20
RICHARD S. MILLER
The case of an “included niche” is particularly interesting, as it
imposes strict conditions for the outcome of competition and, especially,
for the survival of S,. In the simplified, two-dimensional relationship
shown in Fig. 2 (Case l), the niche N, is described by the coordinates
x, - x3 and y, - y3 and is included within the total niche N,, which
is in turn described by the coordinates x, - xp and y, - ya. The following outcomes of competition are possible under the conditions of Case
1: ( a ) competition proceeds in favor of S , in all the elements of B
corresponding to N,.N, and, given adequate time, only S, survives; or
( b ) S, survives in all elements of B corresponding to some part of the
intersection subset and both species survive. The first alternative (a)
implies that S, is the superior competitor and, with its greater ecological
amplitude, will eliminate S , from all parts of the fundamental niche
N,. Coexistence of S, and S, is impossible under the conditions of an
included niche when S , is the superior competitor. The second alternative ( b ) requires that S , be the superior competitor, in spite of its
narrower ecological tolerance. Under these conditions, S, will be excluded from N, but will survive in the parts of N, that lie outside the
intersection subset. The realized niche of S, will therefore be the difference subset N, - N, (N, - N, - N,). As long as the niche space N, - N,
is sufficient to allow the survival of S, there will be coexistence of both
species within the total biotope B.
The conditions described by alternative ( b ) of an included niche
would seem, at first glance, to contradict conventional theories of
competition. We do not ordinarily expect a species with a relatively
narrow range of tolerance to be superior in competition with a closely
related species with greater ecological amplitude, yet later examples
will show that the approximate conditions of an included niche are
relatively common in species relationships, and that Case l ( b ) may in
fact explain some of the species diversity that exists in natural communities.
IV. COMPETITION IN NATURE
It is difficult to identify the actual process of competition in nature,
either as an active or historical factor, although certain patterns of
geographical or habitat distribution and niche relationships between
species are often thought to reflect competitive exclusion. When a
species occupies a broader niche in the absence of a closely rela.ted
species than it does when the two species are sympatric, competitive
exclusion is often inferred (Lack, 1944); contiguous allopatry can only
be explained by a consistent environmental discontinuity or by a competitive interaction which maintains the pattern along a line of contact
(Miller, 1964a); character displacement is usually explained as a product
RICHARD S. MILLER
The case of an “included niche” is particularly interesting, as it
imposes strict conditions for the outcome of competition and, especially,
for the survival of S,. In the simplified, two-dimensional relationship
shown in Fig. 2 (Case l), the niche N, is described by the coordinates
x, - x3 and y, - y3 and is included within the total niche N,, which
is in turn described by the coordinates x, - xp and y, - ya. The following outcomes of competition are possible under the conditions of Case
1: ( a ) competition proceeds in favor of S , in all the elements of B
corresponding to N,.N, and, given adequate time, only S, survives; or
( b ) S, survives in all elements of B corresponding to some part of the
intersection subset and both species survive. The first alternative (a)
implies that S, is the superior competitor and, with its greater ecological
amplitude, will eliminate S , from all parts of the fundamental niche
N,. Coexistence of S, and S, is impossible under the conditions of an
included niche when S , is the superior competitor. The second alternative ( b ) requires that S , be the superior competitor, in spite of its
narrower ecological tolerance. Under these conditions, S, will be excluded from N, but will survive in the parts of N, that lie outside the
intersection subset. The realized niche of S, will therefore be the difference subset N, - N, (N, - N, - N,). As long as the niche space N, - N,
is sufficient to allow the survival of S, there will be coexistence of both
species within the total biotope B.
The conditions described by alternative ( b ) of an included niche
would seem, at first glance, to contradict conventional theories of
competition. We do not ordinarily expect a species with a relatively
narrow range of tolerance to be superior in competition with a closely
related species with greater ecological amplitude, yet later examples
will show that the approximate conditions of an included niche are
relatively common in species relationships, and that Case l ( b ) may in
fact explain some of the species diversity that exists in natural communities.
IV. COMPETITION IN NATURE
It is difficult to identify the actual process of competition in nature,
either as an active or historical factor, although certain patterns of
geographical or habitat distribution and niche relationships between
species are often thought to reflect competitive exclusion. When a
species occupies a broader niche in the absence of a closely rela.ted
species than it does when the two species are sympatric, competitive
exclusion is often inferred (Lack, 1944); contiguous allopatry can only
be explained by a consistent environmental discontinuity or by a competitive interaction which maintains the pattern along a line of contact
(Miller, 1964a); character displacement is usually explained as a product