Introduction

The locomotor behaviors of small, cryptic species of mammals have been studied directly for only a relatively few species. Instead, external and internal morphological characters are typically interpreted to provide insight into how individual species use available substrates, particularly while foraging (^{Shimer 1903}; ^{Reed 1951}; ^{Hildebrand 1985}a, 1985b; ^{Hutterer 1985}; ^{Price 1993}; ^{Samuels and Van Valkenburgh 2008}; ^{Hopkins and Davis 2009}; ^{Nations et al. 2019}).

The typical external morphology of shrews (Mammalia: Eulypotyphla: Soricidae) can be generalized as a long cylindrical body, short legs, and simple feet with five digits used in a plantigrade-to-digitigrade posture, a body plan that is typical of ambulatory small mammals that make use of the ground surface as their primary locomotor substrate (^{Hutterer 1985}; ^{Churchfield 1990}; ^{Woodman and Morgan 2005}). In contrast, the relatively short dense fur, small pinnae, and small eyes of soricids are common mammalian adaptations for fossoriality (^{Shimer 1903}; ^{Eisenberg 1981}). Although ambulation and semi-fossoriality are the two dominant locomotor modes among soricids, members of the family exhibit a range of other locomotor behaviors that assist in exploiting additional substrates. Based on a large sample of 266 species in 20 genera (the recognized diversity of Soricidae at that time), ^{Hutterer (1985)} estimated that almost 77 % of soricid species are primarily ambulatory (terrestrial), nearly 11 % are adapted for semi-fossoriality, about 5 % are scansorial, more than 4 % are semi-aquatic, 2 % are anthrophilic, and one species is psammophilic. In a related study based on a similar sample, ^{Churchfield (1990}:100) estimated that 82 % of soricid species have a dominantly epigeal foraging mode, 11 % are hypogeal, 5 % are aquatic, and 3 % are scansorial, illustrating the seemingly close correspondence of primary locomotor mode and resource use.

Previous studies of soricid skeletal adaptations related to locomotor behavior have focused primarily on understanding morphological variation as it relates to ambulation and semi-fossoriality. Ambulatory and semi-fossorial species are distributed among all three subfamilies of the Soricidae (^{Hutterer 1985}; ^{Churchfield 1990}), and they exhibit considerable intra-modal variation in morphological characteristics related to substrate use (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015b}; ^{Woodman and Wilken 2019}). Herein, I explore skeletal variation as it relates to three of the four dominant locomotory modes identified for shrews by testing the discriminatory power of 34 common locomotor indices, mostly calculated from postcranial measurements. Although ambulatory and semi-fossorial locomotor modes occur in all three subfamilies of Soricidae, semi-aquaticmodes are confined to a smaller number of species in four genera representing two taxonomic tribes of the subfamily Soricinae: Chimarrogale, Nectogale, Neomys, and Sorex (This number increases to five genera if Crossogale is recognized as distinct from Chimarrogale: ^{Wahab et al. 2020}).

Materials and methods

The primary goal of this paper is to better understand skeletal variation among soricids in relation to a traditional, stereotyped classification of locomotor modes. This study of the association between morphology and locomotor behavior is admittedly incomplete, in part because locomotor modes of many soricids are based on inference rather than direct observation. Moreover, phylogeny is a potential primary driver of morphological variation, behavioral variation, or both, but genetic relationships among clades in the Soricidae remain poorly supported at nodes that appear to be crucial to understanding the evolution of locomotor morphology in the family (e. g., ^{He et al. 2015}, ²⁰²¹) and cannot yet be controlled for.

For the purposes of this paper, the word “ambulatory” refers to terrestrial shrews that use the ground surface as their primary locomotor substrate, and lack morphological characters linked to aquatic, fossorial, or scansorial adaptations or behaviors.

In this study, I used measurements and indices from 41 species and subspecies of soricids previously reported by ^{Woodman and Gaffney (2014}), ^{Woodman and Stabile (2015a}, ^2015b), and ^{Woodman et al. (2019)}. To these, I added measurements from 180 individuals representing 11 additional species from the mammal collections of the Field Museum of Natural History, Chicago, IL (FMNH), and the National Museum of Natural History, Washington, DC (USNM; Appendix 1). All 52 species were classified a priori into one of five locomotor groupings based on reported behaviors and suites of external characteristics: ambulatory (n = 16); semi-aquatic (n = 7); semi-fossorial (n = 19); fossorial (n = 2); unknown (n = 5). Semi-fossorial and fossorial taxa tend to have large body size, short tails, small pinnae hidden by the fur, enlarged forefeet, and long, broad foreclaws (^{Hildebrand 1985}b; ^{Hutterer 1985}). Semi-aquatic shrews tend to have large body size, long tails that may be laterally flattened or have one or more keels of stiff bristles, long hind feet, and digits and feet fringed with bristles; some have webbed hind feet (^{Howell 1930}; Hutterer 1985). Ambulatory species exhibit the entire range of body size and lack fossorial or aquatic characters. A complete list of species and their a priori locomotor classifications is provided in Appendix 2.

Skeletal measurements. To assess relative locomotor adaptations, I followed procedures explained in detail by ^{Woodman and Gaffney (2014}; see also ^{Woodman and Stabile 2015b}; ^{Woodman and Wilken 2019}). Total length and tail length are the standard external measurements recorded from skin tags, and head-and-body length was calculated by subtracting tail length from total length. Forty measurements (Table 1) were obtained from the manus, pes, and long bones of the appendicular skeletons. The scapula, humerus, ulna, radius, femur, and tibiofibula were digitally photographed, and the bones of the manus and pes were digitally x-rayed using a Kevex X-Ray Source 4.1.3 (Kevex, Palo Alto, CA) with Varian Image Viewing and Acquisition 2.0 software (VIVA, Waltham, MA) in the Division of Fishes, National Museum of Natural History, Washington, DC. The resulting digital images from both sources were imported into Adobe Photoshop CS3 Extended 10.0.1 (Adobe Systems, San Jose, CA) and variables (Supplementary Table S1) measured using the Custom Measuring Scale in the Analysis menu following ^{Woodman and Gaffney (2014}; see also ^{Woodman and Morgan 2005}; ^{Woodman and Stephens 2010}; ^{Sargis et al. 2013}a, ^2013b; ^{Woodman and Stabile 2015b}; ^{Woodman and Wilken 2019}).

Locomotor indices. Skeletal measurements were used to calculate 34 osteological indices previously employed to characterize locomotor mode and identify potential adaptations for substrate use among soricids (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015a}, ^b; ^{Woodman and Wilken 2019}; ^{Woodman et al. 2019}), rodents (^{Price 1993}; ^{Samuels and Van Valkenburgh 2008}; ^{Elissamburu and De Santis 2011}; ^{Nations et al. 2019}), and other mammals (^{Sargis 2002}; ^{Hopkins and Davis 2009}). To overcome the problem of missing elements, and thereby, missing data, indices (Table 2) were calculated from mean values of variables for each species (Supplementary material Table S1). Abbreviations of measurements used to calculate indices are explained in Table 1.

1. Intermembral index (IM = [HL+RL]/[FL+TL]) compares the lengths of the forelimbs and hind limbs (^{Sargis 2002}).

2. Humerofemoral index (HFI = HL/FL) represents the length of the humerus as a proportion of the length of the femur (^{Sargis 2002}).

