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51 results for “multivariate analyses”
Fig. 18 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 18. Proximal views of the right cuboid and navicular of a human (A) and a common chimpanzee (B) in a closepacked position showing the contribution of the talocuboid angle (v) to the height of the transverse arch (h). In the closepacked position the small angle shown by chimpanzees results in a higher transverse arch than normally seen in humans. The human arch, however, unlike that of chimpanzees, exhibits a fixed height. Owing to a small, irregular, and often absent cuboid facet, the human talocuboid angle could not be accurately measured.
Fig. 17 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 17. Contribution of navicular torsion (v) and the frontal mesoectocuneiform angle (w) to the relative set of the ectocuneiform, mesocuneiform, and the talar facet in the closepacked position as seen in line drawings of an exploded right foot of a human (A) and a gorilla (B) from a dorsodistal view. High values of the frontal mesoectocuneiform angle in humans (w) do not result in marked opposition of the second and third metatarsals given metatarsal, ectocuneiform, and mesocuneiform torsion values which correct for the imparted set. Despite similar torsion values in humans and gorillas, the metatarsal, ectocuneiform, and mesocuneiform torsion all contribute to causing more marked opposition of the second and third metatarsals in gorillas. Marked talar torsion or large frontal mesoectocuneiform angles, are also associated to a high transverse arch (see text).
Fig. 16 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 16. Dorsal view of the exploded left tarsus and metatarsus of a pygmy chimpanzee in the closepacked position showing the contribution of the transverse mesoectocuneiform angle (w) and the transverse cuboectocuneiform angle (v) to the divergence of the second through fourth metatarsals. Correction of the talocuboid angle by the facet sets on the cuboid and ectocuneiform results in third and fourth metatarsals that are nearly alinged (y). A relatively low transverse mesoectocuneiform angle results in a second metatarsal that is divergent from the most lateral three (x) despite a partial correction of this set by the mesocuneiform.
Fig. 15 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 15. Contributions of the entoectocuneiform and sagittal taloectocuneiform angles (w and v respectively) to the relative set of the first through third metatarsal in closepacked position as seen in line drawings of the exploded left foot of a human (A) and of a gorilla (B) in medial view. The large sagittal taloectocuneiform angle in gorillas imparts a dorsiflexed set to the third metatarsal and is associated with a dorsiflexed talar head, i.e. small angle of talar neck inclination (Day and Wood 1968). The gorilla entoectocuneiform angle imparts a plantar set to the entocuneiform relative to the ectocuneiform and is associated with an abducted hallux, i.e. plantar divergence of the hallux relative to second (x) and third metatarsals (y). The human taloectocuneiform and entoectocuneiform angles are associated with a plantar flexed talar head (i.e., large angle of talar neck inclination), nearly aligned first to third metatarsals, and a longitudinal plantar arch. Due to a fixed transverse arch in humans, however, the long axis of the second and third metatarsals must have a more plantar inclination than the hallux, and the value of x and y are negative. Because the major axis of the navicular's talar facet is not necessarily held vertically, the sagittal taloectocuneiform and entoectocuneiform angles may also impart some degree of medial divergence to the hallux.
Fig. 14 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 14. Plot of mean canonical variate scores for studied taxa. All fossils are based on single samples. The actual Mahalanobis D for all of the canonical variates separating taxa is given as the value above each connecting line (table 11). Connecting lines represent a Minimum Spanning Tree (after Rohlf, 1997). Owing to a twodimensional projection, the actual lengths of the connecting lines on the plot represent only a fraction of the D values.
Fig. 13 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 13. Dendrograms of the studied taxa constructed using unweighted pair group method (Rohlf, 1997). Inset shows portion of dendrogram which differs when both Hadar naviculars are considered as a single sample.
