TY - JOUR
T1 - Biodiversity, habitat area, resource growth rate and interference competition
AU - Kuang, Yang
AU - Fagan, William F.
AU - Loladze, Irakli
N1 - Funding Information:
We would like to thank Peter Abrams, Michael Rosenzweig and Lev Ginzburg for providing us with many important references. This manuscript benefited from many invaluable e-mail exchanges with Peter Abrams and discussions with Chris Klausmeier, Michael Rosenzweig, Hal Smith, Claudia Neuhauser and Simon Levin. Last but not least, we are grateful to the two referees for their accurate and insightful comments that improved this manuscript. The first author’s work is partially supported by NSF grant DMS-0077790. I L has been partially supported by NSF grant DEB-0083566 and the Andrew W Mellon Foundation.
PY - 2003/5
Y1 - 2003/5
N2 - For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.
AB - For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.
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U2 - 10.1016/S0092-8240(03)00008-9
DO - 10.1016/S0092-8240(03)00008-9
M3 - Article
C2 - 12749536
AN - SCOPUS:0037406628
SN - 0092-8240
VL - 65
SP - 497
EP - 518
JO - Bulletin of mathematical biology
JF - Bulletin of mathematical biology
IS - 3
ER -