During the decision-making part of the task, the brain explicitly determined how long to work before initiating harvest. During the work and the harvest periods, the brain implicitly controlled the vigor of movements. We imagined that these two forms of behavior were not independent, but rather coordinated via a control policy that maximized a single utility: the sum of rewards acquired, minus efforts expended, divided by time, termed the capture rate. We chose this formulation because it presents a normative approach that ecologists have used to understand the decisions that animals make regarding how far to travel for food, what mode of travel to use, and how long to stay before moving on to another patch (Richardson and Verbeek, 1986; Stephens and Krebs, 1987; Bautista et al., 2001).

During a work period, our subjects decided to complete a number of saccade trials ns , a fraction βs of which were successful, earning food increment α, but expended effort cs that consumed time Ts for each trial. They then stopped working and initiated harvest, producing a number of licks nl , a fraction βl of which succeeded, thus expending effort cl and consuming time Tl for each lick. These actions produced the following capture rate:(1)J=αβsns(1-11+βlnl)-nlcl-ns2csnlTl+nsTs

In the numerator of Equation 1, the first term represents the fact that the food cache increased linearly with successful trials and was then consumed gradually with successful licks. The second term represents the effort expenditure of licking, and the third term represents the effort expenditure of working. Notably, the effort expenditure of work, ns2cs , grows faster than linearly as a function of trials. This nonlinearity is essential to reflect the idea that following a long work period, the capture rate must be more negative than following a short work period (i.e., more work trials produce a greater reduction in utility).

A control policy describes how long to work and harvest, and an optimal policy produces periods of working and harvesting, ns*, nl* , that maximize Equation 1. A closed-form solution for the optimal policy can be obtained (Supplementary file 1), and Figure 2A provides an example. As the work period concludes and the harvest period beings (nl=0), the capture rate is negative. This reflects the fact that the subject has performed a few trials and stockpiled food, thus expended effort but has not been rewarded yet. The capture rate rises when licking commences. Critically, the peak capture rate is not an increasing function of the work period. Rather, there is an optimal work period (ns* , red trace, Figure 2A) associated with a given effort cost of licking cl . If we now move the tube away from the mouth, that is, increase the effort cost of licking cl , the peak of the capture rate shifts and the optimal work period changes: the proper response to an increased effort cost of licking is to work longer, stowing more food before commencing harvest.

Notably, the higher cost of licking inevitably reduces the maximum capture rate (Figure 2A). This should impact movement vigor: animals tend to respond to a reduced capture rate by slowing their movements (Yoon et al., 2018), which can be viewed as an effective way to save energy (Shadmehr et al., 2016). To incorporate vigor into the capture rate, we tried to define the effort cost of a single lick cl in terms of its energetic cost, a relationship that is currently unknown. Fortunately, other movements provide a clue: the energetic cost of reaching (Shadmehr et al., 2016; Huang and Ahmed, 2014) and the energetic cost of walking (Ralston, 1958; Bastien et al., 2005) are both concave upward functions of the movement’s duration. That is, from an energetic standpoint, there is a reach speed and a walking speed that minimize the cost of each type of movement. We generalized these empirical observations to licking and assumed that the energetic cost of a single lick was a concave upward function of its duration:(2)clTl=d2Tl+kTl

In Equation 2, the lick is aimed at a tube located at distance d and has a duration Tl . The parameter k describes the rate with which the cost grows as a function of duration. For example, the lick duration that minimizes the energetic cost is d/k . Thus, for an energetically optimal lick, duration grows linearly with tube distance (Figure 2B). However, our objective is not to minimize the cost of licking, but to maximize the capture rate. To do so, we insert Equation 2 into Equation 1 and find the optimal policy (ns*, nl*, Tl*), which now depends on the distance of the food tube to the mouth (Supplementary file 1).

The theory predicts that to maximize the capture rate (Equation 1), the response to an increased effort cost of harvest (i.e., tube distance) should be as follows: ns* should increase (Figure 2C), nl* should decrease (Figure 2C), and Tl* should increase (Figure 2D). Notably, the rate of increase in Tl* as a function of tube distance is faster than linear, while from an energetic point of view (Equation 2), increase in distance should produce a linear increase in lick duration. Thus, as the harvest becomes more effortful, the subject should work longer to stockpile food, but move slower to save energy.

