The use of marker‐based relationship information to estimate the heritability of body weight in a natural population: a cautionary tale

A number of procedures have been developed that allow the genetic parameters of natural populations to be estimated using relationship information inferred from marker data rather than known pedigrees. Three published approaches are available; the regression, pair‐wise likelihood and Markov Chain Monte Carlo (MCMC) sib‐ship reconstruction methods. These were applied to body weight and molecular data collected from the Soay sheep population of St. Kilda, which has a previously determined pedigree. The regression and pair‐wise likelihood approaches do not specify an exact pedigree and yielded unreliable heritability estimates, that were sensitive to alteration of the fixed effects. The MCMC method, which specifies a pedigree prior to heritability estimation, yielded results closer to those determined using the known pedigree. In populations of low average relationship, such as the Soay sheep population, determination of a reliable pedigree is more useful than indirect approaches that do not specify a pedigree.     

Social recognition and approach in the chick: lateralization and effect of visual experience

Chicks, Gallus gallus domesticus, tested monocularly on day 3 after hatching recognize familiar versus unfamiliar conspecifics and choose to approach one or other when they use the left eye, whereas they approach familiar and unfamiliar chicks at random when they use the right eye. In experiment 1 we investigated the effects of light exposure of embryos prior to hatching on this particular form of lateralization. Irrespective of whether they hatched from eggs incubated in the dark or from eggs exposed to light during the final days of incubation, chicks using the left eye had higher choice scores (meaning they chose to approach either a familiar or an unfamiliar chick) than chicks using the right eye or both eyes. Therefore, light experience prior to hatching did not influence the lateralization of individual recognition or choice behaviour, although it did affect latency to move out of, and time spent in, the centre of the runway. Experiment 2 showed that visual/social experience posthatching influences choice behaviour: chicks housed in a group in the light for 12 h on day 1 posthatching made a clear choice between familiar and unfamiliar chicks when tested on day 3, but chicks kept in a group in the dark on day 1 did not make a choice, instead alternating between the two stimuli. In experiment 3 we found that posthatching visual/social experience increased the choice scores of chicks using the right eye and thereby removed any lateralization of choice behaviour. The results suggest that visual experience of a social group is required before chicks using their right eye (and left hemisphere) will pay attention to the cues that distinguish one chick from another. Chicks using their left eye (and right hemisphere) recognize the difference between individuals without requiring visual experience with other chicks. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

Validation of Bayesian analysis of compartmental kinetic models in medical imaging

IntroductionKinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated.Materials and methodsThe closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach.Results and discussionPosteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P > 0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P < 0.0001).ConclusionsThe results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities.     

A bootstrap assessment of variability in pedigree reconstruction based on genetic markers

The problem of assessing the variability in pedigree reconstruction using DNA markers is considered for the special case of single generation samples with no parents present. Error in pedigree reconstruction is measured through a metric imposed on the space of partitions of the individuals into family groups. A confidence set can therefore be taken to be a neighborhood of a point estimate, analogous to the estimation of a parameter in Euclidean space. The coverage probability is estimated using bootstrap techniques. Although the distributional properties of the sample depend on the population genotype frequencies, these are in practice usually unknown. Confidence sets conditioned on a statistic approximately sufficient for these frequencies are compared with confidence sets obtained by substituting frequency estimates directly into the sampling distribution. In two simulation studies, the difference is found to be of some consequence.     

Statistical mechanics analysis of sparse data

Inferential structure determination uses Bayesian theory to combine experimental data with prior structural knowledge into a posterior probability distribution over protein conformational space. The posterior distribution encodes everything one can say objectively about the native structure in the light of the available data and additional prior assumptions and can be searched for structural representatives. Here an analogy is drawn between the posterior distribution and the canonical ensemble of statistical physics. A statistical mechanics analysis assesses the complexity of a structure calculation globally in terms of ensemble properties. Analogs of the free energy and density of states are introduced; partition functions evaluate the consistency of prior assumptions with data. Critical behavior is observed with dwindling restraint density, which impairs structure determination with too sparse data. However, prior distributions with improved realism ameliorate the situation by lowering the critical number of observations. An in-depth analysis of various experimentally accessible structural parameters and force field terms will facilitate a statistical approach to protein structure determination with sparse data that avoids bias as much as possible.     

