Copyright 1972.
All
righu reservedINTERSPECIFIC COMPETITION AMONG RODENTS 4037
P. R. GRANT
Biology Department, McGill University Montreal,
Quebec,
CanadaThe aim of this paper is to integrate the results of the several experiments reported in this series,1 to review other published evidence of competitive in teraction among rodent species, and to formulate some general statements.
The experiments were stimulated
by
the lackof
a rigorous experimental demonstration of competition between species of vertebrates under field con ditions. There is an abundance of indirect evidence and some direct evidence(96, 97, 110, 111),
but in contrast to the situation with invertebrates(38),
experimental
studies with vertebrates have lackedappropriate controls. Ex
ceptions to this are Inger & Greenberg's(76)
study of frogs
in Borneo,and
more recently Jaeger's(77, 78)
study of salamanders in eastern North America. The
importance of the subject scarcely needsemphasizing
at a time when competition theory plays so conspicuous a role in community ecology and evolution analyses(75,88, 90,96, 98) .
The evidence from other studies o f rodents is reviewed first. Then the experiments reported in this series are discussed. Finally
some generalizations
and theoretical considerations are presented.FIELD OBSERVATIONS
Contiguous, allopatric distributions of rodent species have been inter preted as being the result
of
interspecific competition( 18, 22, 74, 79, 1 15,
124) ,
but the major evidence for interspecific competition is derived from observations of sympatric species. The evidence falls into two categories:(a)
two sympatric species exhibit an inverse numerical relationship, and(b)
two sympatric speciesexhibit an
inversespatial
rel
ati
onship
.In the first category the population numbers of one species rise while those of the other fall. This has been observed and commented upon several times (e.g.
3, 14, 1 7, 49, 56, 61, 70, 91, 92, 128, 129, 138, 146 ) .
In some cases the numerical changes are later reversed, with the common species be coming rare and the rare species becoming common. Numerical phenomena of this sort,and all
the population parameters involved (birth, d'eath, and 1 This is Part V and is entitled Experimental studies of competitive interactionin a two-species system. V. Summary of the evidence for rodent species, and some generalizations.
79
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Further
dispersal
rates,etc),
mayrefiect
the outcome ofcompetitive
interaction ina
temporarily varying environment, although competition clearly need not be involved (e.g. see
127).
At its extreme, this leads to the extinction of one of the species. Such was observed to occur on Brooks Island in California(86,
87). Microtus californicus,
a new immigrant to the island, increased in num bers at a time when the resident species Mus musculus declined in numbers, eventually to extinction. The authors suggested that the decline ofMus mus
culus was actually caused byMicrotus californicus,
due to competition for food and space. Aggressive interaction was indicated for the latter. This sug gestion was supported by the results of work by de Long(45,
46), who provided evidence for the competitive inferiority of Mus musculusin
the field on the mainland, and for the vulnerability of Mus musculus to damaging at tack from M. californicus in the laboratory (also86).
Moreover Quadagno(118)
found that Mus musculus had smaller home ranges in the presence of M.californicus
than in their absence.In the second category, two species sometimes occupy different parts of the same habitat for no clearly discernible reason associated with variations in habitat features, and therefore possibly as a result of interspecific interac tion
(6, 7,
9,
120).
Small-scale spatial sf:paration of this sort should lead to an increased difference in diets, if one species dominates the other and ex cludes it from the best patches of habitat, Cameron(29)
has found evidence of this with woodrats (Neotoma spp.). In allopatry N. fuscipes and N. lepida have similar but not identical diets. In sympatry N. lepida, but not the domi nant N. fuscipes, has shifted its diet to a small extent, as a result of which the diets of the two species are more different in sympatry than in aIIopatry.Species may also be generally contiguously allopatric, but locally sympat ric, and here in the zone of overlap competition between the species prevents one or both from spreading into the other's exclusive domain. Such has been suggested for chipmunk species in western North America
(18,74, 124).
In each of these three independent studies there is evidence from laboratory or the field that one species is aggressively dominant to another and therefore could restrict the movements of the other through aggressive interaction.Moreover, the variety of habitats oC1;upied by a species is smaller in the presence than in the absence of another species (e.g.
1 1, 1 8, 21 , 52, 53, 92,
95,
125, 146,
other references cited in the Introduction). The appearance of one species in a habitat has been observed to coincide approximately with the decline in numbers or absence of another species normally resident in that habitat( 1 7, 19-21, 32, 41,
50,
93, 128, 129, 147).
Once again the difficulty arises that the events may or may not be casually related. Apparently con vincing explanations involving competition sometimes lose force when other factors are taken into account. This point is well illustrated by the changes in distribution of the arctic hare, Lepus arcticus, on Newfoundland, often quoted as a clear example of interspecifi.; competition(27, 89a) .