To test our theory further, we thought it useful to have a way to alter decisions in one direction (say work longer) but change movement vigor in the opposite direction (move faster). In theory, this is possible: if the subject is hungry (darker lines in Figure 2C and D), that is, the reward is more valuable, then they should again work longer before initiating harvest. Paradoxically, they should also move faster.

In summary, if decisions and actions are coordinated via a policy that aims to maximize the capture rate, then in response to an increased cost of harvest, one should work longer, but move with reduced vigor. In response to an increased reward value, as in hunger, one should also work longer, but now move with increased vigor.

To vary the effort cost of harvest, we altered the tube distance to the mouth (but kept it constant during each session). Varying tube distance affected the decisions of the subjects: when the tube was placed farther, they chose to work longer before starting harvest (Figure 3A, left subplot): they attempted more trials during each work period (ANOVA, subject M: F(2,7908) = 41.5, p=5.2 × 10^–25, subject R: F(2,10948) = 88.2, p=7 × 10^–50) and produced more successful trials per work period (ANOVA, subject M: F(2,7908) = 63, p=2.8 × 10^–24, subject R: F(2,10948) = 163, p<10^–50). This policy of delayed gratification was present throughout the recording session (Figure 3A, middle plot). That is, when the harvest required more effort, the subjects worked longer to stockpile more food before initiating their harvest (Figure 3A, right plot, effect of tube distance on food cached: subject M: F(2,9566) = 176, p<10^–50, subject R: F(2,8907) = 204, p<10^–50).

During the work period, the subjects made saccades to visual targets and accumulated their food. They also made saccades that were not toward visual targets and thus were not eligible for reward. For each animal, we computed the relationship between peak saccade velocity and saccade amplitude across all sessions and then calculated the vigor of each saccade: defined as the ratio of the actual peak velocity with respect to the expected peak velocity for that amplitude (Reppert et al., 2015; Reppert et al., 2018). For example, a saccade that exhibited a vigor of 1.10 had a peak velocity that was 10% greater than the average peak velocity of the saccades of that amplitude for that subject. As expected, the reward-relevant saccades, that is, saccades made to visual targets (primary, corrective, and center saccades), were more vigorous than other saccades (Figure 3B, two-way ANOVA, effect of saccade type, subject M: F(1,391459) = 7,248, p<10^–50, subject R: F(1,355839) = 13,641, p<10^–50).

As a work period began, the reward-relevant saccades exhibited high vigor, but then trial-by-trial, this vigor declined, reaching a low vigor value just before the work period ended (Figure 3C vigor). Remarkably, on days in which the tube was placed farther, saccade vigor was lower (RMANOVA, effect of tube distance, subject M: F(2,59033) = 224, p<10^–50, subject R: F(2,50103) = 75.51, p=1.8 × 10^–33). Thus, increasing the effort cost of extracting food during the harvest period reduced saccade vigor during the work period.

By definition, a more vigorous saccade had a greater peak velocity. This might imply that high vigor saccades should suffer from inaccuracy due to signal dependent noise (Harris and Wolpert, 1998). However, we observed the opposite tendency: as saccade vigor increased, both the magnitude and the variance of the endpoint error decreased (Figure 3C, two-way ANOVA, effect of vigor on error magnitude, subject M: F(8,59046) = 480, p<10^–50, subject R: F(8,50184) = 252, p<10^–50, effect of vigor on error variance, subject M: F(8,2673) = 18,200, p<10^–50, subject R: F(8,2673) = 4170, p<10^–50). That is, reducing the effort costs of harvest not only promoted vigor, it also facilitated accuracy (Wang et al., 2016).

Cognitive signals such as effort and reward are associated with changes in pupil size (Joshi and Gold, 2020), as well as transient activation of brainstem neuromodulatory circuits in locus coeruleus (Bornert and Bouret, 2021). We wondered if the changes in tube position altered the output of these neuromodulatory circuits, as inferred via pupil size. For each reward-relevant saccade, we measured the pupil size during a ±250 ms window centered on saccade onset, and then normalized this measure based on the distribution of pupil sizes that we had measured during the entire recording for that session in that subject, resulting in a z-score.

At the onset of each work period, the pupils were dilated, but as the subjects performed more trials, the pupils constricted, exhibiting a trial-by-trial reduction that paralleled the changes in saccade vigor (Figure 3C). Notably, the effort cost of harvest affected pupil size: during the work period, the pupils were more dilated if the tube was placed closer to the mouth (Figure 3C, RMANOVA, effect of tube distance, subject M: F(2,60502) = 20, p=2 × 10^–9, subject R: F(2,50431) = 23.8, p=4.9 × 10^–11). That is, when the effort cost of harvest was lower, the pupils dilated, and the saccades were invigorated.

