University of Kansas Publications MUSEUM OF NATURAL HISTORY The University of Kansas Publications, Museum of Natural History, beginning with volume 1 in 1946, was discontinued with volume 20 in 1971. Shorter research papers formerly pub- lished in the abo^'e series are now published as Occasional Papers, Museum of Natural History. The Miscellaneous Publica- tions, Museum of Natiual History, began with number 1 in 1946. Longer research papers are published in that series. Monographs of the Museum of Natural History were initiated in 1970. All manuscripts are subject to critical review by intra- and extra-mural specialists; final acceptance is at tire discretion of the publications committee. Institutional libraries interested in exchanging publications may obtain the Occasional Papers and Miscellaneous Publica- tions, by addressing the Exchange Librarian, The University of Kansas Library, Lawrence, Kansas 66045. Individuals may pur- chase separate numbers of all series. Prices may be obtained upon request addressed to Publications Secretary, Museum of Natural Historv, The University of Kansas, Lawrence, Kansas 66045. Editor: Linda Trueb PRINTED BY UXIVERSITY OF KANSAS PRINTING SERVICE LAWRENCE, KANSAS 5 ' Ai/1 ' [D^V^ftn Ct LIBRARY APR 1 5 1977 OCCASIONAL PAPERS HARVARO of the UNIVERSITY MUSEUM OF NATURAL HISTORY The University of Kansas Lawrence, Kansas NUMBER 65, PAGES 1-8 APRIL 1, 1977 COMMENTS ON COMPETITIVELY- INDUCED DISJUNCT ALLOPATHY By Norman A. Slade^ and Paul B. Robertson^^ Krebs ( 1972 ) outlined a number of factors, both abiotic and biotic, which might determine the boundary of a special range. Competitive exclusion (Cause, 1934) is among the most studied of these phenomena. When applied to biogeography, interspecific competition is a potential explanation of the absence of a species from areas of favorable physical environment and might be expected to lead to contiguous species ranges, i.e. parapatry. Mac-Arthur (1970, 1972) developed a graphical model which he used to define the environmental conditions necessary for resource competition to lead to sympatry, parapatry, or even disjunct allopatry, i.e., gaps between species boundaries. Although MacArthur (1972) discussed his model in a chapter on competition and predation, he did not clarify the involvement of competition in maintaining these gaps. The purpose of this paper is to expand upon the role of competition in MacArthur's model, and identify some constraints to its applicability. We also cite several additional examples of disjunct allopatry which might be used for testing this model. MacArthur ( 1970, 1972 ) presented a two-species model of ex- ploitative competition. One form of the model (1972:46-58) dealt with a two-resource-two-species system in which each competing species could use both resources, with the benefit derived from each resource being additive. MacArthur constructed a graph (Fig. 1) 1 Museum of Natural History and Department of Systematics and Ecology, The University of Kansas, Lawrence, Kansas 66045, U.S.A. 2 Present address : Department of Biology, Trinity University, San Antonio, Texas 78284, U.S.A. 2 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY in which quantities of each of the two resources were represented. The growth rates of the competing populations were assumed to be detemiined by the amount of resources available. Thus, points on the resource graph representing resources available also represent specific potential growth rates for each of the consumer species starting from any particular joint population density. Points repre- senting equal growth rates for one species could then be connected as dx/dt isoclines. MacArthur dealt with the zero growth isoclines (dx/dt=0) for each of the species when resources were interchange- able (the solid lines in Fig. 1). The various combinations of re- sources which exist along a transect also can be shown on this graph (dotted lines "a", "b", and "c", Fig. 1). Line c represents a more productive transect than b or a, and b is more productive than a. Population densities of the two consumer species were not specified by MacArthur (1972) because the consumers were as- sumed to show no direct density-dependence. The equations used in deriving the graphical model ( MacArthur, 1970) express the relationships of rates of change of resources and consumers more explicitly. For two resources and two consumers, MacArthur's (1970) equations can be written dXi/dt=Xi(an Ri+ai2 R2-T1) dX2/dt=X2(aoi Ri+a,, R2-T0) dRi/dt=Rif(Xi,Xo, Ri) dR2/dt=R,g(Xi,Xo, Ro) Where X's and R's represent quantities of consumers and resources respectively, a's represent effectiveness of consumer use of re- sources, and T's are threshold levels of resources necessary for con- sumer populations to increase. The specific equations for resources are not important for our discussion; any functions f and g are acceptable provided the consumers have a negative impact on rates of change of resources. Note that the model does not provide for density-dependence or interspecific interference except as mediated through levels of resources. It is this property of the system of equations that penults the zero isoclines to be plotted as functions of Ri and R^, but it is a stringent constraint on the applicability of the model (Michael Rosenzweig, pers. com.). According to our understanding of MacArthur's model, neither species can persist as a breeding population on the transect when the available resources are below the zero growth isoclines, ( line "a" in Fig. 1). MacArthur (1972) stated that both species could co- exist in sympatric equilibrium at the intersection of the isoclines under the conditions of resource line c, but the species with the lower requirements would exclude the other at each end of the transect. When the resource states are depicted by line b, species 1 or 2 occurs alone at opposite ends of the resource gradient and COMPETITIVELY-INDUCED DISJUNCT ALLOPATRY Fig. 1. — Population isoclines (solid lines) and resource availabilities (dashed lines) plotted as quantities of resources (RI and R2). (After MacArthur, 1972). A change in resource availability from dashed line c to b as a result of the cost of competition would produce a competitively-induced gap. an intemiediate gap exists which is not occupied by either species. Cody (1974), using a fitness set model, also predicted a gap be- tween species ranges under similar conditions. MacArthur (1972) concluded from this model that sympatry or disjunct allopatry occurred as a result of resource abundance with parapatry a result of behavioral dominance which excludes species from the resource-determined area of sympatry. Therefore the type of boundaiy may fluctuate in both time and space depending upon resource availability. The question we now address is, what are the conditions neces- sary