Conventional measures of predictor importance in linear models are applicable only when the assumption of homoscedasticity is satisfied. Moreover, they cannot be adapted to evaluating predictor importance in models of heteroscedasticity (i.e., dispersion), an issue that seems not to have been systematically addressed in the literature. We compare two suitable approaches, Dominance Analysis (DA) and Bayesian Model Averaging (BMA), for simultaneously evaluating predictor importance in models of location and dispersion. We apply them to the beta general linear model as a test-case, illustrating this with an example using real data. Simulations using several different model structures, sample sizes, and degrees of multicollinearity suggest that both DA and BMA largely agree on the relative importance of predictors of the mean, but differ when ranking predictors of dispersion. The main implication of these findings for researchers is that the choice between DA and BMA is most important when they wish to evaluate the importance of predictors of dispersion.

The “less is more effect” (LIME) occurs when a recognition-dependent agent has a greater probability of choosing the better item than a more knowledgeable agent who recognizes more items. Goldstein and Gigerenzer (2002) define α as the probability that a correct choice is made on the basis of recognition alone and β the probability that a correct choice is made when both items are recognized (via additional cues). They claim that a LIME occurs if α > β (α > 1/2) and α and β remain constant as the number of recognized items, n, varies. In fact, it can be shown that neither of these parameters generally remains constant as n varies, and neither of them are simple functions of n. Therefore, a new theoretical basis for the LIME is needed. This paper provides mathematical results for understanding when the LIME can occur and elucidates implications of these results. The major findings presented here are as follows:

• Demonstrations that the LIME can occur when α ≤ β and fail to occur when α > β, and derivation of the conditions for these co-occurrences;

• A new characterization of the conditions under which the LIME occurs;

• Generalizations of this characterization to handle imperfect recognition; and

• Characterization of when the LIME occurs as more items become recognized.

The primary implication of these results is that the advantage of the recognition cue depends not only on cue validities, but also on the order in which items are learned. This realization, in turn, suggests that research in this area should incorporate a more dynamic focus on learning and memory processes, and the effects of reputational information.

Bone healing is an important survival mechanism, allowing vertebrates to recover from injury and disease. Here we describe newly recognized paleopathologies in the hindlimbs of the early tetrapods Crassigyrinus scoticus and Eoherpeton watsoni from the early Carboniferous of Cowdenbeath, Scotland. These pathologies are among the oldest known instances of bone healing in tetrapod limb bones in the fossil record (about 325 Ma). X-ray microtomographic imaging of the internal bone structure of these lesions shows that they are characterized by a mass of trabecular bone separated from the shaft's trabeculae by a layer of cortical bone. We frame these paleopathologies in an evolutionary context, including additional data on bone healing and its pathways across extinct and extant sarcopterygians. These data allowed us to synthesize information on cell-mediated repair of bone and other mineralized tissues in all vertebrates, to reconstruct the evolutionary history of skeletal tissue repair mechanisms. We conclude that bone healing is ancestral for sarcopterygians. Furthermore, other mineralized tissues (aspidin and dentine) were also capable of healing and remodeling early in vertebrate evolution, suggesting that these repair mechanisms are synapomorphies of vertebrate mineralized tissues. The evidence for remodeling and healing in all of these tissues appears concurrently, so in addition to healing, these early vertebrates had the capacity to restore structure and strength by remodeling their skeletons. Healing appears to be an inherent property of these mineralized tissues, and its linkage to their remodeling capacity has previously been underappreciated.

In Scotland, the base of the Ballagan Formation has traditionally been placed at the first grey mudstone within a contiguous Late Devonian to Carboniferous succession. This convention places the Devonian–Carboniferous boundary within the Old Red Sandstone (ORS) Kinnesswood Formation. The consequences of this placement are that tetrapods from the Ballagan Formation were dated as late Tournaisian in age and that the ranges of typically Devonian fish found in the Kinnesswood Formation continued into the Carboniferous. The Pease Bay specimen of the fish Remigolepis is from the Kinnesswood Formation. Comparisons with its range in Greenland, calibrated against spores, show it was Famennian in age. Detailed palynological sampling at Burnmouth from the base of the Ballagan Formation proves that the early Tournaisian spore zones (VI and HD plus Cl 1) are present. The Schopfites species that occurs through most of the succession is Schopfites delicatus rather than Schopfites claviger. The latter species defines the late Tournaisian CM spore zone. The first spore assemblage that has been found in Upper ‘ORS' strata underlying the Ballagan Formation (Preston, Whiteadder Water), contains Retispora lepidophyta and is from the early latest Famennian LL spore zone. The spore samples are interbedded with volcaniclastic debris, which shows that the Kelso Volcanic Formation is, in part, early latest Famennian in age. These findings demonstrate that the Ballagan Formation includes most of the Tournaisian with the Devonian–Carboniferous boundary positioned close to the top of the Kinnesswood Formation. The Stage 6 calcrete at Pease Bay can be correlated to the equivalent section at Carham, showing that it represents a time gap equivalent to the latest Famennian glaciation(s). Importantly, some of the recently described Ballagan Formation tetrapods are older than previously dated and now fill the key early part of Romer's Gap.

This paper surveys results of a research program investigating human judgments of imprecise probabilities under sample-space ignorance (i.e., ignorance of what the possible outcomes are in a decision). The framework used for comparisons with human judgments is primarily due to Walley (1991, 1996). Five studies are reported which test four of Walley's prescriptions for judgment under sample-space ignorance, as well as assessing the impact of the number of observations and types of events on subjective lower and upper probability estimates. The paper concludes with a synopsis of future directions for empirical research on subjective imprecise probability judgments.