Inbreeding, pedigree size, and the most recent common ancestor of humanity

How many generations ago did the common ancestor of all present-day individuals live, and how does inbreeding affect this estimate? The number of ancestors within family trees determines the timing of the most recent common ancestor of humanity. However, mating is often non-random and inbreeding is ubiquitous in natural populations. Rates of pedigree growth are found for multiple types of inbreeding. This data is then combined with models of global population structure to estimate biparental coalescence times. When pedigrees for regular systems of mating are constructed, the growth rates of inbred populations contain Fibonacci n-step constants. The timing of the most recent common ancestor depends on global population structure, the mean rate of pedigree growth, mean fitness, and current population size. Inbreeding reduces the number of ancestors in a pedigree, pushing back global common ancestry times. These results are consistent with the remarkable findings of previous studies: all humanity shares common ancestry in the recent past.     

Relationship type affects the reliability of dispersal distance estimated using pedigree inferences in partially sampled populations: A case study involving invasive American mink in Scotland

Estimating dispersal—a key parameter for population ecology and management—is notoriously difficult. The use of pedigree assignments, aided by likelihood‐based software, has become popular to estimate dispersal rate and distance. However, the partial sampling of populations may produce false assignments. Further, it is unknown how the accuracy of assignment is affected by the genealogical relationships of individuals and is reflected by software‐derived assignment probabilities. Inspired by a project managing invasive American mink (Neovison vison), we estimated individual dispersal distances using inferred pairwise relationships of culled individuals. Additionally, we simulated scenarios to investigate the accuracy of pairwise inferences. Estimates of dispersal distance varied greatly when derived from different inferred pairwise relationships, with mother–offspring relationship being the shortest (average = 21 km) and the most accurate. Pairs assigned as maternal half‐siblings were inaccurate, with 64%–97% falsely assigned, implying that estimates for these relationships in the wild population were unreliable. The false assignment rate was unrelated to the software‐derived assignment probabilities at high dispersal rates. Assignments were more accurate when the inferred parents were older and immigrants and when dispersal rates between subpopulations were low (1% and 2%). Using 30 instead of 15 loci increased pairwise reliability, but half‐sibling assignments were still inaccurate (>59% falsely assigned). The most reliable approach when using inferred pairwise relationships in polygamous species would be not to use half‐sibling relationship types. Our simulation approach provides guidance for the application of pedigree inferences under partial sampling and is applicable to other systems where pedigree assignments are used for ecological inference.     

The anatomy of choice: dopamine and decision-making

This paper considers goal-directed decision-making in terms of embodied or active inference. We associate bounded rationality with approximate Bayesian inference that optimizes a free energy bound on model evidence. Several constructs such as expected utility, exploration or novelty bonuses, softmax choice rules and optimism bias emerge as natural consequences of free energy minimization. Previous accounts of active inference have focused on predictive coding. In this paper, we consider variational Bayes as a scheme that the brain might use for approximate Bayesian inference. This scheme provides formal constraints on the computational anatomy of inference and action, which appear to be remarkably consistent with neuroanatomy. Active inference contextualizes optimal decision theory within embodied inference, where goals become prior beliefs. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (associated with softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution. Crucially, this sensitivity corresponds to the precision of beliefs about behaviour. The changes in precision during variational updates are remarkably reminiscent of empirical dopaminergic responses—and they may provide a new perspective on the role of dopamine in assimilating reward prediction errors to optimize decision-making.     