In summary, when we increased the effort cost of harvest, both the movements and the decisions changed: the pupils constricted and the movements slowed, but they chose to work more trials before initiating harvest.

The work period ended when the subject chose to stop tracking the target and initiated harvest via a licking bout. As in saccades, we defined lick vigor via the ratio of the actual peak velocity of the lick with respect to the expected velocity for that lick amplitude. As amplitude increased, lick peak velocity increased during both protraction and retraction (Figure 4A). Some of the licks were reward seeking and directed toward the tube, while others were grooming licks, cleaning the tongue and the area around the mouth (Animation 5). Reward-seeking licks were more vigorous than grooming licks (two-way ANOVA, effect of lick type, protraction, subject M: F(1,272233) = 66, p=4.5 × 10^–16, subject R: F(1,229052) = 698, p<10^–50), and retraction was more vigorous than protraction (reward-seeking licks, retraction vs. protraction, subject M: t(241145) = 532, p<10^–50, subject R: t(213674) = 665, p<10^–50).

As the harvest began, the first lick was very low vigor, but lick after lick, the movements gathered velocity, reaching peak vigor by the third or the fourth lick (Figure 4B). As the harvest continued, lick vigor gradually declined. Like saccades, licks had a lower vigor in sessions in which the tube was placed farther from the mouth (RMANOVA, effect of tube distance, subject M: F(2,59033) = 222.5, p<10^–50, subject R: F(2,133502) = 224, p<10^–50), and this pattern was present during the entire recording session (Figure 4C, left subplot). Thus, an increased effort cost of harvest promoted sloth: reduced vigor of saccades during the work period and reduced vigor of licks during the harvest period.

For each reward-seeking lick, we measured pupil size during a ±250 ms window centered on the moment of peak tongue displacement. During licking, the pupil size changed with a pattern that closely paralleled lick vigor: as the harvest began, pupil size was small, but it rapidly increased during the early licks, then gradually declined as the harvest continued (Figure 4B, right subplot). Importantly, the pupils were more dilated in sessions in which the tube was closer to the mouth (Figure 4C, right subplot, effect of tube distance, subject M: F(2,166742) = 583, p<10^–50, subject R: F(2,130493) = 118, p<10^–50). As a result, when the effort cost of reward increased, the pupils constricted, and the vigor of both saccades and licks decreased.

While the theory predicted that moving the tube farther would result in a longer work period and reduced movement vigor, it also predicted that the subjects would reduce their harvest duration (reduced licks, Figure 2C). That is, it predicted that the subjects would work longer, stowing more food, but leave more of it behind. This last prediction did not agree with our data (see ‘Discussion’). For subject R, the number of licks was approximately the same across the various tube distances, and for subject M the number of licks increased with tube distance (Figure 1—figure supplement 1).

In summary, within a harvest period, lick vigor rapidly increased and then gradually declined. Simultaneous with the changes in vigor, the pupils rapidly dilated and then gradually constricted. In sessions where the tube was placed farther from the mouth, the licks had lower vigor and the pupils were more constricted.

As the subject worked, they accumulated food, thus increasing the magnitude of the available reward. To check whether reward magnitude affected movement vigor, for each tube distance we computed the average lick vigor during the harvest as a function of the number of trials completed in the preceding work period. We found that when the work period had included many completed trials, then the movements in the ensuing harvest period were more vigorous (Figure 4D, two-way ANOVA, effect of trials, subject M: F(4, 164242) = 353, p<10^–50, subject R: F(4,123411) = 152, p<10^–50). Thus, the licks were invigorated by the amount of food that awaited harvest.

Because the tube was small, many of the licks missed their goal and failed to contact the food. The success or failure of a lick affected both the vigor of the subsequent lick and the change in the size of the pupil. Following a successful lick, there was a large increase in lick vigor (Figure 4E, subject M: t(85182) = 40, p<10^–50, subject R: t(81378) = 104, p<10^–50), and a large increase in pupil size (subject M: F(84969) = 57, p<10^–50, subject R: t(80318) = 94, p<10^–50). In contrast, following a failed lick the subjects either reduced or did not increase their lick vigor (Figure 4E, subject M: t(114159) = 0.88, p=0.37, subject R: t(97164) = -44, p<10^–50). This failure also produced a smaller increase in pupil size (comparison to successful lick, two-sample t-test, subject M: t(198722) = 14.8, p=4.3 × 10^–50, subject R: t(176044) = 53, p<10^–50). Thus, a single successful lick led to acquisition of reward, which then was followed by a relatively large increase in pupil size, and an invigorated subsequent lick.

