The affective impact of financial skewness on neural activity and choice

Few finance theories consider the influence of "skewness" (or large and asymmetric but unlikely outcomes) on financial choice. We investigated the impact of skewed gambles on subjects' neural activity, self-reported affective responses, and subsequent preferences using functional magnetic resonance imaging (FMRI). Neurally, skewed gambles elicited more anterior insula activation than symmetric gambles equated for expected value and variance, and positively skewed gambles also specifically elicited more nucleus accumbens (NAcc) activation than negatively skewed gambles. Affectively, positively skewed gambles elicited more positive arousal and negatively skewed gambles elicited more negative arousal than symmetric gambles equated for expected value and variance. Subjects also preferred positively skewed gambles more, but negatively skewed gambles less than symmetric gambles of equal expected value. Individual differences in both NAcc activity and positive arousal predicted preferences for positively skewed gambles. These findings support an anticipatory affect account in which statistical properties of gambles--including skewness--can influence neural activity, affective responses, and ultimately, choice.     

The Effect of Positive and Negative Feedback on Risk-Taking across Different Contexts

Preferences for risky choices have often been shown to be unstable and context-dependent. Though people generally avoid gambles with mixed outcomes, a phenomenon often attributed to loss aversion, contextual factors can impact this dramatically. For example, people typically prefer risky options after a financial loss, while generally choosing safer options after a monetary gain. However, it is unclear what exactly contributes to these preference shifts as a function of prior outcomes, as these gain/loss outcomes are usually confounded with participant performance, and therefore it is unclear whether these effects are driven purely by the monetary gains or losses, or rather by success or failure at the actual task. Here, we experimentally separated the effects of monetary gains/losses from performance success/failure prior to a standard risky choice. Participants performed a task in which they experienced contextual effects: 1) monetary gain or loss based directly on performance, 2) monetary gain or loss that was randomly awarded and was, crucially, independent from performance, and 3) success or failure feedback based on performance, but without any monetary incentive. Immediately following these positive/negative contexts, participants were presented with a gain-loss gamble that they had to decide to either play or pass. We found that risk preferences for identical sets of gambles were biased by positive and negative contexts containing monetary gains and losses, but not by contexts containing performance feedback. This data suggests that the observed framing effects are driven by aversion for monetary losses and not simply by the positive or negative valence of the context, or by potential moods resulting from positive or negative contexts. These results highlight the specific context dependence of risk preferences.     

Bayesian QTL mapping using skewed Student-t distributions

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.     

Commingling in the distributions of fat-related measures in Punjabi families

The distribution of anthropometric measurements related to fatness levels is examined to determine if skewness alone accounts for the nonnormality of such measures. A mixture of two normal distributions or a single skewed distribution fit the data significantly better than a single normal in all cases. For maximum hip width, knee diameter, and weight, two skewed distributions give a better fit than one skewed distribution, rejecting the null hypothesis of a single distribution even when skewness is considered. There is evidence for three skewed component distributions for biceps skinfold. Abdomen circumference, upper arm circumference, triceps skinfold, and calf skinfold are best approximated by a one component log-normal distribution. Children and parents show slightly different patterns in skewness and kurtosis when considered separately, but differences between them do not account for the commingling found in the combined distributions.     

Bayesian analysis of multivariate mixed models for a prospective cohort study using skew‐elliptical distributions

Classical multivariate mixed models that acknowledge the correlation of patients through the incorporation of normal error terms are widely used in cohort studies. Violation of the normality assumption can make the statistical inference vague. In this paper, we propose a Bayesian parametric approach by relaxing this assumption and substituting some flexible distributions in fitting multivariate mixed models. This strategy allows for the skewness and the heavy tails of error‐term distributions and thus makes inferences robust to the violation. This approach uses flexible skew‐elliptical distributions, including skewed, fat, or thin‐tailed distributions, and imposes the normal model as a special case. We use real data obtained from a prospective cohort study on the low back pain to illustrate the usefulness of our proposed approach.     