Stochastic modelling of prey depletion processes

The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this approach has the drawbacks of assuming continuous population variables and of being deterministic. We propose a general approach to stochastic modelling based on the concept of functional response for a prey depletion process with a constant number of predators. Our model could involve any kind of functional response, and permits a likelihood-based approach to statistical modelling and stable computation using matrix exponentials. To illustrate the method we use the Holling-Juliano functional response and compare the outcomes of our model with a deterministic counterpart considered by Schenk and Bacher [2002. Functional response of a generalist insect predator to one of its prey species in the field. Journal of Animal Ecology 71 (3), 524-531], who observed the depletion of Cassida rubiginosa due to its exclusive predator, Polistes dominulus. The predation was found to be Holling type III, reflecting the ability of the predator to regulate its prey. Our approach corroborates this result, but suggests that the prey depletion census should have been performed more often, and that predation features were significantly different between the two years for which data are available.     

Maximum likelihood inference implies a high, not a low, ancestral haploid chromosome number in Araceae, with a critique of the bias introduced by 'x'

Background and Aims

For 84 years, botanists have relied on calculating the highest common factor for series of haploid chromosome numbers to arrive at a so-called basic number, x. This was done without consistent (reproducible) reference to species relationships and frequencies of different numbers in a clade. Likelihood models that treat polyploidy, chromosome fusion and fission as events with particular probabilities now allow reconstruction of ancestral chromosome numbers in an explicit framework. We have used a modelling approach to reconstruct chromosome number change in the large monocot family Araceae and to test earlier hypotheses about basic numbers in the family.

Methods

Using a maximum likelihood approach and chromosome counts for 26 % of the 3300 species of Araceae and representative numbers for each of the other 13 families of Alismatales, polyploidization events and single chromosome changes were inferred on a genus-level phylogenetic tree for 113 of the 117 genera of Araceae.

Key Results

The previously inferred basic numbers x = 14 and x = 7 are rejected. Instead, maximum likelihood optimization revealed an ancestral haploid chromosome number of n = 16, Bayesian inference of n = 18. Chromosome fusion (loss) is the predominant inferred event, whereas polyploidization events occurred less frequently and mainly towards the tips of the tree.

Conclusions

The bias towards low basic numbers (x) introduced by the algebraic approach to inferring chromosome number changes, prevalent among botanists, may have contributed to an unrealistic picture of ancestral chromosome numbers in many plant clades. The availability of robust quantitative methods for reconstructing ancestral chromosome numbers on molecular phylogenetic trees (with or without branch length information), with confidence statistics, makes the calculation of x an obsolete approach, at least when applied to large clades.     

Factor analytic and reduced animal models for the investigation of additive genotype-by-environment interaction in outcrossing plant species with application to a Pinus radiata breeding programme

Key message

Modelling additive genotype-by-environment interaction is best achieved with the use of factor analytic models. With numerous environments and for outcrossing plant species, computation is facilitated using reduced animal models.

Abstract

The development of efficient plant breeding strategies requires a knowledge of the magnitude and structure of genotype-by-environment interaction. This information can be obtained from appropriate linear mixed model analyses of phenotypic data from multi-environment trials. The use of factor analytic models for genotype-by-environment effects is known to provide a reliable, parsimonious and holistic approach for obtaining estimates of genetic correlations between all pairs of trials. When breeding for outcrossing species the focus is on estimating additive genetic correlations and effects which is achieved by including pedigree information in the analysis. The use of factor analytic models in this setting may be computationally prohibitive when the number of environments is moderate to large. In this paper, we present an approach that uses an approximate reduced animal model to overcome the computational issues associated with factor analytic models for additive genotype-by-environment effects. The approach is illustrated using a Pinus radiata breeding dataset involving 77 trials, located in environments across New Zealand and south eastern Australia, and with pedigree information on 315,581 trees. Using this approach we demonstrate the existence of substantial additive genotype-by-environment interaction for the trait of stem diameter measured at breast height. This finding has potentially significant implications for both breeding and deployment strategies. Although our approach has been developed for forest tree breeding programmes, it is directly applicable for other outcrossing plant species, including sugarcane, maize and numerous horticultural crops.     