3. Metapodial index (FOOT = ML/hML) indicates the relative sizes of the forefeet and hind feet by comparing the length of metacarpal III to that of metatarsal III.

4. Distal phalanx length index (CLAW = DPL/hDPL) compares the relative size of distal phalanx III of the manus to distal phalanx III of the pes.

5. Claw length index (CLI = CL/hCL) gauges the relative size of claw III of the manus to claw III of the pes.

6. Scapulohumeral index (SHI = SL/HL) indicates relative lengths of the scapula and humerus.

7. Brachial index (BI = RL/HL) shows the relative proportions of the proximal (humerus) and distal (radius) elements of the forelimb.

8. Shoulder moment index (SMI = HDPC/HL) is equivalent to the delto-pectoral crest length index (^{Sargis 2002}). It measures the length of the deltopectoral crest of the humerus relative to the length of the humerus, thereby gauging the size and mechanical advantage of the deltoid and pectoral muscle groups, which are important in the movement, rotation, and counter-rotation of the humerus (^{Reed 1951}).

9. Humeral robustness index (HRI = HLD/HL) indicates the robustness of the humerus and its ability to resist bending and shearing stresses.

10. Humeral rotation lever index (HTI = HTTR/HAR) shows the relative length of the teres tubercle measured at right angles to the longitudinal axis of rotation of the humerus. The teres tubercle is an elongate process unique to the humerus of talpids, soricids, tachyglossids, and a few early mammals (^{Reed 1951}; ^{Hildebrand 1985}b). It serves as the insertion for the latissimus dorsi and teres major muscles and as a lever for rotating the humerus (Reed 1951).

11. Teres tubercle position index (TTP = HTT/HAR) represents the relative position of the teres tubercle along the axis of rotation of the humerus (HAR). In more robust, more fossorially adapted humeri with larger muscle attachment surfaces, the teres tubercle is often more distally positioned (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015}).

12. Humeral epicondylar index (HEB = HDW/HL) measures the width of the distal humerus relative to the length of the humerus and represents the area available for the origins of muscles involved in flexing, pronating, and supinating the forearm.

13. Radial distal width index (RDW = RDW/RL) measures the relative width of the proximal end of the radius, providing a gauge of its robustness and its resistance to stress.

14. Olecranon length index (OLI = UOP/UFL) is one of several variations on the index of fossorial ability of ^{Hildebrand (1985}a). The ulna acts as a lever that pivots at the trochlear notch, and OLI gauges the force exerted by the triceps brachii muscle on the olecranon process that is transmitted to the functional arm of the ulna. Semi-fossorial and fossorial mammals generally have a longer olecranon process to accommodate a larger triceps brachii, resulting in larger OLI (^{Reed 1951}; ^{Vizcaino and Milne 2002}; ^{Samuels and Van Valkenburgh 2008}; ^{Woodman and Gaffney 2014}).

15. Triceps metacarpal outforce index (TMO = UOP/[UFL+ML]), a variant of ^{Hildebrand’s (1985}a) index of fossorial ability (OLI), gives the length of the olecranon process as a proportion of the functional arm provided by the ulna and metacarpal III together. This index measures the amount of force input on the olecranon process that is transmitted to the tip of the metacarpal of ray III (^{Price 1993}).

16. Triceps claw outforce index (TCO = UOP/[UFL+ML+PPL+MPL+CL]) expresses the length of the olecranon process relative to the combined functional lengths of the ulna and the four bones comprising ray III of the manus. An extension of ^{Hildebrand’s (1985}b) index of fossorial ability (OLI) and ^{Price’s (1993}) triceps metacarpal outforce index (TMO), TCO represents the proportion of force input on the olecranon process by the triceps muscle that is transmitted to the tip of the claw of ray III, which is the initial point of contact with the soil.

17. Olecranon crest index (OCI = UPC/UFL) is a measure of the relative length of the olecranon crest on the olecranon process. It serves as the insertion for much of the triceps brachii. OCI is an approximate gauge of muscle size, and, therefore, another measure of the relative input force on the ulna (^{Woodman and Gaffney 2014}).

18. Ulnar robustness index (URI = ULD/UFL) measures the robustness of the ulna and its ability to resist bending and shearing stresses.

19. Manual distal phalanx index [%DPL = DPL/(ML+PPL+MPL)] is the length of distal phalanx III of the manus relative to the combined length of the proximal three bones of ray III.

20. Manual claw index [%CL = CL/(ML+PPL+MPL)] is the length of claw III of the manus relative to the combined length of the proximal three bones of ray III.

21. Manual claw support index (%CLS = DPL/CL) represents the proportion of claw III of the manus that is supported by the underlying distal phalanx III.

22. Metacarpal width index (MW3 = MW/ML) measures the robustness of metacarpal III of the manus in relation to its length.

23. Phalangeal index (PI = (PPL+MPL)/ML) shows the lengths of the proximal and middle phalanges relative to the metacarpal. This index reflects the degree to which the hand is prehensile and used for grasping (higher index value) versus walking on the ground (lower index value), and it has been used mainly for distinguishing arboreal and scansorial species from ambulatory species. PI varies considerably among rays of an individual, so ray III is typically used for comparisons among species (^{Lemelin 1999}; ^{Kirk et al. 2008}). No arboreal or scansorial shrews were included in the present study.

24. Manus proportions index (MANUS = PPL/ML) measures the size of the proximal phalanx relative to the metacarpal of manual ray III (^{Samuels and Van Valkenburgh 2008}), and it is the same as ^{Kirk et al.’s (2008}) proximal phalangeal index. There appears to be a large phylogenetic component to this index across mammalian orders (^{Kirk et al. 2008}), but not within rodent families (^{Nations et al. 2019}), and it is useful for distinguishing arboreally adapted species (larger indices) from ambulatory species (smaller indices).

25. Crural index (CI = TL/FL) measures the relative lengths of proximal (femur) and distal (tibiofibula) long bones of the hind limb.

26. Pes length index (PES = hML/FL) represents the length of metatarsal III relative to femur length and is used to indicate the relative size of the hind foot.

27. Femoral robustness index (FRI = FLD/FL) quantifies the robustness of the femur and its ability to resist bending and shearing stresses.

28. Femoral epicondylar index (FEB = FDW/FL) approximates the area available for the origins of the gastrocnemius and soleus muscles involved in extension of the knee and plantar-flexion of the pes in rodents (^{Samuels and Van Valkenburgh 2008}). In shrews and talpids, this region is the origin for the plantaris, which flexes the toes, the gastrocnemius, which extends the pes, and the extensor digitorum longus, which extends and adducts the digits and dorsoflexes the foot. It is also the insertion for the caudofemoralis, which retracts the femur, and the adductor longis, which adducts the femur (^{Reed 1951}).

29. Distal tibiofibular articulation index (DTA = TDA/TDW) measures the width of the articular region for the astragalus between the lateral and medial malleolus relative to the distal width of the tibia (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015}).

30. Pedal distal phalanx index [%hDPL = hDPL/(hML+hPPL+hMPL)] is the length of the distal phalanx of ray III of the pes relative to the combined length of the proximal three bones of that ray.