Originally the arctic hare occurred in alpine, subalpine,
and
(lower)woodland
habitats; but following the iintrod
uction ofthe snowshoe hare,
Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
Lepus american
us, about100
years ago, it disappeared from the woodland, which was then solely occupied by the snowshoe hare. The situation on New foundland is now similar to the one on the North American mainland. It has suggested to several authors (e.g.27,
46a, 89a) a simple hypothesis to account for the changes in distribution: the arctic hare, upon arrival in New foundland, expanded its range of habitats in the absence of competition from the snowshoe hare, and then contracted the range as a result of competition with it in the woodland. However, the arctic hare is now conspicuously re stricted to terrain with ample escape cover from predators (9a). Furthermore the principle predator, the lynx(Lynx canadensis),
is known to have in creased in numbers substantially following the snowshoe hare introduction. Bergerud (9a) has suggested, therefore, that the disappearance of the arctic hare from the woodland is attributable to increased predation there by lynx, whose numbers increased as a direct result of the availability of snowshoe hare as prey. A complex interaction of the three species is indicated, rather than just a simple competitive interaction between the two hare species. Which of the two species, lynx or snowshoe hare, played the larger role in facilitating the habitatexpansion
of the arctic hare is a matter for conjecture. But one additional factor makes the predation pressure hypothesis for the habitatrestriction
more convincing than the competition hypothesis. The arctic hare no longer occupies large sections of subalpine and alpine habitat that are poor in escape cover, and snowshoe hares have not occupied these areas either (9a). In some instances both the distribution of the presumed interactants, with regard to variety of habitats occupied, and their numbers are inversely re lated (119, 137, 139-141). Thus, the distribution of numbers in time and in space are complementary aspects of the position of a species in the environ ment, and both aspects, according to this circumstantial evidence, are in fluenced by the presence of other interacting species.These dynamic relationships are summarized in two models in Figure 1. In Modell the optima for the two species are widely separated along the habitat axis; in Model
2
they are closer and are nearly identical. The models depict a cycle of reciprocal expansions and contractions, both numerical and spatial, and each cycle is composed of two subcycles. Thus, a given pair of species may progress from Stage1
to2
and back again, and only rarely pass all the way from 1 through2
to 3 and back again. Degree and shape of the overlap segment of the curves depend upon dominance, habitat tolerances, etc. For instance, where a predictable dominance exists, the slope of the curve is likely to be steeper for the subordinate species than for the dominant one, and this may be of use in the testing of a model.FIELD EXPERIMENTS
Experiments, with or without enclosures, have been conducted only in the last 15 years. Enclosing populations gives control over the interactants as well as other elements such as mammalian predators. One study of interspecific interaction has been made with enclosed populations, and it has given
posi-Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
MODEL MODEL 2 habitats habitats N N
�
(J
2\\
fJ 2 \\
WW
3 RW FIGURE 1. Two models of habitat occupancy by competing species. The num ber of animals (N) of two speci
es, A and :B, is shown in a spectrum of habitats linearly ordered along the horizontal axis.tive evidence of interaction.
Caldwell (23)
followed the fate of populationsof
Peromyscus polionotus
andMus musculus
in a1
acre field enclosure. Ini tially the two species occupied separate areas of the enclosure for no discern ible reason connected with variations in the habitat, which suggests an inter action between the species. Thisis
further supported by subsequent events. P.polionotus
gradually invaded the area ofMus musculus,
which declined to extinction in6
months. However, no aggressive interaction was manifested by animals kept together in the laboratory, so Caldwell concluded that de spite the initial spatial separation, the species had competed for food rather than for space. In the laboratory the two species selected the same types of seeds to a large extent(23).
There wall no control enclosure for the field experiment, but six unenclosed and larger plots which had both species were studied at the same time.Mus musculus
became extinct on four of these, but persisted for15
months on the plot most similar in habitat-features to the enclosed area. Without a single-spe
cies control, it is not certain thatMus
musculus
would have persisted in the absence of P.polionotus,
but that it became extinct in the enclosure at least suggests a competitive interaction. Caldwell & Gentry(24)
repeated the experiment with essentially the same result, including the initial spatial separation of the species.Krebs et
al
( 85)
appear to have provided evidence inadvertently of a competitive interaction betweenM. pennrylvanicus
andM. ochrogaster
inen-Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
83
closures containing grassland.
M. ochrogaster
became more numerous in an enclosure without its conspecific than in another with it, suggesting an inter action between the species when together in the same enclosure.Vaughan & Hanson
(144)
experimented with unenclosed populations of two species of pocket gophers, using the technique of removing alI residents from an area and then introducing both species to see if they were capable of coexisting in the same habitat. Three areas were used, each2
to6
acres in size. One area originally had both species, another had onlyThomomys bot
tae,
and the third had only T.talpoides.
Residents were removed, and both species were introduced into each area at high and equal densities. In the following year all the animals were removed, and the experiment was re peated for another year with new animals. At the end of both experimentsT.
bottae
predominated in the area which originally had onlyT. bottae,
andT.
talpoides
predominated in the area which originally had only T.talpoides. T.
talpoides
also predominated at the end of the first experiment in the area originally supporting both species; but at the end of the second experiment only one T.bottae
was found in this area. Unfortunately no estimates were given of the densities of the two species prevailing before the experiments were carried out so that the above results might be compared, nor were single species controls conducted. The results of the experiments might be exactly those predicted on the basis of different habitat affinities of the species, al though interspecific competition could have occurred as well. Vaughan & Hanson also discuss the possible influence of reproduction and dispersal upon the observed changes in numbers. In a later paper dealing with the coexis tence of these two species, Vaughan(143)
gave little emphasis to interspe cific competition. [Clough's(36)
addition experiment is discussed on p.94.]
The opposite of putting two species togetheris
to remove one from an area where previouslyit had coexisted with another.
Ashift
in distribution of the remaining species into the area previously occupied by the removed spe cies is evidence for a previous interaction between the species; just as, analo gously, intraspecific interaction is inferred from the repopulation of an area, from which individuals were removed, by neighbors or more distant members of the same population(4, 5, 13, 15,25,26,31,73, 83, 107, 109, 132-136,
142).
This technique was first used by Sheppe
(125, 126)
and was later adopted by Koplin & Hoffmann(82);
Peterson( 117),
as reported by Baker(7);
Sheppard( 123, 124);
and Stoecker( 137).
Sheppe( 125)
observed thatPeromyscus oreas
was almost entirely restricted to the floors of ravines in parts of British Columbia, and P.maniculatus
was present only on the sides of the ravines and in neighboring areas; the two species were present together in a narrow zone of overlap on the lower slopes of the ravines. Having re corded no P.maniculatus
on the floor of a ravine in2
years, he removed the wholeP.
orear population. This was easy to do because the population was an isolated one. He then recorded15
P. maniculatus on the floor of thera-Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
84
,. vine in the next 2 years.
Thisexperiment was performed without a control, so
it is possible that
P.
maniculatus
wou
ld have occurred on the ravine floor
anyway, irrespective of the presence or ab:;ence of P. o
reas
,particularly if the
population level of
P.man
ic
ulatu
swas higher ill the years following the
removal of
P.areas. However, Sheppe's
,;onclusion that P.oreas
had previ
ously excluded
P.man
icu
latus
from the ravine floor is supported by subse
quent and uncontrolled events. Sometime in the next 6 years P. oreas re-in
vaded the ravine, because when trapping was next performed in the ravine
only
P.oreas were captured on the floor (126) .
Sheppe ( 126) also performed the same type of uncontrolled experiment
with Mus musculus and
P.man
icula
tus
in
a
ranch
buildingwhere the maxi
mum abundance of each species coincided with the least abundance of the
other. The removal of Mus musc
ulu
swas followed by a small invasion of
that area by
P.maniculatus.
