Effects of Methamphetamine on Probability Discounting in rats using Concurrent Chains

How stimulant drugs affect risky choice and the role of reinforcement magnitude has been an important question for research on impulsivity. This study investigated rats’ responding on a rapid acquisition, concurrent chains, probability discounting task under methamphetamine administration. In each block of four sessions, probability of reinforcement delivery was unequal (0.5/1.0, 1.0/0.5) or equal, (1.0/1.0, 0.5/0.5) while amount of reinforcement was constant and unequal. This allowed for an estimate of probability discounting and the magnitude effect (where larger reinforcers are discounted at a greater rate) in each block. Baseline, acute and chronic methamphetamine administration, and re-establish baseline phases were completed. Rats showed sensitivity to probability and magnitude in baseline, as well as a magnitude effect whereby preference for the larger reinforcement was greater with 100% than 50% reinforcement probability. Acute methamphetamine dose-dependently reduced the probability effect. There were no effects of chronic administration and only probability discounting was maintained in the re-establish baseline phase. This was the first procedure to find a magnitude effect with rats in a probability discounting procedure and


INTRODUCTION
Research of impulsive choice can broadly be attributed to two domains.Delay based choice examines how a reward decreases in value as the time until its receipt increases, whereas uncertainty-based choice refers to the decrease in value of a reward as the likelihood of receiving it decreases.Both delay and probability discounting are mediated by the magnitude of the reward, but in different ways.Larger amounts are discounted more slowly in delay discounting, indicating self-control, whereas the same large amount would be discounted more quickly in probability discounting, indicating that a larger amount should promote risk aversion as the chance of receiving it decreases (Green, Myerson, & Ostaszewski, 1999).This 'probability discounting' has been a widely reported phenomena both in human (Dai et al., 2013;Ohmura, Takahashi, & Kitamura, 2005;Richards et al., 1999), and animal paradigms (Green, Myerson, & Calvert, 2010;Kelsey & Niraula, 2013;Wilhelm & Mitchell, 2008), particularly as it has correlations with risk taking behaviours such as gambling (Kyonka & Schutte, 2018;Petry, 2012).Probability discounting can be assessed in several ways including adjusting-amount procedures where the magnitude of the certain reinforcement is systematically changed across blocks or changed according to the previous response and subjects choose between this and an uncertain fixed amount.An indifference point can be determined when subjects shift responses to the alternative option indicating an J o u r n a l P r e -p r o o f approximate equivalence in subjective value between the certain small reinforcement and the uncertain large reinforcement (Green, Myerson, & Ostaszewski, 1999, Green, Myerson, & Calvert, 2010).
Stimulant drug users are impaired in probability discounting tasks.Betzler, Viohl, and Romanczuk-Seiferth (2017) reviewed studies where MDMA users completed impulsive choice tasks.They reported that drug users tended to make riskier choices compared to control groups.Methamphetamine is an illegal stimulant drug with a relatively high rate of use in New Zealand.Approximately 1% of the population reported using it in the past year in 2021.It has a negative influence on the life course of frequent users with poorer occupational, social and health outcomes (Bax, 2021).Thus, methamphetamine also warrants investigation into its influence on probability discounting.
Drug administration and probability discounting can be modelled in animal analogues using concurrent chains with dependent scheduling.Concurrent chains allow for preference to be assessed during the initial links independently from the reinforcement contingencies in the terminal link, while dependent scheduling ensures that subjects receive equal exposure to the terminal links.This is advantageous because it prevents floor effects where a subject responds exclusively on a single option.Yates et al. (2020) administered increasing doses of amphetamine, methylphenidate, and methamphetamine to rats before they completed a concurrent chains procedure in which one lever was associated with a certain small reinforcement and the other with an uncertain larger reinforcement.The probability of receiving the large reinforcement decreased across the session.They found that the highest methylphenidate dose increased risky choice, the highest amphetamine doses increased risky choice and impaired response rates and every methamphetamine dose increased risky choice and impaired response rates.Thus, the decrease in sensitivity to probability indicated an increase in impulsivity.
J o u r n a l P r e -p r o o f larger amounts are discounted more steeply, meaning that participants are less willing to risk losing them, when compared to smaller rewards.Anderson and Dallery (2021) determined indifference points for four uncertain amounts ranging between $20-$500,000 with five probabilities of receipt ranging between 5%-80% presented randomly.Indifference points were found for each uncertain amount and probability of receipt.Results showed that larger amounts were discounted more rapidly than smaller ones (see also Myerson, Green, & Morris, 2011).
A magnitude effect in probability discounting with pigeons was reported by Grace and McLean (2015) using a concurrent-chains procedure.This task had proven effective in finding a magnitude effect for delay discounting with pigeons, in contrast to adjustingamount procedures (e.g., Green, Myerson, Holt, Slevin & Estle, 2004), because it allows choice (i.e., relative response rate) to vary across a wide range rather than titrated to an indifference point (Grace, Sargisson, & White, 2012).In Grace and McLean's (2015) Experiment 1, pigeons responded in the initial links to produce terminal links that delivered either 4-s or 2-s access to food after a 10-s delay.In one component, the probability of receiving reinforcement for both terminal links was 100% but in the other component the probability was 50%.Pigeons showed a stronger preference for the 4-s terminal link in the 100% component, suggesting that the value of the 4-s reinforcer had decreased more when its probability was 50%.In Experiment 2, the reinforcement probabilities were 100% and 50% while across components the reinforcers were either 4-s or 2-s access to food.Choice for the 100% terminal link was greater in the component with 4-s access to food, again suggesting that the larger reward decreased in value more when its receipt was uncertain.These results are similar to the effect of reward magnitude in probability discounting with humans (e.g., Green, Myerson & Ostaszewski, 1999).

