Diffusion about the mean drift location in a biased random walk

Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a two- dimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. we demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. we relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement. © 2010 by the Ecological Society of America

Impact of increasing the availability of healthier vs. less-healthy food on food selection: a randomised laboratory experiment

Abstract: Background: Environmental cues shape behaviour, but few studies compare the impact of targeting healthier vs. less-healthy cues. One online study suggested greater impact on selection from increasing the number of less-healthy (vs. healthier) snacks. The current study aimed to: (1) extend the previous study by using physically-present snacks for immediate consumption; (2) explore responsiveness by socio-economic position; (3) investigate possible mediators (response inhibition, food appeal) of any socio-economic differences in selection. Methods: In a between-subjects laboratory experiment UK adults (n = 417) were randomised according to their ID number (without blinding) to one of three ranges of options: Two healthier, two less-healthy [“Equal”] (n = 136); Six healthier, two less-healthy [“Increased Healthier”] (n = 143); Two healthier, six less-healthy [“Increased Less-Healthy”] (n = 138). Participants completed measures of response inhibition and food appeal, and selected a snack for immediate consumption from their allocated range. The primary outcome was selection of a healthier (over less-healthy) snack. Results: The odds of selecting a less-healthy snack were 2.9 times higher (95%CIs:1.7,5.1) in the Increased Less-Healthy condition compared to the Equal condition. The odds of selecting a healthier snack were 2.5 times higher (95%CIs:1.5,4.1) in the Increased Healthier (vs. Equal) condition. There was no significant difference in the size of these effects (− 0.2; 95%CIs:-1.1,0.7). Findings were inconclusive with regard to interactions by education, but the direction of effects was consistent with potentially larger impact of the Increased Healthier condition on selection for higher-educated participants, and potentially larger impact of the Increased Less-Healthy condition for less-educated participants. Conclusions: A greater impact from increasing the number of less-healthy (over healthier) foods was not replicated when selecting snacks for immediate consumption: both increased selections of the targeted foods with no evidence of a difference in effectiveness. The observed pattern of results suggested possible differential impact by education, albeit not statistically significant. If replicated in larger studies, this could suggest that removing less-healthy options has the potential to reduce health inequalities due to unhealthier diets. Conversely, adding healthier options could have the potential to increase these inequalities. Trial registration: ISRCTN: ISRCTN34626166; 11/06/2018; Retrospectively registered

The impact of 'on-pack' pictorial health warning labels and calorie information labels on drink choice: A laboratory experiment.

Sugar-sweetened beverages (SSBs) are one of the largest added sugar sources to diets in the UK and USA. Health warning labels reduce hypothetical selection of SSBs in online studies but uncertainty surrounds their impact on selection of drinks for consumption. Calorie information labels are also promising but their impact on SSB selection is unclear. This laboratory study assessed the impact on SSB selection of 'on-pack' labels placed directly on physical products: i.a pictorial health warning label depicting an adverse health consequence of excess sugar consumption; and ii.calorie information labels. Potential moderation of any effects by socio-economic position (SEP) was also examined. Participants - 401 adults, resident in England, approximately half of whom were of lower SEP and half of higher SEP, were asked to select a drink from a range of two non-SSBs and four SSBs (subsequent to completing a separate study assessing the effects of food availability on snack selection). The drinks included 'on-pack' labels according to randomisation: Group 1: pictorial health warning label on SSBs; Group 2: calorie information label on all drinks; Group 3: no additional label. The primary outcome was the proportion of participants selecting an SSB. Compared to not having additional labels (39%), neither the pictorial health warning label (40%) nor calorie information labels (43%) affected the proportion of participants selecting an SSB. Lower SEP participants (45%) were more likely to select an SSB compared to those of higher SEP (35%), but SEP did not moderate the impact of labels on drink selection. In conclusion, pictorial health warning labels may be less effective in reducing SSB selection in lab-based compared with online settings, or depending on label design and placement. Findings suggest that effects might be absent when choosing from real products with actual 'on-pack' labels, positioned in a 'realistic' manner. Field studies are needed to further assess the impact of 'on-pack' SSB warning labels in real-world settings to rule out the possible contribution of study design factors

Impact of increasing the availability of healthier vs. less-healthy food on food selection: A randomised laboratory experiment

Background. Environmental cues shape behaviour, but few studies compare the impact of targeting healthier vs. less-healthy cues. One online study suggested greater impact on selection from increasing the number of less-healthy (vs. healthier) snacks. The current study aimed to: (1) extend the previous study by using physically-present snacks for immediate consumption; (2) explore responsiveness by socio-economic position; (3) investigate possible mediators (response inhibition, food appeal) of any socio-economic differences in selection. Methods. In a between-subjects laboratory experiment UK adults (n=417) were randomised according to their ID number (without blinding) to one of three ranges of options: Two healthier, two less-healthy [“Equal”] (n=136); Six healthier, two less-healthy [“Increased Healthier”] (n=143); Two healthier, six less-healthy [“Increased Less-Healthy”] (n=138). Participants completed measures of response inhibition and food appeal, and selected a snack for immediate consumption from their allocated range. The primary outcome was selection of a healthier (over less-healthy) snack.Results. The odds of selecting a less-healthy snack were 2.9 times higher (95%CIs:1.7,5.1) in the Increased Less-Healthy condition compared to the Equal condition. The odds of selecting a healthier snack were 2.5 times higher (95%CIs:1.5,4.1) in the Increased Healthier (vs. Equal) condition. There was no significant difference in the size of these effects (-0.2; 95%CIs:-1.1,0.7). Findings were inconclusive with regard to interactions by education, but the direction of effects was consistent with potentially larger impact of the Increased Healthier condition on selection for less-educated participants, and potentially larger impact of the Increased Less-Healthy condition for higher-educated participants. Conclusions. A greater impact from increasing the number of less-healthy (over healthier) foods was not replicated when selecting snacks for immediate consumption: both increased selections of the targeted foods with no evidence of a difference in effectiveness. The observed pattern of results suggested possible differential impact by education, albeit not statistically significant. If replicated in larger studies, this could suggest that removing less-healthy options has the potential to reduce health inequalities due to unhealthier diets. Conversely, adding healthier options could have the potential to increase these inequalities. Trial registration: Retrospectively registered on ISRCTN 11/06/2018 (https://doi.org/10.1186/ISRCTN34626166).</p

