Appendix A. Results of linear mixed-effects models of within-individual changes in mass.
The presence of age-independent terminal declines in Soay sheep with little evidence for declines in mass in relation to years to death in bighorn sheep and roe deer were supported by plots of within-individual changes (i) in relation to years to death (Fig. A1) and by LMMs of i in elderly females (Table A1). In bighorn sheep, the best fitting model of i included a quadratic term for age, although this model did not perform much better than the null model (age2 vs null model: ΔAIC = 1.3; Table A1, Fig. A1A). In roe deer, the best fitting model of i was the null model, suggesting no consistent variation in within-individual changes across years with respect to age or years to death (Table A1, Fig. A1B). In Soay sheep, the model of i including an effect of last year clearly outperformed other models including age or years to death (ΔAIC > 7.5, Table A1). This confirms the presence of significant, age-independent declines in body mass in the year before death in the Soay sheep population (Table A1, Fig. A1C).
TABLE A1. A comparison of linear mixed-effects models of within-individual changes (i) in body mass across years from elderly females (≥8 years for bighorn sheep and roe deer, ≥7 years for Soay sheep and ≤ 6 years to death for all populations). All models included individual identity as a random effect. The model with the lowest AIC is highlighted in bold.
|Bighorn sheep||Roe deer||Soay sheep|
|N = 301 (88 females)||N = 42 (29 females)||N = 146 (74 females)|
|Years to death||4||1718.55||2.6||4||188.33||1.9||4||545.91||8.1|
|Years to death2||5||1718.01||2.0||5||188.93||2.5||5||545.38||7.6|
FIG. A1. Average within-individual changes in body mass across time steps plotted against years until death, rather than age for (A) Bighorn sheep, (B) roe deer, and (C) Soay sheep (with SE bars). Note the emphatic decline in mass between the last two measurements prior to death in Soay sheep (C) but not in the other two systems (A and B).