J o u r n a l P r e -p r o o f
The prior studies used steady state designs where multiple sessions with the same contingencies are completed until choice responding stabilizes.Alternatively, measures of choice can be obtained within individual sessions if the contingencies are changed unpredictably across sessions.Kyonka and Grace (2008) used this 'rapid acquisition' design with pigeons in concurrent chains.In their study, terminal-link delays, reinforcer magnitudes, and reinforcer probabilities were changed unpredictably (and independently) across sessions.
Kyonka and Grace found that after training with the procedure, pigeons' choice showed rapid adaptation such that by about midway through each session, choice was determined by the contingencies in the current session and with little or no influence of prior sessions.
This study incorporated several of the elements discussed above and examined probability discounting and the magnitude effect in a rapid acquisition concurrent chains design.A baseline was established before a saline and three increasing acute doses of methamphetamine were administered, followed by chronic methamphetamine administration and a re-establishment of the baseline.It was hypothesised that acute and chronic doses of methamphetamine would dose dependently attenuate sensitivity to probability meaning that they would increase impulsivity.The magnitude effect was exploratory as it had not been investigated alongside methamphetamine administration in rats in a rapid acquisition concurrent-chains design.

SUBJECTS
Twelve black hooded/PVG (Piebald Virol Glaxo) male rats were used in this study.
They were bred in the University of Canterbury Animal Lab and were a minimum of 100 days old when training commenced.The subjects were maintained at 85% of their free feeding weight throughout the training and experimental phase with a combination of diluted condensed milk, used as the reinforcer in the testing chambers, and supplemental food pellets J o u r n a l P r e -p r o o f (LabDiet ProLab RMH 1800) given at the conclusion of each session.At the conclusion of the experiment, the subjects were euthanised according to American Veterinary Medical Association guidelines by a trained lab technician.

APPARATUS
Twelve rat operant chambers measuring 250mm x 250mm x 280mm and housed in boxes to which a sound attenuating fan was attached, were used.Each chamber had two retractable levers mounted 100mm above the floor and 140mm apart on the right wall with cue lights 40mm above each lever.An inactive fixed lever and cue light was located on the opposite wall.A house light was positioned on the ceiling of the chamber halfway between the levers and 60mm from the wall.Halfway between the levers and 12mm above the floor, a 65mm diameter circle was positioned from which the subject could collect reinforcement when the dipper arm was raised.Reinforcement consisted of condensed milk diluted with water in a 1:3 ratio.A Med-PC version 1.10 programme controlled the chambers.Statistical analysis was completed with Jamovi 2.3.16software which uses the LME4 R package.
Jamovi uses an unstructured co-variance matrix and restricted maximum likelihood for parameter estimation.The GAMLj module was installed to preform mixed model analysis.

DESIGN
A rapid acquisition concurrent chains design was used.Each day, one of four possible session types (two probability discounting sessions and two magnitude effect session) was arranged pseudo-randomly such that location of the richer terminal link varied unpredictably across sessions.