Endowment effect in capuchin monkeys

In humans, the capacity for economically rational choice is constrained by a variety of preference biases: humans evaluate gambles relative to arbitrary reference points; weigh losses heavier than equally sized gains; and demand a higher price for owned goods than for equally preferred goods that are not yet owned. To date, however, fewer studies have examined the origins of these biases. Here, we review previous work demonstrating that human economic biases such as loss aversion and reference dependence are shared with an ancestrally related New World primate, the capuchin monkey (Cebus apella). We then examine whether capuchins display an endowment effect in a token-trading task. We identified pairs of treats (fruit discs versus cereal chunks) that were equally preferred by each monkey. When given a chance to trade away their owned fruit discs to obtain the equally valued cereal chunks (or vice versa), however, monkeys required a far greater compensation than the equally preferred treat. We show that these effects are not due to transaction costs or timing issues. These data suggest that biased preferences rely on cognitive systems that are more evolutionarily ancient than previously thought-and that common evolutionary ancestry shared by humans and capuchins may account for the occurrence of the endowment effect in both species.     

Body size distributions in North American freshwater fish: large‐scale factors

Aim To document continental‐ and regional‐scale variation in the size distributions of freshwater fish and examine some energetic, evolutionary and biogeographic explanations for these patterns. Location North America. Methods Regional species lists, coupled with habitat and body size information, were used to document the spatial patterns. Results At the continental scale, riverine specialist fishes show a unimodal, right‐skewed, body size distribution whereas habitat generalist and lacustrine specialist species exhibit bimodal size distributions, with only a slight preponderance of small‐mode species. Most large‐mode species are migratory. Resident species, unlike migratory ones, show a latitudinal increase in mean size, but the size increase across all species is steeper because the importance of large migratory species increases with latitude. Size distributions change from right‐ to left‐skewed with increasing latitude. Maximum body size does not change with increasing family richness but minimum size declines and skewness increases, consistent with diversification of small species. Skewness does not vary with mean family body size. Main conclusions Post‐glacial recolonization by large, habitat generalist, migratory species is the main determinant of latitudinal size distribution trends. There is little support for the energetic hypothesis, but the data are consistent with a negative Cope's rule.     

Low-quality females prefer low-quality males when choosing a mate

Mate choice studies routinely assume female preferences for indicators of high quality in males but rarely consider developmental causes of within-population variation in mating preferences. By contrast, recent mate choice models assume that costs and benefits of searching or competing for high-quality males depend on females'' phenotypic quality. A prediction following from these models is that manipulation of female quality should alter her choosiness or even the direction of her mating preferences. We here provide (to our knowledge) the first example where an experimental manipulation of female quality induced a mating preference for low-quality males. Zebra finches (Taeniopygia guttata) reared in small or large experimental broods became high- or low-quality adults, respectively. Only high-quality females preferred high-quality males'' mate-advertising songs, while all low-quality females preferred low-quality males'' song. Subsequent breeding trials confirmed this pattern: latency until egg laying was shortest in quality-matched pairs, indicating that quality-matched birds were accepted faster as partners. Females produced larger eggs when mated with high-quality males, regardless of their own quality, indicating consensus regarding male quality despite the expression of different choices. Our results demonstrate the importance of considering the development of mating preferences to understand their within-population variation and environmentally induced change.     

Bayesian analysis for nonlinear regression model under skewed errors,with application in growth curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew‐t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.     

Rationality in risk-sensitive foraging choices by starlings

Normative models of choice usually predict preferences between alternatives by computing their value according to some criterion, then identifying the alternative with greatest value. An important consequence of this procedure is captured in the economic concept of rationality, defined through a number of principles that are necessary for the existence of an ordinal scale of value upon which organisms base their choices. Violations of these principles, such as some recently reported breaches of transitivity and regularity in birds and honeybees, have strong implications for the understanding of decision mechanisms in humans and nonhumans alike. We investigated rationality in risky choice using European starlings, Sturnus vulgaris. Birds had to choose between two or three food sources, each associated with a different variance in delay to reward. In three experiments, starlings were strongly risk prone, showing regular and consistent preferences in binary and trinary choices. Preferences also satisfied weak and strong stochastic transitivity. Our results extend the generality of previous research in risk-sensitive foraging to situations where more than two alternatives are present and suggest that violations of rationality in risk-sensitive choices may be expressed only under restricted sets of conditions. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.      

