Complex clines: the predictivity of complicated patterns of geographic variation portrayed by multivariate analysis

The stability of complex patterns of geographic variation was investigated by assessing the congruence between multivariate ordinations derived from randomly chosen real characters. Two series of populations were analysed representing two situations with complex patterns of geographic variation. The first, a ‘Eurasian’ series of populations, showed a strongly structured hierarchical pattern, the second, an ‘eastern’ series of populations, showed a more subtle complex pattern of smooth clines and steps. The characters were selected from a total of 81 (Eurasian) or 61 (eastern) within-population independent characters from six different systems. The congruence between ordinations of the geographical populations was measured by the rotational fit statistic, R². Three procedures were used to compare ordinations based on from two to up to 80 characters randomly chosen to give: A, completely independent character sets; B, subsets compared to the total set; and C, potentially overlapping sets. All three procedures showed that congruence between the ordinations was asymptotic in relation to character number. This relationship was described by one of two mathematical models (procedure B did not result in a hyperbolic model as found with simple patterns of geographic variation). Generally speaking, once a sufficient number of characters are used, the complex patterns of geographic variation are stable, reliable and predictive and not substantially influenced by character choice. The strongly structured hierarchical pattern required 15 or so characters to achieve reliability whilst the more subtle patterns required 20 or so characters. However, the addition of further characters does improve reliability in both cases. The greater percentage of variance portrayed by three-dimensional ordinations compared to two-dimensional ordinations is achieved at the cost of lower congruence when a sufficient number of characters are used. If case studies of geographic variation were to adopt these procedures (preferably using completely independent character sets; procedure A) the reliability of their results would be indicated).     

The effect of insignificant characters on the multivariate analysis of simple patterns of geographic variation

The multivariate analysis of a set of significant characters portrays a simple geographic cline which is evident even when very few characters are used. The effect of adding insignificant characters to the set of significant characters is studied, as is the effect of replacing significant characters by insignificant characters. The former (addition) causes only a slight decline in congruence between patterns of geographic variation but the latter (replacement) causes a substantial decline in congruence. The congruence between patterns of geographic variation obtained by multivariate analysis of independent character sets is plotted against character number and gives an S-shaped relationship when insignificant or significant plus insignificant characters are used. This is distinct from the convex asymptotic curve obtained when only significant characters are used. In spite of the reduction in congruence caused by the use of insignificant characters, multivariate analysis of insignificant characters consistently revealed the 'same' geographic pattern (i.e. 'cline') as the set of significant characters. However, it required 10 times as many insignificant characters to achieve this.     

Congruence between independent character systems across a hybrid zone: patterns in geographic space

The hybrid zone between eastern and western grass snakes, which has been independently hypothesized to be due to secondary contact, is investigated using univariate and multivariate analysis of a large number of independent, quantitative characters. Investigation of the patterns of geographic variation show that 5 out of 6 character systems show a congruent pattern of “stepped clinal” change across the zone. Insofar as this case is concerned, secondary contact ‘hybrid’ zones are associated with concordant changes in many character systems and “speciation” involves the origin of a large number of small differences in most character systems rather than the major reorganisation of a single system.     

Comparing patterns of geographic variation in cave crickets by combining geostatistic methods and Mantel tests

Geographic variation patterns of biological characters and environmental variables are compared by using a procedure employing multivariate analyses, production of contour maps by the kriging method with enclosed validation of estimates, and Mantel tests to assess the significance of comparisons. As biological material we chose a sample of Dolichopoda cave crickets populations from Central-Southern Italy. The kriging technique provides estimates of the interpolation error for each true and estimated point. This profitable feature offers the opportunity to use, with ascertained levels of confidence, the estimated z -scores for further analysis and to compare data collected within the same area, but not exactly coincident in location or number. In such a way, we were able to use for subsequent comparisons by means of Mantel tests the maximum number of data points for all data sets, which originally differed in sampling sites. The interpretation of the contour maps and their statistical comparison suggested that allozymes and epiphallus shape data sets follow the phylogenetic pathways within the Dolichopoda populations, whereas variation in leg elongation is almost entirely under the control of an environmental gradient, synthetically described by the cave temperature.     

Late Upper Pleistocene human peopling of the Far East: multivariate analysis and geographic patterns of variation

This research deals with the History of the human peopling of Far East Asia during the Late Upper Pleistocene. It brings some new answers to the question of modern human migrations in the Far East. This study is based on morphometric analysis of 45 fossil crania. The results of the multivariate analyses, combined with the recognition of geographic patterns of variation, separate the fossils into three morphological classes. These three clusters enable us to propose a likely scenario for the human peopling of the Far East from about 67 000 years ago. To cite this article: F. Demeter et al., C. R. Palevol 2 (2003).     

