TY - JOUR
T1 - Persistence and extinction in three species Lotka-Volterra competitive systems
AU - Hallam, Thomas G.
AU - Svoboda, Linda J.
AU - Gard, Thomas C.
N1 - Funding Information:
The authorsw ouldlike to thank Dr. R. V. O’Neill and Dr. D. L. DeAngelis for helpful commentso n the manuscrtptA. refereek indryp ointed out a recent relatedr eferencea nd suggestedre placemenot f our analyticalp roofs by geometric ones. This researchw as supportedin part by the Office of Naval Research under contract N00014-78-C-0256 (T.G.H; L.J.S); in part by the National Science Foundation’sE cosystemS tudies Program under InteragencyA gree-ment No. DEB 77-25781w ith the U.S Departmento f Energy under contract W-7405-eng-26w ith Union Carbide Corporation( T.G.H.); and in part by the EnvironmentalP rotectionA gency under Grant R806161010( T. C. G.).
PY - 1979/9
Y1 - 1979/9
N2 - Extinction in a three species Lotka-Volterra competitive system is classified in terms of the model parameters. Necessary and sufficient conditions are given for one and two species extinction; these are, alternatively, conditions for two and one species persistence. Persistence of the system is studied assuming all pairwise interactions between species are known. An intransitive species arrangement is the only case of persistence where pairwise interactions are, by themselves, sufficient to govern persistence. No persistent arrangement can contain a pair of species that interacts in an unstable manner.
AB - Extinction in a three species Lotka-Volterra competitive system is classified in terms of the model parameters. Necessary and sufficient conditions are given for one and two species extinction; these are, alternatively, conditions for two and one species persistence. Persistence of the system is studied assuming all pairwise interactions between species are known. An intransitive species arrangement is the only case of persistence where pairwise interactions are, by themselves, sufficient to govern persistence. No persistent arrangement can contain a pair of species that interacts in an unstable manner.
UR - http://www.scopus.com/inward/record.url?scp=0018519784&partnerID=8YFLogxK
U2 - 10.1016/0025-5564(79)90018-X
DO - 10.1016/0025-5564(79)90018-X
M3 - Article
AN - SCOPUS:0018519784
VL - 46
SP - 117
EP - 124
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 1-2
ER -