On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting

Previously, we (McKerchar et al., 2009) showed that two-parameter hyperboloid models ( [Green and Myerson, 2004] and [Rachlin, 2006]) provide significantly better fits to delay discounting data than simple, one-parameter hyperbolic and exponential models. Here, we extend this effort by comparing fits of the two-parameter hyperboloid models to data from a larger sample of participants (N = 171) who discounted probabilistic as well as delayed rewards. In particular, we examined the effects of amount on the exponents in the two hyperboloid models of delay and probability discounting in order to evaluate key theoretical predictions of the standard psychophysical scaling interpretation of these exponents. Both the Rachlin model and the Green and Myerson model provided very good fits to delay and probability discounting of both small and large amounts at both the group and individual levels (all R²s > .97 at the group level; all median R²s > .92 at the individual level). For delay discounting, the exponent in both models did not vary as a function of delayed amount, consistent with the psychophysical scaling interpretation. For probability discounting, however, the exponent in both models increased as the probabilistic amount increased—a finding inconsistent with the scaling interpretation.     

Estimates of Genetic Differentiation Measured by F(ST) Do Not Necessarily Require Large Sample Sizes When Using Many SNP Markers

Population genetic studies provide insights into the evolutionary processes that influence the distribution of sequence variants within and among wild populations. F_ST is among the most widely used measures for genetic differentiation and plays a central role in ecological and evolutionary genetic studies. It is commonly thought that large sample sizes are required in order to precisely infer F_ST and that small sample sizes lead to overestimation of genetic differentiation. Until recently, studies in ecological model organisms incorporated a limited number of genetic markers, but since the emergence of next generation sequencing, the panel size of genetic markers available even in non-reference organisms has rapidly increased. In this study we examine whether a large number of genetic markers can substitute for small sample sizes when estimating F_ST. We tested the behavior of three different estimators that infer F_ST and that are commonly used in population genetic studies. By simulating populations, we assessed the effects of sample size and the number of markers on the various estimates of genetic differentiation. Furthermore, we tested the effect of ascertainment bias on these estimates. We show that the population sample size can be significantly reduced (as small as n = 4–6) when using an appropriate estimator and a large number of bi-allelic genetic markers (k>1,000). Therefore, conservation genetic studies can now obtain almost the same statistical power as studies performed on model organisms using markers developed with next-generation sequencing.     

Group size, sex and age composition of chital (Axis axis) and sambar (Rusa unicolor) in a deciduous habitat of Western Ghats

Knowledge of the social structure of a population is important for a range of fundamental and applied purposes. Group characteristics and population structure of chital (Axis axis) and sambar (Rusa unicolor) were studied in a deciduous habitat of Mudumalai Tiger Reserve, Western Ghats, India, during 2008-2009. Vehicle transects were monitored monthly to gather information on group-size and age-sex composition of chital and sambar. The average mean group size and crowding for chital and sambar was 13.1 ± 0.5 (n = 1020), 3.6 ± 0.2 (n = 377) and 33.3, 11.0 respectively. The average adult male:adult female:fawn ratio was 63.4:100:22.3 (n = 9391) and 43.9:100:23.7 (n = 1023) in chital and sambar respectively. The mean group size of chital and sambar varied significantly between seasons (Kruskal-Wallis test, p = <0.001). Peak fawning season was observed from February to May for chital and May to August for sambar. Group's sex-age composition influenced group formation in both species between seasons at different level. Adult male and fawn were the important predicting variables of change in group size. Skewed female sex ratio was probably due to selective male predation by large predators. Although fawning occurred throughout the year, both species showed seasonality in fawning. The above mentioned patterns differed between species depending upon their ecological adaptation in foraging strategies and habitat preference.     

Coupling Demographic and Genetic Variability from Archived Collections of European Anchovy (Engraulis encrasicolus)

It is well known that temporal fluctuations in small populations deeply influence evolutionary potential. Less well known is whether fluctuations can influence the evolutionary potentials of species with large census sizes. Here, we estimated genetic population parameters from as survey of polymorphic microsatellite DNA loci in archived otoliths from Adriatic European anchovy (Engraulis encrasicolus), a fish with large census sizes that supports numerous local fisheries. Stocks have fluctuated greatly over the past few decades, and the Adriatic fishery collapsed in 1987. Our results show a significant reduction of mean genetic parameters as a consequence of the population collapse. In addition, estimates of effective population size (N_e) are much smaller than those expected in a fishes with large population census sizes (N_c). Estimates of N_e indicate low effective population sizes, even before the population collapse. The ratio N_e/N_e ranged between 10⁻⁶ and 10⁻⁸, indicating a large discrepancy between the anchovy gene pool and population census size. Therefore, anchovy populations may be more vulnerable to fishery effort and environmental change than previously thought.     

