA
Entomological Laboratory, College of Agriculture, Kyoto University, Kyoto, Japan
INTRODUCTION
The problem of cyclic fluctuations of insect populations has been approached deductively, starting
from the assumption that the fluctuations are inherent in the relation between predator (e.g. a
parastic wasp) and prey (e.g. a host insect). It
can be shown mathematically that the interacting
species fluctuate in numbers from generation to
generation, and the mathematical predictions have
been verified experimentally (DeBach and Smith
1941; Utida 1950, 1951a). A further inference
from the theoretical model is that the nature of
the predator's ecology should influence both the
amplitude and the period of the fluctuations, and
this was also demonstrated experimentally for
certain host-parasite combinations (Utida 1951b,
1953; Takahasi 1953). It is equally reasonable
to suppose that the host's ecology should have
like effects on amplitude and period. "Ecology"
in this context can be considered to be completely
embraced by the twin concepts of biotic potential
and environmental resistance; in Nicholson's
(1933) mathematical approach only the first (the
power of increase of the host) was taken into account, but the author (Utida 1953) has shown how
both parameters can be allowed for. The mathematical treatment has been published only in
Japanese, but a full account in English, together
with experimental proofs, is being published elsewhere. For the purpose of the present paper,
which reports part of the experimental work, only
a brief summary of the theory is needed.
The problem of predator-pDreyinteraction is
1 Contribution
from the Entomological
Kyoto University, No. 224.
Laboratory,
somewhat simplified, in the case of insect combinations consisting of host and parasite, by the fact
that time can be measured in generations, within
which mortality is complete. That is, members
of one generation do not survive to contribute to
the census of the next generation, and the numbers observed in one generation are purely the
product of events during the time of the preceding
generation. Since this advantage applies to both
parasite and host, and since it can be arranged that
both species have approximately the same generation time, the approach reduces to a simplified
version of the Lotka-Volterra model.
We begin with an expression for logistic growth
of either species:
N
- 1+{(
/~N)
1 + I (W/7No)
-1
1}~
}e -
(1)
where Nr is the number of individuals at the end
of any generation time x, No is the initial number,
and the upper asymptote of population growth
(K in the usual notation) has been partitioned into
E, the biotic potential, and 4, the coefficient of en-
vironmental resistance. This is equation (2) of
Fujita and Utida (1953), and in this equation it
is obvious that neither e nor 7 depends on the
initial number of population No. Thus the quantities b and c, defined as
b =e
,
(1-b)E
are regarded as constants. The total population
at the end of any generation is of course NaNo,
where a is the coefficient of mortality of adult insects in one generation, here taken as 1; letting the
April, 1955
INTERACTING
HOST AND
total population be P, equation (7) of Fujita and
Utida gives
P= No
(bN+ c
).
TABLE I. Mathematical expectation of the relations between the ecological characters of host species and the
mode of fluctuations in the interacting population of host
and parasite.
Conditions given
'hn + 1
203
POPULATION
(2)
For the dynamic interaction between host and
parasite populations, it is important to realize ( 1 )
that intrinsic oscillations are expected in P, even
in the absence of the parasite (Fujita and Utida
1953), and (2) that the number of parasite progeny does not increase linearly with the population of adult parasites. Thus the initial density
of host population in the (n + 1)th generation is
not the simple product of the final density of the
host in the nth generation and the host's power of
increase. But, if we assume that equation (2)
holds for both species, and that the number of
emerged parasites depends on the ratio of parasite
and host populations -n
PARASITE
Biotic
potential
of host
great
Mode of fluctuations obtained
Envirornmental resistance
Level of
of host
steady state
Amplitude of Period of
fluctuation
fluctuation
of density
of density
great
relatively
narrow
relatively
long
A
relatively
low
Symbol
in
Figure 1
great
small
high
wide
short
B
small
great
low
narrow
long
C
small
small
relatively
high
relatively
wide
relatively
short
D
A
, we may
,w
a write
rt equaqa
4.1
a
%~~~~~~~I
tion (2) in the form of simultaneous equations
hn + 1=
Pn +
= Pn
Hn (bh+
I-
ab) + c
)
cHn
h
1'--
i)
(3)
J
tak difrnIaus.(Rgrig
figre se
Tabl
I.