TRAINING
Training commenced with five sessions of dipper training where reinforcement was presented regardless of a response on a lever.An auto-shaping procedure followed where the left lever was presented constantly and subjects were required to respond on the lever once J o u r n a l P r e -p r o o f (FR1) in order to receive reinforcement, if the subjects failed to respond, reinforcement was delivered after 8 seconds.For subjects that failed to respond in these sessions, manual shaping was given to develop lever responding.Subjects then completed FR1 schedules with the right lever extended for five sessions until all subjects collected 72 reinforcers per session.Auto-shaping with both levers randomly alternating was completed for two sessions before variable interval (VI) schedules were introduced.VI15s initial links were added until subjects collected reinforcement reliably before fixed interval (FI) 6 second terminal links were added.Magnitude differences were then introduced for five sessions with one dipper cycle of reinforcer on the left lever and four dipper cycles of reinforcer on the right.
Magnitudes were then equalized at two dipper cycles for each lever and the probability of reinforcement was changed with 0.5 reinforcement on the left lever and 1.0 reinforcement on the right lever.Delay to reinforcement was held constant across both levers at 2.83 seconds.
After eight sessions, the probabilities were switched to the opposing levers for two sessions.Differential magnitudes were then reinstated for 40 sessions before magnitude effect sessions were introduced where the probability of reinforcement was either 0.5 or 1.0 on both levers.
The differential reinforcer amount remained the same.Training then continued for a further 30 sessions where for every four days, two probability effect sessions and two magnitude effect sessions occurred in a pseudo-random order.

PROCEDURE
Each trial commenced with an initial link in which the house light was illuminated, the left and right levers extended and the lights above both levers illuminated.Lever presses on both alternatives were recorded until the VI 8 second timer elapsed and a reinforcer was assigned to either the left or right lever.A further lever press on the alternative to which the reinforcer was assigned, retracted the remaining lever, extinguished the light above that lever and illuminated the lamp above the active lever to which reinforcement was assigned to start  Session types A and B provided a measure of sensitivity to probability.In session A, the left and right probabilities of receiving reinforcement were 0.5 and 1.0 respectively, and in session B they were 1.0 and 0.5.The difference between the log response ratios of each session type gave a measure of the subject's sensitivity to probability.The amount of reinforcement was held constant across sessions, with the left lever providing one dipper cycle of reinforcer and the right lever providing four dipper cycles of reinforcer.The J o u r n a l P r e -p r o o f probability of receiving reinforcement and dipper cycle amounts were counter-balanced between subjects.
Session types C and D provided a magnitude effect.In session C, both levers had a probability of receiving reinforcement of 1.0 and in session D, both levers had a probability of receiving reinforcement of 0.5.Terminal link durations were always 2.83 seconds.The difference between the log response ratios of each session type gave a magnitude effect.The amount of reinforcement was held constant across sessions, with the left lever providing one dipper cycle of reinforcer and the right lever providing four dipper cycles of reinforcer.The probability of receiving reinforcement and dipper cycle amounts were counter-balanced between subjects.The experiment itself started with a baseline phase before acute and chronic drug administration stages were completed with a re-establish baseline stage to conclude.

Phase
60 baseline sessions, one session per day, were completed before the commencement of drug administration.For every four sessions, two probability effect sessions and two magnitude effect sessions occurred in a pseudo-random order.
In the acute drug phase, subjects completed a session everyday regardless of the presence or absence of methamphetamine.The sequencing of sessions was arranged from In the acute phase, sessions were arranged so that the effect to be tested under drug administration was first tested in non-drug administration sessions.For example, if a probability discounting effect was to be tested, the two non-drug sessions preceding the drug session would also measure a probability discounting effect.The first drug administration session for probability discounting (A or B) was then followed by two non-drug days in which the magnitude effect would be assessed (C and D).The second of the probability discounting sessions would then be run and a probability discounting effect under drug administration could be measured.This procedure would then be repeated in order to obtain a non-drug and drug measure of the remaining effect; in this example, the magnitude effect.
Thus, a block of twelve sessions was required to obtain estimates of the probability and magnitude effects under drug administration.Two such blocks were run for each drug dose, and the order was counterbalanced across rats.
A saline control and three drug doses were administered in the acute phase half an hour prior to the start of a session.In order to examine the effects of the receipt of an injection, a saline only solution was administered first (0.0mg/kg).This was followed by 0.5mg/kg of methamphetamine solution, then 1.0mg/kg of methamphetamine solution and finally, 2.0mg/kg of methamphetamine solution.All solutions were administered intraperitoneally, at a volume of 1ml/kg.Each drug administration day was followed by two non-drug administration days.Six days were required to measure a single effect, two probability and two magnitude effects were obtained per dose with four doses measured which resulted in 96 days of acute methamphetamine measurement.

