Table 1.
Linear mixed model (LMM) selection parameters of gray whale fecal glucocorticoid metabolite (fGC) concentrations relative to vessel counts, sex, year, progestin metabolites (fP), androgen metabolites (fA) and body condition (Body Area Index: BAI).
| Models | DF | AIC | R2m | R2c |
|---|---|---|---|---|
| 0) fGC ~ sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 67.81511 | 0.45 | 0.49 |
| 1) fGC ~ vesselssameday + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 64.21275 | 0.54 | 0.54 |
| 2) fGC ~ vesselsprev1 + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 58.5528 | 0.64 | 0.64 |
| 3) fGC ~ vesselsprev2sum + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 59.86415 | 0.61 | 0.61 |
| 4) fGC ~ vesselsprev3sum + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 64.81003 | 0.5 | 0.5 |
| 5) fGC ~ vesselsprev4sum + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 68.19622 | 0.41 | 0.43 |
| 6) fGC ~ vesselsprev5sum + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 67.24901 | 0.45 | 0.56 |
| 7) fGC ~ vesselsprev6sum + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 68.38497 | 0.4 | 0.4 |
| 8) fGC ~ vesselsprev7sum + sex + month + year + fP + fA + BAI + (1|whale ID) | 14 | 68.10813 | 0.4 | 0.4 |
| A) fGC ~ vesselsprev1 + sex + month + year + fP + fA + (1|whale ID) | 13 | 91.82038 | 0.28 | 0.3 |
| B) fGC ~ vesselsprev1 + sex + month + year + fP + (1|whale ID) | 12 | 103.6393 | 0.2 | 0.2 |
| C) fGC ~ vesselsprev1 + sex + month + year + (1|whale ID) | 11 | 110.6568 | 0.1 | 0.1 |
| D) fGC ~ vesselsprev1 + sex + month + (1|whale ID) | 9 | 106.5958 | 0.08 | 0.08 |
| E) fGC ~ vesselsprev1 + sex + (1|whale ID) | 5 | 97.52082 | 0.05 | 0.05 |
| F) fGC ~ vesselsprev1 + month + (1|whale ID) | 8 | 104.8685 | 0.04 | 0.04 |
| G) fGC ~ vesselsprev1 + year + (1|whale ID) | 6 | 100.0222 | 0.05 | 0.05 |
| H) fGC ~ vesselsprev1 + fP + (1|whale ID) | 5 | 88.37007 | 0.13 | 0.13 |
| I) fGC ~ vesselsprev1 + fA + (1|whale ID) | 5 | 84.47714 | 0.09 | 0.09 |
| J) fGC ~ vesselsprev1 + (1|whale ID) | 4 | 95.57796 | 0.01 | 0.01 |
| K) fGC ~ vesselsprev1 + sex + month + year + fP + BAI + (1|whale ID) | 13 | 67.12452 | 0.54 | 0.68 |
| L) fGC ~ vesselsprev1 + sex + month + year + fA + BAI + (1|whale ID) | 13 | 60.16235 | 0.61 | 0.61 |
| M) fGC ~ vesselsprev1 + sex + month + year + BAI + (1|whale ID) | 12 | 71.2999 | 0.48 | 0.48 |
| N) fGC ~ vesselsprev1 + sex + month + BAI + (1|whale ID) | 10 | 67.72778 | 0.48 | 0.52 |
| O) fGC ~ vesselsprev1 + sex + BAI + (1|whale ID) | 6 | 65.35813 | 0.37 | 0.37 |
| P) fGC ~ vesselsprev1 + month + BAI + (1|whale ID) | 9 | 64.00439 | 0.49 | 0.51 |
| Q) fGC ~ vesselsprev1 + BAI + (1|whale ID) | 5 | 61.61131 | 0.37 | 0.37 |
All models used whale identification (whale ID) as a random factor to account for pseudoreplication. Models 1–8 included the same predictor variables except vessel counts, which was assessed at different temporal scales in each model and ranged from the count of vessels on the same day of the fecal sample collection (vesselssameday, model 1) to the count of vessel within the seven previous days (vesselsprev7sum, model 8). Model zero is the null model, which does not include vessels. Once the most influential temporal scale for vessel counts was determined (i.e., previous day; Model 2), 17 additional LMMs were run with varied combinations of the fixed effects (stepwise process, models A-Q; below the thin black line). Model in bold represents the selected model based on the lowest Akaike Information Criterion (AIC). The degrees of freedom for each model are indicated by DF. The fit of each model is represented by the marginal R2 (R2m; variance explained by fixed effects) and the conditional R2 (R2c; variance explained by both fixed and random effects).