Estimating the proportion of guilty suspects and posterior probability of guilt in lineups using signal-detection models

Background The majority of eyewitness lineup studies are laboratory-based. How well the conclusions of these studies, including the relationship between confidence and accuracy, generalize to real-world police lineups is an open question. Signal detection theory (SDT) has emerged as a powerful framework for analyzing lineups that allows comparison of witnesses’ memory accuracy under different types of identification procedures. Because the guilt or innocence of a real-world suspect is generally not known, however, it is further unknown precisely how the identification of a suspect should change our belief in their guilt. The probability of guilt after the suspect has been identified, the posterior probability of guilt (PPG), can only be meaningfully estimated if we know the proportion of lineups that include a guilty suspect, P(guilty). Recent work used SDT to estimate P(guilty) on a single empirical data set that shared an important property with real-world data; that is, no information about the guilt or innocence of the suspects was provided. Here we test the ability of the SDT model to recover P(guilty) on a wide range of pre-existing empirical data from more than 10,000 identification decisions. We then use simulations of the SDT model to determine the conditions under which the model succeeds and, where applicable, why it fails. Results For both empirical and simulated studies, the model was able to accurately estimate P(guilty) when the lineups were fair (the guilty and innocent suspects did not stand out) and identifications of both suspects and fillers occurred with a range of confidence levels. Simulations showed that the model can accurately recover P(guilty) given data that matches the model assumptions. The model failed to accurately estimate P(guilty) under conditions that violated its assumptions; for example, when the effective size of the lineup was reduced, either because the fillers were selected to be poor matches to the suspect or because the innocent suspect was more familiar than the guilty suspect. The model also underestimated P(guilty) when a weapon was shown. Conclusions Depending on lineup quality, estimation of P(guilty) and, relatedly, PPG, from the SDT model can range from poor to excellent. These results highlight the need to carefully consider how the similarity relations between fillers and suspects influence identifications

Strategies for Using a Spatial Method to Promote Active Learning of Probability Concepts

We developed and tested strategies for using spatial representations to help students understand core probability concepts, including the multiplication rule for computing a joint probability from a marginal and conditional probability, interpreting an odds value as the ratio of two probabilities, and Bayesian inference. The general goal of these strategies is to promote active learning by introducing concepts in an intuitive spatial format and then encouraging students to try to discover the explicit equations associated with the spatial representations. We assessed the viability of the proposed active-learning approach with two exercises that tested undergraduates’ ability to specify mathematical equations after learning to use the spatial solution method. A majority of students succeeded in independently discovering fundamental mathematical concepts underlying probabilistic reasoning. For example, in the second exercise, 76% of students correctly multiplied marginal and conditional probabilities to find joint probabilities, 86% correctly divided joint probabilities to get an odds value, and 69% did both to achieve full Bayesian inference. Thus, we conclude that the spatial method is an effective way to promote active learning of probability equations

Effects of pyric herbivory on prairie-chicken (\u3ci\u3eTympanuchus\u3c/i\u3e spp) habitat

The reduction and simplification of grasslands has led to the decline of numerous species of grassland fauna, particularly grassland-obligate birds. Prairie-chickens (Tympanuchus spp.) are an example of obligate grassland birds that have declined throughout most of their distribution and are species of conservation concern. Pyric herbivory has been suggested as a land management strategy for enhancing prairie-chicken habitat and stabilizing declining population trends. We assessed differences in vegetation structure created by pyric herbivory compared to fire-only treatments to determine whether pyric herbivory increased habitat heterogeneity for prairie-chickens, spatially or temporally. Our study was performed at four sites in the southern Great Plains, all within the current or historic distribution of either lesser (T. pallidicinctus), greater (T. cupido), or Attwater’s (T. cupido attwateri) prairie-chick-ens. Key vegetation characteristics of grass cover and vegetation height in pyric herbivory and fire-only treatments were within the recommended range of values for prairie-chickens during their distinct life history stages. However, patches managed via pyric herbivory pro-vided approximately 5% more forb cover than fire-only treatments for almost 30 months post-fire. Additionally, pyric herbivory extended the length of time bare ground was present after fires. Pyric herbivory also reduced vegetation height and biomass, with mean vegetation height in pyric herbivory treatments lagging behind fire-only treatments by approximately 15 months. Canopy cover in fire-only treatments exceeded levels recommended for prairie-chicken young within 12 months post-fire. However, canopy cover in pyric herbivory treatments never exceeded the maximum recommended levels. Overall, it appears that pyric herbivory improves vegetation characteristics reported as critical to prairie-chicken reproduction. Based on our results, we suggest pyric herbivory as a viable management technique to promote prairie-chicken habitat in the southern Great Plains, while still accommodating livestock production