J o u r n a l P r e -p r o o f
The chronic phase consisted of twelve injections administered 23 hours before the start of a session with one injection given per day for 12 subsequent days.Three probability and three magnitude effects were obtained in this phase.
The final phase of the experiment re-established a baseline measurement of probability discounting and the magnitude effect.No drug was administered in this phase.
This phase commenced immediately after the completion of the chronic phase and ran for 16 sessions allowing for four probability discounting and four magnitude effects to be measured.

STATISTICAL ANALYSIS
Analyses were based on a generalised matching model: where B is response rate, P is probability of reinforcer receipt, M is magnitude, and subscripts L and R indicate the choice alternatives.There are three parameters: sensitivity to probability (  ), sensitivity to magnitude (  ) and bias, log b.By examining differences in log response ratios between sessions in which probability was unequal (0.5/1.0 or 1.0/0.5)or equal (1.0/1.0 or 0.5/0.5),we were able to obtain estimates of probability discounting (i.e., sensitivity to probability) and the magnitude effect in each block of four sessions.Because reinforcement magnitudes were constant, bias and sensitivity to magnitude were estimated as a single parameter.
To determine the effects of reinforcement probability and magnitude on choice, we conducted a lag regression analysis using the final 20 sessions of baseline training.This analysis used a model with predictors for both current and prior session contingencies, and was applied to successive blocks of training within sessions so that we could conceptualise the acquisition of choice: J o u r n a l P r e -p r o o f In Equation 2, B is response rate, P is probability of reinforcement, and subscripts indicate the left/right lever (L, R) and lag (0 = current session; 1 = prior session).There are five parameters: Bias (log b), sensitivity to probability (p; lag 0 and 1), and magnitude effect (m; lag 0 and 1).Definitions for sensitivity to probability and the magnitude effect in terms of session type log response ratios (A, B, C, D) are shown in Table 2.Because the reinforcer magnitudes for the left and right levers were constant, the magnitude effect was defined as a change in preference for sessions when the terminal link probabilities were both certain (i.e., 100%; Type C) or both uncertain (50%; Type D) relative to sessions where the probabilities were unequal (50% and 100% or 100% and 50%; Type A or B), such that m > 0 indicated that preference for the larger reinforcement was greater when probabilities were certain than when they were uncertain.Sensitivity to probability was calculated as (log (BL/BR)Alog  Best-fitting parameter estimates for Equation 2were obtained for each of the six session blocks for individual rats (overall average R 2 = 0.40).The left panel of Figure 2 displays the sensitivity to probability for both the current (Lag0) and prior session (Lag1) averaged across all subjects.Sensitivity to probability increased across subsequent blocks up to block 5 for Lag0, while Lag1 sensitivity remained greater than, but near zero throughout the entire session.A linear mixed effects model with lag and block as fixed effects and a random intercept was applied to the sensitivity to probability data.The intra-class correlation was significant, rICC = .364,p<.001, showing that the random effect accounted for 36.4% of the variance.There was a significant effect of Lag, F(1,121)=266.660,p<.001 showing that sensitivity to probability was greater for Lag0 (M = 0.361; 95% CI [0.301, 0.420]) than Lag1 (M = 0.055, 95% CI [-0.005,0.115]).There was a significant effect of Block, F(5,121)= 4.131, p=.002 and a significant Lag by Block interaction, F(5,121)=4.932, p<.001.Analysis of simple effects showed that for Lag 0, sensitivity to probability was significantly lower in Block 1 than all other blocks.For Lag 0, there was a significant linear component, demonstrating that there was a magnitude effect for the current session.The results of the baseline lag regression analysis establish that subjects could reliably distinguish between the previous probability or magnitude session and the current one, therefore rates of responding from the entire session were used in subsequent analysis.

ACUTE
J o u r n a l P r e -p r o o f        Baseline Lag 1, (M= -0.017, 95% CI [-0.036, -0.002]).There was a significant Re-Establish Baseline Lag 0 linear contrast, t(5,253)=-3.682,p<.001.These results demonstrate that subjects were able to maintain their sensitivity to probability following acute and chronic drug administration and reliably differentiate the previous session from the current one.
However, subjects' magnitude effect which was present in baseline, was not evident by the 1.0mg dose in the acute phase, the chronic drug administration phase or in re-establish baseline.