Semicircular canal system in early primates

Mammals with more rapid and agile locomotion have larger semicircular canals relative to body mass than species that move more slowly. Measurements of semicircular canals in extant mammals with known locomotor behaviours can provide a basis for testing hypotheses about locomotion in fossil primates that is independent of postcranial remains, and a means of reconstructing locomotor behaviour in species known only from cranial material. Semicircular canal radii were measured using ultra high resolution X-ray CT data for 9 stem primates (“plesiadapiforms”; n = 11), 7 adapoids (n = 12), 4 omomyoids (n = 5), and the possible omomyoid Rooneyia viejaensis (n = 1). These were compared with a modern sample (210 species including 91 primates) with known locomotor behaviours. The predicted locomotor agilities for extinct primates generally follow expectations based on known postcrania for those taxa. “Plesiadapiforms” and adapids have relatively small semicircular canals, suggesting they practiced less agile locomotion than other fossil primates in the sample, which is consistent with reconstructions of them as less specialized for leaping. The derived notharctid adapoids (excluding Cantius) and all omomyoids sampled have relatively larger semicircular canals, suggesting that they were more agile, with Microchoerus in particular being reconstructed as having had very jerky locomotion with relatively high magnitude accelerations of the head. Rooneyia viejaensis is reconstructed as having been similarly agile to omomyids and derived notharctid adapoids, which suggests that when postcranial material is found for this species it will exhibit features for some leaping behaviour, or for a locomotor mode requiring a similar degree of agility.     

An exact test of the Hardy-Weinberg law.

An exact distribution of a finite sample drawn from an infinite population in Hardy-Weinberg Equilibrium is described for k-alleles. Accordingly, an exact test of the law is presented and compared with two x2-tests for two and three alleles. For two alleles, it is shown that the "classical" c2-test is very adequate for sample sizes as small as ten. For three alleles, it is shown that a simpler formulation based on Leven's distribution approximates the exact test of this paper rather closely. However, it is recommended that researchers continue to employ the standard x2-test for all sample sizes and abide by it if the corresponding probability value is not "too close" to the critical level; otherwise, an exact test should be used.     

Determination of the specific activities of methionine sulfoxide reductase A and B by capillary electrophoresis

A capillary electrophoresis (CE) method for the determination of methionine sulfoxide reductase A and methionine sulfoxide reductase B activities in mouse liver is described. The method is based on detection of the 4-(dimethylamino)azobenzene-4′-sulfonyl derivative of l-methionine (dabsyl Met), the product of the enzymatic reactions when either dabsyl l-methionine S-sulfoxide or dabsyl l-methionine R-sulfoxide is used as a substrate. The method provides baseline resolution of the substrates and, therefore, can be used to easily determine the purity of the substrates. The method is rapid (∼20 min sample to sample), requires no column regeneration, and uses very small amounts of buffers. Separation was performed by using a 75-μm internal diameter polyimide-coated fused silica capillary (no inside coating) with 60 cm total length (50 cm to the detector window). Samples were separated at 22.5 kV, and the separation buffer was 25 mM KH₂PO₄ (pH 8.0) containing 0.9 ml of N-lauroylsarcosine (sodium salt, 30% [w/v] solution) per 100 ml of buffer. Prior to use, the capillary was conditioned with the same buffer that also contained 25 mM sodium dodecyl sulfate. The CE method is compared with high-performance liquid chromatography (HPLC) as determined by comparing results from measurements of hepatic enzyme activities in mice fed either deficient or adequate selenium.     

