Figures and data in Rats exhibit similar biases in foraging and intertemporal choice tasks

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7 figures, 2 tables and 3 additional files

Figures

Figure 1 with 1 supplement

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Rat foraging behavior.

Rat foraging behavior in the (A) Travel Time, (B) Depletion Rate, (C) Scale, and (D) Pre-vs-Post Experiments. In (A), points and error bars represent mean ± standard error. In (**B-D**), points and connecting lines represent behavior of each individual rat. Red lines indicate optimal behavior (per MVT).

https://doi.org/10.7554/eLife.48429.003

Figure 1—source data 1 Trial-by-trial foraging behavior.: https://doi.org/10.7554/eLife.48429.005
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Figure 1—figure supplement 1

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Diagram of the foraging task.

Rats press a lever to harvest reward from the patch then receive reward in an adjacent port following a pre-reward delay (handling time or HT). After receiving reward, there is a post-reward delay (inter-trial interval or) before rats can make their next decision. Rats can leave the patch by nose poking in the back of the chamber (trial n+2), which initiates a delay simulating time to travel to the next patch, after which, rats can harvest from a new replenished patch.

https://doi.org/10.7554/eLife.48429.004

Figure 2

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Post-reward delay foraging and intertemporal choice behavior.

(A) Rat behavior in the Post-Reward Delay Experiment. Points and lines represent behavior of individual rats. Red line indicates optimal behavior (per MVT). (B) Rat behavior in the intertemporal choice task. Points and error bars represent mean ± standard error for each condition.

https://doi.org/10.7554/eLife.48429.007

Figure 2—source data 1 Trial-by-trial intertemporal choice behavior.: https://doi.org/10.7554/eLife.48429.008
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Figure 3 with 5 supplements

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Model predictions for foraging tasks.

(**A-E**) Predictions of the best fit quasi-hyperbolic discounting model to all foraging tasks. Points and error bars represent mean ± standard deviation of the means for each individual rat; lines and ribbon represent the mean ± standard deviation of the means of the model-predicted behavior for each individual rat. (F) The sum of iBIC scores across all foraging tasks for each model. Cost = subjective cost model, util-pwr and util-crra = nonlinear reward utility with power and CRRA function respectively, pre-del = linear overestimation of pre-reward delays, post-del = linear underestimation of post-reward delays, post-del-pwr=underestimation of post-reward delays according to a power function, disc-exp = exponential discounting, disc-hyp = hyperbolic discounting, disc-cs = constant sensitivity discounting, disc-quasi = quasi hyperbolic discounting.

https://doi.org/10.7554/eLife.48429.010

Figure 3—figure supplement 1

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State space diagram of the foraging task.

State space diagram for the semi-markov model of the foraging task. Decisions to stay vs. leave are made in Decision states. A decision to stay causes a transition to the handling time, then reward, ITI, and to the Decision state on the next trial. Reward is delivered uniformly throughout time spent in the each reward state. Reward depletion is achieved via shorter time spent in the reward state (resulting in longer stay in the ITI state). A decision to leave causes a transition to the Travel state, then to the first trial of the patch.

https://doi.org/10.7554/eLife.48429.011

Figure 3—figure supplement 2

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Predictions of the best fit subjective cost and nonlinear reward utility models.

Predictions of the best fit subjective cost and nonlinear reward utility models (power law = util pwr; constant relative risk aversion = util CRRA). Black points and error bars represent mean ± standard error of observed behavior. Colored lines represent the mean model predicted behavior across rats.

https://doi.org/10.7554/eLife.48429.012

Figure 3—figure supplement 3

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Predictions of the best fit biased time perception models.

Predictions of the best fit models of overestimation of pre-reward delays (pre-delay), linear underestimation of post-reward delays (post-delay), and nonlinear underestimation of post-reward delays (post-delay-nonlinear). Points and errorbars are the mean ± standard deviation of rat behavior, colored lines represent the mean model predicted number of harvests across all rats.

https://doi.org/10.7554/eLife.48429.013

Figure 3—figure supplement 4

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Predictions of the best fit discounting models.

Predictions of the best fit exponential discounting model (disc-exp), hyperbolic discounting model (disc-hyp), and constant sensitivity discounting model (disc-cs). Points and error bars are the mean ± standard deviation of rat behavior; colored lines represent the mean predicted number of harvests across all rats.

https://doi.org/10.7554/eLife.48429.014

Figure 3—figure supplement 5

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iBIC for each model for each foraging experiment.

Cost = subjective cost model, util-pwr and util-crra = nonlinear reward utility with power and CRRA function respectively, pre-del = linear overestimation of pre-reward delays, post-del = linear underestimation of post-reward delays, post-del-pwr=underestimation of post-reward delays according to a power function, disc-exp = exponential discounting, disc-hyp = hyperbolic discounting, disc-cs = constant sensitivity discounting, disc-quasi = quasi hyperbolic discounting.

https://doi.org/10.7554/eLife.48429.015

Figure 4 with 2 supplements

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Model predictions for the intertemporal choice task.

(A) Quasi-hyperbolic model predictions for the intertemporal choice task. Points and error bars represent the mean ± standard error of individual rat behavior; lines and ribbon represent mean ± standard error of model predicted behavior for each individual rat. (B) The iBIC score for each model for the delay discounting experiment. Util-pwr and util-crra = nonlinear reward utility with power and CRRA function respectively, pre-del = linear overestimation of pre-reward delays, post-del = linear underestimation of post-reward delays, post-del-pwr=underestimation of post-reward delays according to a power function, disc-exp = exponential discounting, disc-hyp = hyperbolic discounting, disc-cs = constant sensitivity discounting, disc-quasi = quasi hyperbolic discounting.

https://doi.org/10.7554/eLife.48429.016

Figure 4—figure supplement 1

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State space diagram of the intertemporal choice task.