31. Pedal claw index [%hCL = hCL/(hML+hPPL+hMPL)] is the length of the claw of ray III of the pes relative to the combined length of the proximal three bones of that ray.

32. Pedal claw support index (%hCLS = hDPL/hCL) is the proportion of the claw of ray III of the pes supported by the distal phalanx.

33. Tail length index (%TAIL = tail length/head-and-body length) measures the length of the tail relative to head-and-body length. This index was effective for distinguishing between arboreal and terrestrial species of murid rodents (^{Nations et al. 2019}).

34. Relative robustness index (RR = HLD/FLD) measures the least breadth of the humerus relative to the least breadth of the femur.

Analyses of locomotor indices. The effectiveness of the 34 indices for distinguishing locomotor mode was initially evaluated by calculating standard univariate statistics (mean, SD, range) in Excel (Microsoft Corporation, Redmond, Washington) for each locomotor group and plotting as box-and-whisker plots (Supplementary material Figure 1). To provide overviews of interspecific variation and to determine relative grades of locomotor modes among taxa, analyses of percentile ranks and multivariate analyses were employed to combine multiple indices. Percentile ranks were calculated for each taxon for each of 23 locomotor indices (IM, HFI, FOOT, CLAW, CLI, SMI, HRI, HTI, TTP, HEB, TCO, OCI, URI, %DPL, %CL, MW3, CI, PES, FEB, %hDPL, %hCL, RR, %TAIL) using the percentile rank calculator at Statisticshelper.com (https://statisticshelper.com/percentile-rank-calculator/). A mean percentile rank was then calculated for each taxon from all indices for which it could be scored. Mean percentile ranks provide a convenient means of comparing all 52 taxa on a possible scale from 0 to 100. This permits broader taxonomic coverage, but the lack of data for some taxa means that morphological comparisons are not even across all taxa.

Figure 1 Plot of the indices PES and %TAIL showing separation between semi-aquatic and ambulatory species. The three species of unknown locomotor mode (C. gracilis, C. endersi, C. thomasi) plot with ambulatory and semi-fossorial taxa. 

The largest complete dataset (i. e., no missing data) that I could compile included 17 indices (CLI, CLAW, %CL, %DPL, SHI, HEB, HTI, %hCL, FOOT, TTP, SMI, %hDPL, MW3, HRI, PI, MANUS, %TAIL) from six semi-aquatic, 12 ambulatory, 13 semi-fossorial, and two fossorial species. To test the ability of this dataset to discriminate locomotor modes, I carried out both principal components analyses (PCAs) and discriminant function analyses (DFAs) in Past4.03 (^{Hammer et al. 2001}).

To investigate the possible locomotory modes of four species (Cryptotis gracilis, C. endersi, C. meridensis, C. thomasi) for which locomotory mode was uncertain, I carried out PCA and DFA on a subset of 10 indices (CLAW, CLI, SHI, SMI, HRI, HTI, TTP, %CLS, FEB, %TAIL) from these species and 33 species of known locomotory mode. All four unknown species lacked sufficient data to be included in the 17-variable model (Table S1).

Results

Effectiveness of individual indices. Most of the indices tested individually show identifiable patterns of variation among locomotor modes in soricids, most typically either ascending or descending in mean values from semi-aquatic to ambulatory to semi-fossorial to fossorial. Only a few indices, however, exhibit ranges of variation that are sufficiently constrained to be useful for clearly distinguishing one or more modes.

Individual locomotor indices that appear to be the most reliable for distinguishing semi-aquatic species are PES (n = 37 species), FOOT (n = 46), CLI (n = 44), CI (n = 28), %TAIL (n = 52), and %hCL (n = 45). All but PES have ranges that overlap in value with one or more ambulatory species (Figure 1). The indices CLAW, OCI, MW3, %DPL, %CL, HTI, and CLI are useful for differentiating semi-aquatic and semi-fossorial species.

The ranges of individual locomotor indices of ambulatory species most commonly group with those of semi-aquatic species and often overlap the ranges of some semi-fossorial species. The most reliable indices for distinguishing ambulatory species from semi-aquatic species are PES, FOOT, CLI, FEB (n = 41), and %TAIL. The most efficient indices for distinguishing ambulatory species from semi-fossorial species are CLAW (n = 43), OCI (n = 30), and RDW (n = 30), followed by MW3 (n = 45), %DPL (n = 44), %CL (n = 45), HRI (n = 49), HTI (n = 49), SHI (n = 44), CLI, HEB (n = 48), TTP (n = 49), OLI (n = 30), TMO (n = 29), and TCO (n = 28).

The combination of semi-fossorial and fossorial species can be distinguished most effectively from the other two locomotory modes by OCI and CLAW, followed by MW3, %DPL, CLI, TMO, TCO, HTI, HRI, TTP, RDW, and %CL. The most useful indices for differentiating semi-fossorial from fossorial shrews are %DPL, %CL, %hDPL (n = 45), CLI, SMI (n = 49), HRI, and HTI, followed by CLAW, HEB, PI (n = 45), MANUS (n = 46), and %hCL.

1. Intermembral index (IM), which compares the lengths of the forelimbs and hind limbs, typically increases in rodents from semi-aquatic species to ambulatory, to semi-fossorial, and to fossorial species (^{Samuels and Van Valkenburgh 2008}). The index shows a similar pattern with soricids (Supplementary material Figure 1a), indicating a tendency for semi-aquatic species to have relatively longer hind limbs (and/or shorter fore limbs) and for more fossorial forms to have relatively shorter hind limbs. Overlap among most locomotor groups, however, limits the usefulness of this index for determining locomotory mode for any one species.

2. Humerofemoral index (HFI) represents the length of the humerus as a proportion of the length of the femur. Among soricids, this index decreases from semi-aquatic species to ambulatory, to semi-fossorial, and to fossorial species (Supplementary material Figure 1b), indicating that semi-aquatic species have a longer humerus relative to the femur, whereas more fossorial species have a shorter humerus. This pattern seems counterintuitive in light of the pattern displayed by the IM, but the longer hind limb in semi-aquatic shrews is a result of their relatively longer tibiofibula (see #25, crural index). Overlap among most locomotor groups makes this index most useful for distinguishing semi-aquatic species from semi-fossorial and fossorial species.

3. Metapodial index (FOOT) indicates the relative sizes of the forefeet and hind feet by comparing the lengths of metacarpal III and metatarsal III. Soricids exhibit an increase in the index from semi-aquatic species to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1c), indicating that semi-aquatic species have a relatively longer hind foot (metatarsal III) than other species, particularly the most fossorial species. This index is useful for distinguishing semi-aquatic (low values) and the most fossorial species (high values) from most other species.

4. Distal phalanx length index (CLAW) compares the relative lengths of manual distal phalanx III and pedal distal phalanx III. It increases with increasing fossoriality in rodents (^{Samuels and Van Valkenburgh 2008}), indicating a relatively longer foreclaw than hind claw in more fossorial groups. Among soricids, CLAW clearly distinguishes most semi-fossorial and fossorial species from each other and from other locomotor modes (Supplementary material Figure 1d).

