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
n = 10

Woodlands
n = 15

Plains
n = 13

Woodlands
n = 13

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


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