Computational annotation of plant metabolomics profiles via a novel network-assisted approach

Mass spectrometry (MS) has become the analytical method of choice in plant metabolomics. Nevertheless, metabolite annotation remains a major challenge and implies the integration of structural searches in compound libraries with biological knowledge inferred from metabolite regulation studies. Here we propose a novel integrative approach to process and exploit the rich structural information contained in in-source fragmentation patterns of high-resolution LC–MS profiles. In this approach, a correlation matrix is first calculated from individual mass features extracted by xcms processing. Mass feature co-regulation patterns corresponding to metabolite in-source fragmentation are then detected and assembled into compound spectra using the R package CAMERA and processed for in silico fragment-based structure elucidation using MetFrag. We validate the performance of this approach for the rapid annotation of the twelve largest compound spectra, including four O-acyl sugars and six 17-hydroxygeranyllinalool diterpene glycosides in metabolic profiles of insect-attacked Nicotiana attenuata leaves. Additionally, we demonstrate the power of refining MetFrag metabolite annotations based on co-regulation patterns between known and unknown compounds in the correlation matrix and proposed structural annotations on two previously un-characterized O-acyl sugars. In summary, this novel approach facilitates compound annotation from in-source fragmentation patterns using correlation between intensities of mass features of one or several metabolites. Additionally, this analysis provides further support that insect herbivory activates major metabolic reconfigurations in N. attenuata leaves.     

Optimal marker-assisted selection to increase the effective size of small populations

An approach to the optimal utilization of marker and pedigree information in minimizing the rates of inbreeding and genetic drift at the average locus of the genome (not just the marked loci) in a small diploid population is proposed, and its efficiency is investigated by stochastic simulations. The approach is based on estimating the expected pedigree of each chromosome by using marker and individual pedigree information and minimizing the average coancestry of selected chromosomes by quadratic integer programming. It is shown that the approach is much more effective and much less computer demanding in implementation than previous ones. For pigs with 10 offspring per mother genotyped for two markers (each with four alleles at equal initial frequency) per chromosome of 100 cM, the approach can increase the average effective size for the whole genome by approximately 40 and 55% if mating ratios (the number of females mated with a male) are 3 and 12, respectively, compared with the corresponding values obtained by optimizing between-family selection using pedigree information only. The efficiency of the marker-assisted selection method increases with increasing amount of marker information (number of markers per chromosome, heterozygosity per marker) and family size, but decreases with increasing genome size. For less prolific species, the approach is still effective if the mating ratio is large so that a high marker-assisted selection pressure on the rarer sex can be maintained.     

Bayesian species delimitation in West African forest geckos (Hemidactylus fasciatus)

Genealogical data are an important source of evidence for delimiting species, yet few statistical methods are available for calculating the probabilities associated with different species delimitations. Bayesian species delimitation uses reversible-jump Markov chain Monte Carlo (rjMCMC) in conjunction with a user-specified guide tree to estimate the posterior distribution for species delimitation models containing different numbers of species. We apply Bayesian species delimitation to investigate the speciation history of forest geckos (Hemidactylus fasciatus) from tropical West Africa using five nuclear loci (and mtDNA) for 51 specimens representing 10 populations. We find that species diversity in H. fasciatus is currently underestimated, and describe three new species to reflect the most conservative estimate for the number of species in this complex. We examine the impact of the guide tree, and the prior distributions on ancestral population sizes (θ) and root age (τ₀), on the posterior probabilities for species delimitation. Mis-specification of the guide tree or the prior distribution for θ can result in strong support for models containing more species. We describe a new statistic for summarizing the posterior distribution of species delimitation models, called speciation probabilities, which summarize the posterior support for each speciation event on the starting guide tree.     