Examining determinants of geographic variation in colorectal cancer mortality in North Carolina: A spatial analysis approach

PurposeA recent study using national data from 2000 to 2009 identified colorectal cancer (CRC) mortality “hotspots” in 11 counties of North Carolina (NC). In this study, we used more recent, state-specific data to investigate the county-level determinants of geographic variation in NC through a geospatial analytic approach.MethodUsing NC CRC mortality data from 2003 to 2013, we first conducted clustering analysis to confirm spatial dependence. Spatial economic models were then used to incorporate spatial structure to estimate the association between determinants and CRC mortality. We included county-level data on socio-demographic characteristics, access and quality of healthcare, behavioral risk factors (CRC screening, obesity, and cigarette smoking), and urbanicity. Due to correlation among screening, obesity and quality of healthcare, we combined these factors to form a cumulative risk group variable in the analysis.ResultsWe confirmed the existence of spatial dependence and identified clusters of elevated CRC mortality rates in NC counties. Using a spatial lag model, we found significant interaction effect between CRC risk groups and socioeconomic deprivation. Higher CRC mortality rates were also associated with rural counties with large towns compared to urban counties.ConclusionOur findings depicted a spatial diffusion process of CRC mortality rates across NC counties, demonstrated intertwined effects between SES deprivation and behavioral risks in shaping CRC mortality at area-level, and identified counties with high CRC mortality that were also deprived in multiple factors. These results suggest interventions to reduce geographic variation in CRC mortality should develop multifaceted strategies and work through shared resources in neighboring areas.     

Patterns of morphological and geographic variation in trophic bill morphs of the African finch Pyrenestes

Intra- and inter-population variability was studied in three species of tropical African estrildid finches comprising the genus Pyrenestes. Eleven characters were measured on P. ostrinus captured on a study area in Cameroon. Most of these same characters were also measured on museum specimens of this species and P. saguineus and P. minor. Data were analysed using univariate and multivariate statistical methods in order to characterize variation within and between populations and species.
Variation in all three species of Pyrenestes is greatest in bill size, resulting from an exceptional non-sex-linked polymorphism. Bill size differences between morphs are as high as between congeneric species, with extremely large coefficients of variation, while other body characters show comparatively little variation. Sexual dimorphisms and differences in size due to age occur, but contribute little to overall size variation. Distributions of bill characters in each age and sex class are bimodal or greatly skewed, and in some geographical regions tend to be trimodal. Distributions of other body characters tend not to be significantly different from normal. Bill morphs differ in both shape and size and may be separated using principal component analysis. Static allometries of bill morphs differ significantly: relative to body size, bill size increases more rapidly in the large morph. Bill size and shape also vary geographically. The three species differ in mean size but show much overlap. Bill size is negatively correlated with total annual rainfall. In regions characterized by ecotonal transition zones between forest and savanna, tentative evidence suggests that a third, yet larger bill mode occurs. This third mode apparently results from the presence of a distinct larger species of hard-seeded sedge found only in these regions. The taxonomic implications of the polymorphism are discussed.     

Physiological variation in insects: large-scale patterns and their implications

In this paper we demonstrate how broad scale comparative physiology has an important role to play in informing a variety of assumptions made in macroecology. We do so by examining large-scale geographic variation in insect development, thermal tolerance and metabolic rate. From these studies, and those from the literature on insect water loss and thermoregulation, we show that there is often a bias to the geographic extent of available empirical data. Studies of cold hardiness are most usually undertaken at high latitudes, while investigations of upper thermal tolerances and water loss are most common in warm arid regions. Likewise, we demonstrate that much variation in insect physiological tolerances is partitioned at higher taxonomic levels, which has important implications for comparative physiology. Intriguingly, data on the full range of variables we review are available for only three species. We also show that, despite its importance, body size is regularly reported in only some kinds of investigations (metabolic rate, water loss rate), whereas in others (upper lethal temperature, cold hardiness, development) this variable is often ignored. In short, although large-scale comparative physiology can contribute considerable understanding to both physiology and ecology, there is much that remains to be done.     

