Predicting and correcting bias caused by measurement error in line transect sampling using multiplicative error models

Line transect sampling is one of the most widely used methods for animal abundance assessment. Standard estimation methods assume certain detection on the transect, no animal movement, and no measurement errors. Failure of the assumptions can cause substantial bias. In this work, the effect of error measurement on line transect estimators is investigated. Based on considerations of the process generating the errors, a multiplicative error model is presented and a simple way of correcting estimates based on knowledge of the error distribution is proposed. Using beta models for the error distribution, the effect of errors and of the proposed correction is assessed by simulation. Adequate confidence intervals for the corrected estimates are obtained using a bootstrap variance estimate for the correction and the delta method. As noted by Chen (1998, Biometrics 54, 899-908), even unbiased estimators of the distances might lead to biased density estimators, depending on the actual error distribution. In contrast with the findings of Chen, who used an additive model, unbiased estimation of distances, given a multiplicative model, lead to overestimation of density. Some error distributions result in observed distance distributions that make efficient estimation impossible, by removing the shoulder present in the original detection function. This indicates the need to improve field methods to reduce measurement error. An application of the new methods to a real data set is presented.     

High variation in developmental instability under non-normal developmental error: a Bayesian perspective

The developmental mechanisms behind developmental instability (DI) are only poorly understood. Nevertheless, fluctuating asymmetry (FA) is often used a surrogate for DI. Based on statistical arguments it is often assumed that individual levels of FA are only weakly associated with the underlying DI. Patterns in FA therefore need to be interpreted with caution, and should ideally be transformed into patterns in DI. In order to be able to achieve that, assumptions about the distribution of developmental errors must be made. Current models assume that errors during development are additive and independent such that they yield a normal distribution. The observation that the distribution of FA is often leptokurtic has been interpreted as evidence for between-individual variation in DI. This approach has led to unrealistically high estimates of between-individual variation in DI, and potentially incorrect interpretations of patterns in FA, especially at the individual level. Recently, it has been suggested that the high estimates of variation in DI may be biased upward because either developmental errors are log-normal or gamma distributed and/or low measurement resolution of FA. A proper estimation of the amount (and shape) of heterogeneity in DI is crucial for the interpretation of patterns in FA and their transformation into patterns in DI. Yet, incorrect model assumptions may render misleading inferences. We therefore develop a statistical model to evaluate the sensitivity of results under the normal error model against the two alternative distributions as well as to investigate the importance of low measurement resolution. An analysis of simulated and empirical data sets indicated that bias due to misspecification of the developmental error distribution can be substantial, yet, did not appear to reduce estimates of variation in DI in empirical data sets to a large extent. Effects of low measurement resolution were neglectable. The importance of these results are discussed in the context of the interpretation of patterns in FA.     

The statistics of detecting positional fluctuating asymmetry

The detection of asymmetry can be difficult because the signals indicating right–left differences are frequently weak. When bilaterally symmetric organisms can be further inspected for positional asymmetry (differences between body sides in the placement of meristic traits) anterior–posterior allocation may provide additional evidence for fluctuating asymmetry. Statistical power comparisons were made for indices used to measure fluctuating (FA) and positional fluctuating asymmetry (PFA) in meristic traits. Monte Carlo simulations of developmental and random processes were used to generate null and alternative distributions of a hypothetical meristic trait (such as bristle counts). The counts were used to calculate the corresponding distributions of six indices used to detect fluctuating and positional fluctuating asymmetry. Power comparisons show that there is no single best index. If positional deviations are strong relative to bilateral errors then pfa1 is generally the most powerful, while fa, the G-statistic, and in some instances the procrustes-distance measure do best when there is little positional deviation relative to side-to-side deviations. The decision on what index is best is thus influenced by knowledge of the likely sources of error. As a consequence, all three indices (fa, G and pfa1) should be explored when little a priori knowledge is available. © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 77 , 491–498.     