Impact of increasing the availability of healthier vs. less-healthy food on food selection: A randomised laboratory experiment

Background. Environmental cues shape behaviour, but few studies compare the impact of targeting healthier vs. less-healthy cues. One online study suggested greater impact on selection from increasing the number of less-healthy (vs. healthier) snacks. The current study aimed to: (1) extend the previous study by using physically-present snacks for immediate consumption; (2) explore responsiveness by socio-economic position; (3) investigate possible mediators (response inhibition, food appeal) of any socio-economic differences in selection. Methods. In a between-subjects laboratory experiment UK adults (n=417) were randomised according to their ID number (without blinding) to one of three ranges of options: Two healthier, two less-healthy [“Equal”] (n=136); Six healthier, two less-healthy [“Increased Healthier”] (n=143); Two healthier, six less-healthy [“Increased Less-Healthy”] (n=138). Participants completed measures of response inhibition and food appeal, and selected a snack for immediate consumption from their allocated range. The primary outcome was selection of a healthier (over less-healthy) snack. Results. The odds of selecting a less-healthy snack were 2.9 times higher (95%CIs:1.7,5.1) in the Increased Less-Healthy condition compared to the Equal condition. The odds of selecting a healthier snack were 2.5 times higher (95%CIs:1.5,4.1) in the Increased Healthier (vs. Equal) condition. There was no significant difference in the size of these effects (-0.2; 95%CIs:-1.1,0.7). Findings were inconclusive with regard to interactions by education, but the direction of effects was consistent with potentially larger impact of the Increased Healthier condition on selection for less-educated participants, and potentially larger impact of the Increased Less-Healthy condition for higher-educated participants. Conclusions. A greater impact from increasing the number of less-healthy (over healthier) foods was not replicated when selecting snacks for immediate consumption: both increased selections of the targeted foods with no evidence of a difference in effectiveness. The observed pattern of results suggested possible differential impact by education, albeit not statistically significant. If replicated in larger studies, this could suggest that removing less-healthy options has the potential to reduce health inequalities due to unhealthier diets. Conversely, adding healthier options could have the potential to increase these inequalities. Trial registration: Retrospectively registered on ISRCTN 11/06/2018 (https://doi.org/10.1186/ISRCTN34626166)

Impact of increasing the availability of healthier vs. less-healthy food on food selection: a randomised laboratory experiment

Abstract Background Environmental cues shape behaviour, but few studies compare the impact of targeting healthier vs. less-healthy cues. One online study suggested greater impact on selection from increasing the number of less-healthy (vs. healthier) snacks. The current study aimed to: (1) extend the previous study by using physically-present snacks for immediate consumption; (2) explore responsiveness by socio-economic position; (3) investigate possible mediators (response inhibition, food appeal) of any socio-economic differences in selection. Methods In a between-subjects laboratory experiment UK adults (n = 417) were randomised according to their ID number (without blinding) to one of three ranges of options: Two healthier, two less-healthy [“Equal”] (n = 136); Six healthier, two less-healthy [“Increased Healthier”] (n = 143); Two healthier, six less-healthy [“Increased Less-Healthy”] (n = 138). Participants completed measures of response inhibition and food appeal, and selected a snack for immediate consumption from their allocated range. The primary outcome was selection of a healthier (over less-healthy) snack. Results The odds of selecting a less-healthy snack were 2.9 times higher (95%CIs:1.7,5.1) in the Increased Less-Healthy condition compared to the Equal condition. The odds of selecting a healthier snack were 2.5 times higher (95%CIs:1.5,4.1) in the Increased Healthier (vs. Equal) condition. There was no significant difference in the size of these effects (− 0.2; 95%CIs:-1.1,0.7). Findings were inconclusive with regard to interactions by education, but the direction of effects was consistent with potentially larger impact of the Increased Healthier condition on selection for higher-educated participants, and potentially larger impact of the Increased Less-Healthy condition for less-educated participants. Conclusions A greater impact from increasing the number of less-healthy (over healthier) foods was not replicated when selecting snacks for immediate consumption: both increased selections of the targeted foods with no evidence of a difference in effectiveness. The observed pattern of results suggested possible differential impact by education, albeit not statistically significant. If replicated in larger studies, this could suggest that removing less-healthy options has the potential to reduce health inequalities due to unhealthier diets. Conversely, adding healthier options could have the potential to increase these inequalities. Trial registration ISRCTN: ISRCTN34626166; 11/06/2018; Retrospectively registered. </jats:sec

Appendix A. Simulating biased random walks.

Simulating biased random walks