RESPONSE RATES
J o u r n a l P r e -p r o o f  A linear mixed effects model with Drug Administration Type as the fixed effect and a random intercept were applied to the chronic data.The intra-class correlation was significant, rICC=0.909,p<.001, showing that the random effect accounted for 90.9% of the variance.
There was a significant effect of drug administration type, F( 4 CI [1.669,2.216]).These results demonstrate that subjects' response rates dose dependently decreased with acute drug administration and by the third chronic dose, decreased compared to the acute no-drug days and the re-establish baseline.
Because both probability effects and overall response rates showed a similar dose dependent decrease and significant linear trend with acute drug administration, it is possible that the decrease in sensitivity to probability was a consequence of the decrease in overall responding and not the effect of methamphetamine.To test this, we calculated the differences between the non-drug and drug effect sizes for probability and response rate for individual rats at each dose and conducted a correlation analysis.If the decrease in sensitivity to probability was caused by a decrease in overall response rate then these correlations should be positive.However, only the correlation for saline was positive and none were significant: 0.0mg/kg (r(10)= 0.317, p=.316), 0.5mg/kg (r(10)= -0.103, p=.751), 1.0mg/kg (r(10)= -0.433, p=.160), 2.0mg/kg (r(9)= 0.034, p=.921.This suggests that the decrease in sensitivity to probability is not caused by a decrease in overall response rate but is a result of the increasing methamphetamine doses.

3.5.SENSITIVITY TO MAGNITUDE
J o u r n a l P r e -p r o o f According to Equation 2, sensitivity to magnitude cannot be found independent of bias but as location of reinforcer delivery as well as session type was counter balanced across subjects, bias can be assumed to be negligible which allows for a point estimate of sensitivity to magnitude to be calculated for every session by dividing response rates by the magnitude ratio of reinforcement.These values were averaged across subjects and displayed in Figure 9.
Sensitivity to magnitude in acute drug sessions decreased compared to non-drug sessions and increased in chronic drug administration compared to the non-drug sessions in acute and the re-establish baseline.Linear mixed effects models with Dose and Drug/Non-Drug as fixed effects and a random intercept were applied to the acute sensitivity to magnitude data.The intra-class correlation was significant, rICC=0.380,p<.001, showing that the random effect accounted for 38% of the variance.There was a significant effect of Drug/Non-Drug, ).Subjects' sensitivity to magnitude dose dependently decreased across drug sessions in the acute phase whereas it increased in the chronic drug administration sessions.