Karyology of some Brazilian species of Alismataceae

The family Alismataceae ( sensu Cronquist) comprises 11 genera and 75 species of aquatic and semiaquatic herbs. In Brazil, only the two most speciose genera, Echinodorus Rich. ex Engelm. and Sagittaria L., are present. The chromosome number 2 n  = 22 is common to all species. We present karyotypes for eight species, together with their asymmetry index (TF%) and total chromatin length (TCL). All karyotypes have high karyotypic asymmetry and TCL, due to their large and mostly acrocentric chromosomes. The chromosomal evolution of the Alismatidae group is discussed.  © 2003 The Linnean Society of London, Botanical Journal of the Linnean Society , 2003, 143 , 159−164.     

Geometric morphometrics, neural networks and diagnosis of sibling Taterillus species (Rodentia, Gerbillinae)

The lack of diagnostic traits in sibling species means that great quantities of biogeographical and ecological data held in museum collections cannot be utilized effectively, leading to underestimates of biodiversity. In this study we applied neural networks (NN) and canonical variates analyses (CVA) to landmark measurements on the skulls of the West African species Taterillus arenarius , T. petteri , T. gracilis and T. pygargus in an attempt to discriminate species previously identified unambiguously from their karyotypes. Among suggested differences, the relationship between inflation of the tympanic bullae and lower population density is discussed. Cross-validated classification rates did not exceed 73%. Two hypotheses are proposed to explain such high phenotypic similarity: morphological plasticity limited by environmental constraints and the possibility that speciation has been too recent to allow significant morphological divergence.  © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 77 , 319−327.     

Statistical methods for estimating doubling time in in vitro cell growth

Summary Doubling time has been widely used to represent the growth pattern of cells. A traditional method for finding the doubling time is to apply gray-scaled cells, where the logarithmic transformed scale is used. As an alternative statistical method, the log-linear model was recently proposed, for which actual cell numbers are used instead of the transformed gray-scaled cells. In this paper, I extend the log-linear model and propose the extended log-linear model. This model is designed for extra-Poisson variation, where the log-linear model produces the less appropriate estimate of the doubling time. Moreover, I compare statistical properties of the gray-scaled method, the log-linear model, and the extended log-linear model. For this purpose, I perform a Monte Carlo simulation study with three data-generating models: the additive error model, the multiplicative error model, and the overdispersed Poisson model. From the simulation study, I found that the gray-scaled method highly depends on the normality assumption of the gray-scaled cells; hence, this method is appropriate when the error model is multiplicative with the log-normally distributed errors. However, it is less efficient for other types of error distributions, especially when the error model is additive or the errors follow the Poisson distribution. The estimated standard error for the doubling time is not accurate in this case. The log-linear model was found to be efficient when the errors follow the Poisson distribution or nearly Poisson distribution. The efficiency of the log-linear model was decreased accordingly as the overdispersion increased, compared to the extended log-linear model. When the error model is additive or multiplicative with Gamma-distributed errors, the log-linear model is more efficient than the gray-scaled method. The extended log-linear model performs well overall for all three data-generating models. The loss of efficiency of the extended log-linear model is observed only when the error model is multiplicative with log-normally distributed errors, where the gray-scaled method is appropriate. However, the extended log-linear model is more efficient than the log-linear model in this case.     

Geometric morphometrics as a tool for understanding Dactylorhiza (Orchidaceae) diversity in European Russia

Geometric morphometric techniques were employed to assess the diversity of lip shapes (305 samples from 83 populations) in flowers of European Russian Dactylorhiza (Orchidaceae: Orchidinae). We found significant agreement between the results from geometric morphometrics, classic morphometrics and the distribution of certain nuclear DNA markers. The lip shapes from Arctic Dactylorhiza samples occupied an intermediate position between D. maculata and D. fuchsii samples from Central Russia, supporting a hybrid origin of 'northern tetraploids'. Lip shapes of the taxonomically controversial allotetraploid D. baltica were found to form a distinct group, with members having definite relationships with diploid D. incarnata samples from the same localities, indicating either their local origin or introgression with D. incarnata . In addition to demonstrating the value of geometric morphometric methods in studies of plant taxonomy and hybridization, we suggest future applications designed to explore pollinator-driven directional selection, developmental constraints and fluctuating asymmetry.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 85 , 1–12.     