Fig. 12. A in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 12. A plot of the first two canonical variates with vectors representing the contribution of each of the measured variables to the scatter within and among measured taxa. Arrows point to fossils. Note the distinctiveness of H. sapiens, the uniqueness of Oreopithecus and the similarities of Hadar and African apes, of OH 8 and Homo, and of great ape species or subspecies within genera. The vectors representing the frontal mesoectocuneiform angle (EctMsFn) and the mediolateral diameter of the entocuneiform facet (EntFml) are nearly overlapping. Vector lengths are exagerated by a factor of ten, and owing to a twodimensional projection, are not proportional to their actual length. Eighty percent of the variance among means relative to the withingroup variance is summarized by the first two canonical variates (see figure 14 for plotted means of the first two canonical variates). Program written in Matlab version 5.1. This ''biplot'' is after Rohlf (1997); see Marcus (1993) for a discussion. The program and navicular data are available from one of us (LM). TalFlng = talar facet dorsoplantar (major axis) diameter, TalFwd = talar facet mediolateral (minor axis) diameter, EctFpd= ectocuneiform facet dorsoplantar diameter, EctFml= ectocuneiform facet mediolateral diameter, MesFdp= mesocuneiform facet dorsoplantar diameter, MesFml= mesocuneiform facet mediolateral diameter, EntFml= entocuneiform facet mediolateral diameter, EntFdp= entocuneiform facet dorsoplantar diameter, MaxLng= navicular maximum length, CuFdp= cuboid facet dorsoplantar diameter, CuFml= cuboid facet mediolateral diameter, TalFlDp= depth of talar facet along major axis, TalTrDp= depth of talar facet along minor axis; CubEcto = transverse cuboectocuneiform angle, EctMstr= transverse mesoectocuneiform angle, Tor= navicular torsion, EctMsFn= frontal mesoectocuneiform angle, TalEct= sagittal taloectocuneifrom angle, EctEmt= entoectocuneiform angle.
Fig. 11 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 11. Cube root of lower limbvolume (mm) vs. square root of total navicular crosssectional area (mm) in humans, great apes, and fossil hominoids.
Fig. 10 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 10. The sum of the femoral and tibial crosssectional areas (mm2) vs. talar facet crosssectional area (mm2) in humans, great apes, and fossil hominoids.
Fig. 9 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 9. Bivariate plot of cube root of body weight (kg⅓) vs. square root of total navicular facet crosssectional area (mm) in great apes. N = 62, Slope = 6.58, y intercept = 143.77. At 95% confidence limits OH 8, the two Hadar naviculars, and Oreopithecus were calculated to have body weights of 12.0– 100.3 kg, 17.6–143.6 kg (AL 33347), 18.6–155.1 kg (AL 33336), and 4.4–39.5 kg respectively.
Fig. 7 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 7. Dorsoplantar (major axis) diameter (mm) vs. mediolateral (minor axis) diameter (mm) of the talar facet (i.e., talar facet length vs. talar facet width) in humans, great apes, and fossil hominoids. Arrows point to fossils.
Fig. 4 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 4. Mesocuneiform facet crosssectional area (mm2) vs. total navicular facet crosssectional area
Fig. 3 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 3. Ectocuneiform facet crosssectional area (mm2) vs. total navicular facet crosssectional area
Fig. 5 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 5. Entocuneiform facet crosssectional area (mm2) vs. total navicular facet crosssectional area
Fig. 6 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 6. Cuboid facet crosssectional area (mm2) vs. total navicular facet crosssectional area (mm2) in humans, great apes, and fossil hominoids. Arrows point to fossils.