Geographic variation in the garter snakes (Thamnophis sirtalis) of the north-central United States, a multivariate study

A study of geographic variation in three subspecies of garter snake (Thamnophis sirtalis sirtalis, T. s. parietalis, T. s. semifasciata) in the north-central United States indicates patterns of irregular non-clinal microgeographic variation for 40 characters of coloration, scalation, and internal anatomy. Multivariate analyses show that geographically close populations are not always phenetically close and that overall differentiation of the phenotype is greater in males than in females. Univariate and multivariate studies indicate that T. s. semifasciata Cope 1892, restricted to the Chicago area, is not uniform within its small range and that it has no constant distinguishing features: it is shown to be taxonomically invalid.     

Corresponding patterns of geographic variation among populations ofSilene latifolia (=S. alba =S. pratensis) (Caryophyllaceae)

Morphological and biochemical data were analysed from 30 greenhouse-grown populations of EuropeanSilene latifolia. Six separate character sets (flavones, seed, pollen, capsules, male and female flower morphology) were used in the analyses. There was broad-scale congruence between trends of geographic variation in most character sets, with the populations being assigned to western (or southern and western) and eastern clusters. The eastern and western clusters abut along a transition zone that runs roughly from Belgium to the northern Balkans; this zone represents a region of relatively rapid change and contains populations intermediate between the eastern and western clusters. Variation in flower morphology was weak and discordant with variation in the other character sets. The origin and maintenance of the variation pattern is discussed in terms of migrational history and hybrid zones.     

Regional isolation in the Balkan region: an analysis of craniofacial variation

Biological variation is investigated among contemporary Croatians, Bosnians, American whites, and other multitemporal Balkan populations (World War II Croatians, Macedonians, and Greeks) via multivariate statistics and distance measures of the craniofacial complex. This study demonstrates that there is considerable variation among groups of European ancestry. Bosnians and Croatians who are thought to be relatively homogenous and historically to originate from the same Slav ancestry show local variations. While environmental plasticity has been used to explain cranial changes among human groups, it does not adequately explain the variation observed between Bosnians and Croatians. It is an oversimplification to exclusively attribute the vast range of variability observed among local as well as geographic populations to environmental adaptations.     

Craniometrical variation among South American prehistoric populations: climatic, altitudinal, chronological, and geographic contributions

The independent contributions of climate, altitude, chronology, and geographic location of archeological sites to craniometrical variation are analyzed in a sample of 1,119 skulls from South America. Geographic location is responsible for the highest proportion of craniometrical variation, followed by climate and altitude. It is concluded that geographic isolation has partially prevented gene flow from counterbalancing craniometrical microdifferentiation produced by founder effect.     

The effect of seed traits on geographic variation in body size and sexual size dimorphism of the seed‐feeding beetle Acanthoscelides macrophthalmus

Explaining large‐scale patterns of variation in body size has been considered a central question in ecology and evolutionary biology because several life‐history traits are directly linked to body size. For ectothermic organisms, little is known about what processes influence geographic variation in body size. Changes in body size and sexual size dimorphism (SSD) have been associated with environmental variables, particularly for Bruchinae insects, which feed exclusively on seeds during the larval stage. However, the effect of important seed traits on body size variation has rarely been investigated, and whether SSD varies substantially among populations within bruchine species is poorly known. Using the seed‐feeding beetle Acanthoscelides macrophthalmus infesting its host plant Leucaena leucocephala, we investigated whether specific seed traits (hardness, size, water content, carbon/nitrogen ratio, and phenolic content) were determinant in generating geographic variation in body size and SSD of A. macrophthalmus. We also examined the relationships between body size and SSD with latitude and altitude. The body size of both sexes combined was not related to latitude, altitude, and any of the physical and chemical seed traits. However, the female body size tended to vary more in size than the males, generating significant variation in SSD in relation to latitude and altitude. The females were the larger sex at higher latitudes and at lower altitudes, precisely where seed water content was greater. Therefore, our results suggest that water content was the most important seed trait, most severely affecting the females, promoting geographic variation in SSD of A. macrophthalmus.     

Finding the Minimum Sample Richness (MSR) for multivariate analyses: implications for palaeoecology

Many techniques have been developed to estimate species richness and beta diversity. Those techniques, dependent on sampling, require abundance or presence/absence data. Palaeontological data is by nature incomplete, and presence/absence data is often the only type of data that can be used to provide an estimate of ancient biodiversity. We used a simulation approach to investigate the behaviour of commonly used similarity indices, and the reliability of classifications derived from these indices, when working with incomplete data. We drew samples, of varying number and richness, from artificial species lists, which represented original life assemblages, and calculated error rates for classifications of the parent lists and samples. Using these results, we estimated the Minimum Sample Richness (MSR) needed to achieve 95% classification accuracy. Results were compared for classifications derived from several commonly used similarity indexes (Dice, Jaccard, Simpson and Raup–Crick). MSR was similar for the Dice, Jaccard and Simpson indices. MSR for the Raup–Crick index was often much lower, suggesting that it is preferable for classifying patchy data, however the performance of this index was less stable than the other three in the simulations, which required an even lower MSR. MSR can be found for all presence/absence data from the contour graphs and equations as long as the absolute species richness and the beta diversity can be estimated.     