Can effective population size estimates be used to monitor population trends of woodland bats? A case study of Myotis bechsteinii

Molecular approaches to calculate effective population size estimates (Ne) are increasingly used as an alternative to long‐term demographic monitoring of wildlife populations. However, the complex ecology of most long‐lived species and the consequent uncertainties in model assumptions means that effective population size estimates are often imprecise. Although methods exist to incorporate age structure into Ne estimations for long‐lived species with overlapping generations, they are rarely used owing to the lack of relevant information for most wild populations. Here, we performed a case study on an elusive woodland bat, Myotis bechsteinii, to compare the use of the parentage assignment Ne estimator (EPA) with the more commonly used linkage disequilibrium (LD) Ne estimator in detecting long‐term population trends, and assessed the impacts of deploying different overall sample sizes. We used genotypic data from a previously published study, and simulated 48 contrasting demographic scenarios over 150 years using the life history characteristics of this species The LD method strongly outperformed the EPA method. As expected, smaller sample sizes resulted in a reduced ability to detect population trends. Nevertheless, even the smallest sample size tested (n = 30) could detect important changes (60%–80% decline) with the LD method. These results demonstrate that genetic approaches can be an effective way to monitor long‐lived species, such as bats, provided that they are undertaken over multiple decades.     

Filling of eco-climatological niches in a polyploid complex – A case study in the plant genus Leucanthemum Mill. (Compositae,Anthemideae) from the Iberian Peninsula

In order to assess the effects of polyploidisation on distribution patterns of species in a polyploid complex, we compared potential and actual distribution ranges of representatives from the genus Leucanthemum Mill. (Compositae, Anthemideae), which occur on the Iberian Peninsula with 20 taxa spanning ploidy levels between 2n = 2x = 18 and 2n = 22x = 198. Actual distribution ranges of taxa were derived from geo-referenced herbarium specimens by defining buffer circles around the collection localities to account for geographical uncertainties and haphazardness of specimen collecting. Eco-climatologically potential ranges were modelled with the maximum entropy method (Maxent) based on the actual distributions. By comparison of sizes of realised and eco-climatologically potential areas for each taxon we computed taxon-specific overlap indices that express the filling of eco-climatological niches. The correlation between overlap indices and ploidy levels was tested by Spearman's rank correlation coefficient. We observed a significant negative correlation between ploidy level and sizes of realised distribution ranges and no significant correlation of ploidy level and sizes of potential ranges. Finally, we found that diploid and low-ploidy taxa are filling their potential eco-climatological distribution ranges more exhaustively than highly polyploid taxa. Assuming that ascending polyploidisation is the prevailing mode compared to descending polyploidisation, our results demonstrate that the distribution patterns of members of the Leucanthemum polyploid complex on the Iberian Peninsula are mainly influenced by the age of taxa and not by ecological advantages or disadvantages connected with polyploidy.     

Improved prediction of Canada lynx distribution through regional model transferability and data efficiency

The application of species distribution models (SDMs) to areas outside of where a model was created allows informed decisions across large spatial scales, yet transferability remains a challenge in ecological modeling. We examined how regional variation in animal‐environment relationships influenced model transferability for Canada lynx (Lynx canadensis), with an additional conservation aim of modeling lynx habitat across the northwestern United States. Simultaneously, we explored the effect of sample size from GPS data on SDM model performance and transferability. We used data from three geographically distinct Canada lynx populations in Washington (n = 17 individuals), Montana (n = 66), and Wyoming (n = 10) from 1996 to 2015. We assessed regional variation in lynx‐environment relationships between these three populations using principal components analysis (PCA). We used ensemble modeling to develop SDMs for each population and all populations combined and assessed model prediction and transferability for each model scenario using withheld data and an extensive independent dataset (n = 650). Finally, we examined GPS data efficiency by testing models created with sample sizes of 5%–100% of the original datasets. PCA results indicated some differences in environmental characteristics between populations; models created from individual populations showed differential transferability based on the populations'' similarity in PCA space. Despite population differences, a single model created from all populations performed as well, or better, than each individual population. Model performance was mostly insensitive to GPS sample size, with a plateau in predictive ability reached at ~30% of the total GPS dataset when initial sample size was large. Based on these results, we generated well‐validated spatial predictions of Canada lynx distribution across a large portion of the species'' southern range, with precipitation and temperature the primary environmental predictors in the model. We also demonstrated substantial redundancy in our large GPS dataset, with predictive performance insensitive to sample sizes above 30% of the original.     