Fig. 1 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 1. Proximal (A), distal (B), lateral (C) and dorsal (D) views of the OH 8 navicular showing the measured lengths, and proximal (E), distal (F), lateral (G) and dorsal (H) views of a left gorilla navicular showing the measured angles; a = talar facet major axis (dorsoplantar) diameter, b = talar facet minor axis (mediolateral) diameter, c = ectocuneiform facet dorsoplantar diameter, d = ectocuneiform facet mediolateral diameter, e = mesocuneiform facet dorsoplantar diameter, f = mesocuneiform facet mediolateral diameter, g = entocuneiform facet mediolateral diameter, h = entocuneiform facet dorsoplantar diameter, i = navicular maximum length, j = cuboid facet dorsoplantar diameter, k = cuboid facet mediolateral diameter, l = depth of talar facet along major axis, m = depth of talar facet along minor axis; 1 = frontal talocuboid angle, 90° 2 = navicular torsion, 3 = frontal mesoectocuneiform angle, 4 = entoectocuneiform angle 5 = sagittal taloectocuneifrom angle, 6 = transverse mesoectocuneiform angle, 7 = transverse cuboectocuneiform angle. In all cases the lines chosen for angular measurements bisect facets into approximately equal halves. For comparative purposes the major bisecting axes of the talar head and cuneiform facets are referred to in the text as the dorsoplantar axes. In neither great apes nor humans do all these axes have a dorsoplantar orientation, but are held in varying inclination to a dorsoplantar axis according to talar head and navicular torison and the frontal mesoectocuneiform angle. The crosssectional area of the talar, ectocuneiform, mesocuneiform entocuneiform and cuboid facets are given by the products of a and b, c and d, e and f, g and h, and j and k, respectively. Relative crosssectional area for each facet is compared as a percentage of the sum of all of the navicular facets. The subtended angle of curvature and the radius of curvature of the talar facet along the dosoplantar (major) and mediolateral (minor) axes are given by 4 arctan(2l/a) and (l2 + a2/4)/ 2l, and 4 arctan(2m/b) and (m2 + b2/4)/2m, respectively.
Fig. 2 in The Os Navicular of Humans, Great Apes, OH 8, Hadar, and Oreopithecus: Function, Phylogeny, and Multivariate Analyses
Fig. 2. Talar facet crosssectional area (mm2) vs. total navicular facet crosssectional area (mm2) in humans, great apes, and fossil hominoids. Arrows point to fossils.
FIGURE 1. Scatterplots from multivariate statistical analyses. Ellipses define the 95 in Morphological Variation in a Unisexual Whiptail Lizard (Aspidoscelis exsanguis) and One of Its Bisexual Parental Species (Aspidoscelis inornata) (Reptilia: Squamata: Teiidae): Is the Clonal Species Less Variable?
FIGURE 1. Scatterplots from multivariate statistical analyses. Ellipses define the 95% confidence limits of score distributions. A. Principal component scores of 14 field A. exsanguis, 42 laboratory A. exsanguis of two lineages pooled, and 19 field A. inornata. Axis percentages reflect variance explained by PC1 and PC2 (table 5). B. Canonical variate scores of the same specimens as in A. Axis percentages are relative contributions of CV1 and CV2 to the discrimination (table 5).
Prior choice and data requirements of Bayesian multivariate mixed effects models fit to tag-recovery data: The need for power analyses
<p>1. Recent empirical studies have quantified correlation between survival and recovery by estimating these parameters as correlated random effects with hierarchical Bayesian multivariate models fit to tag-recovery data. In these applications, increasingly negative correlation between survival and recovery has been interpreted as evidence for increasingly additive harvest mortality. The power of these hierarchal models to detect non-zero correlations has rarely been evaluated and these few studies have not focused on tag-recovery data, which is a common data type.</p> <p>2. We assessed the power of multivariate hierarchical models to detect negative correlation between annual survival and recovery. Using three priors for multivariate normal distributions, we fit hierarchical effects models to a mallard (<em>Anas</em> <em>platyrhychos</em>) tag-recovery dataset and to simulated data with sample sizes corresponding to different levels of monitoring intensity. We also demonstrate more robust summary statistics for tag-recovery datasets than total individuals tagged.</p> <p>3. Different priors lead to substantially different estimates of correlation from the mallard data. Our power analysis of simulated data indicated most prior distribution and sample size combinations could not estimate strongly negative correlation with useful precision or accuracy. Many correlation estimates spanned the available parameter space (–1,1) and underestimated the magnitude of negative correlation. Only one prior combined with our most intensive monitoring scenario provided reliable results. Underestimating the magnitude of correlation coincided with overestimating the variability of annual survival, but not annual recovery.</p> <p>4. The inadequacy of prior distributions and sample size combinations previously assumed adequate for obtaining robust inference from tag-recovery data represents a concern in the application of Bayesian hierarchical models to tag-recovery data. Our analysis approach provides a means for examining prior influence and sample size on hierarchical models fit to capture-recapture data while emphasizing transferability of results between empirical and simulation studies.</p>
Prior choice and data requirements of Bayesian multivariate mixed effects models fit to tag-recovery data: The need for power analyses
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