A multivariate analysis of geographic variation in morphology inPersoonia mollis (Proteaceae)

This study highlights the utility and limitations of multivariate procedures for the analysis and taxonomic interpretation of geographic variation within a complex species. Morphological data from herbarium specimens ofPersoonia mollis (Proteceae) were analyzed by two ordination procedures, multidimensional scaling (MDS) and canonical variate analysis (CVA). Support for the earlier recognition of nine infraspecific taxa was found. However, plots of canonical variate scores against latitute or longitude across parapatric subspecies boundaries revealed unexpected phenetic homogeneity within subspecies with sharp transitions between subspecies. The geographic variation in morphology withinP. mollis can be best described as a mosaic of nine recognisably distinct and internally homogeneous allopatric or parapatric taxa, where neighbouring taxa share surprisingly narrow zones of morphological transition at ecotones. The utility of these procedures was highlighted by the recovery of unexpected patterns of variation. However, questions of rank remain unresolved by phenetic analysis alone.     

Interpopulational variation in recovery time from chill coma along a geographic gradient: a study in the common woodlouse, Porcellio laevis

Extreme temperatures restrict the performance of terrestrial arthropods and variations in low temperatures on a latitudinal scale influence physiological variables. Recovery time from chill coma is a measure of cold tolerance and it is a good index of climatic adaptation. We tested differences in recovery time of the common woodlouse (Porcellio laevis) exposed to different thermal conditions. Individuals were sampled from four different populations in Chile, spanning a latitudinal range of approximately 10 degrees . Significant differences were found in recovery time among experimental temperatures and among populations, but no interaction between these factors. The results of recovery time in P. laevis showed a positive increment with annual mean minimum temperature, indicating that there is geographical variation in recovery time. While body mass presented interpopulational variation, this variation was not associated with thermal variables or latitude. Overall, our results agree with previous studies in the sense that recovery time from chill coma decreases towards high latitudes, and it is independent of taxa, continent and hemisphere.     

Allozyme differentiation of populations of the dogwhelk Nucella lapillus, (L.): the relative effects of geographic distance and variation in chromosome number

Geographic patterns of genie differentiation were compared with differentiation between karyotypes in the intertidal snail Nucella lapillus. Samples from 24 sites covering the species range in Europe and North America were analysed for allozyme variation at 16 soluble enzyme loci. Two homokaryotypes have been identified with diploid numbers 2n = 26 and 2n= 36 (variation is Robertsonian and hybrids have intermediate chromosome numbers) and samples were classified (on the basis of published data) according to karyotype. Group 1 consisted of samples from three English Channel populations of higher chromosome number (on average 2n > 32) and Group 2 consisted of the remaining 21 samples (presumed to be 2n= 26). Karyotype variation accounts for roughly the same amount of the absolute allozyme variance as geographic variation (46.3 °, and 53.7°, respectively). Yet the patterns of differentiation seen between karyotypes and with geographic separation are very different. In samples classified as 2n= 26 (Group 2), while there is a significant amount of heterogeneity (F_ST per locus averaged 0.128 for 10 polymorphic loci), allozyme variation occurs independently at different loci so mean genetic identity (Nei) is high: 0.972. There is only a slight decline in genetic identity with distance (genetic identity averaged 0.965 for amphi-atlantic comparisons) indicating that passive transport of juveniles or adults may contribute significantly to gene flow. Conversely, allozyme variation between karyotypes was concordant. High chromosome number populations possessed a suite of alleles at four allozyme loci (Esl-3, Lap-2, Mdh-1 and Pep-2) which were absent or rare in Group 2 samples resulting in high F_ST values for these loci (from 0.294 to 0.472) when karyotypic classes were combined. Consequently the mean genetic identity between these Robertsonian races is low, 0.856, and falls within the range more usually associated with congeneric comparisons than with con-specific comparisons. The mechanisms maintaining this genie difference are unclear. However the distribution of the karyotypes and physiological and morphological differences (in shell shape) between them strongly suggest that karyotypic variation in Nucella is adaptive.     