5. Claw length index (CLI) gauges the relative lengths of manual claw III and pedal claw III. CLI increases from semi-aquatic species to ambulatory to semi-fossorial to fossorial species with only minor overlap among locomotor modes (Supplementary material Figure 1e). It clearly distinguishes semi-fossorial and fossorial species from each other and from other locomotor modes, and it also distinguishes semi-aquatic species from most ambulatory species. In this study, only ambulatory Suncus hututsi (CLI = 81) and Sorex cinereus (86) overlapped with semi-aquatic species, and only semi-fossorial Congosorex phillipsorum (107) overlapped with the ambulatory species.

6. Scapulohumeral index (SHI) shows the relative lengths of the scapula and humerus (Supplementary material Figure 1f). This index is typically greater (relatively shorter humerus) for more semi-fossorial and fossorial soricids and lower for ambulatory and aquatic species (^{Woodman and Gaffney 2014}), but its ability to distinguish individual locomotor modes is limited.

7. Brachial index (BI) shows the relative lengths of the humerus and radius. Mean values of this index decrease (relatively shorter radius) among rodents from semi-aquatic to ambulatory to semi-fossorial to fossorial species (^{Samuels and Van Valkenburgh 2008}). The pattern is less apparent among soricids, and ranges of the four modes overlap too extensively for this to be a useful index (Supplementary material Figure 1g).

8. Shoulder moment index (SMI) measures the length of the deltopectoral crest relative to humerus length. In rodents, the index increases from ambulatory to semi-fossorial to semi-aquatic to fossorial species (^{Samuels and Van Valkenburgh 2008}). In contrast, in soricids there is a tendency to increase from semi-aquatic to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1h). Extensive overlap among groups makes the index useful only for distinguishing some semi-aquatic and some of the most fossorial species.

9. Humeral robustness index (HRI) indicates the relative thickness of the humerus, which increases (more robust humerus) from ambulatory to semi-fossorial to semi-aquatic to fossorial species among rodents (^{Samuels and Van Valkenburgh 2008}). Among soricids, mean values increase from ambulatory to semi-aquatic to semi-fossorial to fossorial species (Supplementary material Figure 1i). Indices for ambulatory and semi-aquatic species overlap extensively, but most semi-fossorial and fossorial species are distinct. Two exceptions are semi-fossorial Myosorex blarina (HRI = 9), which has a lower index than expected, and Nectogale elegans (12), which has a higher index than is typical for a semi-aquatic species.

10. Humeral rotation lever index (HTI) shows the relative length of the teres tubercle of the humerus. HTI exhibits little difference between semi-aquatic and ambulatory soricids (Supplementary material Figure 1j), but increases substantially with increased semi-fossoriality and fossoriality (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015}). Exceptions are Myosorex varius (HTI = 18) and M. zinki (18), which have lower index values than is typical for semi-fossorial soricids, and Blarinella quadricaudata (21), which has a higher index than expected for an ambulatory species.

11. Teres tubercle position index (TTP) measures the position of the teres tubercle along the humerus. TTP exhibits little difference between semi-aquatic and ambulatory soricids, but increases substantially with increased semi-fossoriality and fossoriality (Supplementary material Figure 1k). Exceptions are include Congosorex phillipsorum (TTP = 39) and Myosorex blarina (41), which have lower index values than expected for semi-fossorial shrews, and ambulatory Blarinella quadricaudata (46), with a higher index than expected.

12. Humeral epicondylar index (HEB) is the width of the distal humerus relative to its length. The index typically increases (greater relative width) in mammals with increasing fossoriality (^{Hildebrand 1985}b), and among rodents HEB increases (broader distal humerus) from ambulatory to semi-fossorial to semi-aquatic to fossorial species (^{Samuels and Van Valkenburgh 2008}). Among soricids, mean values increase from ambulatory to semi-aquatic to semi-fossorial to fossorial species (Supplementary material Figure 1l). There is extensive overlap in index values among ambulatory, semi-aquatic, and semi-fossorial groups, making this index useful for distinguishing only the more fossorial species.

13. Radial distal width index (RDW) measures the relative width of the proximal end of the radius. Ambulatory and semiaquatic soricids tend to have lower RDW (narrower proximal radius), whereas semi-fossorial and fossorial species tend to have larger RDW (Supplementary material Figure 1m). There is extensive overlap, however, between terrestrial and semiaquatic species and between semi-fossorial and fossorial species.

14. Olecranon length index (OLI) represents the relative length of the olecranon process of the ulna. Semi-fossorial and fossorial mammals generally have a longer olecranon process to accommodate a larger triceps brachii, resulting in larger OLI (^{Reed 1951}; ^{Vizcaino and Milne 2002}; ^{Samuels and Van Valkenburgh 2008}; ^{Woodman and Gaffney 2014}). Among rodents, OLI increases from ambulatory to semi-fossorial to semi-aquatic to fossorial species (Samuels and Van Valkenburgh 2008). Among soricids, mean values for this index increase from ambulatory to semi-aquatic to semi-fossorial to fossorial species (Supplementary material Figure 1n). Overlap among groups, however, limits the usefulness of this index for identifying locomotor modes for individual species.

15. Triceps metacarpal outforce index (TMO), like OLI, measures the relative length of the olecranon process. As for OLI, mean values among soricids increase from ambulatory to semi-aquatic to semi-fossorial to fossorial species (Supplementary material Figure 1o), but there is greater separation between semi-aquatic and semi-fossorial species. The one outlier causing overlap between these two groups is semi-fossorial Myosorex varius (TMO = 14), which has a lower index than is typical.

16. Triceps claw outforce index (TCO), like OLI and TMO, expresses the relative length of the olecranon process, and it exhibits a pattern similar to those shown by these two indices. Mean values increase from ambulatory to semi-aquatic to semi-fossorial to fossorial species (Supplementary material Figure 1p). Overlap between semi-aquatic and semi-fossorial species is again a result of a lower-than-expected index for semi-fossorial Myosorex varius (TMO = 10).

17. Olecranon crest index (OCI) measure of the relative length of the olecranon crest on the olecranon process. Among soricids, there is little difference in TCO between ambulatory and semi-aquatic species, but semi-fossorial and fossorial species exhibit a noticeable increase in the length of the olecranon crest and, therefore, in the index (Supplementary material Figure 1q).

18. Ulnar robustness index (URI) measures the robustness of the ulna. Among rodents, URI increases from ambulatory to semi-fossorial to semi-aquatic to fossorial species (^{Samuels and Van Valkenburgh 2008}). In soricids, this index exhibits a clear pattern of increasing mean values from semi-aquatic to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1r). Overlap among groups, however, limits the usefulness of this index for identifying locomotor modes for most individual species. The semi-fossorial Myosorex varius (URI = 5), in particular, has a much lower URI than would be predicted.

19. Manual distal phalanx index (%DPL) gauges the length of the manual distal phalanx III. There is little difference in this index between ambulatory and semi-aquatic species, but there are clear distinctions among those two locomotor groups combined, and the semi-fossorial and fossorial species (Supplementary material Figure 1s). The overlap in ranges between ambulatory and semi-fossorial groups results from a lower-than-expected %DPL (and shorter distal phalanx) of semi-fossorial Blarina shermani (%DPL = 21) and greater-than-expected index of ambulatory Myosorex kihaulei (23).