/o paast
bu
dfeignbioti
ineniomna
Hn + 1
hn + 1 -Pn
+ 1
where Hn and Pn, are the adult densities of host
and parasite populations in the nth generation,
hn ? 19Hn + 1, and Pn + 1 are the initial host, final
host, and parasite densites in the (n + 1)th generation, and b and c of equation (2) have been
appropriately transformed into bh, ch, bp, and cp
for host and parasite, respectively.
Unfortunately, equations (3) are non-linear
difference equations and cannot be solved analvtically. In the full version of the theory solutioins
are obtained by approxiinative methods with numerical examples, ancl they are summarized in
Table I, with special reference to the modes of
population fluctuation expected when the coefficients of biotic potential and enviroinmental resistance of the host are varied through wide ranges.
Figure 1 summarizes the same results graphically.
Experimental evidence is given below to support the deduction that in a host-parasite svstem
the amplitude and period of fluctuations of the
host population depend on the "ecologv" of the
host.
figure, see Table
site Nectlc/
th
syblnth
poe
eitne
ineth
I.)
tia
n
aui'ba
I
mneopiausIhieNga
on
othe
Types
pouatind futuatio whenthe suiotic
ther
weevies, Cal musotc eitsL
peiment
rssetac hotoste
of
potntal andsith enioi mensytal
expecies
taent differenthe
v lues. (Rgringcobntiesmols with the
andth
wressac
oftl
species
thos
spoential,
enviutprfonmena
differentcales.(eadnth
takelslatecl(il
monrarasit\\e
have
dtherinaore
figure,osee Tablies.)
bitchesybolsein
ptentia
the
ande
mwon
parasit ofu differimngainpbioticotntiale
andi
inedwl
envirnmetaleresistnce.
Sinte itheracukin bean
eecslewe
h
seemhtoelntohesmd ecological
tively,
nihean
ho to
hs
species.
aesmlreooy
menlt witlypesofltller ioneinlctationw the
biotic
To1;1I feperiment;othohehand
vevomiplutheyoare
MATERIAL AND M-\ETHOD
As material for the present purpose, we slhould ulationof calliebsis
C.
an(i Neocatolaccits and the
choose two species of host insect, having a com- otper is that of C. qloadrimacuslatdisand Neo-
204
SYUNRO
Ecology, Vol. 36, No. 2
UTIDA
catola;ccus. As the method used is the same as counted in three consecutive censuses. For simthat of the author's previous experiment (Utida plicity, the same treatment is accorded the data
1950), only a brief outline of it is given here. for wasps, although some error is thus introTwenty grams of azuki bean are used as food duced, the life cycle of the wasp being completed
for each population, which is maintained in a in about 2 weeks. The observations continued
perti dish of 4.3 cm. radius and 1.8 cm. depth about half a year and only eight generations were
(24.2 cc. capacity). The cultures are kept in obtained. Thus the results leave something to
darkness at 30?c. and 75% R.H. At each weekly be desired, as compared to those for C. chinensis
census the adults (male and female) of weevils and Neocatolaccus, which continued for over 50
and wasps are counted, dead as well as living. generations. Figure 2 gives the result of the first
Food is renewed every three weeks, which cor- experiment, in which C. quadrimcacula&tsand
responds to the time required for one generation Neocatolaccus were introduced simultaneously,
of both species of weevil under these conditions. and Figure 3 gives the results when the wasp was
Since the population fluctuation resulting from introduced into a flourishing weevil population.
interaction of C. chinensis and Neocatolaccus was
All four populations show fluctuations, but they
fully studied in the author's previous work (Utida differ in detail, even between duplicate experi1950), this combination was not repeated, and ments. In one of the first experiments (left half
the previous data are used again. The other of Fig. 2), the host population maintained an alhost-parasite pair (C. quadrimaculatus and Neo- most constant level of density, while the parasite
catolaccus) was studied in two experiments, each population increased rapidly at first, attaining a
being set up in duplicate. In one experiment, high level of density, and then decreased in the
small numbers of both host and parasite species 7th and 8th generations. In the duplicate of this
were introduced simultaneously at the beginning experiment (right half of Fig. 2), the fluctuation
of the experiment, and in the other a small num- was at first similar, but after the 6th generation
ber of the parasite species was introduced after the host population increased gradually while the
the host population had attained its equilibrium parasite population fell.
state.