For saccades, we had found that increased vigor was associated with greater accuracy. To quantify the relationship between lick vigor and accuracy, for each tube distance we labeled each reward-seeking lick as being high or low vigor. For subject M, high vigor licks tended to be more successful, but this was not the case for subject R (Figure 4F). Moreover, tube distance did not produce a consistent effect on lick success.

In summary, the subject licked more vigorously following a long work period in which they had accumulated more reward. Moreover, when a lick was successful in acquiring reward, they increased the vigor of the subsequent lick.

Our theory predicted that it should be possible to change decisions in one direction (say work longer), while altering movement vigor in the opposite direction (move faster). An increase in the subjective value of reward, as might occur when the subject is hungry, should have two effects: increase the number of trials that the subject chooses to perform before commencing harvest and increase movement vigor.

We did not explicitly manipulate the weight of the subjects. Indeed, to maintain their health, we strived to keep their weights constant during the roughly 2.5-year period of these experiments. However, there was natural variability, which allowed us to test the predictions of the theory.

We found that when their weight was lower than average, the subjects chose to work a greater number of trials before commencing harvest (Figure 5A, two-sample t-test, subject M: t(11052) = 7.9, p=3.4 × 10^–25, subject M: t(12549) = 10.1, p=9.3 × 10^–24). This result was similar to the effect that we had seen when the effort cost of harvest was increased. However, the theory had predicted that the effect on vigor should be in the opposite direction: if hunger increased reward valuation, then one should speed the movements and hasten food acquisition. Notably, weight did not have a consistent effect on saccade vigor across the two subjects (Figure 5A), yet during the harvest, both subjects licked with greater vigor when their weight was lower (Figure 5A, subject M: t(219752) = 88, p<10^–50, subject R: t(205163) = 22, p<10^–50).

Thus, while both the effort cost of reward and hunger promoted greater work, effort promoted sloth while hunger promoted lick vigor.

Finally, we considered the data across both the work and the harvest periods and asked how well movement vigor tracked pupil size. The results demonstrated that in both the work and the harvest periods, for both saccades and licks, an increase in pupil size was associated with an increase in vigor (Figure 5B, reward-relevant saccades, subject M: r = 0.989, p=7.7 × 10^–9, subject R: r = 0.97, p=7.1 × 10^–7; reward-seeking protraction licks, subject M: r = 0.969, p=9.8 × 10^–7, subject R: r = 0.989, p=6.3 × 10^–9). Moreover, when the pupil was dilated, the work periods tended to be shorter (Figure 5C, subject M: r = −0.90, p=0.00014, subject R: r = −0.97, p=6.3 × 10^–7), while harvest durations tended to be longer (Figure 5C, subject M: r = 0.894, p=0.00021, subject R: r = 0.935, p=2.4 × 10^–5). Thus, pupil dilation was associated with choosing to work less, while moving faster.

Following recovery from head-post implantation surgery, the animals were trained to make saccades to visual targets and rewarded with a mixture of apple sauce and lab diet (Sedaghat-Nejad et al., 2019). They were placed in a monkey chair and head-fixed while we presented visual targets on an LCD screen (Curved MSI 32” 144 Hz, model AG32CQ) and tracked both eyes at 1000 Hz using an EyeLink-1000 system (SR Research, USA). The timing of target presentation on the video screen was measured using a photo diode. Tongue movements were tracked with a 522 frame per second Sony IMX287 FLIR camera, with frames captured at 100 Hz.

Each trial began with a saccade to the center target followed by fixation for 200 ms, after which a primary target (0.5 × 0.5° square) appeared at one of eight randomly selected directions at a distance of 5–6.5°. Onset of the primary target coincided with the presentation of a tone. As the animal made a saccade to the primary target, that target was erased and a secondary target was presented at a distance of 2–2.5°, also at one of eight randomly selected directions. The subject was rewarded if following the primary saccade it made a corrective saccade to the secondary target, landed within 1.5° radius of the target center, and maintained fixation for at least 200 ms. Onset of reward coincided with the presentation of another distinct tone. Following an additional 150–250 ms period (uniform random distribution), the secondary target was erased and the center target was displayed, indicating the onset of the next trial. Thus, a successful trial comprised of a sequence of three saccades: center, primary, and corrective, after which the subject received a small increment of food (0.015 mL).