20. Manual claw index (%CL) is the relative length of manual claw III. Among soricids, %CL shows increases in mean length from semi-aquatic to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1t). Overlap between the ranges for semi-aquatic and ambulatory species precludes its use for distinguishing individual species having those locomotor modes. In contrast, the ranges for semi-fossorial and fossorial species are distinct from each other and mostly from the other two modes. Exceptions are greater indices than expected for ambulatory Myosorex geata (%CL = 42) and M. kihaulei (46) and lower indices than expected for semi-fossorial Congosorex phillipsorum (39) and Blarina brevicauda jerryrchoatei (41).

21. Manual claw support index (%CLS) represents the proportion of manual claw III supported by underlying distal phalanx III. Mean values of this index increase from ambulatory to semifossorial to semi-aquatic to fossorial species (Supplementary material Figure 1u), but the great range of variation among semi-aquatic species and the consequent overlap with other locomotor groups prevents this index from being useful for identifying locomotor modes for individual species.

22. Metacarpal width index (MW3) represents the relative robustness of manual metacarpal III. There is a clear pattern of increase in this index, indicating relatively more robust bones of the manus, from semi-aquatic to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1v). Overlaps in values between semi-aquatic and ambulatory species and between semi-fossorial and fossorial species limit the usefulness of this index for distinguishing individual modes, but there is clear separation of most species with adaptations for digging.

23. Phalangeal index (PI) shows the relative lengths of the proximal and middle phalanges of manual ray III. Among the soricid species tested, mean indices increased from fossorial to semi-aquatic species to semi-fossorial species to ambulatory species (Supplementary material Figure 1w). The ranges in values of semi-aquatic, semi-fossorial, and ambulatory species overlap extensively. Fossorial species, however, have extremely low PI.

24. Manus proportions index (MANUS) measures the relative length of the proximal phalanx of manual ray III. Among rodents, mean MANUS increases from fossorial to semi-aquatic to semi-fossorial to ambulatory to arboreal and gliding species (^{Samuels and Van Valkenburgh 2008}; ^{Nations et al. 2019}). In the Soricidae tested, values for MANUS overlap extensively among semi-aquatic, ambulatory, and semi-fossorial modes (Supplementary material Figure 1x). Fossorial species (i. e., Surdisorex) exhibit particularly low MANUS values and are distinct from all other species except semi-aquatic Nectogale elegans (MANUS = 48) and semi-fossorial Myosorex blarina (50).

25. Crural index (CI) measures the relative lengths of the femur and tibiofibula. Among rodents, this index decreases (longer femur, shorter tibiofibula) with increasing fossoriality, but increases in semi-aquatic species (^{Samuels and Van Valkenburgh 2008}). Although shrews have a relatively longer tibiofibula to begin with, they show a similar pattern, with mean values increasing from fossorial to semi-fossorial to ambulatory to semi-aquatic species (Supplementary material Figure 1y). Overlap in range among fossorial, semi-fossorial, and ambulatory modes is relatively large, making locomotor mode difficult to determine for most individual species. Semi-aquatic species are mostly distinct, overlapping only with Sorex sonomae (CI = 175) and S. cinereus (177), which have large indices for ambulatory species.

26. Pes length index (PES) represents the relative length of the hind foot. Among rodents, this index increases (relatively longer foot) from fossorial to semi-fossorial to ambulatory to semi-aquatic species (^{Samuels and Van Valkenburgh 2008}). Soricids exhibit a similar pattern, and PES is particularly good for distinguishing semi-aquatic species (Supplementary material Figure 1z).

27. Femoral robustness index (FRI) quantifies the breadth of the femur shaft. Among rodents, this index increases (more robust femur) from ambulatory to semi-fossorial to fossorial to semi-aquatic species (^{Samuels and Van Valkenburgh 2008}). Among rodents, mean values for FRI increase from ambulatory to semi-fossorial to semi-aquatic to fossorial species (Supplementary material Figure 1 α). In both groups, there is considerable overlap among locomotor groups, making it difficult to distinguish locomotor mode for a particular species.

28. Femoral epicondylar index (FEB) is the relative distal breadth of the femur. Among rodents, mean FEB is lowest (relatively smaller muscle attachment area) in ambulatory species and is sequentially larger in semi-fossorial, fossorial, and semi-aquatic species (^{Samuels and Van Valkenburgh 2008}). FEB exhibits a slightly different pattern in soricids, increasing from ambulatory to fossorial to semi-fossorial to semi-aquatic species (Supplementary material Figure 1β). There is extensive overlap among groups, but some ambulatory species and some semi-aquatic species are distinguishable.

29. Distal tibiofibular articulation index (DTA) measures the relative width of the articular region for the astragalus. The ranges of this index overlap extensively among groups, rendering this index essentially useless (Supplementary material Figure 1γ).

30. Pedal distal phalanx index (%hDPL) is the relative length of the pedal distal phalanx III. This index shows a clear pattern of increasing (relatively longer distal phalanx) from semi-aquatic to ambulatory to semi-fossorial to fossorial species. Although this index clearly separates semi-fossorial and fossorial locomotor modes. there is considerable overlap between the ranges of semi-aquatic and ambulatory modes (Supplementary material Figure 1δ).

31. Pedal claw index (%hCL) is the relative length of the claw of pedal ray III. Like the pedal distal phalanx index (%hDPL), %hCL shows a clear pattern of increasing (longer claw) mean values from semi-aquatic to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1ε). Although there is greater overlap among the ranges of the four locomotory modes, there is greater separation of some semi-aquatic species from ambulatory species.

32. Pedal claw support index (%hCLS) is the proportion of the claw of pedal ray III supported by the distal phalanx. Values of this index for ambulatory and semi-aquatic species overlap nearly completely but show higher values (relatively greater support) in semi-fossorial and fossorial species (Supplementary material Figure 1ζ).

33. Tail length index (%TAIL) measures the relative length of the tail. Among shrews, there is a clear pattern of increase in the mean index (greater relative tail length) from fossorial and semi-fossorial species to ambulatory species to semi-aquatic species. There is considerable overlap in ranges among groups, but most semi-aquatic species have longer tails than those in other locomotor modes (Supplementary material Figure 1 η). The longer tail of semi-aquatic species may be used to provide added thrust and to prevent yaw rotation while swimming (^{Fish 1982}, ²⁰⁰0). Overlap in the ranges of tail lengths between ambulatory and semi-aquatic shrews is mostly a result of the relatively short tail of semi-aquatic Nectogale elegans (%TAIL = 51) and the relatively long tails of ambulatory Sorex cinereus (72) and S. sonomae (73). As expected (^{Shimer 1903}), semi-fossorial and fossorial species have the shortest tails, with the exception of semi-fossorial Congosorex phillipsorum, which has an unexpectedly long tail (58).

34. Relative robustness index (RR) compares the breadths of the humerus and femur. This index exhibits a progressive increase in mean values (increasing robustness of the humerus) from semi-aquatic to ambulatory to semi-fossorial to fossorial species (Supplementary material Figure 1θ). There is considerable overlap among ranges of values, making it difficult to distinguish locomotor mode for a particular species.