In the other experiment, in which the parasite
was introduced after the host population had
RESULTS
From the number of dead and living individuals reached equilibrium, the results of the duplicates
at each census, the number of individuals emerg- are essentially indentical: the parasite increased as
ing between two successive counts can be cal- the host decreased, but the trend was reversed
culated. Since the duration of development of a after the 6th host generation, and the host ingeneration of the weevils is about 3 weeks, the creased as the parasite population fell.
total number of weevils that emerge in a generaThese fluctuations are very distinct and seem
tion is obtainable by summing up the numbers to be due to interaction between host and parasite
40C
'bZ300I
0
/
'
''
f
tI's''
T
2
'1
I
~
~
~
G
IERA
/0\
FIG. 2. Population fluctuations when C. quadrimacuilatus ( O
(- o - -). Both populations of host and parasite start simultaneously.
)
is
parasitized
by
ATeocatolaccus
April, 1955
HOST AND
INTERACTING
PARASITE
205
POPULATION
400
300
t3> 300
0~~~~~~~
o~~~~~~~~~~~~
0~~~~~
2
4
-6
8
4
2
6
TIOI'
GENVERA
Population fluctuations when C. quadrimaculatus (
O ) is parasitized by Neocatolaccus
FIG. 3.
Parasite population starts after the host population attains the steady state.
(-- * --).
species as predicted by the mathematical theories.
The minor differences, e.g. those between the
duplicate parts of the first experiment, may be attributed to random error but the reciprocal fluctuation in host and parasite populations is clearly reproducible.
We may now come to the comparison between
these results and the analogous ones from the C.
chinensis-Neocatolaccu, combination. The interest of this comparison is that C. chinensis,
though extremely similar to C. quadrimaculatus,
is known to deposit a slightly smaller number of
eggs in an optimum environment (Yosida 1952).
This would mean that its biotic potential (e in
equation (1)) is slightly smaller, and, as Table
I shows, a species with a smaller potential should
not give such violent fluctuations in numbers when
it lives with its parasite. Results for C. chinensis,
the species with the smaller biotic potential, are
given in Figure 4, which is reproduced from the
author's previous paper (Utida 1950), and, as may
be seen, the amplitude and period of the fluctuations of the host population are smaller than those
for C. quadrimaculatus. That is, particularly in
respect to amplitude, the difference between the
experimental results (comparing especially the
right half of Fig. 2 with Fig. 4) is like the difference predicted theoretically (comparing A with
C or B with D in Fig. 1). On the other hand,
in- respect to the absolute density attained by the
host species at equilibrium, the results are not so
clear-cut; at least, while there appears to be a
slight difference in favor of the species with the
higher potential (Fig. 2, especially the right half),
the difference is not obvious in the relatively short
span of available observations, and may not be
significant.
If the theory is only partially verified by this
comparison, it may be because of unconsidered
variations in 4, the coefficient of environmental
resistance. We have assumed that 4 remains constant, as seems reasonable when the major deterrent to potential increase of the weevils, the
presence of the wasp, is the same for both species.
However, this may not be correct, and since variation of 4 will have an influence on the mode of
population fluctuations that is of like magnitude
400
~300
I'
/0
0'~200
I
10
ol
2
4
6
8
10
(-EAE RAT I 0N
FIG. 4. Population fluctuation when C. chinensis (-O
- -) (from
is parasitized by Neocatolaccus (-)
Utida 1950).
206
LEWIS E. ANDERSON
AND PHILIPPE
but opposite sign to variation of e, different experiments will have to be designed to test this
possibility. For the present, we conclude that
the amplitude of the fluctuation in host and parasite populations is dependent on the intrinsic rate
of increase of the host population. This conclusion is the same as that deduced mathematically by Nicholson (1933) and the present author
(1953).