DISCUSSION
We used a 'rapid acquisition' choice task in which probability of reinforcement changed unpredictably across sessions to study how rats' choices between certain and uncertain reinforcers were affected by methamphetamine administration.Our procedure was novel and assessed both probability discounting (i.e., 'effect of probability', or sensitivity to probability) and how discounting was modulated by reinforcement amount (i.e., 'magnitude effect').In each block of four sessions during baseline training, probability of reinforcement was unequal (0.5 vs 1.0; or 1.0 vs 0.5) or equal (0.5 vs 0.5; or 1.0 vs 1.0), while reinforcement amounts were constant and unequal (4 presentations of sweetened condensed milk vs 1 presentation).Rats reliably preferred the alternative with the certain reinforcement in the unequal probability sessions, and had a stronger preference for the larger amount when probability of reinforcement was equal and certain.This shows that the subjective value of the larger amount decreased more quickly when it was delivered 50% of the time compared to 100%, confirming a magnitude effect in rats' probability discounting.
J o u r n a l P r e -p r o o f were administered followed by a twelve-session chronic dose phase.Results of the acute phase confirmed a significant linear trend across drug sessions such that choice for the 100% reinforcement decreased as dose increased, indicating that the acute methamphetamine dosedependently caused the subjects to be more risk prone.For the chronic drug phase, probability discounting was not significantly different from non-drug sessions in the acute phase, or re-establish baseline phase.When baseline training was re-established, results showed that strong control by the contingencies in the current session was recovered.
The present study was novel in that we also investigated whether probability discounting was modulated by reinforcement amount, and effects of methamphetamine.This 'magnitude effect' has been commonly reported in humans, (Yi, Carter, & Landes, 2012) but less so with non-humans (Grace & McLean, 2015).Baseline results confirmed the magnitude effectrats showed a stronger preference for large reinforcement when probability of reception was certain than when it was uncertain.Acute drug sessions had no influence on the magnitude effect compared to the non-drug sessions at any dose, but it was no longer evident for both the non-drug and drug sessions by the 1.0mg/kg dose.For the chronic drug administration, no significant differences were found between the non-drug average and the 12 sessions of chronic training.The re-establish baseline data showed that the magnitude effect was significantly reduced compared to baseline, showing that rats' ability to adjust their risk preference depending on reinforcement amount was impaired by the acute and chronic drug administration sessions.Bodeker and Grace (Unpublished Results) used the same design and drug administration regimen as the current study, but assessed delay discounting and found similar results in the acute drug phase where both sensitivity to delay and the magnitude effect decreased as dose increased.However, the interpretation of these results differ in that a decrease in delay sensitivity indicates a reduction in impulsivity as the J o u r n a l P r e -p r o o f subject shows a weaker preference for the smaller, immediate reinforcement.By contrast, a decrease in probability discounting implies an increase in choice for the risky alternative and thus an increase in impulsivity.The reduction in probability discounting in the acute phase coupled with the failure of the magnitude effect to recover after drug administration suggests that methamphetamine promoted risky choice and that probability discounting was more adversely affected by methamphetamine than delay discounting.
Our results that sensitivity to probability in rats decreased dose dependently with acute methamphetamine such that they showed increasing preferences for the large risky alternative, are of interest when compared with the results of other experiments where impulsivity has been manipulated.Cardinal and Howes (2005) lesioned the nucleus accumbens core in rats, an area associated with impulsivity, before rats completed a probability discounting task.They reported that lesioned rats were more risk averse and chose the large uncertain reinforcers less than sham lesioned controls to the point where they collected fewer reinforcers.They suggested that subjects behaved as if they were less likely to receive reinforcement than they actually were.Perhaps the opposite could be said in our study with acute methamphetamine, that as the dose increased, subjects behaved as if they were more likely to receive reinforcement than they actually were and consequently responded more on the larger uncertain alternative.
Other studies involving a different behavioural procedure have also reported an increase in risky choice with relatively small doses of acute amphetamine.Yang, Cheng, and Liao ( 2018) used a T-maze design where rats choose between a small certain reinforcer and a larger uncertain reinforcer that changed in both probability of receipt and magnitude of reinforcement across conditions.When 1.0mg/kg of amphetamine was administered prior to the experiment, rats' choice for the uncertain alternative increased slightly but only when the difference in reinforcement ratio was 1:8 and the equivalent value between the two options J o u r n a l P r e -p r o o f became more risk averse in blocks with increasing doses of amphetamine although only results for the largest dose approached significance.The authors suggest that the discrepancy between how subjects responded to a stimulant drug in experiments like ours, where methamphetamine increased preference for the risky alternative, and their results, was that the punishment was a more salient cost than reinforcement omission meaning that the punishment controlled the behaviour to a greater degree than the reinforcement.However, Leland and Paulus (2005) used a risky gains task where points on a screen increased every second until participants stopped the trial.The greater the number, that is, the longer the participant waited to stop the trial, the greater the risk that the points would be deducted from their total.They found that stimulant using participants made more risky responses at baseline, but that a loss of points attenuated the subsequent trial lengths to the same degree in both the stimulant and control groups, indicating that although punishment reduced risky responding, it did so to the same degree in both groups.It would be interesting to examine how subjects' preference may be influenced with a more salient cost within our experimental design as this may more accurately reflect the outcomes of human impulsive choice.Dai et al. (2013) investigated probability discounting in a population with ADHD, an impulsivity control disorder when they tested adults diagnosed with ADHD on delay and probability discounting and gambling simulations.Participants completed a task where they chose between certain rewards of $50 or $5000 (hypothetical) and an uncertain reward with probabilities of receipt ranging from 95%-5%.They found that people with ADHD had both higher rates of delay discounting and lower rates of probability discounting for both amounts of money than the non-ADHD controls.These results support the concept that acute stimulant use and impulsivity control disorders are related in terms of their influence on probability discounting, meaning that further research that aims to ameliorate risky choice behaviour may be applicable to both populations.
J o u r n a l P r e -p r o o f discount probabilistic rewards.Madden, Petry, and Johnson (2009) tested men diagnosed with pathological gambling on a series of questions where they chose between a certain amount of money and a larger amount with varying probabilities of receipt.They found that pathological gamblers discounted the probabilistic rewards less steeply than non-gambling controls and suggest that gamblers may overvalue the opportunity to gamble or they display greater risk tolerance than controls.It would be of interest if future animal research could attempt to elucidate this perception of or preference for risk in order to better inform treatment direction.