Evidence for female-biased juvenile dispersal in corophiid amphipods from a New Zealand estuary

This study examined the distribution and dispersal of corophiid amphipods (Paracorophium spp.) in a temperate New Zealand estuary. Individuals in the sediment (resident population) and those caught in bed-load (local-scale movement) and suspended-load (larger-scale movement) were counted, measured, and sexed, during two tidal cycles at 4-6 week intervals spanning 13 months. Gravid females and juveniles were present in the resident population on all sample dates suggesting near continuous reproduction. Juveniles (< 2.2 mm body length) accounted for 49.8% of individuals in the sediment, compared to 65.4% of those caught in the bed-load and suspended-load traps. For the majority of sample dates, there was a net export of juveniles from the estuary. The total number of juveniles captured in suspended-load traps was significantly greater during the ebb tide relative to the flood tide (n = 541 versus 256), whereas no significant differences were found for adults. Similarly, numbers in the bed-load traps were significantly greater for juveniles during the ebb versus the flood tide (n = 900 versus 484), and also for adult females (n = 180 versus 86). Juvenile sex ratios were female biased in the sediment (9.8:1) and in suspended-load traps (7.6:1) and both were significantly more female-biased than that recorded for juveniles caught in bed-load traps (5.8:1). By contrast, there was a significantly lower proportion of adult females to adult males found in bed-load traps (1.7:1) and in suspended-load traps (0.98:1) compared to the resident population in the sediment (3.6:1). The mean size of juvenile females caught on a flood tide was significantly larger compared to those on the ebb tide, yet juvenile males were not significantly different, suggesting that smaller females were not returning on the flood tide. We suggest that female-biased juvenile dispersal for estuarine Paracorophium spp. lowers the risk of inbreeding and reduces competition. This may have evolved in response to a polygamous breeding system with little or no social organisation where a female produces more female offspring to maximise her inclusive fitness.     

Quantitative metabolome analysis using liquid chromatography-high-resolution mass spectrometry

In this report, we introduce a liquid chromatography single-mass spectrometry method for metabolome quantification, using the LTQ Orbitrap high-resolution mass spectrometer. Analytes were separated with hydrophilic interaction liquid chromatography. At a working resolution of 30,000 (at m/z 400), the limit of detection varied from 50 fmol to 5 pmol for 25 metabolites tested. In terms of metabolite concentration, the linearity was about 2 to 3 orders of magnitude for most compounds (R² > 0.99). To determine the accuracy of the system in complex sample matrices, the isotope dilution method was evaluated from mixtures of pure compounds and uniformly ¹³C-labeled cell extracts. With the application of this method, quantification was possible within single runs even when the pool sizes of individual metabolites varied from 0.13 to 55.6 μM. As a case study, intracellular concentrations of central metabolites were determined for Methylobacterium extorquens AM1 during growth on two different carbon sources, methanol and succinate. Reproducible results from technical and biological repetitions were obtained that revealed significant variations of intracellular metabolite pool sizes, depending on the carbon source. The LTQ Obitrap offers new perspectives and strategies for metabolome quantification.     

FOUNDER EFFECTS AND PEAK SHIFTS WITHOUT GENETIC DRIFT: ADAPTIVE PEAK SHIFTS OCCUR EASILY WHEN ENVIRONMENTS FLUCTUATE SLIGHTLY

Two similar evolutionary theories, the shifting balance theory and founder-flush models, invoke random genetic drift to allow evolution on complex adaptive landscapes. These models, in their usual incarnations, deal with fitness as a static entity, and the probability of transition from one form to another is predicted to be quite small by analysis of these models. Fitness itself can change, however, and the amount of change in the parameters of the fitness functions required to allow deterministic evolution to new adaptive peaks is very small. The probability of environmental changes sufficient to allow substantial morphological evolution or reproductive isolation is large relative to the probability that similar changes could occur by processes requiring genetic drift, even with very small population sizes. The rapid evolution or speciation following a population founding event is more closely linked with environmental changes than genetic drift.     

A Fast Estimate for the Population Recombination Rate Based on Regression

Recombination is a fundamental evolutionary force. Therefore the population recombination rate ρ plays an important role in the analysis of population genetic data; however, it is notoriously difficult to estimate. This difficulty applies both to the accuracy of commonly used estimates and to the computational efforts required to obtain them. Some particularly popular methods are based on approximations to the likelihood. They require considerably less computational efforts than the full-likelihood method with not much less accuracy. Nevertheless, the computation of these approximate estimates can still be very time consuming, in particular when the sample size is large. Although auxiliary quantities for composite likelihood estimates can be computed in advance and stored in tables, these tables need to be recomputed if either the sample size or the mutation rate θ changes. Here we introduce a new method based on regression combined with boosting as a model selection technique. For large samples, it requires much less computational effort than other approximate methods, while providing similar levels of accuracy. Notably, for a sample of hundreds or thousands of individuals, the estimate of ρ using regression can be obtained on a single personal computer within a couple of minutes while other methods may need a couple of days or months (or even years). When the sample size is smaller (n ≤ 50), our new method remains computational efficient but produces biased estimates. We expect the new estimates to be helpful when analyzing large samples and/or many loci with possibly different mutation rates.     