The author wishes to express hearty thanks
to Dr. E. S. Deevey of Yale University for reading through his manuscript and polishing its style.
SUM MARY
When the cowpea weevil Callosobruchus quadrimaculatus is maintained in controlled conditions
with its parasite, the wasp Neocatolaccus mamezophagus, reciprocal fluctuations of numbers are
observed in host and parasite. A similar result
was obtained earlier with another species of weevil, C. chinensis, in interaction with the same parasite and in identical conditions of culture. The
mode of the fluctuations is not quite identical in
the two host-parasite combinations, however, the
amplitude being greater when the host is C. quadrimaculatus. This difference is attributed to the
slightly greater biotic potential that C. quadrimaculatus is known to have, for it can be shown
theoretically that the amplitude of population
WATER RELATIONS
F. BOURDEAU
Ecology, Vol. 36, No. 2
fluctuation depends in high degree upon the reproductive potential of the host species.
REFERENCES
DeBach, P., and H. S. Smith. 1941. Are population
oscillations inherent in the host-parasite relation?
Ecology, 22: 363-369.
Fujita, H., and S. Utida. 1953. The effect of population density on the growth of an animal population.
Ecology, 34: 488-498.
Nicholson, A. J. 1933. The balance of animal populations. J. Anim. Ecol., 2: 132-178.
Takahasi, H. 1953. On the difference between two
parasitic wasps on their actions to the population
fluctuations of host and parasite.
Researches on
Population Ecology, 2: 47-54. (In Japanese.)
Utida, S. 1950. On the equilibrium state of the interacting population of an insect and its parasite.
Ecology, 31: 165-175.
-.
1951a. Population fluctuations caused by hostparasite interaction, II. Jap. J. Appl. Zool., 16: 111118. (In Japanese, but Mimeographed copy of the
English version is available on request.)
. 1951b. Role of parasite in determining equilibrium state of interacting population of a host and
its parasite.
Oyo-Kontyu, 7: 1-7. (In Japanese.)
. 1953. Population fluctuation in the system of
host-parasite interaction.
Researches on Population
Ecology, 2: 22-46. (In Japanese.)
Yosida, T. 1952. Experimental analysis of emergency
curve. Researches on Population Ecology, 1: 152165. (In Japanese.)
IN TWO SPECIES OF TERRESTRIAL
MOSSES
LEWIS
E. ANDERSON
AND PHILIPPE
F. BOURDEAV1
Department of Botany, Duke University, Durham, North Carolina
As every bryologist with field experience
knows, there is a sharp correlation between the
occurrence and distribution of many species of
mosses and the conditions of moisture of the habitat. As in vascular plants, most species can be
grouped ecologically into xero-, meso-, and hydrophytes. Little is known, however, concerning
water relations in the moss plant itself, so that
interrelationships of structure, physiology and
habitat are not well understood.
It is rather generally accepted that rhizoids are
not responsible for much, if any, water absorption
and that in most mosses only negligible amounts
are translocated internally. Water obtained by the
moss plant from the substrate is presumed, therefore, to rise by capillary movement on the outside
of the plant. Atmospheric moisture is absorbed
directly through the leaves and stems either in
1 Present address: Department of Botany, North Carolina State College, Raleigh, North Carolina.
liquid or vapor form or both. Corticolous and
rupestral mosses presumably obtain water principally from the atmosphere while terrestrial
mosses are generally assumed to absorb water from
both soil and atmosphere. The present study on
two species of terrestrial mosses, Atrichum angustatum Brid. and Polytrichum commune Hedw.,
was made in an attempt to determine and compare
the relative amounts of water these species absorb,
(1) from the substrate, and (2) from the atmosphere. Such information might be useful in explaining the distribution of mosses according to
conditions of moisture.
Apparently most of the early investigators assumed that water conduction in mosses takes place
entirely in the central strand of the stem and some
even went so far as to refer to this structural feature as "the conducting strand." Bowen (1931,
1933), however, in a series of ingeniously devised
experiments, demonstrated conclusively that