Ecological Archives M084-012-A4
J. Grant C. Hopcraft, J. M. Morales, H. L. Beyer, Markus Borner, Ephraim Mwangomo, A. R. E. Sinclair, Han Olff, Daniel T. Haydon. 2014. Competition, predation, and migration: individual choice patterns of Serengeti migrants captured by hierarchical models. Ecological Monographs 84:355–372. http://dx.doi.org/10.1890/13-1446.1
Appendix D. A comparison between the full models presented in the manuscript and simplified models from a backward elimination process.
Table D1. Model selection was performed by backward elimination starting from the full model for (a) wildebeest on the plains, (b) wildebeest in the woodlands, (c) zebra on the plains, and (d) zebra in the woodlands. Covariates were systematically dropped from subsequent models if their coefficients did not differ from zero (i.e., the 80th percentiles of the highest probability density (HPD) estimating the credible interval of the coefficient included zero). An increase in the Deviance Information Criterion (ΔDIC) suggests poorer model fit. The full models presented in the manuscript contain the following variables: distance to high nitrogen patches, distance to high nitrogen patches², NDVI, dNDVI (i.e., NDVI change), distance to high grass biomass patches, distance to high grass biomass patches², distance to water, distance to dense woody cover, distance to dense woody cover², distance to drainages, distance to drainages², distance to human habitation, and distance to human habitation².
(a) Wildebeest on the plains
|
Variables included (Wildebeest Plains) |
DIC |
ΔDIC |
||
|
ρ |
μ |
α |
||
Full Model |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
5598.2 |
|
1 |
Nitrogen, Grass Biomass, Woody Cover, Human, Intercept |
Nitrogen, NDVI, dNDVI, Grass Biomass, Woody Cover, Human, Intercept |
Nitrogen, Nitrogen², Human, Intercept |
5598.8 |
+0.6 |
2 |
Nitrogen, Grass Biomass, Woody Cover, Human, Intercept |
Nitrogen, dNDVI, Grass Biomass, Woody Cover, Human, Intercept |
Nitrogen, Nitrogen², Intercept |
5603.4 |
+4.6 |
3 |
Grass Biomass, Woody Cover, Human, Intercept |
Nitrogen, dNDVI, Grass Biomass, Woody Cover, Human, Intercept |
Intercept |
5612.6 |
+9.2 |
(b) Wildebeest in the woodlands
|
Variables included (Wildebeest Woodlands) |
DIC |
ΔDIC |
||
|
ρ |
μ |
α |
||
Full Model |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
23073.1 |
|
1 |
Woody Cover, Woody Cover², Intercept |
Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Water, Water², Woody Cover, Woody Cover², Human, Humans², Intercept |
23059.9 |
-13.2 |
2 |
Woody Cover, Woody Cover², Intercept |
Grass Biomass, Grass Biomass², Woody Cover, Woody Cover², Drainage, Intercept |
Nitrogen, NDVI, dNDVI, Woody Cover, Human, Intercept |
23097.8 |
+37.9 |
3 |
Woody Cover, Woody Cover², Intercept |
Grass Biomass, Grass Biomass², Woody Cover, Woody Cover², Drainage, Intercept |
Nitrogen, NDVI, dNDVI, Woody Cover, Intercept |
23106.2 |
+8.4 |
(c) Zebra on the plains
|
Variables included (Zebra Plains) |
DIC |
ΔDIC |
||
|
ρ |
μ |
α |
||
Full Model |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
21162.3 |
|
1 |
dNDVI, Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Woody Cover, Woody Cover², Drainage, Intercept |
Nitrogen, NDVI, Woody Cover, Drainage, Human, Humans², Intercept |
21160.9 |
-1.4 |
2 |
Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Drainage, Intercept |
Nitrogen, NDVI, Woody Cover, Drainage, Human, Humans², Intercept |
21165.2 |
+4.3 |
3 |
Intercept |
NDVI, dNDVI, Intercept |
NDVI, Woody Cover, Drainage, Human, Humans², Intercept |
21165.7 |
+0.5 |
4 |
Intercept |
NDVI, dNDVI, Intercept |
NDVI, Drainage, Human, Humans², Intercept |
21163.2 |
-2.5 |
(d) Zebra in the woodlands
|
Variables included (Zebra Woodlands) |
DIC |
ΔDIC |
||
|
ρ |
μ |
α |
||
Full Model |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
Nitrogen, Nitrogen², NDVI, dNDVI, Grass Biomass, Grass Biomass², Water, Water², Woody Cover, Woody Cover², Drainage, Drainage², Human, Humans², Intercept |
45240.1 |
|
1 |
Grass Biomass, Grass Biomass², Intercept |
Nitrogen, Nitrogen², Grass Biomass, Woody Cover, Woody Cover², Human, Intercept |
Nitrogen, NDVI, Grass Biomass, Grass Biomass², Water, Intercept |
45241.0 |
+0.9 |
2 |
Grass Biomass, Intercept |
Nitrogen, Nitrogen², Grass Biomass, Woody Cover, Human, Intercept |
Nitrogen, NDVI, Grass Biomass, Grass Biomass², Water, Intercept |
45237.9 |
-3.1 |
Table D2. Estimates of the population level variance of α for the full model. Large variance suggests more inter-individual variation in response while small variance suggests all individuals behave somewhat similarly. Variables where the credible interval of the mean coefficient at the population level is non-zero are in bold and correspond to the bold values in Table 2 and 3.
|
|
Wildebeest |
Zebra |
||
|
|
Plains |
Woodlands |
Plains |
Woodlands |
Food quality |
Nitrogen |
0.30 |
0.10 |
0.19 |
0.10 |
|
(Nitrogen)² |
0.27 |
0.08 |
0.07 |
0.22 |
|
NDVI |
0.61 |
0.13 |
0.07 |
0.13 |
|
dNDVI |
0.26 |
0.26 |
0.18 |
0.03 |
Food abundance |
Grass Biomass |
0.58 |
0.27 |
0.07 |
0.24 |
|
(Grass Biomass)² |
0.17 |
0.12 |
0.02 |
0.14 |
Water |
Water |
X |
0.17 |
X |
0.06 |
|
(Water)² |
X |
0.07 |
X |
0.03 |
Predation |
Woody Cover |
0.30 |
0.12 |
0.10 |
0.17 |
|
(Woody Cover)² |
0.32 |
0.15 |
0.16 |
0.05 |
|
Drainage |
0.42 |
0.12 |
0.09 |
0.05 |
|
(Drainage)² |
0.36 |
0.05 |
0.03 |
0.04 |
Anthropogenic |
Human |
0.55 |
0.21 |
0.26 |
0.17 |
|
(Human)² |
0.49 |
0.10 |
0.14 |
0.02 |
Intercept |
|
0.72 |
0.33 |
0.26 |
0.18 |