Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population

2018 ◽  
Vol 77 (6-7) ◽  
pp. 1689-1720 ◽  
Author(s):  
J. M. Cushing ◽  
Shandelle M. Henson
Keyword(s):  
Matrix Models ◽  
Seasonal Dynamics ◽  
Structured Populations ◽  
Periodic Matrix ◽  
Seabird Population

Sensitivity Analysis of Periodic Matrix Models

Ecology ◽  
1994 ◽  
Vol 75 (5) ◽  
pp. 1299-1303 ◽  
Author(s):  
Hal Caswell ◽  
Maria Cristina Trevisan
Keyword(s):  
Sensitivity Analysis ◽  
Matrix Models ◽  
Periodic Matrix

scholarly journals Sensitivity analysis in periodic matrix models: A postscript to Caswell and Trevisan

2003 ◽  
Vol 37 (9-10) ◽  
pp. 945-948 ◽  
Author(s):  
M. Lesnoff ◽  
P. Ezanno ◽  
H. Caswell
Keyword(s):  
Sensitivity Analysis ◽  
Matrix Models ◽  
Periodic Matrix

scholarly journals Individual-based Integral Projection Models: The role of size-structure on extinction risk and establishment success

2015 ◽  
Author(s):  
Sebastian Schreiber ◽  
Noam Ross
Keyword(s):  
Matrix Models ◽  
Extinction Risk ◽  
Branching Processes ◽  
Structured Populations ◽  
Integral Projection Models ◽  
Integral Projection ◽  
Analytic Methods ◽  
Continuous State ◽  
The Individual ◽  
Over Time

1. Matrix models or integral projection models (IPMs) are commonly used to study the dynamics of structured populations, where discrete or continuous traits influence survival, growth, or reproduction. When a population's size is small, as is often the case for threatened species or potentially invasive species arriving in novel habitats, extinction risk may be substantial due to demographic stochasticity. 2. Branching processes, which are individual-based counterparts to matrix models and IPMs, allow one to quantify these risks of extinction. For discretely structured populations, the theory of multi-type branching processes provides analytic methods to compute how extinction risk changes over time and how it depends on the size and composition of the population. Building on prior work on continuous-state branching processes, we extend these analytic methods to individual-based models accounting for any mixture of discrete and continuous population structure. 3. The individual-based IPMs are defined by probabilistic update rules at the level of the individual which determine how each individual with a given trait value dies, changes trait value (e.g. grows in size), or produces individuals with the same or other trait values. Probabilities of extinction are shown to be analytically determined by probability generating functionals associated with the individual-based IPMs. In particular, we present analytical expressions for how extinction probabilities change over time and depend on the initial abundance and trait distribution of the population. We illustrate how to numerically implement these methods using data from the short-lived desert shrub species \emph{Cryptantha flava}, and provide a more general discussion of how to implement these methods to other data sets including those involving fluctuating environmental conditions. 4. As most IPM studies have the necessary data to parameterize individual-based IPMs, these methods provide a computationally efficient means to explore how continuously structured populations differing in their evolutionary history and environmental context may differ in their vulnerability to extinction or ability to colonize new habitats.

scholarly journals Matrix Models for Size-Structured Populations: Unrealistic Fast Growth or Simply Diffusion?

PLoS ONE ◽  
2014 ◽  
Vol 9 (6) ◽  
pp. e98254 ◽  
Author(s):  
Nicolas Picard ◽  
Jingjing Liang
Keyword(s):  
Matrix Models ◽  
Fast Growth ◽  
Structured Populations

scholarly journals A net reproductive number for periodic matrix models

2012 ◽  
Vol 6 (2) ◽  
pp. 166-188 ◽  
Author(s):  
J. M. Cushing ◽  
A. S. Ackleh
Keyword(s):  
Matrix Models ◽  
Reproductive Number ◽  
Periodic Matrix

scholarly journals TRANSIENT POPULATION DYNAMICS IN PERIODIC MATRIX MODELS: METHODOLOGY AND EFFECTS OF CYCLIC PERMUTATIONS

Ecology ◽  
2006 ◽  
Vol 87 (9) ◽  
pp. 2338-2348 ◽  
Author(s):  
Shana K. Mertens ◽  
Jonathan M. Yearsley ◽  
Frank van den Bosch ◽  
Christopher A. Gilligan
Keyword(s):  
Population Dynamics ◽  
Matrix Models ◽  
Periodic Matrix ◽  
Transient Population
Sign in / Sign up

Export Citation Format

Share Document