Again, this might have occurred anyway, espe
cially as recruits were entering the
P.maniculatus
populationat this time and
might be expected to disperse. In contrast to the results of Caldwell's study,
there was evidence, from the type
ofwound scars on
P.maniculatus
individu
als, of an aggressive interaction between the species (see also King
81).
It is
possible, therefore, that the two species tended to exclude one another from
different parts of the building by aggressive interaction.
As reported by Baker
(7),
Peterson
(11 7)
performed a
similar removal experiment withcotton
rats(Sigmodon)
in agrassland community in Du
rango, Mexico. The numerically dominant and "spatially unrestricted"
S.lul
viventer were removed serially. As the numbers of
S./ulviventer declined, the
numbers of
S.hispidus
increased, and their ranges, previously restricted, ex
panded. One year later
S. fulviventerhad increased and regained its position
of numerical dominance. These results suggest that
S.lulviventer
competi
tively interacted with
S.hispidus in some way, to the detriment
of
S.hispidus,
although no controls for this experiment are mentioned by Baker (7).
Koplin
&Hoffmann
(82)
used the removal te
chniq
ue in a 1lLudy of Mi
cro
tus montanus
and M. pennsylvanicus, but also provided a contemporaneous
control. They
usedtwo neighboring areas of unequal size as control and ex
perimental conditions. Both areas had "hydric-mesic" and "xeric" habitats, in
approximately the same proportions, and both contained the
twospecies,
wi
th M. pennsylvanicus
mainly in mesic and M. montanus solely in xeric
habitats. After M. pennsylvanicus was removed from the experimental plot,
M. montanus was
cap
tured in both habitats. This contrasts
with the com
ple
te
absen'ce of M. montanus from the mesic: habitat on the control area through
out the study. The authors concluded that M. pennsylvanicus competitively
excluded M. mon
tan
usfrom the mesic habitat on the control area throughout
the study, and on the experimental area before M. pennsylvanicus was re
moved. The dominance of M. p
ennsy
lvani
cusover M. montanus in the labo
ratory
(103)
supports the conclusion.
The conclusion
may becorrect,
but the (nonstatistical)comparison
ofcontrol and experimental data is marred
bythe fact that the population sizes
Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
were quite different on the two areas; hence, the behavior of the populations may not be strictly comparable. Prior to the removal period, M. montanus (like M. pennsylvanicus) was present in much higher numbers on the experi mental plot than on the larger control plot. The authors believe this to be due to the grazing effects of Bison bison on the control plot during the study, and to the absence of such effects on the (fenced) experimental plot. Therefore, the failure of
M.
montanus to move from xeric to mesic habitat on the con trol plot may have been due to the absence of high-density conditions, rela tive to the resources, which might bee
xpe
cted to promote dispersal from one ha
bitat to the other. If this is correct, the movement ofM.
montanus from xeric to mesic habitat on the experimental plot, following the removal of M.pennsylvanicus,
may have been due solely to an increasein M. montanus
density at
this time. Unfortunately, the density of M.montanus
is not known, because no trapping was done in the xeric habitat on tbe experimental plot at that time. Thus, the hypothesis of Findley(53),
which predicts the results obtained, is supported but not adequately tested.A
more recent study of these two species conducted more than300
km from the Koplin and Hoffmann study area has produced somewhat different results (Stoecker, in press) .If
one species is consistently dominant to the other in this location it is M. montanus, notM.
pennsylvanicus, as revealed by laboratory observations in simulated natural habitat. The field evidence for interspecific competition is equivocal.M.
pennsylvanicus was present in xeric habitat with M. montanus in one year, when theM.
pennsylvanicus density was high andM.
montanus density was low, and not in another yearwhen the populations
wereabout
equal. These results canbe
accounted for solely interms
ofintraspecific interaction
in the M. pennsylvanicus popula tion sufficient to cause movementinto
the xeric habitat at high density but not at low den
sity. Stoecker(137)
made a similar point. Nevertheless, inter specific interaction with generallydominant M. montanus
may also be in volved, and it is indicated by a small-scale removal experiment. In one small areaM.
pennsylvanicus was trapped for the first time only after M. montanus· had been removed.Thus, a comparison of the results of the two studies of these two species leads to the conclusion that if the species compete with each other for space, the outcome varies regionally. This implies that competitive attributes, such as aggressiveness, vary regionally, perhaps in relation to habitat factors (cf.
8).
Although plausible, this need not be so, because aggressiveness also varies in relation to the stage in a population cycle, at least inM.
pennsylvanicus(34);
Krebs(84)
has also demonstrated this withM.
ochrogaster. Hence, the outcome of competitive interaction between species such as these can be expected to vary at the same location according to the position of one popu lation
in relation to itsc
yc
le, and according to the relative densities of the two species.Sheppard's
( 1 23, 1 24)
stUdy concerned two species of Chipmunks
which are partly sympatric and partly allopatric. Eutamias amoenus
occurs
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mainly in forested areas at generally low altitudes, while E.
minimusoccurs
in alpine meadows and rocky areas at high altitude; there is a narrow zone of overlap in altitudinal ranges where the two species coexist.S
h
ep
pard
took15
E.minimus
from al
pine
habitat and introduced them toa
forested area fromwhich 20
E.amOenus had been removed. From the description
gi
ven of
the habitatin the area
ofintroduction
it appearsto
have
been
suitable
for
either
s
peci
es and to have been
more suitable for the introduced E.minimus
than
wasthe habitat in any neighboring area. On two subsequent
trappingocca
sions, first three and then one of the introduced animals were captured. Ten
E.amoenus
were introduced into an
are:a fromwhich 14
E. minimushad
beenremoved, and another 10 were
introduced intoan area in which 14 r
es
i dent E. minimusw
er
eallowed
to remain.None of
th
e introduced E.amoenus
were subsequently retrapped in either arc�a. But since
the neighboringareas
had
habitat(forest) more suitable for E. clmoenus,
it isl
ikely that E.amoenus
moved into them,a
possibility noted'by
S
hep
par
d.