The size distribution of conspecific populations: the peoples of New Guinea

The size distribution of the language populations in New Guinea, which represent over 15% of the world's languages, is analysed using models analogous to the resource division models of species abundance distribution in ecological communities. A model distribution of resource segments reflecting population size is created by repeated selection of an existing resource segment and its division into two. We found that any dependency of the selection probability on the size of the segment generated negatively skewed abundance distributions after log transformation. Asymmetric segment division further exacerbated the negative skewness. Size-independent selection produced lognormal abundance distributions, irrespective of the segment division method. Size-dependent selection and asymmetric division were deemed reasonable assumptions since large language populations are more likely to generate isolates, which develop into new populations, than small ones, and these isolates are likely to be small relative to the progenitor population. A negatively skewed distribution of the log-transformed population sizes was therefore expected. However, the observed distributions were lognormal, scale invariant for areas containing between 100 and over 1000 language populations. The dynamics of language differentiation, as reflected by the models, may therefore be unimportant relative to the effect of variable growth rates among populations. All lognormal distributions from resource division models had a higher variance than the observed one, where half of the 1053 populations had between 350 and 3000 individuals. The possible mechanisms maintaining such a low variance around a modal population size of 1000 are discussed.     

Skew‐normal/independent linear mixed models for censored responses with applications to HIV viral loads

Often in biomedical studies, the routine use of linear mixed‐effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew‐normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral‐load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew‐normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy‐tailed distributions that includes the skew‐normal, skew‐t, skew‐slash, and skew‐contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left‐ or right‐censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case‐deletion influence diagnostics based on the Kullback–Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.     

Evolution of female multiple mating: A quantitative model of the “sexually selected sperm” hypothesis

Explaining the evolution and maintenance of polyandry remains a key challenge in evolutionary ecology. One appealing explanation is the sexually selected sperm (SSS) hypothesis, which proposes that polyandry evolves due to indirect selection stemming from positive genetic covariance with male fertilization efficiency, and hence with a male's success in postcopulatory competition for paternity. However, the SSS hypothesis relies on verbal analogy with “sexy-son” models explaining coevolution of female preferences for male displays, and explicit models that validate the basic SSS principle are surprisingly lacking. We developed analogous genetically explicit individual-based models describing the SSS and “sexy-son” processes. We show that the analogy between the two is only partly valid, such that the genetic correlation arising between polyandry and fertilization efficiency is generally smaller than that arising between preference and display, resulting in less reliable coevolution. Importantly, indirect selection was too weak to cause polyandry to evolve in the presence of negative direct selection. Negatively biased mutations on fertilization efficiency did not generally rescue runaway evolution of polyandry unless realized fertilization was highly skewed toward a single male, and coevolution was even weaker given random mating order effects on fertilization. Our models suggest that the SSS process is, on its own, unlikely to generally explain the evolution of polyandry.     

Food web stability and weighted connectance: the complexity-stability debate revisited

How the complexity of food webs relates to stability has been a subject of many studies. Often, unweighted connectance is used to express complexity. Unweighted connectance is measured as the proportion of realized links in the network. Weighted connectance, on the other hand, takes link weights (fluxes or feeding rates) into account and captures the shape of the flux distribution. Here, we used weighted connectance to revisit the relation between complexity and stability. We used 15 real soil food webs and determined the feeding rates and the interaction strength matrices. We calculated both versions of connectance, and related these structural properties to food web stability. We also determined the skewness of both flux and interaction strength distributions with the Gini coefficient. We found no relation between unweighted connectance and food web stability, but weighted connectance was positively correlated with stability. This finding challenges the notion that complexity may constrain stability, and supports the ‘complexity begets stability’ notion. The positive correlation between weighted connectance and stability implies that the more evenly flux rates were distributed over links, the more stable the webs were. This was confirmed by the Gini coefficients of both fluxes and interaction strengths. However, the most even distributions of this dataset still were strongly skewed towards small fluxes or weak interaction strengths. Thus, incorporating these distribution with many weak links via weighted instead of unweighted food web measures can shed new light on classical theories.     