Mean percentile ranks. A univariate plot of the mean percentile ranks calculated for each of the 52 soricid taxa is shown in Figure 2a. The four locomotor modes mostly form distinct groupings, although there is overlap among some of the modes. As in previous studies of locomotor mode in soricids (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015b}; ^{Woodman and Wilken 2019}), there is a clear trend of increase in mean percentile rank from ambulatory to semi-fossorial to fossorial taxa. Semi-aquatic species all have relatively low mean ranks, and their range overlaps that of the lower ranked ambulatory species (Sorex cinereus, Suncus hututsi, Sorex hoyi). There is also overlap of one semi-fossorial species (Cryptotis phillipsii) with the highest-ranked ambulatory species. In the latter case, the overlap may result from a lack of data, as C. phillipsii is represented by only six indices (Table 3). Among the five species of unknown locomotor mode, four species (Cryptotis endersi, C. gracilis, C. meridensis, C. monteverdensis) plot with the higher-ranked ambulatory species. The fifth species (C. thomasi) plots between the ambulatory species (and Cryptotis phillipsii) and the bulk of the semi-fossorial species, but is more closely allied to the latter.

PCA of locomotor indices. In the PCA of 17 locomotor indices, the first three principal components had high eigenvalues and together accounted for >94 % if the variation in the model. Fourteen indices contributed positively to the first principal component (PC1), which alone represented nearly 79 % of the variation. PC1 was most strongly influenced by four variables: CLI, CLAW, %CL, and negatively weighted %TAIL (Table 4). The second principal component (PC2) represented %TAIL and constituted about 12 % of variation. The third principal component (PC3), accounting for <4 % of the variation, was most influenced by PI, SHI, and negatively weighted FOOT.

In a plot of factor scores on PC1 (Figure 2b), a priori locomotory groups are mostly separated along PC1, with semi-aquatic species having the lowest scores, and ambulatory, semi-fossorial, and fossorial groups having increasingly greater scores, respectively. Ambulatory species exhibit two distinct clusters along this axis. The ambulatory group with the lower scores includes species of Sorex and Cryptotis, and the group with the larger scores includes Cryptotis parvus, Blarinella quadricaudata, and species of Myosorex. There are also two clusters of semi-fossorial species. The group with the lower scores includes species of Myosorex and Blarina, and that with the larger scores is comprised of Myosorex zinki and species of Cryptotis. The bimodal patterns within the ambulatory and semi-fossorial groups indicate that species in different genera have somewhat different suites of characters associated with a particular locomotor mode (^{Woodman and Wilken 2019}).

One exception to the general pattern is ambulatory Sorex cinereus, which plotted with semi-aquatic species. Its low score on PC1 resulted from its low CLI and %CL (relatively short foreclaw) and high %TAIL (relatively long tail). Another exception is semi-fossorial Congosorex phillipsorum, which plotted with the ambulatory species. Its low score also resulted from its low CLI, %CL, and %DPL (short foreclaw and distal phalanx relative to other semi-fossorial species) and high %TAIL (long tail). The unique combination of ambulatory and semi-fossorial traits in C. phillipsorum previously was discussed in detail in ^{Woodman and Stabile (2015}b).

In a plot of factor scores on PC1 and PC2 (Figure 2c), the second factor axis separates fossorial species and most semi-aquatic species from ambulatory and semi-fossorial species. It also separates subgroupings of semi-fossorial shrews with semi-fossorial Cryptotis and Myosorex zinki plotting along the positive portion of PC2, whereas Blarina and other semi-fossorial Myosorex plot along the negative part of the axis.

The third factor axis (not shown) provides no discrimination among the a priori locomotor groupings. Within the ambulatory group, however, the low scores of the three species of Myosorex separate them from ambulatory taxa in other genera. Within the semi-fossorial group, PC3 separates three subgroupings that consist of three species of Myosorex (low scores); most taxa of Blarina, Congosorex phillipsorum, and Cryptotis celaque (intermediate scores); and Blarina carolinensis and four species of Cryptotis.

Figure 2 Scaling of locomotory modes: (a) Plot of mean percentile ranks calculated from up to 23 locomotor indices from 52 taxa of soricids, including species of unknown locomotor mode (Table 3). (b) Univariate plot of scores on PC1 (78.8% of variance) from PCA of 17 locomotor indices from 33 taxa (Table 4). (c) Bivariate plot of scores on PC1 and PC2 (12.2%) from a PCA of 17 locomotor indices from 33 taxa (Table 4). Species of unknown locomotor mode were not included in the PCA because of missing data. Key to all symbols is in Figure 2c. 

DFA of locomotor indices. Plots of scores from the DFA of 17 locomotor indices show clear separation of the four locomotor groups along combinations of the first three canonical variates (Table 5; Figure 3). Fossorial species are strongly separated along CV1, and the other three locomotor groups are separated from each other along CV2 (Figure 3a). Semi-aquatic and semi-fossorial species overlap along CV3, but are separated from both ambulatory and fossorial species (Figure 3b).

The post hoc classification matrix indicates that 100 % of taxa were correctly classified into their a priori locomotor groups by the DFA (Table 5). In the jack-knifed classification, five species were misclassified as belonging to a locomotor mode other than their a priori mode. Ambulatory Sorex cinereus and Cryptotis tropicalis were both misclassified as being semi-aquatic; ambulatory Myosorex cafer was misclassified as semi-fossorial; and semi-fossorial Myosorex blarina and M. varius were misclassified as being ambulatory.

PCA of species having unknown locomotor mode. In the PCA carried out in an attempt to classify four species whose locomotor mode was unknown, eight of 10 locomotor indices contributed positively to the first principal component (PC1). PC1 accounted for more than 77 % of the variation in the model (Table 6), and it was most strongly influenced by three variables: CLI, CLAW, and negatively weighted %TAIL. As in the 17-variable model, a priori locomotory groups are mostly separated along this axis, from semi-aquatic species with the lowest scores to ambulatory to semi-fossorial to fossorial groups having increasingly higher scores (Figure 4). As in the 17-variable model, semi-fossorial species plotted in two primary clusters with the same compositions as in that model. In contrast, ambulatory species were more cohesive. Ambulatory Sorex cinereus, which plotted with semi-aquatic species, and semi-fossorial Congosorex phillipsorum, which plotted with ambulatory species, again proved to be exceptions to the general pattern.

Among the species of uncertain locomotor mode, Cryptotis gracilis and C. meridensis plotted within the distribution of ambulatory species; C. thomasi occurred between the ambulatory species (and Congosorex phillipsorum) and semi-fossorial species; and C. endersi plotted with the Blarina grouping of semi-fossorial species rather than with the Cryptotis grouping of semi-fossorial species (Figure 4, Table 6).

Figure 3 Plots of scores a) on CV1 and CV2 and b) on CV2 and CV3 from a DFA of 17 locomotor indices from 33 species (Table 5). 

DFA of species of unknown locomotor mode. Plots of scores from the DFA of 10 locomotor indices exhibit similar patterns as those from the 17-variable model, although the separations among locomotor groups are generally not as clear (Table 7; Figure 5). Fossorial species are again strongly separated along CV1, whereas the other three locomotor groups are separated from each other along a combination of CV1 and CV2 (Figure 5a). Semi-aquatic and semi-fossorial species overlap along CV3, but are separated from both ambulatory and fossorial species (Figure 5b).