The food was provided in two small tubes (4.4 mm diameter), one to the left and the other to the right of the animal (Figure 1A). A successful trial produced a food increment in one of the tubes and would continue to do so for 50–300 consecutive trials, then switch to the other tube. Because the food increment was small, the subjects naturally chose to work for a few consecutive trials, tracking the visual targets and allowing the food to accumulate, then stopped tracking and harvested the food via a licking bout. The licking bout typically included a sequence of 15–40 licks. The subjects did not work while harvesting. As a result, the behavior consisted of a work period (targeted saccades), followed by a harvest period (targeted licking), repeated hundreds of times per session.

The critical variables were the number of trials that the subject chose to perform before initiating harvest, the vigor of their saccades during the work period, and the vigor of their licks during the harvest period.

All saccades, regardless of whether they were instructed by presentation of a visual target or not, were identified using a velocity threshold. Saccades to primary, secondary, and central targets were labeled as reward-relevant saccades, while all remaining saccades were labeled as task irrelevant.

We analyzed tongue movements using DeepLabCut (Mathis et al., 2018). Our network was trained on 89 video recordings of the subjects with 15–25 frames extracted and labeled from each recording. The network was built on the ResNet-152 pre-trained model, and then trained over 1.03 × 10⁶ iterations with a batch size of 8, using a GeForce GTX 1080Ti graphics processing unit (He et al., 2016). A Kalman filter was further applied to improve quality and smoothness of the tracking, and the output was analyzed in MATLAB to quantify varying lick events and kinematics.

We tracked the tongue tip and the edge of the food in the tube, along with control locations (nose position and tube edges). We tracked all licks, regardless of whether they were aimed toward the tube (reward seeking) or not (grooming). Reward-seeking licks were further differentiated based on whether they aimed to enter the tube (inner-tube licks), hit the outer edge of the tube (outer-edge licks), or fell below the tube (under tube). If any of these licks successfully contacted the tube, we labeled that lick as a success (otherwise, a failed lick).

Pupil area was measured during a ±250 ms period centered at the onset of each reward-relevant saccade and the onset of each lick. We then normalized the pupil measurements by representing it as a z-score with respect to the mean value for that session.

We relied on previous work to define vigor of a movement (Yoon et al., 2020; Yoon et al., 2018; Reppert et al., 2015; Reppert et al., 2018). Briefly, if the amplitude of a movement is x and the peak speed of that movement is v, then for each subject the relationship between the two variables can be described as:(3)v=α1-11+βx

In the above expression, α,β≥0 and are subject-specific parameters. For a movement with amplitude x, its vigor was defined as the ratio of the actual peak speed with respect to the expected value of its peak speed, that is, vEvx . Expected value was computed by fitting Equation 3 to all the data acquired across all sessions. When vigor is greater than 1, the movement had a peak velocity that was higher than the mean value associated with that amplitude.

We chose a formulation of utility (Equation 1) based on a normative approach that ecologists have used to understand the decisions that animals make regarding how far to travel for food, what mode of travel to use, and how long to stay before moving on to another reward opportunity (Richardson and Verbeek, 1986; Stephens and Krebs, 1987; Bautista et al., 2001). In a typical formulation of the theory, the numerator represents the reward gained (in units of energy), minus the effort expended (also in units of energy), while the denominator represents the amount of time spent during that behavior. We represented this idea in Equation 1 with saccades that produced reward accumulation and licks that produced reward consumption. Thus, the utility that we aim to maximize is the rate of energy gained.

The specific functions that we used to represent the energy gained through reward acquisition and the energy expended through effort expenditure came either from experiment design or from the measurements we have made in other experiments. We modeled reward accumulation as a linear rise in energy stored because successful saccades produced a linear increase in the food cache. We modeled harvesting of the food as a hyperbolic function of the number of licks to represent the fact that as the licking bout began, each successful lick depleted the food, and thus the first few licks produced a greater amount of food consumption than the last few licks. We modeled the effort cost of licking as a linear function of the number of licks.

