Major insights into the relationship between life-history features and fitness have come from Lotka’s proof that population growth rate is determined by the level (expected amount) of reproduction and the average timing of reproduction of an individual. But this classical result is limited to age-structured populations. Here we generalize this result to populations structured by stage and age by providing a new, unique measure of reproductive timing (Tc) that, along with net reproductive rate (R0), has a direct mathematical relationship to and approximates growth rate (r). We use simple examples to show how reproductive timing Tc and level R0 are shaped by stage dynamics (individual trait changes), selection on the trait, and parent-offspring phenotypic correlation. We also show how population structure can affect dispersion in reproduction among ages and stages. These macroscopic features of the life history determine population growth rate r and reveal a complex interplay of trait dynamics, timing, and level of reproduction. Our results contribute to a new framework of population and evolutionary dynamics in stage-and-age-structured populations.
Killer Whale example code and matrix
Matlab code for the killer whale example including stage structured transition matrix. Initial data published by Caswell (2001) based on Brault & Caswell (1993)
simple_stage.m
Killer Whale example output
Output from the matlab code for the killer whale example.
killer_out.mat
Matlab code for two patch model run first
This generates the matrices and information that is later used in the patches-analysis.m file. So run this file first.
patches0.m
Matlab code two patch example run second
Matlab code for the two patch model that estimating the data used in Fig. 3 of the article
patches_analysis.m
Matlab output file for two patch model
This is the Matlab output generated from the patches_analysis file
patches1_out.mat
Matlab code for two age class four size class example: matices
Matlab code that generates the data for the two age class four size class model. It generates an output file called small_neutral
small_neutral.m
Matlab output file small_neutral
Matlab output file for two stage four age class model: small_neutral output file. Generated from small_neutral.m file
small_neutral.mat
Matlab code two age four stage class example run second
Matlab code for the two age four stage class example that generates the data for Fig. 3
comp_smallmats.m
Matlab output two age four stage class example
Matlab output for the two age class four stage class example generated by comp_smallmats.m file
smallouts.mat
Matlab function for two age four stage class model 1
Matlab function that is called by the small_neutral.m file and comp_smallmats.m file
makesmallmats.m
Matlab function for two age four stage class model
A matlab function that is called by small_neutral.m and comp_smallmats.m file for the two age and four stage class example.
smallmat.m
Matlab code for generating Fig. 2-4
Matlab code for generating Fig. 2-4 using Output files: killer_out, patches1_out, small_neutral, and smallouts
misc_graphs.m
Soay Sheep IPM matrices used for Appendix
Data base that has been used for the Soay Sheep example including the matrices (Age-stage structured with dimensions of 900x900).
base_June_2012.mat