Reliability of reliability coefficients in the estimation of asymmetry

Although promising to provide insight into the interaction between genotype and environment, investigations into fluctuating asymmetry suffer from a lack of standardization in the reporting of measurement error. In the present paper we show, using both anthropometric and odonto-metric data, that the use of the reliability coefficient calculated for a bilateral measurement provides no indication of the reliability of the corresponding asymmetry estimate, because reliability of asymmetry depends on the relationship between measurement error and the difference between sides. Thus, we suggest that future investigations either provide reliability coefficients for asymmetry estimates specifically, or use methods that account for measurement error. © 1995 Wiley-Liss, Inc.     

Assemblage and population-level consequences of forest fragmentation on bilateral asymmetry in tropical montane birds

Habitat fragmentation has the potential to influence the development and thus the phenotype of organisms. The asymmetry of bilateral traits may be indicative of the extent to which developmental stability is compromised by the stressful conditions underlying fragmentation. Using an assemblage- and population-level approach, we explored asymmetry differences in tarsus and outermost tail feathers of birds inhabiting fragmented landscapes in the tropical Andes of Colombia. More than 2500 individuals of 185 species were mist-netted at nine forest sites representing continuous forest (> 1000 ha), medium- (70–110 ha), and small-sized (8–20 ha) fragments. Feathers showed true fluctuating asymmetry (FA), whereas tarsus presented a mixture of FA and directional asymmetry. Overall, asymmetry was lowest in continuous forest, and highest in small and medium fragments. These patterns remained unchanged when directionality and differences in species composition, abundance, and foraging tactics were considered. The population-level analyses showed a general trend of increased asymmetry variation in fragments, yet the responses were not always in the same direction. Increased asymmetry may represent an outcome of processes that contribute to the persistence of species in changing environments, and to the generation of phenotypic innovation, which suggests individual adjustments of development to deal with stress. This calls into question the deliberated application of FA as a biomonitoring tool for conservation.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 92 , 119–133.     

Effects of the mixture of avermectin and imidacloprid on mortality and developmental stability of Copera annulata (Odonata: Zygoptera) larvae

The present study explored the effects of mixture of avermectin and imidacloprid on the level of fluctuating asymmetry (FA) and mortality of Copera annulata larvae. The results showed that the mortality of larval damselflies treated with different concentrations of insecticide did not differ significantly. However, we found that the levels of FA of two traits were significantly different with different treatments but the others did not show any differences. Explicitly, FA of two traits increased with increasing pesticide concentration. There was a significantly negative relationship between first femur length and the absolute difference between its right and left sides. There was no relationship with respect to the absolute difference between the right and left sides of all traits and their body size. FA was not associated with mortality. Our results emphasized that insecticide had potential effects on bilaterally symmetrical traits of damselfly larvae, although they were no longer treated with insecticide during the last rearing.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society , 2009, 96 , 44–50.     

Measurement errors in line transect surveys where detectability varies with distance and size

When using bivariate line transect methods to estimate the biomass density of a tightly clustered biological population, it is generally assumed that both the perpendicular distance from the trackline to the cluster and the cluster size, or biomass, are measured without error. This is unlikely to be the case in practice. In this article, assuming additive mean zero errors in distance and multiplicative errors in size, we develop an estimator of density that corrects for these errors. We use the method of moments for the case of gamma cluster size, randomly placed transect lines, and the generalized exponential detection function. We derive results that show that it may not be necessary to correct for errors in distance or size when the distance and size estimates are not biased. When the size estimates are biased, the biomass density estimate has approximately the same bias as the size estimates. The work is illustrated in the context of annual aerial surveys for juvenile southern bluefin tuna in the Great Australian Bight.     