In our study, the chronic administration of a relatively high dose of methamphetamine 23 hours prior to completing the behavioural task for 12 consecutive days had no effect on the sensitivity to probability.This may have been because the rapid acquisition design, where the probabilities of reinforcement associated with each lever changed unpredictably across sessions as opposed to a more traditional steady-state design, precluded the development of a cumulative effect of the drug that a chronic administration requires.Few animal studies report the influence of chronic use and most human studies report on previous users who are currently seeking treatment.
Results from the re-establish baseline phase of our procedure showed that subjects retained their sensitivity to probability and that it did not significantly differ from baseline, indicating that the acute and chronic methamphetamine did not significantly alter responding in abstinence.Floresco and Whelan (2009) trained rats on a probability discounting task where they responded for one certain pellet or 4 pellets with the probability of receiving them decreasing from 100% to 12.5% across blocks.Subjects then received repeated amphetamine injections before completing probability discounting in three days of acute withdrawal immediately following.Amphetamine pre-treated rats did not significantly differ in their J o u r n a l P r e -p r o o f allocation of responses compared to the saline pre-treated group.However, following a wash out period of 12 days, a further 12 days of testing revealed that amphetamine pre-treated rats made significantly more responses on the large risky alternative compared to controls meaning they earned significantly fewer pellets.Perhaps if the re-establish baseline phase of the present experiment had been extended beyond 16 sessions, an effect of the acute and chronic drug administration may have become evident.Bornovalova et al. (2005) tested previous cocaine users in a computerised risk-taking task where a balloon could be inflated to earn more money, but the risk that the balloon would explode and all the money would be lost increased as the balloon was inflated, meaning that the relative gain decreased as the amount that could be lost increased.The task could be stopped and the acquired money collected at any point.The cocaine users took more risks in the task compared to past heroin users, although these differences lost significance once age and gender were factored in.
Therefore, studies of sensitivity to probability in withdrawal reveal that the influence of effects from previous stimulant use can persist in particular circumstances even when abstinence has been established.
Few studies have examined the chronic effects of stimulants on the magnitude effect in probability discounting, but Yi, Carter, and Landes (2012) did so with currently using, non-treatment seeking methamphetamine users who had been using the drug for at least 12 months.They found indifference points for certain adjusting amounts of $50 and $10000 or a standard amount at 75, 50 or 10% chance of receipt.They found that methamphetamine users discounted only the larger amount more quickly than non-using controls, meaning they were more risk averse with the large amount, although both groups discounted the large amount more than the small amount.The authors noted that although this result may seem contradictory, it may reflect an overall insensitivity to risk, where variations in the chances of receiving reinforcement are treated equivocally.
J o u r n a l P r e -p r o o f Sensitivity to magnitude can also be examined in order to understand why subjects' preference changed throughout the experimental conditions.In the present experiment, sensitivity to magnitude dose dependently decreased in the acute drug administration phase compared to non-drug days, whereas it increased in the chronic administration phase.This was a contrast to Bodeker and Grace (Unpublished Results) where the same experimental paradigms were applied to delay discounting, but no changes in sensitivity to magnitude were found throughout the different drug administration phases.Therefore, in this procedure, methamphetamine had greater impact on reinforcement sensitivity in probability discounting than in delay discounting.Perhaps something akin to the Mazur (1988) conclusion that propensity to risk can change as experimental variables change could be applied here.With acute doses of methamphetamine, sensitivity to magnitude decreased as did sensitivity to probability which resulted in an increased propensity to risk, whereas in the chronic phase an increase in sensitivity to magnitude and no change in sensitivity to probability resulted in no difference in preference compared to non-drug stages.Therefore, sensitivity to magnitude and sensitivity to probability as well as having different degrees of influence on preference, may also have differing influences on preference depending on when and at what dose the drug was administered.
The conclusions of this experiment are limited by a number of factors.Animal models can never hope to reflect the complexity of human decision making and although they are useful to isolate individual factors in laboratory conditions, they must always be constrained by the multiplicity of influences that cannot be captured.The fact that rats failed to respond at acute methamphetamine doses over 2mg/kg also precludes the investigation of relatively large doses that may be more analogous to abuse amounts in humans.Our rapid acquisition design where conditions changed unpredictably between four possible session types may have impeded effects that steady state procedures could have exposed especially in the J o u r n a l P r e -p r o o f chronic drug phase.Anselme (2015) also highlights an important consideration in using probability discounting procedures when he questions if a loss of potential reinforcement equates to a negative consequence and a genuine cost or simply a loss of optimal gain that has no true impact on energy cost or overall impact on likelihood of survival.A true cost of a risky choice will be difficult to implement in a laboratory setting where animal welfare must be maintained however, being able to replicate facets of risky choice if not the entire phenomenon remains of value when attempting to investigate how probability of reinforcement receipt will be impacted by varying factors.
In summary, we found that acute methamphetamine dose dependently reduced probability discounting.The magnitude effect which was present at baseline was abolished by drug administration alongside the probability discounting task, and not recovered in reestablish baseline.This remains the first procedure to demonstrate the influence of acute and chronic methamphetamine in a probability discounting, rapid acquisition, concurrent chains design and provides a method of measurement that can be applied to future considerations of choice behaviour in the presence of drugs.
J o u r n a l P r e -p r o o f blinking four times per second until the terminal link delay of 2.83 seconds had elapsed.Responses on the active lever were recorded during the terminal link.Once the terminal link time had elapsed, a final response on the active lever extinguished the house light, and the blinking lever light.If reinforcer was delivered, the dipper box light was illuminated and the dipper initiated to deliver the programmed number of cycles of reinforcer (1 cycle or 4 cycles) at one cycle per 0.75 seconds.Following the reinforcer delivery, the dipper lowered, the dipper box light was extinguished and another initial link commenced.If reinforcer was not delivered, a 2 second blackout occurred before the next trial commenced.This process repeated until 72 cycles had occurred or an hour elapsed.