The results of these experiments have been quoted by Miller
(96)
as ev
i
dence
for
interspecific co
mpe
tit
io
n,
but th
ey might eq
ua
ll
ywell be e
xplai
ned
on the basis of d
iffe
re
nt
habit
at
pref
ere
nc
es and the availability or lack of more suitable habitat adjacent to the area into which the introductions were made. Nevertheless, the possibility of in
ters
peci
fi
c competition in the wild,
with
E.a
moe
nu
s tending
to e
xclu
de
E.minimus
from forested areas, is sup portedby
the results of Sheppard's laboratory studies. These showed E.amoenus
to be
generallydominant to the smaller
E. minimus.LABORATORY EXPERIMENTS
Some of the
ev
i
denc
e has beenmentioned already, and most of
it has been di
sc
us
s
ed in Part IIof
this seri
es(64;
see also8, 99, 103, 104, 108) , s
oonly
the essentialswill
bestated here. Individuals of different species are fre
quently aggressive to each other under the confined conditions of thelabora
tory test arena. Aggressive interactions have been observed occasionally inthe wild
aswell (2, 80) ,
indi
cati
ng that the laboratory studies reflect, how ever imperfectly, behavior exhibited in the wild. Many ofthe species which
app
ear
to interact competitively for space in the wild interact aggressively in the laboratory, the outcome being the establishment of a dominance relation ship. Thisis
generally stable(8).
In those instances where the field evidence indicates that one species mi
ght co
nsist
en
tly
beco
mpe
titiv
ely
superiorto the
other, it is alsog
en
er
all
y
the dominant o:ne in the laboratorytests (29,45, 82,
106, 124, 144, 147 ) ; conflicting results
from laboratoryte
sts(99, 104)
are
probably attributable to differences in t€�st procedures, and to different envi
ronmental conditions from which the animals were drawn (92, 103, 137; see
also p. 85) .
Ith
asalso been s
hown
that whentwo
spe
ci
es of different habitataffinity are
placed
together in a
la
b
ora
t
ory
test
arena which hassegments of
both habitats, the species disperse into their usual or "preferred"
habitats, apparently as a consequenceof
the
ago:nistic behavior exhibited under those
conditions
(64, 137) .
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THE SERIES OF EXPERIMENTS WITH WOODLAND AND GRASSLAND SPECIES Choice of specie
s.
-The experiments were designed to demonstrate com
petitive interaction between species under near-natural conditions. It was de
cided to use species which might compete for space, because the results of
competition for space are easier to measure than are the results of competi
tion for food. It was further decided to use two species of animals whose
activities are more or less restricted to the surface of the ground (two-dimen-
sional space) for ease of recording their distributions.
Afinal requirement
was small individual body size, hence potentially large population size, in an
area sufficiently small for suitable experimental manipulations.
The choice of species was made on the basis of indirect evidence of com
petitive interaction in areas of sympatry. The species were rodents of the
family Microtinae:
Microtus pennsylvanicus pennsylvanicus(Ord) from
grassland; and from woodland,
Clethrionomys gapperi gapperi(Vigors) in
some experiments and Peromyscus maniculatus gracilis (Wagner) in others.
On the mainland of North America these species are sympatric overlarge
areas, yet the grassland and woodland species are rarely found outside their
usual habitats. On islands the restriction to habitat is not so pronounced. On
islands in Notre Dame Bay off Newfoundland
(121) and Penobscot Bay in
Maine
(K. L.
Crowell personal communication), M. pennsylvanicus occur in
both grassland and woodland in the absence of the two woodland species.
Conversely, P. maniculatus have been recorded in grassland on islands
largely or entirely devoid of M. pennsylvanicus
(27,
51, 114,
K.L.
Crowell
personal communication).
C.gapperi
have not been reported in grassland on
islands without M. pennsylvanicus (28); but on islands lacking a Microtus
species in the British Isles
(40,44, 55) and in Japan (113) , species of
Cleth rionomyssimilar to
C. gapperihave been found to occupy the grassland to
a
greater extent than on the nearby mainland where Microtus species are pres
ent. These facts indicate, but by no means prove, that the habitat restriction
in mainland areas is caused by other species.
Acompetitive interaction be
tween species, however rarely it might occur, would adequately account for
the restriction observed in areas of sympatry; and the lack of restriction on
islands
isaccounted for by a hypothesis of ecological release (28, 65, 66).
The requirements for a demonstration of interaction.-For
a demonstra
tion of competitive interaction in a two-species two-habitat system, one of the
species (Species 1) should occur in the other's habitat more frequently in the
absence that in the presence of the other species (Species 2). This result can
be obtained more clearly with enclosed populations than with unrestrained
ones. Two approaches to the conduct of such an experiment in enclosures are
possible:
(a)a contemporaneous approach, with control (one-species) and
experimental (two-species) conditions in separate enclosures at the same
time; and (b) a sequential approach, with control and experimental condi
tions in the same enclosure either at different times of the year or, prefer
a
bly,
Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
at the same time in different years. Each approach has its advantages and disadvantages. For example, the contemporaneous approach is more costly to follow in terms of materials, but it does allow one to eliminate the (un known) effects of time (season, years) upon the results. However, if con ducted in this way the experiment should be repeated, with experimental and control conditions reversed, in order to eliminate the effects upon the results of small differences in habitat features between enclosures.
Conclusive evidence for interaction is then obtained if, following the in troduction of Species
2
into its usual habitat, where Species1
has been occur ring frequently, Species1
leaves this habitat and now stays more or less en tirely in its own usual habitat.These steps in the demonstration are shown diagrammatically and hypo thetically in Figure
2.
