TABLE 1.
Parameters in the model, their interpretation, and their default values.
| Symbol | Interpretation | Default parameter values | Range of parameter where play is predicted for at least 5% of lifetime (other parameters held constant) | |||
|---|---|---|---|---|---|---|
| Model 1 | Model 2 | Model 3a | Model 3b | |||
| X | Maximum energy reserves | 300 | All values (150–600) | All values (150–600) | All values (150–600) | All values (150–600) |
| A | Maximum ability level | 100 | A ≤ 121 | 40 ≤ A ≤ 100 | All values (10–250) | 60 ≤ A ≤ 150 |
| T | End time of model | 200 | 175 ≤ T | 200 ≤ T | All values (50–350) | 150 ≤ T ≤ 300 |
| τ | End time of parental provisioning | 50 | τ ≤ 80 | 10 ≤ τ ≤ 50 | All values (1–100) | All values (1–100) |
| w e | Provisioned energy amount | 3 | w e ≤ 5 | 1 ≤ w e ≤ 3 | All values (0–10) | All values (0–10) |
| w z | Provisioned energy probability | 0.7 | All values (0–1) | 0.2 ≤ w z ≤ 0.7 | All values (0–1) | All values (0–1) |
| y e | Foraging energy amount | 5 | 3 ≤ y e | 5 ≤ y e | 3 ≤ y e | 4 ≤ y e |
| y z | Foraging energy probability | 0.7 (Model 2: y z (a): y z (0) = 0.1, y z (A) = 0.9) | 0.5 ≤ y z | y z (0) ≤ 0.1 | 0.4 ≤ y z | 0.5 ≤ y z |
| cf | Energy cost of foraging | 2 | cf ≤ 3 | cf = 2 | cf ≤ 3 | cf ≤ 3 |
| c p | Energy cost of play | 3 | c p ≤ 5 | c p ≤ 3 | All values (1–14) | c p ≤ 12 |
| c r | Energy cost of rest | 1 | 1 ≤ c r | 1 ≤ c r | All values (−1 to 3) | c r ≤ 2 |
| m f | Predation risk of foraging | 0.002 (Model 1: m f (a): m f (0) = 0.005, m f (A) = m p ) | 0.0012 ≤ m f (0) | 0.0017 ≤ m f | m f ≤ 0.06 | 0.0003 ≤ m f ≤ 0.015 |
| m p | Predation risk of play | 0.0002 | m p ≤ 0.006 | m p ≤ 0.00015 | All values (0–0.06) | m p ≤ 0.001 |
| m r | Predation risk of rest | 0.0001 | All values (0–0.06) | 0.0001 ≤ m r | All values (0–0.06) | All values (0–0.06) |
| s f | Probability of improving ability from foraging | 0.8 (Model 3a: s f = 0) | 0.5 ≤ s f | s f ≤ 0.27 & 0.46 ≤ s f ≤ 0.8 | All values (0–1) | All values (0–1) |
| s p | Probability of improving ability from play | 0.5 | 0.3 ≤ s p | 0.5 ≤ s p | 0.01 ≤ s p | 0.05 ≤ s p |
| x crit | Critical level of energy for reproduction at time T | 150 | 90 ≤ x crit | 150 ≤ x crit | All values (1–265) | All values (1–265) |
| q | Exponent transformation on final reserves to value | 0 | All values (0–2) | All values (0–2) | All Values (0–2) | q ≤ 0.05 |
| ω z (a) | Probability of final reproduction | Model 3a & 3b: ω z (0) = 0.1, ω z (A) = 0.9 | N/A | N/A | ω z (0) ≤ 0.75 | ω z (0) ≤ 0.85 |
| x start | Starting energy for Forward Model | 50 | x start ≤ 160 | 30 ≤ x start ≤ 100 & 280 ≤ x start | All values (1–280) | All values (1–280) |
| a start | Starting ability for Forward Model | 0 | a start ≤ 85 | a start = 0 | a start ≤ 90 | a start ≤ 40 |
Note: The final four columns show the range of values for each model over which the proportion of predicted lifetime activity of playing is at least 5% (holding all other parameters constant). This was done through a one‐at‐a‐time sensitivity analysis, by using the parameter values of each basic model, and varying the parameter in each row. For each parameter value variation, we would run the forward model to predict the amount of time individuals spent doing each activity over the total time modelled (t = 0 to T). The default parameters are usually the same for every model, although for each model variation, one of these is a variable that is a function of ability (shown in bold). How each activity changes with the varying parameter can be seen in the figures in the Appendix (Figures A1, A2, A3, A4), and explanations of those of interest are also given.