The post hoc classification matrix had a correct classification rate of nearly 97 % (Table 7). The only misclassification was ambulatory Sorex sonomae, which was misclassified as semi-aquatic. Among the species of uncertain locomotor mode, Cryptotis gracilis was classified as semi-aquatic, C. meridensis and C. thomasi as ambulatory, and C. endersi as semi-fossorial (Figure 5; Table 7). In multivariate space, C. gracilis actually plots by itself away from the a priori locomotor groups, although it is physically closest to semi-aquatic species. Similarly, C. endersi plots in its own multivariate space between the ambulatory and semi-fossorial groups of species, but it is physically closest to the semi-fossorial group.

Discussion

As noted previously, there is considerable variation among soricids in skeletal characteristics that are typically associated with locomotion (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015b}; ^{Woodman and Wilken 2019}). Such variation suggests that individual species’ abilities to use various substrates are more nuanced and diverse (e. g., ^{Mendes-Soares and Rychlik 2009}; ^{Tapisso et al. 2013}). Rather than representing discrete categories permitted by classification, locomotor modes exhibit diverse ranges in morphology that are not always easily defined or distinguished. This observation suggests that not all morphological traits associated with a particular locomotor mode-or the indices used to gauge them-are necessarily adaptive. Instead, phylogeny may control or at least contribute to some traits. Hence, a morphological trait that varies among species or groups of species within a particular locomotor mode may not be employed, or may not be employed to the same extent or purpose, in each species.

Morphological diversity may also reflect the reality that individuals are not entirely restricted in their use of substrate or in their locomotor behavior by either the possession or lack of specialized traits. Morphological traits that are related to particular modes of locomotion may simply reflect enhanced abilities that permit a species to specialize to a greater extent in certain behaviors that, given a shrew’s high metabolism, are most likely related to foraging strategies. This likely accounts for the close correspondence between the numbers of species that appear specialized for ambulatory, semi-fossorial, and semi-aquatic locomotor behaviors (^{Hutterer 1985}) and those that specialize on foraging for epigeal, hypogeal, and aquatic prey (^{Churchfield 1990}). Despite this, ambulatory species can be vigorous scratch-diggers despite the lighter bone structure of their arms and their relatively short foreclaws (^{Chamberlain 1929}). Ambulatory Cryptotis parvus, Sorex cinereus, and S. hoyi, and the semi-aquatic S. palustris are reported to excavate subterranean tunnels of varying lengths, depths, and degrees of complexity (^{Cahn 1937}; ^{Davis and Joeris 1945}; ^{Sorenson 1962}; ^{Tuttle 1964}; ^{Beneski and Stinson 1987}). Similarly, non-aquatic shrews, such as ambulatory Sorex araneus, S. cinereus, S. fumeus, and S. minutus, have been documented to be capable swimmers (^{Dagg and Windsor 1972}; ^{Hanski 1986}). Based on the diversity of species and numbers of individuals that have been found in the digestive tracts of various freshwater fishes (e. g., ^{Huish and Hoffmeister 1947}; ^{Hodgson 1986}; ^{Moore and Kenagy 2004}; ^{Jung et al. 2011}; ^{Lisi et al. 2013}), a number of additional ambulatory and semi-fossorial species readily take to water.

There is also no reason to assume that any particular species cannot possess traits that enhance its abilities for more than one locomotor mode. A ready example in the Talpidae is the Condylura cristata, which possesses numerous anatomical traits associated with fossorial locomotion, but which is also an active swimmer and may forage dominantly on hypogeal or aquatic prey, depending on where it lives (^{Petersen and Yates 1980}).

Figure 4 Plot of scores on PC1 from a PCA of 10 locomotor indices from 33 species of known locomotor mode and four species of uncertain locomotor mode (Table 6). 

Despite the foregoing caveats, a number of generalizations can be suggested regarding the external and skeletal morphological traits marking common, generalized locomotor modes in soricids.

Ambulatory shrews. Most species of shrews are ambulatory and have short legs and a moderately long tail (^{Hutterer 1985}). The foreclaws and hind claws are short (%DPL, %CL, %hDPL, %hCL), the manual distal phalanges are typically somewhat shorter than the pedal distal phalanges (CLAW), although the claws on the fore feet and hind feet may be of approximately the same length (CLI). This means the foreclaw is less supported by the underlying distal phalanx (%CLS) than the hind claw (%hCLS). This relatively unspecialized body form is assumed to be the basic plan for soricids from which more specialized swimming, climbing, and digging forms evolved, but such singular directionality remains to be substantiated. Regardless, the generalized body morphology of ambulatory shrews represents the model to which more specialized shrews are compared and contrasted (^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015b}; ^{Woodman and Wilken 2019}).

Figure 5 Plots of scores a) on CV1 and CV2 and b) on CV2 and CV3 from a DFA of 10 locomotor indices from 33 species of known locomotor mode and four species of uncertain locomotor mode (Table 7). 

Semi-aquatic shrews. Externally, semi-aquatic shrews typically possess long tails relative to other shrews, and there may be a dorsal; dorsal and ventral; or dorsal, ventral, and lateral keels of stiff hairs. The tail probably functions like that of a muskrat (Ondatra zibethicus) tail, by providing a small amount of forward thrust, but more importantly, by preventing the animal from yawing (^{Fish 1982}). In contrast with the muskrat, which swims with just the hind limbs (^{Fish 1984}), however, semi-aquatic and terrestrial shrews typically paddle by alternately stroking the front and hind limbs (^{Jackson 1928}; ^{Dagg and Windsor 1972}; ^{Mendes-Soares and Rychlik 2009}). There is also a fringe of stiff hairs on the lateral edges of the digits of the hands and feet. In some species, notably Nectogale, the digits are partly webbed (^{Hutterer 1985}). The foreclaws and hind claws are generally short (%DPL, %CL, %hDPL, %hCL), the foreclaws and manual distal phalanges typically are somewhat shorter than the hind claws and pedal distal phalanges (CLI, CLAW). The underlying manual distal phalanx, however, supports a greater proportion of the foreclaw than is typical in, for example, ambulatory shrews (%CLS). Semi-aquatic shrews typically have long hind limbs and hind feet relative to other shrews. Proportionally, the femur averages 28 % (range 27 to 29 %, n = 6 species), tibiofibula 50 % (44 to 52), and metacarpal III 22 % (19-26) of their combined length. This is in contrast to ambulatory shrews in which the femur averages 33 % (range 29 to 36 %, n = 9 species), tibiofibula 50 % (49 to 52), and metacarpal III 17 % (15 to 19) of their combined length, and to semi-fossorial and fossorial shrews, in which the femur averages 35 % (range 33 to 36 %, n = 9 species), tibiofibula 50 % (48 to -52), and metacarpal III 15 % (14 to 16) of their combined length. Moreover, the humerus of semi-aquatic shrews tends to be long in proportion to the femur (HFI), so much of the length of hind limb is a result of the proportionally longer tibiofibula (CI) and hind foot (PES).

Skeletally, the emphasis on the hind limbs in semi-aquatic shrews may be further illustrated by the relatively broad epicondyles of the femur (FEB), from which the plantaris, gastrocnemius, and the extensor digitorum longus muscles originate. The long bones of the limbs and manus bones are not particularly robust (HRI, RDW, URI) and are generally similarly proportioned to those of ambulatory shrews, with the exception of the femur (FRI), which can be considerably more robust than those of ambulatory and even semi-fossorial shrews (RR). The humerus has relatively small muscle attachment areas in the short deltopectoral crest (SMI) and small teres tubercle of the humerus (HTI), but can have a relatively broad epicondylar region (HEB) relative to ambulatory shrews. The olecranon process of the ulna tends to be slightly longer than in ambulatory shrews (OLI, TMO, TCO), suggesting the transmission of greater force from the triceps brachii muscle, although the insertion for that muscle (OCI) is no larger than in ambulatory shrews and the ulna averages slightly less breadth, therefore rendering it somewhat less resistant to bending and shearing stresses.