The contemporane:ous approach is used. For the pur pose of illustration, steps1
and2
show the woodland species C.gapperi,
as Species1,
occurring in the grassland more frequently in the absence than in the presence of the grassland speciesM. pennsylvanicus
as Species2
(these steps could have been illustrated just as well withM. pennsylvanicus
entering the woodland). Step3
shows that, following the transposition ofM. pennsyl
vanicus
from Enclosure I grassland to Enclosure II grassland, C.gapperi
oc curs in EnclosureII
grassland less frequc:ntIy than before, and also less fre quently than in Enclosure III grassland (control). In addition, C. gapperi now occur more frequently in Enclosure I grassland than whenM. pennsylvanicus
were there.The most obvious biases are eliminated by this procedure. One set, which is difficult to control, comprises those population factors that cause members of a species to leave their usual habitat and enter another. These include the density. sex and age composition of the population and associated behavior, which may not be the same in two enclosures. Replicates of experimental and control conditions would help to minimize the effects upon the results of dif ferences
in
these factors. A further value of replicates liesin
providing an assessment of the consistency, and hence reliability. of the results. However, for practical reasons replicates are not feasible in studies of this type and scale with vertebrates. Therefore, in their absence, it must be shown that dif fernces in the population features of a species between enclosures do not account for the difference between enclosures in the frequency of occurrence of that species in the habitat of the other species.There are alternative outcomes of these experiments which lead to an op posite conclusion (providing that all biases have been eliminated). One spe cies might occur in the other's habitat as jfrequently. or even more frequently, in the presence as in the absence of the other species. The conclusion from both of these outcomes is that competitivl� interaction between the species did not occur. Therefore, the results allow a decision to be made as to whether or not the two species interact competitively.
The experimental evidence jor interaction in the grassland.-Experiments
were conductedin
three enclosures in soJuthern Quebec in three successiveAnnu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
1. Wood c -
i
--i
--Groll 2. c --t---M 3. c --t
--i
--Enclolures II III c ---i----M c --t--i-c . ,tt-ti
\_, '-' M c --l-
--l-
--c -i
---r
- e-ctt
-FIGURE 2. The requirements for a demonstration of interaction between Species C (Clethrionomys gapperi) and M (Microtus pennsylvanicus) in grass land habitat. Arrows indicate degree of movement but do not represent move ment of all animals from one habitat to another. Steps
1
and 2 are shown as separate experiments. Step 3 is a second part of Experiment2
and involves the transposition, by the experimenter, of all of Species M from Enclosure I to II. years and have been reported in detail(63,65).
The disposition of the enclo sures and habitats is as shown in Figure2.
Each contained0.5
acre of grass land and the same area of deciduous woodland. The distribution of the ani mals was determined by weekly trapping with Longworth live-traps for a pe riod of4
to5
months. The significance of the difference in distribution of a species in woodland and grassland habitat in control and experimental enclo sures was assessed by X2.Animals used in the experiments were collected at another locality in southern Quebec. C.
gapperi
was used in the first experiment. Unexpectedly it was almost completely absent from the source locality in the second andAnnu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
90
third years. Rather than use animals of this species from a different locality, and hence with different experience, in the second and third experiments, it was decided to use another woodland spl:cies, P.
maniculatus,
from the same locality.M.
pennsylvanicus
was used inall
three experiments.The first requisite for these experiments was that one species enter the other's habitat. This happened in all three years; the woodland species en tered the grassland.
The results of the three experiments go most of the way towards fulfilling the requirements outlined in the previous section. In the first experiment the result was identical to the hypothetical f€�sult given in Figure
2
(1)
for enclo sures I and II (Enclosure III hadM. pennsylvanicus
only). It needs no fur ther comment. In the second- and third experiments with P.maniculatus,
Step2
of the progression illustrated in Figure2
was by-passed. Step1
was re peated, and a modified Step3
was performed, in the course of which part of Step2
was demonstrated. The results of the second and third experiments are given diagrammatically in Figure3,
which may be compared with the scheme in Figure 2.The first part of the second experiment duplicated the findings with C.
gapperi,
which justified the tacit assumption that these two species are similar with respect to their response toM. pennsylvanicus.
In both ex:periments1
and2
the numbers, sex, and age distributions of the woodland species in con trol and experimental enclosures varied in approximately the same way, so the results are not obviously biased by these population factors. There are two small differences between experiments1
and2.
Two control enclosures(I
and III) were used in the second experiment, instead of just one as in the first experiment, andP. maniculatus
occurred frequently in the grassland of both (Figure3,
1).
Although it was pronounced, the difference in occurrence ofP . maniculatus
in the grassland of c:ontrol and experimental enclosures was not statistically significant, due to small sample sizes.In the second part of the second experiment
M. pennsylvanicus
was trans posed to the grassland of Enclosure III (Figure3, 2) ,
with two results. There occurred an immediate and 'significant increase in the frequency of occur rence ofP. maniculatus
in the grassland of EnclosureII,
from whichM.
pennsylvanicus
had been removed. Within3
weeks the frequency of occur rence there was indistinguishable from that in the remaining control enclo sure(I).
The other result was that in Ellclosure III, into whichM.
pennsyl
vanicus
had been newly introduced, the frequency of occurrence ofP. mani
culatus
in the grassland did not decline, but P.maniculatus
were only captured in the area of grassland close to the habitat interface. A comparison of the distribution ofP. maniculatus
captures in the grassland before and after the introduction ofM. pennsylvanicus
shclwed that P.maniculatus
captures were significantly restricted within the grassland after the introduction ofM.
pennsylvanicus.
Complete exclusion of P.
maniculatus
from the grassland was demon strated in the third experiment. M.pennrylvanicus,
at a much higher densityAnnu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
1. Wood Grass 2.
-91
II III 3. p p p-tt- --t--
-tt-M 4. p p p -t
--r
---t-t-
--t
--t
:
;
M p �--t
---p ---t---p --t�r--p .. ..t-t-t-+
1_,
)
M p ---i---M p ----t
----FIGURE 3. The demonstration of interaction between Species P(Peromyscus
maniculatus)
and M(Microtus pennsylvanicus)
in grassland habitat. The mean ing of the arrows is the same as in Figure 2. Steps1
and 2 were performed in the second experiment, steps 3 and4 in
the third experiment.than in the second experiment, were introduced into the grassland of Enclo sure II, in which P.
m
an
i
c
ulat
us had been occurring frequently (Figure3, 3).
The frequency of occurrence of P.maniculatus
declined to zero in the next3
weeks (Figure3, 4),
despite recruitment and generally higher numbers of P.maniculatus
i
n Enclosure II than in the preceding4
weeks. It remained at �ro forthe
following5
weeks. Contemporaneous controls cannot be used to assess the significance of this result, because P.maniculatus
rarely occurred in the grassland of enclosures I and III, despite the absence of M.pennsyl
vanicus
(Figure3, 4).
