Ecological Archives A025-009-A7
Alexandre Robert, Stéphane Chantepie, Samuel Pavard, François Sarrazin, and Céline Teplitsky. 2015. Actuarial senescence can increase the risk of extinction of mammal populations. Ecological Applications 25:116–124. http://dx.doi.org/10.1890/14-0221.1
Appendix G. Relationships between changes in population dynamics associated with actuarial senescence and life history trait predictors in 58 species of mammals: details of statistical relationships.
In order to quantify demographic changes associated with actuarial senescence, four indices of change were computed, based on the comparison between the senescence model and the null model: Δλ, ΔT, ΔR0 and ΔText. (details in Appendix D). These indices were regressed against four life history trait predictors using Phylogenetic Generalized Least Squares (PGLS) models using the maximum likelihood estimate of Pagel's λ (Freckleton et al. 2002). All values of Pagel's λ provided below are significantly lower than 1. Values significantly higher than 0 are indicated by symbols (*, p<0.05, **, p<0.01, ***, p<0.001).
Only best multiple regression models (obtained after AIC-based selection, details in methods) are presented. se: standard error of the estimate; t: Student statistics; F: Fisher statistics; R²: corrected coefficient of determination.
Predictors are the body mass (Mass), peak adult survival rate (Smax), litter size (LittSize) and number of litters per year (#Litt).
I. Univariate models
1. Change in annual deterministic growth rate between the null and senescence models (Δλ)
Predictor |
Estimate |
se |
t |
p value |
R² |
Pagel's λ |
Mass |
-0.03 |
0.04 |
-0.92 |
0.36 |
0% |
<10-3 |
Smax |
0.48 |
0.78 |
0.64 |
0.52 |
0% |
<10-3 |
LittSize |
0.02 |
0.22 |
0.09 |
0.92 |
0% |
<10-3 |
#Litt |
0.02 |
0.24 |
0.08 |
0.93 |
0% |
<10-3 |
2. Change in generation time between the null and senescence models (ΔT)
Predictor |
Estimate |
se |
t |
p value |
R² |
Pagel's λ |
Mass |
0.01 |
0.002 |
2.52 |
0.014 |
8% |
<10-3 |
Smax |
0.13 |
0.04 |
3.45 |
0.001 |
16% |
<10-3 |
LittSize |
-0.05 |
0.01 |
-4.67 |
0.0001 |
27% |
<10-3 |
#Litt |
-0.07 |
0.01 |
-5.58 |
0.0000 |
35% |
0.124 |
3. Change in per generation deterministic growth rate between the null and senescence models (ΔR0)
Predictor |
Estimate |
se |
t |
p value |
R² |
Pagel's λ |
Mass |
0.11 |
0.09 |
1.42 |
0.1400 |
2% |
0.600 |
Smax |
6.17 |
0.81 |
7.68 |
0.0000 |
51% |
0.330 |
LittSize |
-1.20 |
0.38 |
-3.16 |
0.0024 |
14% |
0.543 |
#Litt |
-1.30 |
0.33 |
-3.97 |
0.0002 |
21% |
0.239 |
4. Change in median time to extinction between the null and senescence models (ΔText)
Predictor |
Estimate |
se |
t |
p value |
R² |
Pagel's λ |
Mass |
0.04 |
0.03 |
1.05 |
0.2976 |
0% |
0.609** |
Smax |
1.34 |
0.41 |
3.24 |
0.0020 |
14% |
0.606** |
LittSize |
-0.31 |
0.16 |
-1.95 |
0.0569 |
5% |
0.583** |
#Litt |
-0.68 |
0.12 |
-5.62 |
0.0000 |
35% |
0.374* |
II. Multiple regression models
1. Change in annual deterministic growth rate between the null and senescence models (Δλ)
|
estimate |
se |
t |
p value |
Mass |
-0.05 |
0.053 |
-0.97 |
0.3355 |
Smax |
12.72 |
4.436 |
2.87 |
0.0060 |
LittSize |
0.18 |
0.304 |
0.58 |
0.5625 |
#Litt |
0.02 |
0.295 |
0.07 |
0.9439 |
Smax2 |
-5.53 |
2.176 |
-2.54 |
0.0142 |
F6,51=2.045; p value=0.076; R²=8.5%; Pagel's λ<10-3
2. Change in generation time between the null and senescence models (ΔT)
|
estimate |
se |
t |
p value |
Mass |
0.04 |
0.016 |
2.71 |
0.0092 |
Smax |
0.21 |
0.112 |
1.89 |
0.0642 |
LittSize |
0.03 |
0.030 |
1.04 |
0.3014 |
#Litt |
-0.06 |
0.013 |
-4.55 |
<10-4 |
Mass×Smax |
-0.04 |
0.013 |
-2.67 |
0.0102 |
Mass×LittSize |
-0.01 |
0.004 |
-2.57 |
0.0132 |
F7,50=9.53; p value<10-4; R²=47%; Pagel's λ<10-3
3. Change in per generation deterministic growth rate between the null and senescence models (ΔR0)
|
estimate |
se |
t |
p value |
Mass |
-0.94 |
0.303 |
-3.10 |
0.0032 |
Smax |
-0.11 |
2.109 |
-0.05 |
0.9585 |
LittSize |
-0.46 |
0.601 |
-0.76 |
0.4527 |
#Litt |
-5.53 |
0.948 |
-5.84 |
<10-4 |
Smax×#Litt |
4.48 |
0.793 |
5.65 |
<10-4 |
Mass×Smax |
0.78 |
0.253 |
3.07 |
0.0035 |
Mass × LittSize |
0.14 |
0.074 |
1.84 |
0.0712 |
F8,49=20.87; p value<10-4; R²=71%; Pagel's λ=0.217
4. Change in median time to extinction between the null and senescence models (ΔText)
|
estimate |
se |
t |
p value |
Mass |
-0.044 |
0.014 |
-3.08 |
0.003 |
Smax |
0.91 |
0.33 |
2.74 |
0.008 |
LittSize |
0.06 |
0.087 |
0.78 |
0.43 |
#Litt |
-1.47 |
0.27 |
-5.34 |
<10-4 |
#Litt2 |
0.65 |
0.078 |
8.40 |
<10-4 |
Mass×#Litt |
0.13 |
0.034 |
3.76 |
0.0004 |
F7,50=34.1; p value<10-4; R²=78%; Pagel's λ<10-3
Literature cited
Freckleton, R. P., P. H. Harvey, and M. Pagel. 2002. Phylogenetic analysis and comparative data: A test and review of evidence. American Naturalist 160:712–726.