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A simple persistence condition for structured populations
Author(s) -
Hastings Alan,
Botsford Louis W.
Publication year - 2006
Publication title -
ecology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.852
H-Index - 265
eISSN - 1461-0248
pISSN - 1461-023X
DOI - 10.1111/j.1461-0248.2006.00940.x
Subject(s) - persistence (discontinuity) , population , simple (philosophy) , ecology , biology , population model , vital rates , interpretation (philosophy) , population size , statistics , population biology , population growth , mathematics , econometrics , demography , computer science , philosophy , geotechnical engineering , epistemology , sociology , engineering , programming language
The fundamental question in both basic and applied population biology of whether a species will increase in numbers is often investigated by finding the population growth rate as the largest eigenvalue of a deterministic matrix model. For a population classified only by age, and not stage or size, a simpler biologically interpretable condition can be used, namely whether R 0 , the mean number of offspring per newborn, is greater than one. However, for the many populations not easily described using only age classes, stage‐structured models must be used for which there is currently no quantity like R 0 . We determine analogous quantities that must be greater than one for persistence of a general structured population model that have a similar useful biological interpretation. Our approach can be used immediately to determine the magnitude of changes and interactions that would either allow population persistence or would ensure control of an undesirable species.