for a gap between species to be termed competitively-induced. In order to explore this we must identify two sets of zero isoclines- competitive isoclines, representing growth in the presence of the other species, and non-competitive isoclines, representing the ab- sence of the other species. We assume that the presence of one species increases the resources required to support the other species, but that there are no further density-dependent efi^ects. The pres- ence of such a competitor can be represented by increased resource requirement thresholds (T's) in the previous equations, and raised isoclines for either or both species on the graphs. This increase represents the cost of competition and could reflect additional re- sources required for defending interspecific territories, producing allelopathtic sulxstances in proximate response to a competitor, etc. The focal point of the graph is the position of the dashed resource line relative to the solid or dashed and dotted competitor isoclines. Therefore, the only difference between lowering resource lines or raising isoclines is that differential impacts of competition on the two species can be shown by differentially raising the two isoclines. 4 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY In figure 2 the effect of competition is more severe on species 1 than on species 2. MacArthur's model explains disjunct allopatry whenever re- source abundance is sufficient to support populations at either end of a geographical transect but insufficient in between ( line "b", Fig. 1). For competition to be necessary to explain disjunct allopatry, the shortage of resources must result from the cost of competition. That is, a gap resulting from the movement of the resource line from c to b in figure 1 as a result of competition is competitively-induced. The gap shown by the competitive isoclines in figure 2 is not com- petitively-induced because it exists without competition. Given the above explanation, there is an obvious experiment to demonstrate the necessity of competition in maintaining a gap-the removal of one of the competing species should result in the gap's being occu- pied by the other. The competitively-induced gap between species ranges appears to be a paradox. It is a gap where neither species can maintain a population but which persists only with the presence or at least potential presence of both species. This restriction is less trouble- some if we remember that dx/dt<0 means that populations cannot replace themselves; transients, residents, and even unsuccessful breeding attempts are not excluded. Thus competitive gaps should occur only where there is a sufficient supply of transients to present a challenge to transients of the other species. However, if there are too many transients, the observer may not recognize an area where dx/dt<0 without extensive demographic studies. The necessity of dispersal into the gap limits the cases where competition may be Fig. 2. — Competitive (dashed and dotted lines) and non-competitive (solid lines) isoclines, and resonrce a\ailability (dashed line) illnstrating differential costs of competition. The gap is wider with competition but is not com- petitively-induced. COMPETITR'ELY-INDUCED DISJUNCT ALLOPATHY 5 expected to play an important role to geographically narrow gaps. The actual width of a gap will vary in direct relation to the dispersal powers of the competing species. At present we cannot suggest exact or even approximate distance ranges for most species. Cur- rently, J. Antonovics and his students are attempting to measure the distance of influence of plant species but we know of no similar work by zoologists. MacArthur (1972) also pointed out that the biogeographic effects of competition may be the results of sporadic, but intense, competitive episodes during which one or both species are elim- inated from areas of sympatry. If periods of low resources occur frequently, species that were eliminated during intense competition might not reinvade completely. Although this hypothesis may ex- plain much wider gaps than would that of sustained levels of com- petition, it seems much more difficult to verify experimentally. Interestingly, Cornell's (1974) explanation of gaps also requires low levels of dispersal into and, at least indirect, interspecific con- tact within the gap. Cornell proposed that each species might carry parasites much more virulent to the competing species than to the host. This might be modeled as a competitive effect because each competing species has a negative impact on the per capita rate of increase of the other. There is one principal difference between the explanations of MacArthur and Cornell; unless susceptability to pathogens is mediated by the limiting resource, the gaps of Cornell bear no relationship to resource abundance. Alternatively, if sus- ceptability is related to resources, Cornell's explanation becomes a specific type of resource-related interference competition and might represent a special case of MacArthur's model. We believe that removal experiments are the only reliable method for identifying competitively-induced allopatry. Neverthe- less, certain conditions are prerequisite to such an experiment. First, the gap should not occur in an area of obvious environmental dis- continuity. MacArthur proposed the model for areas of gradual replacement of one resource by another. Secondly, if competition is necessary for maintenance, the gap must be narrow relative to the dispersal powers of the competing species. Finally the width (and perhaps location) of the gap should fluctuate in time or space in relation to critical resources, being wider where resources are low, and narrower or absent where resources are abundant. Although several gaps between ranges of potentially strong com- petitors (similarly-sized, congeneric species with similar habits) have been reported, there is little information on the causes of these gaps or the role of competition in their maintenance. MacArthur (1972) cited several gaps in altitudinal distributions of Peruvian birds (Terborgh, 1971). liecause the widest of these gaps is less than 600 m vertically (most are less than 300 m) and resource 6 OCCASIONAL PAPERS MUSEUM OF NATURAL HISTORY gradients seem likely, competition cannot be ruled out. Unfortu- nately little is known about spatial or temporal variation in size or location of the gaps or of resource abundance. The best documented example (of which we are aware) of a gap between the ranges of two species is found in the report of Brewer (1963) on Carolina and Black-capped chickadees (Parus carolinensis and P. articapiUus). The gap between the two species is as wide as 24 km but there are many areas of contiguity or over- lap along the approximately 3840 km of potential contact. In cer- tain mountain regions, the gap averages 1