The meaning of significant mean group differences for biomarker discovery

Over the past decade, biomarker discovery has become a key goal in psychiatry to aid in the more reliable diagnosis and prognosis of heterogeneous psychiatric conditions and the development of tailored therapies. Nevertheless, the prevailing statistical approach is still the mean group comparison between “cases” and “controls,” which tends to ignore within-group variability. In this educational article, we used empirical data simulations to investigate how effect size, sample size, and the shape of distributions impact the interpretation of mean group differences for biomarker discovery. We then applied these statistical criteria to evaluate biomarker discovery in one area of psychiatric research—autism research. Across the most influential areas of autism research, effect size estimates ranged from small (d = 0.21, anatomical structure) to medium (d = 0.36 electrophysiology, d = 0.5, eye-tracking) to large (d = 1.1 theory of mind). We show that in normal distributions, this translates to approximately 45% to 63% of cases performing within 1 standard deviation (SD) of the typical range, i.e., they do not have a deficit/atypicality in a statistical sense. For a measure to have diagnostic utility as defined by 80% sensitivity and 80% specificity, Cohen’s d of 1.66 is required, with still 40% of cases falling within 1 SD. However, in both normal and nonnormal distributions, 1 (skewness) or 2 (platykurtic, bimodal) biologically plausible subgroups may exist despite small or even nonsignificant mean group differences. This conclusion drastically contrasts the way mean group differences are frequently reported. Over 95% of studies omitted the “on average” when summarising their findings in their abstracts (“autistic people have deficits in X”), which can be misleading as it implies that the group-level difference applies to all individuals in that group. We outline practical approaches and steps for researchers to explore mean group comparisons for the discovery of stratification biomarkers.     

Inferences on the common mean of several log-normal populations: the generalized variable approach

This paper proposes a novel approach for the confidence interval estimation and hypothesis testing of the common mean of several log-normal populations using the concept of generalized variable. Simulation studies demonstrate that the proposed approach can provide confidence intervals with satisfying coverage probabilities and can perform hypothesis testing with satisfying type-I error control even at small sample sizes. Overall, it is superior to the large sample approach. The proposed method is illustrated using two examples.     

Growth, size and age at maturity of the agile frog (Rana dalmatina) in an Iberian Peninsula population

The mean age of a population of agile frogs (Rana dalmatina) from the Iberian Peninsula was estimated using mark and recapture and skeletochronology. Life-history parameters, including growth rate, body length, age and size at maturity, sexual dimorphism and longevity, were studied. The regression between age and snout-vent length (SVL) was highly significant in both sexes. Males reached sexual maturity at two years of age, although sometimes they can reach it at only one year of age. The average SVL at maturity was 51.75 mm (standard error (SE) = 0.71; n = 45). Females reached sexual maturity at two years of age with an average SVL of 62.14 mm (SE = 2.20; n = 14). A subset of the female population reached sexual maturity at three years of age. Growth was rapid until sexual maturity was reached. There was an overlap of SVL between different age classes. Growth was continuous, fulfilling the conditions of Von Bertalanffy's model. The growth coefficient (K) was 0.840 in males and 0.625 in females. The maximum SVL was greater in females (73.00 mm) than in males (59.50 mm). Sexual dimorphism was significantly biased towards females in all age classes. The maximum longevity observed was 6 years in females and 8 years in males. Management strategies for agile frogs should take into account factors such as these life-history characteristics.     

Assessment of agreement under nonstandard conditions using regression models for mean and variance

The total deviation index of Lin and Lin et al. is an intuitive approach for the assessment of agreement between two methods of measurement. It assumes that the differences of the paired measurements are a random sample from a normal distribution and works essentially by constructing a probability content tolerance interval for this distribution. We generalize this approach to the case when differences may not have identical distributions -- a common scenario in applications. In particular, we use the regression approach to model the mean and the variance of differences as functions of observed values of the average of the paired measurements, and describe two methods based on asymptotic theory of maximum likelihood estimators for constructing a simultaneous probability content tolerance band. The first method uses bootstrap to approximate the critical point and the second method is an analytical approximation. Simulation shows that the first method works well for sample sizes as small as 30 and the second method is preferable for large sample sizes. We also extend the methodology for the case when the mean function is modeled using penalized splines via a mixed model representation. Two real data applications are presented.