DNA-based parentage verification in two Australian goat herds

This study aimed to evaluate a set of DNA markers for their effectiveness in parentage inference, to quantify the level of pedigree errors in Australian Angora and Cashmere goat herds using different pedigree recording methods, and to investigate genotype mismatches between parent and offspring. The 14 microsatellite markers evaluated in this study provided a high level of power (probability of exclusion, PE >99.70%) for parentage testing. The extent of PE depended on polymorphic information content (PIC) and number of alleles for each marker. The minimum number of MS markers essential for accurate determination of parentage was 12, when neither parent is known (PE1) and 10, when one parent is known (PE2). In both populations, the error rates of recorded sire and dam pedigree were significant, averaging around 12%. The error rates of sire and dam pedigree varied considerably between the two populations, reflecting management differences on the two properties. Of 14 MS markers, one locus, SRCRSP07, had null alleles present in the heterozygous state. This null allele was revealed by mismatches of genotypes of parent-offspring pairs. Highly significant deviation from Hardy–Weinberg Equilibrium and significant heterozygote deficiency was also observed at this locus.     

An autosomal genetic linkage map of the domestic cat,Felis silvestris catus

We report on the completion of an autosomal genetic linkage (GL) map of the domestic cat (Felis silvestris catus). Unlike two previous linkage maps of the cat constructed with a hybrid pedigree between the domestic cat and the Asian leopard cat, this map was generated entirely with domestic cats, using a large multi-generational pedigree (n = 256) maintained by the Nestlé Purina PetCare Company. Four hundred eighty-three simple tandem repeat (STR) loci have been assigned to linkage groups on the cat's 18 autosomes. A single linkage group spans each autosome. The length of the cat map, estimated at 4370 cM, is long relative to most reported mammalian maps. A high degree of concordance in marker order was observed between the third-generation map and the 1.5 Mb-resolution radiation hybrid (RH) map of the cat. Using the cat 1.9 × whole-genome sequence, we identified map coordinates for 85% of the loci in the cat assembly, with high concordance observed in marker order between the linkage map and the cat sequence assembly. The present version represents a marked improvement over previous cat linkage maps as it (i) nearly doubles the number of markers that were present in the second-generation linkage map in the cat, (ii) provides a linkage map generated in a domestic cat pedigree which will more accurately reflect recombination distances than previous maps generated in a hybrid pedigree, and (iii) provides single linkage groups spanning each autosome. Marker order was largely consistent between this and the previous maps, though the use of a hybrid pedigree in the earlier versions appears to have contributed to some suppression of recombination. The improved linkage map will provide an added resource for the mapping of phenotypic variation in the domestic cat and the use of this species as a model system for biological research.     

Analysis of founders and performance test effects on an autochthonous horse population through pedigree analysis: structure,genetic variability and inbreeding

The Maremmano is an autochthonous Italian horse breed, which probably descended from the native horses of the Etruscans (VI century B.C.); the Studbook was acknowledged in 1980, and it includes 12 368 horses born from that year up to 2015. The aim of this study was to evaluate the effect of the selection program on the genetic variability of the Maremmano population; the analysis was performed using both the ‘Endog v 4.8’ program available at http://webs.ucm.es/info/prodanim/html/JP_Web.htm and in-house software on official pedigree data. Four Reference Populations were considered, and the most important one was the population of the 12 368 Maremmano horses officially registered in the National Studbook. The pedigree completeness of this population was very good because it was more than 90% at the third parental generation and more than 70% at the fifth generation; the pedigree traced back to a maximum of 10.50 generations with an average of 3.30 complete generations and 5.70 equivalent complete generations. The average generation interval was 10.65±4.72 years, with stallions used for longer periods than mares. The intervals ranged from 10.15±4.45 (mother–daughter) to 10.99±4.93 (father–daughter). The effective number of founders (f_e) was 74 and the effective number of ancestors (f_a) was 30 so that the ratio f_e/f_a was 2.47. The founder genome equivalents (f_g) was 13.72 with a ratio f_g/f_e equal to 0.18. The mean of the genetic conservation index was 5.55±3.37, and it ranged from 0.81 to 21.32. The average inbreeding coefficient was 2.94%, with an increase of 0.1%/year, and the average relatedness coefficient was 5.52%. The effective population size (N_e) computed by an individual increase in inbreeding was 68.1±13.00; the N_e on equivalent generations was 42.00, and this value slightly increased to 42.20 when computed by Log regression on equivalent generations. The analysis confirmed the presence of seven traditional male lines. The percentage of Thoroughbred blood in the foals born in 2015 was 20.30% and has increased 0.21%/year since 1980; in particular, it increased more than twice (0.51%/year) until 1993 and afterwards slightly fluctuated. The pedigree analysis confirmed the completeness of genealogical information and the traditional importance that breeders gave to the male lines; although the genetic diversity of Maremmano seemed to be not endangered by the selection program, some effects on the population structure were found and a more scientific approach to genetic conservation should be incorporated in the selection plans.     