Therefore, the distribution,of P.maniculatus
in Enclo sure IIwhen
M.pennsy[vanicus
waspresent
mustbe compared
with sequential controls in the same enclosure, (a) earlier
inthe same year, and (b) at
the same time of year in the previous year (Figure3, 2).
The results of the two comparisons are the same. Following the introduction of M.pennsylvani
cus
into the grassland of Enclosure II, the frequency of occurrence of P.maniculatus
there was significantly lower than when M.pennsylvanicus
was absent earlier in the year· ana "lower than at the same time of year in the previous year.The
purpose of Step2
in the progression illustrated in Figure2
was to show that differences in habitat features between enclosures I and II were notresponsible
for theresult
in Step1. Th
at
a woodland species could occurAnnu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
frequently in the grassland of Enclosure II, in the absence of
M. pennsylvani
cus,
was shown in the second and third experiments (Figure 3, 2 and 3), us
ing P. maniculatus
asthe woodland species. It is still
possible, however, that
C.gapperi,
unlike
P. ma
nic
u
l
a
tu
s
,would not occur frequently in the grass
land of Enclosure II for reasons independent of the presence of
M. pennsyl
vanicus. This is extremely unlikely becam:e the Woodlands in enclosures I and
II
we
re
sosimilar, and the grasslands were similar
too(63). Furt
herm
ore
,the population sizes of
C.gapperi in the two enclosures were nearly the same
throughout the experiment.
The other aspect of Step
2
is the demonstration that the woodland species occurs rarely in the grassland in the presence ofM. pennsylvanicus i
n one year,and frequently in the grassland
ofthe same enclosure in the absence
ofM.
p
e
n
n
sylva
n
icus
inanother year. In other words the experimental
result, differing from the control result, is demonstrated in more than one enclosure.This
wasnot attempted in these e
xp
erime
ntsdue
to shortage of time, but it isnot essential for the
demonstration of compet
itive interaction.
Thus, the chief features of the results which demonstrate an interaction
between the woodland and grassland
species in the
grasslandhabitat are: (a)
awoodland species occurs more frequently
in the grassland withoutthan
with a grassland species, and (b) a wotJdland species no longer occurs in
grassland, oroccurs there rarely,
aftera
grass
lan
d speciesis
introduced there. The ecological release hypothesis is tested. and supported by the results.The one piece of conflicting evidencl� is that in the third experiment P.
maniculatus did
notoccur frequently
in the
grassland ofenclosures I and III,
even
in the
absence of M.pennsylvanicus
(Figure
3, 3
and4).
However, this conflict is more apparent than real, because on all occasionsP. maniculatus
occurred frequently in the grassland only following recruitment, and recruitment
didn
ottake place
inenclosures I and III
in the third experiment (i.e.conditions necessary for frequent movement into the grassland did not
occur
in enclosures I and III) .
The animals can be observed in
thefiJ�ld only
with considerable difficulty,so the mechanism of the interaction is
Dot
known.Nevertheless, lab
ora
tor
yexperiments with these species give a strong indication that the mechanism is
aggression and avoidance. When
toge
ther
, thegrassland and woodland
spe cies weremore
restricted totheir
usual habitats(r
ecreated
in alaboratory
testarena)
than when alone, and apparently this resulted from the agonisticbehavior exhibited (and observed) under these conditions (64).
The experimental evidence for interaction in the woodland.-M. pennsyl
vanicus
did not enter the woodland inth��
above experiments, even when thew
oodla
nd was without
a woodland speci��s. Asubsequent
expe
riment
inEn
closure II (66)
showed that thep
robab
l
ereason for this
wasthat the densi
tyin the gr
as
sl
and was
insufficient to induce movement into the woodland.In
this subsequent e
xperi
me
ntM. pennsylvllnicus
did e
nt
er thew
ood
land
,but
Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
only when the density
inthe grassland was considerably higher than the den
sities prevailing in the previous three experiments. The single-species experi
ment was not designed to investigate the possibility that
M.pennsylvanicus
interacts competitively with woodland species in the woodland, but
R. D.Morris has conducted such investigations in an enclosure in Saskatchewan
(102).
T
h
e singl
ee
nclos
ure
co
nta
ine
d a continuous pieceof g
rass
l
and,1.4
acres in area, and three pieces of aspen woodland with grasses and sedges in the herb layer,0.6
acres in combined area. Differing from the Quebec experi ments'in some details, but similar in plan, three experiments withC. gapperi
and
M.pennsylvanicus
were conducted in successive years.The requirements for a demonstration of interaction in this system are shown dia
gr
amm
atic
ally
in
Figu
re 4.
In the presence ofC. gapperi
inthe
woodland,
M.pennsylvanicus
are shown to occur infrequently
in the wood land (Step1).
Following the removal of
C.gapperi from the
woodland,the
frequency of occurrence there of
M.pennsylvanicus
increases (Step 2).
Following the re-introduction of C.gapperi
to the woodland, the frequencyof occurrence there of
M.pennsylvanicus decreases (Step 3).
The three experiments were conducted as follows. In the first experiment
M.pennsylvanicus
were introduced alone, and their distribution was recorded in six trappingp
erio
ds in4
months. Inthe
second year M.pennsylvanicus
andC. gapperi
were introduced into their appropriate habitats and their distributions were recorded in two subsequent trapping period's. C. gapperi were then
removed and the distribution of M.
pennsylvanicus
was recorded. C.gapperi
were re-introduced, and distributions were determined once more. Since theC.
gapperi
population declined drasticall
y following re-introduction, a third ex periment was performed in thenext year
torepeat
there
-in
tro
duc
tion phase.
M.pennsylvanicus
which had survived the winter were allowed to remain,
1. 2. 3. Wood C C ,-,
---t---
- ---�
--i-
- - ---l
---H
-, Grass M M MFIGURE
4.
The demonstration of interaction between Species
C (C.gapperi)
and
M (M.pennsylvanicus)
in woodland habitat. The meaning of the arrows is the same as in Figure 2. Thes
hape of the enclosure and habitat is notas
shown; the enclosure is octagonal and the three pieces of woodland are peripheral. Steps 1 and 2 were performed in one experiment. Step 3 in the next one.Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
alone, in the enclousre for a 3-month period, during which trapping was per
formed weekly.