Semi-fossorial and fossorial shrews. In contrast to semi-aquatic shrews, the emphasis in semi-fossorial and fossorial shrews is on the changes in the morphology of the forelimb, particularly the humerus, ulna, and manus (^{Woodman and Morgan 2005}; ^{Woodman and Stephens 2010}; ^{Woodman and Gaffney 2014}; ^{Woodman and Stabile 2015a}, ^2015b; ^{Woodman and Timm 2016}; ^{Woodman and Wilken 2019}; ^{Woodman et al. 2019}). Among species in these two locomotor groups, morphological changes can appear to be gradual and progressive (e. g., Figs. 2, 3, 5), but traits do not necessarily co-vary in the same way or to the same degree (e. g., Figs. 1, 4, 6).

Externally, semi-fossorial and fossorial shrews are typically characterized by having small (or absent) pinnae, short tails, broadened forefeet, and elongated and broadened foreclaws (%DPL, %CL). They also have elongated and broadened hind claws (%hDPL, %hCL), although not to the same degree as the foreclaws (CLI,CLAW), and there is increasing support from the underlying distal phalanx as the claws increase in size (%CLS, %hCLS). There may be a tendency to reduce the overall length of the hind limbs relative to the forelimbs (IM) and the hind feet relative to the fore feet (FOOT), but, in contrast, there is a definite trend toward reduction of the length of the humerus relative to that of the femur (HFI).

Skeletally, the long bones of the limbs and manus bones become increasingly robust (HRI, RDW, URI, FRI, RR), particularly relative to those of ambulatory shrews. The humerus shortens, but becomes much broadened with enlarged teres tubercle (HTI), deltopectoral crest (SMI), epicondyles (HEB), and other regions involved in muscle attachment. The olecranon process of the ulna elongates and broadens relative to the functional arm (OLI, TMO, TCO), allowing for the transmission of much greater force from the triceps brachii muscle, and the insertion for that muscle on the olecranon process (OCI) greatly increases. In contrast, the breadth of the distal epicondyles of the femur (FEB) are only slightly enlarged relative to those of ambulatory shrews, and they are generally smaller than those of semi-aquatic shrews.

Locomotory modes of the “unknowns”. Cryptotis gracilis and members of the C. thomasi group of species (C. endersi, C. meridensis, C. monteverdensis, C. thomasi) have defied easy characterization of their locomotory modes based on external and skeletal characters (Supplementary material Figure 1). These shrews all have relatively long foreclaws and hind claws and associated distal phalanges, like semi-fossorial shrews, but the claws are not particularly broad, and their tails in some cases (e. g., C. gracilis, C. endersi, C. monteverdensis) are rather long, as in ambulatory shrews. Previous analyses of these species showed most of them to plot between the ambulatory and semi-fossorial shrews, with C. gracilis somewhat more semi-fossorial (^{Woodman and Timm 2016}; ^{Woodman 2019}; ^{Woodman and Wilken 2019}).

In the current analyses, most of these species remain ambiguous, in part because of a continued lack of data regarding relevant characters, particularly for the rare C. endersi and C. monteverdensis (^{Pine et al. 2002}; ^{Woodman and Timm 2016}). Cryptotis gracilis plots out as ambulatory based on mean percentile ranks (Figure 1; Table 2) and PCA (Figure 5; Table 5), but it was classified by DFA (Figure 5; Table 6) as semi-aquatic. In reality, it is separate from all other species in multivariate space between the ambulatory and semi-aquatic groups of species. It is unlikely to be truly semi-aquatic, as it plots as an ambulatory species for two of the more relevant characteristics of semi-aquatic species, represented by the locomotor indices PES and %TAIL (Figure 1; Table 2), and because it lacks more obvious external characteristics of typical semi-aquatic shrews, such as the fringes of short hairs lining the digits and tail.

The four members of the C. thomasi group all plot as ambulatory, semi-fossorial, or intermediate between those two modes. Cryptotis meridensis is consistently ambulatory, and C. monteverdensis plots as ambulatory based on mean percentile rank, the only analysis in which it could be included. Cryptotis endersi plots as ambulatory in the mean percentile rank analysis, and it is classified as semi-fossorial based on both PCA and DFA, but it really plots as somewhat intermediate between both groups (Figure 5; Table 6). In contrast, C. thomasi plots as intermediate between the ambulatory and semi-fossorial groupings in both the mean percentile rank analysis and the PCA, but was classified as ambulatory in the DFA.

All five of these species occupy high elevation habitats in southern Central America and Andean South America, and they may represent one or more unique locomotor adaptations or combinations of adaptations for foraging in high-elevation forests and páramo-like habitats.

1. Of 34 locomotor indices tested in this study, 23 (IM, HFI, FOOT, CLAW, CLI, SMI, HRI, HTI, TTP, HEB, TCO, OCI, URI, %DPL, %CL, MW3, CI, PES, FEB, %hDPL, %hCL, RR, %TAIL) proved effective for discriminating one or more of the four a priori locomotor groups (ambulatory, semi-aquatic, semi-fossorial, fossorial).

2. Among three analyses of locomotor indices, percentile ranking was the only analysis that permitted the inclusion of all 52 taxa, including species of unknown locomotor mode. The lack of data for some taxa, however, results in uneven morphological comparisons across taxa, and there was considerable overlap of some locomotor groups, particularly the semi-aquatic and ambulatory groups.

In contrast, PCA and DFA require complete datasets, and the largest sample I could compile was 17 indices from 33 taxa, which excluded the unknowns in this study. The first principal component (PC1) from PCA distinguished the major (and some minor) locomotor groupings, but there was overlap between locomotor groups that makes it difficult to identify locomotor mode for some species. Plotting PC1 and PC2 provided greater discrimination among groups, but some overlap remains.

DFA classification of a priori locomotor groups provided the best discrimination among locomotor groups, but requires complete datasets.

3. Classification of four species of unknown locomotor mode using PCA and DFA of 10 locomotor indices provided contrasting results. One species was classified as ambulatory by PCA and semi-aquatic by DFA; one species was classified as ambulatory by both analyses; one species was classified as intermediate between ambulatory and semi-fossorial by PCA and semi-fossorial by DFA; and one species was classified as semi-fossorial by both. The lack of complete datasets clearly hampered the analyses, but there is also strong indication that some of these species have unique combinations of morphological traits that are not easily explained by comparison with other shrews, even those in the same genus.

4. Results here confirm that variation in skeletal traits typically exists within defined locomotor modes. Such variation probably results in part from the reality that 1) most species (and individuals) are not restricted to a single mode, but engage in a variety of locomotor behaviors to varying degrees; 2) the traits that we can measure or otherwise gauge are not necessarily adaptive for a particular locomotor mode; and 3) seemingly similar traits may be employed in different ways by different species or populations.