厦门海域浮游植物夏季赤潮期间分布变异的多元分析

根据2000年6月至7月夏季藻华期在11个监测站10个航次获取的表层浮游植物和现场测定的理化参数数据,采用多元分析方法揭示浮游植物聚群在污染胁迫下的动态特征。结果表明：（1）该区调查期间浮游植物群落的物种多样性时空变异显著,各站多样性指数值（H′）变动在0．45—4．23之间;（2）聚类分析和多维排序（MDS）结果显示,浮游植物聚群可分为3个与浮游植物阶段性演替以及各水域间不同的理化特征相关联的群落。群落Ⅰ系2000年6月赤潮暴发时主要出现于西海域的低盐港湾群落,由微型（nano一）浮游植物组成,包括硅藻门的角毛藻、骨条藻等属种类以及金藻门的单鞭金藻属种类等,如中肋骨条藻（Skeletonema costatum）、聚生角毛藻（Chaetoceros socialis）等和一种单鞭金藻（Chromulina sp．）（未鉴定到种,藻径3～5μm）,它们是赤潮原因种。群落Ⅱ和群落Ⅲ都以小型（micro-）浮游植物占优势。群落Ⅱ为赤潮前后广泛出现于调查区各水域的亚热带近岸广布群落,代表种有具槽帕拉藻（Paralia sulcata）、翼鼻状藻（Proboscia alata）、菱形海线藻（Thalassionema nitzschioides）和冰河拟星杆藻（Asterionellopsis glacialis）．群落Ⅲ主要分布于本海区东一东北部,由我国东南沿海常见的近海广布性种类组成,包括旋链角毛藻（Chaetoceros curvisetus）、地中海细柱藻（Leptocylindrus mediterraneus）、尖刺伪菱形藻（Pseudonitzschia pungens）、优美施罗藻（Schroederella delicatula）和斯氏几内亚藻（Guinardia striata）等;（3）丰度-生物量曲线（ABC）分析结果显示,当微藻赤潮出现时,数值丰度的K-优势曲线位于生物量K-优势曲线上方,而无赤潮时2条曲线大体上重叠。其模式可指示厦门海区西部海域污染严重以及东-东北部中度污染的状况;（4）根据各航次全部调查数据所作的PCA分析得到的前3个最主要成分,包括浮游植物丰度和溶解氧,铵氮和磷酸盐,盐度和温度等,大约解析本调查总差异的78．5％。     

Impact of geographic area level on measuring socioeconomic disparities in cancer survival in New South Wales,Australia: A period analysis

BackgroundArea-based socioeconomic measures are widely used in health research. In theory, the larger the area used the more individual misclassification is introduced, thus biasing the association between such area level measures and health outcomes. In this study, we examined the socioeconomic disparities in cancer survival using two geographic area-based measures to see if the size of the area matters.MethodsWe used population-based cancer registry data for patients diagnosed with one of 10 major cancers in New South Wales (NSW), Australia during 2004–2008. Patients were assigned index measures of socioeconomic status (SES) based on two area-level units, census Collection District (CD) and Local Government Area (LGA) of their address at diagnosis. Five-year relative survival was estimated using the period approach for patients alive during 2004–2008, for each socioeconomic quintile at each area-level for each cancer. Poisson-regression modelling was used to adjust for socioeconomic quintile, sex, age-group at diagnosis and disease stage at diagnosis. The relative excess risk of death (RER) by socioeconomic quintile derived from this modelling was compared between area-units.ResultsWe found extensive disagreement in SES classification between CD and LGA levels across all socioeconomic quintiles, particularly for more disadvantaged groups. In general, more disadvantaged patients had significantly lower survival than the least disadvantaged group for both CD and LGA classifications. The socioeconomic survival disparities detected by CD classification were larger than those detected by LGA. Adjusted RER estimates by SES were similar for most cancers when measured at both area levels.ConclusionsWe found that classifying patient SES by the widely used Australian geographic unit LGA results in underestimation of survival disparities for several cancers compared to when SES is classified at the geographically smaller CD level. Despite this, our RER of death estimates derived from these survival estimates were generally similar for both CD and LGA level analyses, suggesting that LGAs remain a valuable spatial unit for use in Australian health and social research, though the potential for misclassification must be considered when interpreting research. While data confidentiality concerns increase with the level of geographical precision, the use of smaller area-level health and census data in the future, with appropriate allowance for confidentiality