Figure 1 .
Figure 1.Probability Discounting and Magnitude Effect Procedure.

J
o u r n a l P r e -p r o o f four possible session types (A-D), two of which, (A and B) assessed probability discounting, and two (C and D) which assessed the magnitude effect.
Figure 2. Lag Regression Analysis Results displaying average Sensitivity to Probability (Left) J o u r n a l P r e -p r o o f t(5,121)=5.495,p<.001, and a quadratic component, t(5,121)=-3.284,p=.001.For Lag 1, there were no significant differences between Block 1 and the remaining Blocks.Thus, choice responding was controlled by the probabilities in the current session with virtually no effect of the prior session.The right panel of Figure2displays the magnitude effect for both the current session (Lag0) and the previous day's session (Lag1) averaged across subjects.The magnitude effect decreased for Lag0 across blocks, whereas Lag 1 remained consistently below zero.A linear mixed effects model with lag and block as fixed effects and a random intercept was applied to the data.The intra-class correlation was significant, rICC =0.227, p<.001, showing that the random effect accounted for 22.7% of the variance.There was a significant effect of Lag, F(1,121)=46.338,p<.001  showing that the magnitude effect was greater for Lag0 (M = 0.028; 95% CI [0.016, 0.041]) than Lag1 (M = -0.006,95% CI [-0.019,0.006]).For Lag 0, block 6 was significantly smaller than block 1, t(5,121)=-2.095,p=.038.Baseline Lag 0, (M= 0.028, 95% CI [0.020, 0.037]), Baseline Lag 1, (M= -0.006, 95% CI [-0.013, 0.001]).There were no other significant results.Lag 0 was significantly greater than zero, (t(5)=11.160,p<.001),

Figure 3 .
Figure 3. Average Probability Effect size for Acute Non-Drug sessions and 0, 0.5, 1.0 and

Figure 3
Figure 3 displays the averaged probability effects across the four drug doses for both

Figure 4 .
Figure 4. Average Magnitude Effect size for Acute Non-Drug sessions and 0, 0.5, 1.0 and

Figure 4
Figure 4 displays the averaged magnitude effects across the four drug doses for both

Figure 5
Figure 5 displays the averaged no drug administration day probability effect size for

Figure 6
Figure 6 displays the averaged no drug administration day magnitude effect size for

Figure 7
Figure 7 displays the same lag regression analysis data as Figure 2 with the addition

Figure 8 .
Figure 8.Average Response Rates of combined Probability Discounting and Magnitude

Figure 8
Figure8displays the average response rates for the acute, chronic and re-establish

Figure 9 .
Figure 9. Point Estimates of Sensitivity to Magnitude in Acute Phase with Average Drug and

Table 1 .
Order of experimental phases.

Table 2 .
The probabilities, magnitudes and log response ratio calculations of session types, BL/BR)B / 2*log (2).whereLR is left responses and RR is right responses.Arrangement of reinforcement location was counter balanced across subjects.