Decisions made in Decision states cause transition to the Delay, Reward, and ITI states for the option chosen (either SS or LL), then back to the next Decision state. The model consisted of 10 consecutive trials — the number of free choice trials — plus the value of rewards in future games.

https://doi.org/10.7554/eLife.48429.017

Figure 4—figure supplement 2

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Comparison of all-future horizon and one-trial horizon discounting models.

(A) iBIC for the full horizon and one-trial horizon discounting models (B) Measured log-transformed discount factors for the full horizon and one-trial horizon discounting models. Bars and errorbars represent mean ± standard error.

https://doi.org/10.7554/eLife.48429.018

Figure 5

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Cross-task model predictions.

(A) Predicted foraging behavior for quasi-hyperbolic model parameters fit to either the foraging task (red line) or delay discounting task (DD; blue line). Black points and error bars represent mean ± standard error of rat data. (B) Predicted intertemporal choice behavior for quasi-hyperbolic model parameters fit to data from either the foraging or delay discounting task, plotted against rat behavior. (C) The difference in negative log likelihood of the left out sample of foraging data (left) or intertemporal choice data (right) between parameters fit to the intertemporal choice task and parameters fit to the foraging task. A negative -LL difference indicates the negative log likelihood of the data for parameters fit to the intertemporal choice task was lower than for parameters fit to the foraging task. Each point and line represents data from individual rats.

https://doi.org/10.7554/eLife.48429.019

Figure 6

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Discount function of the μAgent hyperbolic discounting model vs. standard hyperbolic discounting.

Points represent the standard hyperbolic discounting function, $1 / (1 + k * t i m e)$ . Lines represent the μAgent discount function in which the discount factor for each of the 10 μAgents was equal to the 5–95% quantile of an exponential distribution with rate parameter $λ = 1 / k$ .

https://doi.org/10.7554/eLife.48429.020

Author response image 1

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Tables

Table 1

Parameters for each of the first four foraging experiments.

Harvest time = time to make a decision to harvest + pre-reward delay + post-reward delay (inter-trial interval). To control reward rate in the patch, the post-reward delay was adjusted relative to the decision time to hold the harvest time constant.

https://doi.org/10.7554/eLife.48429.006

Experiment	Condition	Start Reward	Depletion Rate	Pre-Reward Delay	Harvest Time	Travel Time
travel time	10 s	60, 90, or 120 μL^†	−8 μL	0 s	10 s	10 s
travel time	30 s	60, 90, or 120 μL^†	−8 μL	0 s	10 s	30 s
depletion rate	−8 μL	90 μL	−8 μL	0 s	12 s	12 s
depletion rate	−16 μL	90 μL	−16 μL	0 s	12 s	12 s
scale	90 μL/10 s	90 μL	−8 μL	0 s	10 s	10 s
scale	180 μL/20 s	180 μL	−16 μL	0 s	20 s	20 s
handling time	0 s	90 μL	−8 μL	0 s	15 s	15 s
handling time	3 s	90 μL	−8 μL	3 s	15 s	15 s
post-reward delay*	3 s	90 μL	−8 μL	0 s	5–8 s**	10 s
post-reward delay*	12 s	90 μL	−8 μL	0 s	13–16 s**	10 s

^†Rats encountered all three patch types in both conditions.

^*One group of rats (n = 8) was tested on the first four experiments, but a separate group (n = 8) was tested on this final foraging experiment.
^**In this experiment, the harvest time was not held constant — the post-reward delay was always 3 s or 12 s regardless of the time to make a decision.

Table 2

Description of the hypotheses for overharvesting with general, qualitative predictions for the degree of overharvesting in each experiment.

Quantitative predictions depend on the exact formalization of each model and its specific parameters.

https://doi.org/10.7554/eLife.48429.009

	Hypothesis	Experimental predictions
Subjective Costs	A cost term $c$ reduces the value of leaving a patch. Predicts greater overharvesting with higher $c$ . Not affected by specific manipulations to reward or time.	Rats will follow qualitative predictions of the Marginal Value Theorem, but exhibit an equal degree of overharvesting across conditions in each experiment.
Nonlinear Reward Utility	Subjective value increases sublinear to reward magnitude. Predicts greater overharvesting with steeper utility functions with larger rewards.	Rats will exhibit an equal degree of ovarharvesting in all experiments except for the Scale experiment. In the Scale experiment, rats will overharvest more in the conditions with larger rewards.
Biased Time Perception	i) Post-reward delays perceived as shorter, ii) pre-reward delays perceived as longer, or iii) longer delays (irrespective of their placement) perceived as shorter. All three hypotheses predict greater overharvesting with longer delays.	Rats will exhibit a greater degree of overharvesting in the condition with longer delays in the Scale environment, in the condition with the longer post-reward delay in the Pre-vs-Post experiment, and in the condition with longer post-reward delay in the Post-Reward Delay experiment
Temporal Discounting	Value of future rewards discounted due to delay to receive them. Predicts greater overharvesting with greater levels of discounting and with longer delays	Rats will overharvest to a greater degree in the conditions with longer delays in the Scale and Post-Reward Delay experiments and they will leave patches earlier due to the longer pre-reward delay in the Pre-vs-Post experiment.