A critical assumption that we made is that energy expended performing the saccade trials (which grew faster than linearly as a function of the number of trials attempted) grew faster than the time spent attempting those same trials (which grew linearly with the number of trials). This assumption is based on the heuristic that the average rate of energy lost following a large number of attempted trials is greater than the average rate of energy lost following a small number of attempted trials.

The model’s simplicity provided closed-form solutions across all parameter values, allowing us to make predictions without having to fit the model to the measured data. For example, for all parameter values that produce a real solution (as opposed to imaginary), the optimal number of saccade trials increases with the square root of the cost of licking. Thus, the basic prediction of the model is that to maximize the capture rate, regardless of parameter values, an increase in the effort required for harvest should be met with a greater willingness to work. The closed-form solutions are presented in the supplementary document (simulations.nb).

In composing our utility (Equation 1), we chose to combine reward and effort additively. This is in contrast to other approaches in which effort discounts reward multiplicatively (Sugiwaka and Okouchi, 2004; Prévost et al., 2010; Klein-Flügge et al., 2015). Our reasoning is that multiplicative interactions have the limitation that they are incompatible with the observation that reward invigorates movements.

To compare additive and multiplicative approaches, let us consider an arbitrary function U(T) that specifies how effort varies with movement duration T. Typically, this is a U-shaped function that describes energy expenditure as a function of movement duration, as in Shadmehr et al., 2016. In the case of multiplicative interaction between reward and effort, we can consider the following representation of utility:(4)J=α1+TU-1(T)

In the above formulation, reward α is discounted hyperbolically with time and an increase in reward increases the utility of the action. The optimum movement vigor has the duration T∗ that maximizes this utility. Notably, because increasing reward merely scales this utility, it has no effect on vigor. Thus, a utility in which reward is multiplied by a function of effort generally fails to predict dependence of movement vigor on reward.

The optimal policy specifies the decisions and movements that for the effort cost defined in Equation 2 maximizes the capture rate defined in Equation 1. This policy selects the number of saccade trials ns to perform during the work period, the number of licks nl to perform during the harvest period, and the vigor of each lick, represented by the average duration of a lick Tl . To compute the optimal policy, we found the derivative of the capture rate with respect to each policy variable ns , nl , and Tl , then set each derivative equal to zero, producing three simultaneous nonlinear equations. In all three cases, we were able to solve for the relevant control variable analytically (see Supplementary file 1 for the derivations). We found that if the solution was a real number, then regardless of parameter values, an increase in d (distance of the tube to the mouth), the optimal policy produced an increase in ns* , decrease in nL* , and increase in TL* . Thus, the results illustrated in Figure 2 are robust to changes in parameter values.

To generate the plots in Figure 2A, we used the following parameter values: α=20, βs=0.5, βL=0.3, cs=0.5, Ts=1, TL=0.2, cL=0.5 (low effort), and cL=2.5 (high effort). For the plots in Figure 2C and D, we used the same parameter values, but cL was defined via Equation 2. Thus, tube distance d varied, and TL was unknown and was solved for. In Equation 2, kL=1. In the simulations, to describe state of hunger, we set α=20 for a sated state and α=25 for a hungry state.

Hypothesis testing was performed using the functions provided by the MATLAB Statistics and Machine Learning Toolbox, version R2021b. For t-tests, across the one-sample, paired-sample, and two-sample conditions, p-values were computed using the ttest and ttest2 functions with data that was combined across sessions, separated by condition. For ANOVA, in the one-way condition, p-values were computed using a nonparametric Kruskal–Wallis test, using the kruskalwallis function. In the two-way condition, the anovan function was used to compute p-values, accounting for an unbalanced design resulting from a varied number of samples across conditions. In both cases, like in the t-tests, data was combined across sessions, separated by condition. In the repeated measures condition, each session was treated as a subject with multiple repeated measures representing a given variable (i.e., lick vigor per lick in a harvest period). To fit a repeated measures model, the fitrm function was used, then analyzed using the ranova function. In all cases of repeated measures ANOVA, compound symmetry assumptions were tested using the Mauchly sphericity test with the maulchy function. In cases where the assumption was violated (Maulchy test p<0.05), epsilon adjustments were used, with the epsilon function, to compute corrected p-values (for ε > 0.75, use Huynh–Feldt p-value; and for ε < 0.75, use Greenhouse–Geisser p-values). For correlation analyses, Pearson’s correlation coefficient, r, and corresponding p-values were computed using the corrcoef function.