Effects of Pyric Herbivory on Prairie-Chicken (Tympanuchus spp) Habitat

The reduction and simplification of grasslands has led to the decline of numerous species of grassland fauna, particularly grassland-obligate birds. Prairie-chickens (Tympanuchus spp.) are an example of obligate grassland birds that have declined throughout most of their distribution and are species of conservation concern. Pyric herbivory has been suggested as a land management strategy for enhancing prairie-chicken habitat and stabilizing declining population trends. We assessed differences in vegetation structure created by pyric herbivory compared to fire-only treatments to determine whether pyric herbivory increased habitat heterogeneity for prairie-chickens, spatially or temporally. Our study was performed at four sites in the southern Great Plains, all within the current or historic distribution of either lesser (T. pallidicinctus), greater (T. cupido), or Attwater’s (T. cupido attwateri) prairie-chickens. Key vegetation characteristics of grass cover and vegetation height in pyric herbivory and fire-only treatments were within the recommended range of values for prairie-chickens during their distinct life history stages. However, patches managed via pyric herbivory provided approximately 5% more forb cover than fire-only treatments for almost 30 months post-fire. Additionally, pyric herbivory extended the length of time bare ground was present after fires. Pyric herbivory also reduced vegetation height and biomass, with mean vegetation height in pyric herbivory treatments lagging behind fire-only treatments by approximately 15 months. Canopy cover in fire-only treatments exceeded levels recommended for prairie-chicken young within 12 months post-fire. However, canopy cover in pyric herbivory treatments never exceeded the maximum recommended levels. Overall, it appears that pyric herbivory improves vegetation characteristics reported as critical to prairie-chicken reproduction. Based on our results, we suggest pyric herbivory as a viable management technique to promote prairie-chicken habitat in the southern Great Plains, while still accommodating livestock production

Recoupling fire and grazing reduces wildland fuel loads on rangelands

Fire suppression and exclusion, the historically dominant paradigm of fire management, has resulted in major modifications of fire-dependent ecosystems worldwide. These changes are partially credited with a recent increase in wildfire number and extent, as well as more extreme fire behavior. Fire and herbivory historically interacted, and research has shown that the interaction creates a unique mosaic of vegetation heterogeneity that each disturbance alone does not create. Because fire and grazing have largely been decoupled in modern times, the degree to which the interaction affects fuels and fire regimes has not yet been quantified. We evaluated effects of fire-only and pyric herbivory on rangeland fuels and fire behavior simulated using BehavePlus at four sites across the southern Great Plains.We predicted patches managed via pyric herbivory would maintain lower fuel loads, and less intense simulated fire behavior than fire alone. We found that time since fire was a significant predictor of fuel loads and simulated fire behavior characteristics at all sites. Fuel loads and simulated fire behavior characteristics (flame length and rate of spread) increased with increasing time since fire in all simulated weather scenarios. Pyric herbivory mediated fuel accumulation at all sites. Mean fuel loads in fire-only treatments exceeded 5000 kg/ha within 24 months, but pyric herbivory treatments remained below 5000 kg/ha for approximately 36 months. Simulated flame lengths in fire-only treatments were consistently higher (up to 3 9 ) than in pyric herbivory treatments. Similarly, fire spread rates were higher in fire-only than in pyric herbivory treatments in all simulated weather conditions. Although all sites had potential to burn in the most extreme weather conditions, pyric herbivory reduced fuel accumulations, flame lengths, and rates of spread across all weather patterns simulated. These reductions extended the amount of time standard wildland firefighting techniques remain effective. Therefore, incorporating pyric herbivory into fuel management practices, in areas of high herbaceous productivity, increases the effectiveness of fuel treatments

Recoupling Fire and Grazing Reduces Wildland Fuel Loads on Rangelands

Fire suppression and exclusion, the historically dominant paradigm of fire management, has resulted in major modifications of fire-dependent ecosystems worldwide. These changes are partially credited with a recent increase in wildfire number and extent, as well as more extreme fire behavior. Fire and herbivory historically interacted, and research has shown that the interaction creates a unique mosaic of vegetation heterogeneity that each disturbance alone does not create. Because fire and grazing have largely been decoupled in modern times, the degree to which the interaction affects fuels and fire regimes has not yet been quantified. We evaluated effects of fire-only and pyric herbivory on rangeland fuels and fire behavior simulated using BehavePlus at four sites across the southern Great Plains. We predicted patches managed via pyric herbivory would maintain lower fuel loads, and less intense simulated fire behavior than fire alone. We found that time since fire was a significant predictor of fuel loads and simulated fire behavior characteristics at all sites. Fuel loads and simulated fire behavior characteristics (flame length and rate of spread) increased with increasing time since fire in all simulated weather scenarios. Pyric herbivory mediated fuel accumulation at all sites. Mean fuel loads in fire-only treatments exceeded 5000 kg/ha within 24 months, but pyric herbivory treatments remained below 5000 kg/ha for approximately 36 months. Simulated flame lengths in fire-only treatments were consistently higher (up to 3 x ) than in pyric herbivory treatments. Similarly, fire spread rates were higher in fire-only than in pyric herbivory treatments in all simulated weather conditions. Although all sites had potential to burn in the most extreme weather conditions, pyric herbivory reduced fuel accumulations, flame lengths, and rates of spread across all weather patterns simulated. These reductions extended the amount of time standard wildland firefighting techniques remain effective. Therefore, incorporating pyric herbivory into fuel management practices, in areas of high herbaceous productivity, increases the effectiveness of fuel treatments