Social learning of novel route preferences in adult humans

Non-human animals can acquire novel route preferences by following knowledgeable individuals. Such socially learned route preferences can be stably maintained over multiple transmission episodes, sometimes forming long-lived traditions. In humans, preferences for familiar routes or heavily used worn trails over unfamiliar ones have been described in various contexts. However, social learning of route preferences has not been experimentally demonstrated in humans. Here, we demonstrate that social learning and tradition influence route choice. We led adult male and female participants into a room by one of two routes. Participants followed the demonstrated route choices, and later remembered and preferred this choice even when determinably suboptimal (i.e. longer and not preferred by control participants) or when the choice was indicated as arbitrary (the demonstrator took one route to retrieve a poster that had ostensibly fallen). Moreover, route preferences were stably maintained over multiple transmission episodes. We suggest that simple social learning processes, often neglected in human and primate research, can result in long-lived route preferences that may influence a range of additional behaviour patterns.     

Selection of carrion by the Australasian harrier (Circus approximate) in New Zealand

Abstract

The selection of carrion by Australasian harriers was studied by offering a choice of baits in the field. These trials tested preferences for carrion species, amount of flesh exposed, body posture, and colour of the carrion. Domestic hen pullets and Norway rats were chosen significantly more often than rabbits, opossums, or eels. Skinned rabbits were preferred to unskinned ones. Body posture of rabbit carcasses did not appear to affect a harrier's choice. White and blue baits were preferred to red, brown, or green baits. The most important factors involved in the selection of carrion by harriers appear to be the ease of handling of the carrion, and the colour of the bait.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

Disentangling the influences of mean body size and size structure on ecosystem functioning: an example of nutrient recycling by a non‐native crayfish

Body size is a fundamental functional trait that can be used to forecast individuals' responses to environmental change and their contribution to ecosystem functioning. However, information on the mean and variation of size distributions often confound one another when relating body size to aggregate functioning. Given that size‐based metrics are used as indicators of ecosystem status, it is important to identify the specific aspects of size distributions that mediate ecosystem functioning. Our goal was to simultaneously account for the mean, variance, and shape of size distributions when relating body size to aggregate ecosystem functioning. We take advantage of habitat‐specific differences in size distributions to estimate nutrient recycling by a non‐native crayfish using mean‐field and variance‐incorporating approaches. Crayfishes often substantially influence ecosystem functioning through their omnivorous role in aquatic food webs. As predicted from Jensen's inequality, considering only the mean body size of crayfish overestimated aggregate effects on ecosystem functioning. This bias declined with mean body size such that mean‐field and variance‐incorporating estimates of ecosystem functioning were similar for samples at mean body sizes >7.5 g. At low mean body size, mean‐field bias in ecosystem functioning mismatch predictions from Jensen's inequality, likely because of the increasing skewness of the size distribution. Our findings support the prediction that variance around the mean can alter the relationship between body size and ecosystem functioning, especially at low mean body size. However, methods to account for mean‐field bias performed poorly in samples with highly skewed distributions, indicating that changes in the shape of the distribution, in addition to the variance, may confound mean‐based estimates of ecosystem functioning. Given that many biological functions scale allometrically, explicitly defining and experimentally or statistically isolating the effects of the mean, variance, and shape of size distributions is necessary to begin generalizing relationships between animal body size and ecosystem functioning.     

Embracing asymmetry in nature: How to account for skewness in ecological data

Asymmetric regression is an alternative to conventional linear regression that allows us to model the relationship between predictor variables and the response variable while accommodating skewness. Advantages of asymmetric regression include incorporating realistic ecological patterns observed in data, robustness to model misspecification and less sensitivity to outliers. Bayesian asymmetric regression relies on asymmetric distributions such as the asymmetric Laplace (ALD) or asymmetric normal (AND) in place of the normal distribution used in classic linear regression models. Asymmetric regression concepts can be used for process and parameter components of hierarchical Bayesian models and have a wide range of applications in data analyses. In particular, asymmetric regression allows us to fit more realistic statistical models to skewed data and pairs well with Bayesian inference. We first describe asymmetric regression using the ALD and AND. Second, we show how the ALD and AND can be used for Bayesian quantile and expectile regression for continuous response data. Third, we consider an extension to generalize Bayesian asymmetric regression to survey data consisting of counts of objects. Fourth, we describe a regression model using the ALD, and show that it can be applied to add needed flexibility, resulting in better predictive models compared to Poisson or negative binomial regression. We demonstrate concepts by analyzing a data set consisting of counts of Henslow’s sparrows following prescribed fire and provide annotated computer code to facilitate implementation. Our results suggest Bayesian asymmetric regression is an essential component of a scientist’s statistical toolbox.