Effects of habitat heterogeneity and local adaptation on the body condition of a forest passerine at the edge of its distributional range

We studied fluctuating asymmetry and feather growth rates as indicators of fitness of blackcaps ( Sylvia atricapilla ) breeding at the border of their distribution range in the Iberian Peninsula. Iberian blackcaps increase their abundance with increasing rainfall and ground cover of brambles. In border habitats, they are sedentary and morphologically different from migrants, suggesting that they could be adapted to peripheral conditions. We tested whether juvenile body condition depends on (1) distance from the centre of the range, (2) mean precipitation or (3) bramble cover. Controlling for environmental variation, we tested for differences between migratory and sedentary populations. Body condition varied across the Iberian gradient in parallel with changes in precipitation. Controlling for this effect, sedentary populations were in better body condition than migratory populations. Our results support the idea that environmental heterogeneity causes fitness to fluctuate across species' ranges, and also that local adaptation may mean that peripheral populations are more than a 'tail end' of the species.  © 2003 The Linnean Society of London . Biological Journal of the Linnean Society , 2003, 78 , 479–488.     

Sexual selection for symmetrical male medflies (Diptera: Tephritidae) confirmed in the field

The role of fluctuating asymmetry as an indicator of fitness to females in mate choice remains controversial. Previous studies indicated that male medflies with symmetrical supra-fronto-orbital (SFO) bristles achieve relatively high mating success under laboratory conditions. Here we present data from field cage studies of wild collected medflies in Guatemala and Crete, which reveal the same association between fluctuating asymmetry in SFO bristle length and mating success as that seen in the laboratory. The experiments in Crete included males that were missing one or both of their bristles. A comparison of mating success between the three groups indicated that the mere presence of bristles did not exert a major influence. Analysis of attempted courtships suggests that the association between male mating success and FA in bristle length appears to be generated as a result of females being more likely to enter into courtships with symmetrical males, rather than through a rejection of asymmetrical males during or after it. This raises the possibility that the primary stimulus that makes a symmetrical male attractive is acting at too great a distance to depend on symmetry itself. Alternatives might include superior pheromone emissions or the occupation of a prime location within the lek.  © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 81 , 347–355.     

Condition-dependent asymmetry is fluctuating asymmetry

Asymmetry has been demonstrated to play a role in signalling systems such as sexual selection and pollination, with receivers showing a preference for symmetrical signals. Large signals often have the smallest degree of asymmetry, a finding that is consistent with signal asymmetry being condition-dependent. The kind of asymmetry displayed by signals was supposed or shown to be fluctuating asymmetry, and signals revealing individual differences in the ability to stabilize developmental processes, despite a hostile developmental environment, was supposed to be the basis for the preference for symmetric signals. Recently, it has been suggested that condition-dependent signals display antisymmetry rather than fluctuating asymmetry, based on analyses of the relationship between asymmetry and mean length of the left and the right character in a few published graphs of absolute asymmetry of signals. Here I demonstrate on the basis of a much larger number of data sets, including those previously published, that the previous results are biased because of the methods used for the analyses, and that characters with condition-dependent asymmetry show fluctuating asymmetry rather than antisymmetry. In particular, frequency distributions of signed left-minus-right character values display leptokurtosis, as predicted if asymmetry distributions reflected individual differences in developmental precision, rather than platykurtosis. Platykurtosis is predicted if the traits are antisymmetric. The preponderance of leptokurtic distributions is consistent with recent modelling showing that inherent differences in the ability of individuals to control developmental processes invariably leads to leptokurtic distributions of signed left-minus-right character values.     