C.gapperi
were then introduced and distributions were re
corded in the following 3 months.
For a study with only one enclosure the sequential approach to compar
ing experimental and control results must be used. Unfortunately, the density
of traps varied from year to year, and only in the third experiment was it the
same in woodland and grassland. Since frequency of capture is a function of
trap density over a large range of animal densities, statistical comparisons
cannot be �de between years, but only within years.
Steps
1and
2
were demonstrated in the second experiment: following the
removal of C. gapperi, the frequency of ,[)ccurrence of
M.pennsylvanicus in
the woodland increased significantly. No Buch increase was found at that time
of year in the first experiment, in which
M.pennsylvanicus
were alone
throughout. Step 3 was attempted in the second experiment, but it failed due
to the disappearance and presumed dea1h of most of the re-introduced C.
gapped. Step 3 was then demonstrated in the third experiment. Although not
immediately influenced by the introduced C. gapperi,
M.pennsylvanicus oc
curred in the woodland less frequently, overall, after the introduction of
C.gapperi
than before. Furthermore, the relationship between frequency of oc
currence of
M.pennsylvanicus in the woodland and population size was dif
ferent before and after the introduction of
C.gapperi.
For a given population
size of
M.pennsylvanicus there were fewer captures of
M.pennsylvanicus
inthe woodland in the presence of
C.gappeti
than
intheir absence.
Although the Quebec and Saskatchewan experiments were all single repli
cate ones, they provide a demonstration of competitive interaction between a
woodland and a grassland species in both habitats. Competitive exclusion
( 69) of some or all individuals of an invading species is the result of inter
specific interaction. The only other experiment with any two of these three
species, which was performed by Clough (36) with unconstrained populations
of
M.pennsylvanicus
and
C.gapperi,
lacked a control but yielded somewhat
similar results.
C.gapperi were added to two areas which had only
M.penn
sylvanicus but appeared to be favorable,
mterms of habitat, for both species.
Later it was found that
C.gapperi had completely disappeared from one area
and that
M.pennsylvanicus
had completely disappeared from the other.
Clough ( 36) concluded that competitive: interaction had occurred between
the species, and he suggested that the mechanism might be interspecific ag
gression.
Conclusions.-Thus, several studies have provided evidence of varying
degrees of completeness that competitiv(: interaction occurs between rodent
species. Owing to the difficulties of obtaining critical evidence, it is striking
that so much has been obtained with 50 many 5pe<;ies. Therefore. it is likely
that competitive interaction for space
isa general phenomenon among rodent
species and is not restricted to the few slPecies that have been studied in
de-Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
tail. We may inquire why this is so, and ask under what conditions it occurs and what are the selective forces upon the interactants.
SOME GENERALIZ:ATIONS AND THEORETICAL CONSIDERATIONS To understand why interspecific competition for space is apparently wide spread among rodents, let us first consider a simple situation, with Species
1
in Habitat A and Species2
in HabitatB.
They can only compete when indi viduals of one species enter the other habitat. There is an abundance of evi dence to suggest that at the time of reproduction animals seek space first in the habitat to which they are most adapted. They are forced to seek space else where if, as a result of interactions with other animals of the same species in that habitat, they are unable to acquire the sought-after space(33, 37,
63-67,
145) .
They enter another habitat ( let us call them members of Species1
which enter HabitatB) .
Whether or not they secure space and remain there depends upon two classes of factors:(a)
the suitability of HabitatB
in terms of food and cover, nest-holes, microclimate, etc, and(b)
the frequency of interaction with Species 2. Having once left Habitat A, an individual of Spe cies1
will eventually settle in Habitat A orB
according to which side of the following equation is the largerSA
-111
�SB
-112
where S represents the suitability of a habitat and I represents a product of interaction frequency and intensity. Of course, S and I are measured in dif ferent (although unspecified) units, but they could be converted' to a com mon scale of energy units to make them comparable.
With this as background we now ask why Species
1
and2
are not mutu ally tolerant in HabitatB.
A possible reason is that they are not able to dis criminate between members of their own and of the other species. In this case, interspecific interaction would be an inadvertent consequence of similar ity in body size, behavior, etc. However, many interacting species are not particularly similar in appearance or behavior; For example, M.pennsyl
vanicus,
C. gapperi,.
andP. maniculatus
differ conspicuously in size, color, pattern, behavior, vocalizations, and possibly odor (unpublished data) . There fore, the species can probably distinguish each other fairly readily in the wild. An alternative view is that the interactive behavior is advantageous. If it were not, it would be selected against, because interactions between individuals are energy-consuming, and they may also render the animals more con spicuous to a searching predator.There could be an advantage to competitive interaction for space if the diets of the two species overlapped, i.e. pre"emptive competition for food. Put another way, in the event of mutual tolerance in Habitat
B,
Species1
might appreciably reduce part of the food supply of Species2,.
and this could have' serious consequences for Species2
in terms of reproduction,. survival, etc. There could also be an advantage if the probability of succumbing' to a pred-Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
ator increased as the overall density of the two species increased.
A
predator species which preyed upon both Species1
and2
in Habitat B might be ex pected to exhibit a numerical and functional response to an increase in the overall density of the two species combiIled (cf.116).
For the reasons of food and predation, there should be a selective advantage to those individuals of Species2
which respond to the presence of individuals of Species1
by attempting to drive them away.The same considerations apply to situations more complex than this sim ple two-species two-habitat situation, such as two or more species within a single habitat. They may achieve complete spatial separation within the same habitat. The occupation of overlapping areas is more likely to occur, but still there will be a tendency to minimize the overlap by competitive interaction. Since use of the same space by two species is of more frequent and regular occurrence in this situation than in the two-habitat situation described above, selection will also tend to minimize the overlap in diet, spatial and temporal patterns of activity, etc. At the extreme, this would result in ecological differ ences between two species being so large that, providing the predator factor (above) was unimportant, mutually interactive behavior might confer no benefits and would in fact be selected again:;t.