Multiple marker mapping of quantitative trait loci in an outbred pedigree of loblolly pine

A multiple marker least squares approach is presented for the analysis of a single three-generation pedigree for quantitative trait locus (QTL) characterisation. It is an extension of the approach by Haley et?al. (1994) to the situation where grandparents cannot be assumed to be homozygous at QTLs for the trait of interest. The method is applied to the analysis of wood specific gravity in loblolly pine (Pinus taeda L.). Within a similar framework, a series of preliminary analyses are carried out, followed by a more detailed search of the genome for one or more QTLs. The preliminary analyses provide information about whether the contribution from each linkage group appears to be polygenic, localised to a small region (e.g. a single QTL) or oligogenic (i.e. several QTLs). Significance levels are obtained using a permutation test that uses the observed phenotypes and marker genotypes. The conclusion of these analyses is that in this pedigree single QTLs with very large effect on wood specific gravity do not appear to be segregating, although there is evidence for QTLs with small effect. Finally, in order to assess the potential power of this pedigree, we simulated QTLs within the framework of the actual marker data. As expected, QTL effects would need to be large to be reliably detected in this study, and the power to detect QTLs varies at different positions in the genome depending on the level of information in the local markers.     

N-Demethylation of N-methyl alkaloids with ferrocene

Under Polonovski-type conditions, ferrocene has been found to be a convenient and efficient catalyst for the N-demethylation of a number of N-methyl alkaloids such as opiates and tropanes. By judicious choice of solvent, good yields have been obtained for dextromethorphan, codeine methyl ether, and thebaine. The current methodology is also successful for the N-demethylation of morphine, oripavine, and tropane alkaloids, producing the corresponding N-nor compounds in reasonable yields. Key pharmaceutical intermediates such oxycodone and oxymorphone are also readily N-demethylated using this approach.     

Estimation of genealogical coancestry in plant species using a pedigree reconstruction algorithm and application to an oil palm breeding population

Key message

Explicit pedigree reconstruction by simulated annealing gave reliable estimates of genealogical coancestry in plant species, especially when selfing rate was lower than 0.6, using a realistic number of markers. Genealogical coancestry information is crucial in plant breeding to estimate genetic parameters and breeding values. The approach of Fernández and Toro (Mol Ecol 15:1657–1667, 2006) to estimate genealogical coancestries from molecular data through pedigree reconstruction was limited to species with separate sexes. In this study it was extended to plants, allowing hermaphroditism and monoecy, with possible selfing. Moreover, some improvements were made to take previous knowledge on the population demographic history into account. The new method was validated using simulated and real datasets. Simulations showed that accuracy of estimates was high with 30 microsatellites, with the best results obtained for selfing rates below 0.6. In these conditions, the root mean square error (RMSE) between the true and estimated genealogical coancestry was small (<0.07), although the number of ancestors was overestimated and the selfing rate could be biased. Simulations also showed that linkage disequilibrium between markers and departure from the Hardy–Weinberg equilibrium in the founder population did not affect the efficiency of the method. Real oil palm data confirmed the simulation results, with a high correlation between the true and estimated genealogical coancestry (>0.9) and a low RMSE (<0.08) using 38 markers. The method was applied to the Deli oil palm population for which pedigree data were scarce. The estimated genealogical coancestries were highly correlated (>0.9) with the molecular coancestries using 100 markers. Reconstructed pedigrees were used to estimate effective population sizes. In conclusion, this method gave reliable genealogical coancestry estimates. The strategy was implemented in the software MOLCOANC 3.0.