Population genetics of Dioon edule Lindl. (Zamiaceae, Cycadales): biogeographical and evolutionary implications

Dioon edule Lindl. (Zamiaceae) is a cycad endemic to Mexico, that occurs as one species D. edule and the geographical variety D. edule var. angustifolium (Miq.) Miq. Dioon edule has a north to south distribution in eastern Mexico. In this study, we analysed 14 allozymic loci in eight populations of D. edule from its total distribution range by sampling all known populations. Patterns of diversity and genetic variability, within and among populations, were obtained. The mean number of alleles per locus ( A ) was 1.44 and the percentage of polymorphic loci was relatively high ( P  = 54.78). The mean observed ( H _O ) and expected heterozygosity ( H _E ) were 0.27 and 0.24, respectively. F -statistics revealed an excess of heterozygous genotypes, locally and globally ( F  = −0.17 and f  = −0.27, respectively). The genetic variation explained by differences among populations was only 7.5%. We also detected a negative relationship between genetic diversity and latitude. On average, the gene flow between population pairs was relatively high ( Nm  = 2.98); furthermore, gene flow between population pairs was significantly correlated with geographical distances ( r  = −0.38, P  = 0.025). Therefore, patterns of genetic diversity in D. edule appear to be associated with the post-Pleistocene spread of the species, from its southerly (origin) to its northerly range (derived populations, including its central distribution). The biogeographical and evolutionary aspects of the results of this study are discussed. We recognize Dioon angustifolium Miq. for the northernmost disjunct populations.  © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 80 , 457–467     

Asymmetry patterns across the distribution range: does the species matter?

An important question in evolutionary ecology is whether different populations across a species range, from core to periphery, experience different levels of stress. The estimation of developmental instability has been proposed as a useful tool for quantifying the degree of environmental and genetic stress that individuals experience during their development. Fluctuating asymmetry, the unsigned difference between the two sides of a bilaterally symmetrical trait, has been suggested to reflect the levels of developmental instability in a population. As such, it has been proposed as a useful tool for estimating changes in developmental instability and in stress response in populations across a range of environmental conditions. Recent studies focusing mostly on birds have detected increasing fluctuating asymmetry from core to periphery across the distribution range, suggesting that peripheral populations may experience higher levels of environmental and/or genetic stress. Most of these comparisons were done for single taxa across a single gradient. However, different species are predicted to respond differently to environmental shifts across the range. We compared asymmetry patterns in wing morphology in populations of two Euchloe butterfly species across their opposing ranges in Israel. Contrary to the patterns observed in birds across the same gradient, bilateral asymmetry did not increase or shift towards the periphery in either of the butterfly species. If fluctuating asymmetry in these traits reflects levels of stress, these results may partly reflect the fact that the range of these two butterfly species is limited by the distribution of their host plant, rather than by abiotic environmental variables. In addition, developing pierids can diapause during harsh seasons and can persist in resource‐rich patches, thus minimizing the environmental stress perceived by developing individuals. We conclude that accounting for differences in species’ life histories and range‐limiting factors is necessary in order to better predict patterns of developmental instability across spatial and environmental gradients. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 81 , 313–324.     

Simultaneous analysis of basal Hymenoptera (Insecta): introducing robust-choice sensitivity analysis

Molecular characters are analysed on their own and in combination with morphological data to examine the phylogenetic relationships of the basal lineages of Hymenoptera ('Symphyta'). This study covers 47 sawfly genera and nine apocritan families and includes molecular sequences from five genes − 12S, 16S, 18S and 28S ribosomal genes and cytochrome oxidase 1 − as well as 343 morphological characters. A robust-choice sensitivity analysis is performed with the data. First, the simultaneous analysis is repeated three times, each time employing a different step matrix for weighting the transformations of the molecular characters. Then, the results of all three simultaneous analyses are summarized in a strict consensus in order to avoid basing the conclusions on a narrow set of assumptions. This methodology is discussed in the paper. The relationships among superfamilies largely confirm previous hypotheses, being (Xyeloidea (Tenthredinoidea s.l. (Pamphilioidea (Cephoidea (Siricoidea (Xiphydrioidea (Orussoidea Apocrita))))))), where Siricoidea is understood as Siricidae+Anaxyelidae. However, the relationships within Tenthredinoidea s.s. proposed here are novel: ({Argidae Pergidae}[ Athalia {(Diprionidae Cimbicidae) Tenthredinidae minus Athalia }]).  © 2003 The Linnean Society of London . Biological Journal of the Linnean Society , 2003, 79, 245–275.