Diets are not well-enough known to enable one to say whether the species which compete for space have generally overlapping diets. However, there is substantial overlap in diets of at least three pairs of inferred competitors:
Mi
crotus ochrogaster
andM. pennsyZvanicus
( 1 48), M. ochrogaster and Sigmo
don hispidus
(54),
andPeromyscus Zeucopus
andP. manicuZatus bairdii
(47 ) .
The foregoing reasoning is consistent with the generally accepted view of the significance of competition for space in birds [for a different view see
( 105)].
Much more is known about birds than rodents because they are eas ier to study and have been studied more extensively. Numerous studies have shown that where systematically related spi�cies of birds use the same volume of space, they forage in it in different ways" thereby harvesting different foods (e.g.12, 59, 72, 89) .
Conversely, where rdated species use different and ad jacent volumes of space, they forage in their separate spaces in a similar manner and harvest similar foods(62, 71, 97, 111, 112).
The latter spatial separation is achieved by means of interspecific territorialism. Such studies have led to the conclusion that, under conditions where the variety of food resources is too small to permit division between species, selection favors aggressive behavior which results in mutual dispersion of the species. Inter specific territoriality is exhibited most frequently in structurally simple habi tats or portions of habitats, where the foraging space is restricted in the verti cal plane( 1 12).
The activity of many rodents is more or less restricted to a single (hori zontal) plane of the environment. In general, they have not been able to achieve the spatial niche separation in the vertical plane, unlike birds and the shrew species
Sorex araneus
andS. minutus (94 ) .
Thus, they are unable toAnnu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
avoid each other and forage in different
ways to the extent
that birds can( 82 ) ;
this
isparticularly true of the principally subterranean species (95,
1 15 ) . The absence of strict territoriality among many rodent species (but see
1 30), in contrast to its prevalence among birds, does not undermine the argu
ment since spacing-out of conspecifics is achieved to some degree by the be
havior associated with the establishment and maintenance of home ranges.
From this c
o
mparisonwith
birds, it may be predi
ct
edthat i
nte
rspe
ci
fic competit
ion for spacei
s relativ
el
y more widespread among rodents thanamong birds. It probably also occurs widely among other grou
nd
-livi
ngmam
mals, such as shrews (42, 94) , and ground-living forms of other vertebrate
classes, such as lizards ( 100), salamanders (48, 68, 77, 78) , and frogs (76).
The conditions under which interaction occurs are not uniform.
Thishas
been alludedto
already.Our
knowledgeof
the interspecific interactionsin
nature
istoo fragmentary to offer a comprehensive theory of when and under
what conditions interaction occurs. There are, however, three identifiable
states of coexistence between rodent species, and these are illustrated in Fig
ure 5. They represent coexistence with or without competitive interaction,
and, in the former, with or without predictable outcomes. Predictable, in this
Habitats A C 0) 1 (2
1·<, I
I) 2 �I
·I
1 =2FIGURE 5. Three stages of coexistence of Species
1
and 2. A, B, and C referto
habitats (the precise definition of habitat is unimportant prOViding that eachs
pa
ceso
designated has its own characteristic plant and animal composition ) . The symbols indicate dominance or lack of it (equal sign). The consistent dominance
of Species1
in Habi
tat B(2)
tends to lead to the exclusion of Species 2and
therefore to minimal coexistence, unless Species2
possess
es
some compen sating adv
ant
age (see text, p. 98).Annu. Rev. Ecol. Syst. 1972.3:79-106. Downloaded from www.annualreviews.org
sense, means on the average. Since the animals are not at maximum size at .the age of first maturity
(
-50%
in the case of M. pennsylvanicus) , their interactive behavior is likely to change wilth age(64)
and reproductive status(34),
which introduces a varying component into the determination of an outcome.Type l' coexistence represents coexistence over a small area. The two spe cies generally select different habitats, in which they are dominant to the other species should the other species ·enter. In a small area of overlap
(B)
the habitat characteristics are intermediatf:. Coexistence is permanent, or near permanent, and the outcome of .competiHve interaction is indeterminate. It may be determined by a "beachhead" pheJilomenon(39, 101 ) ;
whichever ani mal arrives first at a piece of ground holds sway. HabitatsA
and C may be adjacent at some localities or else may be separated by such a thin strip of intermediate habitat,B,
that there is insufficient space in it for the home range requirements of any animal. An ex.ample of this type of coexistence is M. pennsylvanicus with C. gapperi orP.
maniculatus, which was described in detail in an earlier section (see also1 02 ) .
Type
2
coexistence represents coexistence in a moderately large area of overlap. Habitat characteristics are intermediate here, and competitive inter action yields a predictable outcome since Species1
is consistently dominant to the other. However, Habitat C does not offer the requirements of Species I, and so Species1
will rarely enter it and will not remain there long when it does. There are really two variants of this type of coexistence, which may be designateda
and b. As a result of competitive interaction, the subordinate Species 2 tends to be excluded from Habitat B and is never abundant there in the presence of Species1 ;
this is Variant a.An
example of this is given by Wirtz & Pearson( 1 47 ) .
M. pennsylvaniclls occurs in grassland (HabitatA) ;
P.
leucopus occurs in shrubbery and gOlden-rod plant association (HabitatC) .
In an intermediate habitat of broomsedge (HabitatB) ,
M. pennsylvaniCIlS
is
apparently dominant to and tends to excludeP.
leucopus. Alternatively, Species
1
does not exclude Species 2 from HabitatB
because Species2
enjoys some compensating advantage; this might reside in the foods( 1 3 1 )
or structural aspects of the habitat( 1 8, 74 ) ,
which it is better able to exploit, or in its superior ability to avoid predators( 1 22 ) .
This is Variant b. It might be widespread if many of the rodent species which coexist over large areas ex hibit a regular dominance-subordinate relationship( 1 , 2 5 ) .
Coexistence types1
and2
may be expected to give rise to the numerical and spatial dynamics depicted in ModelI
of Figure1 .
Type
3
coexistence represents largely coextensive ranges and either no interaction between the species, as is shown, or else infrequent and unpredict able interaction. According to Catlett & Shellhammer(30),
Reithrodontomys megalotis and Mus musculus do not inteJC3ct aggressively; and because they coexist in the wild, they may constitute an example of Type3
coexistence.Obviously, the three types of coexistence do not exhaust all possibilities. They are presented in this way in order to suggest a possible sequence of