The role of population inertia in predicting the outcome of stage-structured biological invasions.
Deterministic dynamic models for coupled resident and invader populations are considered with the purpose of finding quantities that are effective at predicting when the invasive population will become established asymptotically. A key feature of the models considered is the stage-structure, meaning that the populations are described by vectors of discrete developmental stage- or age-classes. The vector structure permits exotic transient behaviour-phenomena not encountered in scalar models. Analysis using a linear Lyapunov function demonstrates that for the class of population models considered, a large so-called population inertia is indicative of successful invasion. Population inertia is an indicator of transient growth or decline. Furthermore, for the class of models considered, we find that the so-called invasion exponent, an existing index used in models for invasion, is not always a reliable comparative indicator of successful invasion. We highlight these findings through numerical examples and a biological interpretation of why this might be the case is discussed.
Environment and Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: c.guiver@ex.ac.uk.
Chris
C
Guiver
Mathematics Research Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Streatham Campus, Exeter, EX4 4QF, UK.
Hanan
H
Dreiwi
Mathematics Research Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Streatham Campus, Exeter, EX4 4QF, UK.
Donna-Maria
DM
Filannino
Centre for Ecology and Conservation, College of Life and Environmental Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: d.j.hodgson@ex.ac.uk.
Dave
D
Hodgson
Environment and Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK.
Stephanie
S
Lloyd
Environment and Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: s.b.townley@ex.ac.uk.
Stuart
S
Townley
D017753:Ecosystem; D008954:Models, Biological
Biological invasion; Lyapunov functions; Non-linear system; Population inertia; Positive system