Ecology

Exp 1: chemo-tactile conditioning of the proboscis extension response (PER)Bee foragers may assess the quality of floral nectars through chemo-sensilla located on their antennae47. In this first experiment, we asked whether nectar-relevant concentrations of GABA, β-alanine, taurine, citrulline and ornithine can be detected by bees through their antennae. To this aim, we used a chemo-tactile differential conditioning of PER protocol48 in which different groups of bees were trained to discriminate one of the five NPAAs from water. Briefly, tethered bees experienced five pairings of a neutral stimulus (either NPAA-laced water or water) (CS+) with a 30% sucrose solution reinforcement (US) and five pairings (either water or NPAA-laced water) (CS−) with a saturated NaCl solution (US) used as punishment. The results showed that bees increased their response to both the rewarded (CS+) and the punished (CS−) stimuli over the ten conditioning trials (GLMM, trial: GABA: n = 76, χ2 = 65.75, df = 1, p  More

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OverviewWe used long-term time series of lake temperature profiles to determine the magnitude of thermal habitat change in 139 widely distributed lakes. Time series were interpolated across depth and season to generate data with consistent resolutions across lakes. To assess temperature change, we used a metric, ‘thermal non-overlap’, based on the percentage of two kernel density estimations of lake temperature which are non-overlapping. We calculated the metric for a range of plausible seasonal and depth habitat restrictions for aquatic species in the face of climate change. We used BRT to explain variability across lakes in their thermal habitat non-overlap as a function of lake characteristics (mean depth and latitude), characteristics of the time series for each lake (starting day of the year, ending day of the year, starting year and ending year, average number of sampling dates per year, long-term trend in the number of sampling dates per year, long-term trend in the yearly seasonal range of sampling dates), the habitat restriction values (season and depth) and the location of the time series delineation for thermal non-overlap calculations (30th, 50th and/or 70th quantiles of the years included in each lake’s time series).Study sitesWe compiled long-term lake temperature data from 139 lakes across the globe. Temperature variations in many of these lakes have already been linked to climate change1,2,19,20,57,58, but temperature change in at least one lake may be partially due to background climate variation in addition to anthropogenic climate change (Atlantic Multidecadal Oscillation in Lake Annie)59. The lakes included in our analysis represent a wide range of surface area (0.02 to 68,800 km2), maximum depth (2.3 to 1,642 m), latitude (60 °S to 69 °N) and elevation (−212 to 1,987 m above sea level) (see Supplementary Table 1 for more information).Temperature dataIn total, we used more than 32 million lake temperature measurements for our analyses. The number of observations per lake ranged from 368 (Lake Stensjon) to 7,636,767 (Lake Superior) with approximately 232,000 observations per lake on average. Temperature data from each lake came from in situ temperature profiles60,61,62,63,64 for lakes smaller than 169 km2 and from a combination of in situ temperature profiles and remotely sensed surface water temperatures for 21 larger lakes. Remote sensing data were used in recognition that temperature and warming rates can vary substantially across latitude and longitude for large lakes19,20,21.The mean length of the temperature time series was 36 years with a range from 15 to 101 years. All lakes had temperature data which started in the year 2000 or earlier and ended in 2000 or later. Lakes had on average 29 temperature profiles per year (inner quartile range: 7–26). In situ temperature data were measured using a wide variety of temperature sensors. Data collection methods included regularly collected discrete temperature profiles, high-resolution thermistor chains and other commonly accepted tools for measuring aquatic temperature. The in situ data are publicly available through the environmental data initiative60.Remotely sensed lake surface temperatures were measured using the Advanced Very High-Resolution Radiometer (AVHRR) and processed by the Group for High Resolution Sea Surface Temperature (GHRSST) project65. AVHRR data have been validated against buoy data from the North American Great Lakes and found to have a root mean squared error of 0.55 °C compared with in situ measurements2. AVHRR temperature data were included to capture horizontal variability in temperature and warming in 21 of the 139 lakes that would not be captured by temperature profiles from a single central location19,20,21. AVHRR data were pooled with in situ data for temperature interpolation.Temperature interpolationTemperature data were spatially and temporally interpolated for each lake. All temperature profile data were first linearly interpolated across depth because temperature variability with depth is highly constrained by lake physics and typically allows for robust interpolations. The largest data gap over which depth interpolation occurred was 0.1 × mean depth of each lake. Following interpolation across depth, data were interpolated across time using standard spline interpolation models with a Kalman filter66. The model output was used to fill data gaps to produce a continuous, daily time series over the day of the year range for which temperature profiles had been regularly measured. Some times of the year were excluded from specific lakes because they lacked regular measurements throughout the length of the long-term time series. Thus, the same starting and ending day of the year was used for each lake throughout its time series, and was often shorter than the full annual cycle (Supplementary Table 1). The largest gap in time over which interpolation occurred was 30 days and this included extrapolations for lakes with missing data at the beginning or end of seasonal coverage in a specific year. Years with longer gaps were omitted from the analysis and the length of the seasonal coverage was optimized to minimize the number of years that needed to be removed. For large lakes with many sampling points (for example, Baikal, Superior, Victoria), temperature data were divided into 1,000 km2 latitude–longitude bins and interpolated across depth and across time separately for each bin. The mean seasonal coverage of the interpolated lake time series was 245 days per year with a minimum of 17 days per year and a maximum of 365 days per year.The interpolated temperature output had a daily temporal resolution and a depth resolution which varied continuously over depth. At the lake surface, we interpolated temperatures every 0.1 m (for example, 0 m, 0.1 m, 0.2 m), to every 1 m starting at a depth of 10 m (for example, 10 m, 11 m, 12 m) and every 100 m starting at a depth of 1,000 m (for example, 1,000 m, 1,100 m, 1,200 m). These depth increments were used because they consistently gave good coverage over all major lake strata, regardless of each lake’s morphometric characteristics, while minimizing computational intensity by eliminating redundancy within lake strata.Thermal habitat non-overlap calculationsAfter interpolating the temperature data across depth and season for each lake, we bisected it into an early part (part a) and a later part (part b). Parts a and b were iteratively delineated at three points positioned serially along the time series—at the 30th, 50th and 70th quantiles. We averaged the final non-overlap values across these three delineations for each lake so that the results depended less on the somewhat arbitrary decision of where to split the time series. For each delineation, we randomly sampled 10,000 temperature values from each of parts a and b. This was repeated ten times resulting in a total of 300,000 temperature values across all three time series delineations and all ten repetitions for each lake (10,000 × 3 × 10). The sampling probability for temperature values in each comparison was weighted by the volume increment associated with each temperature value (depth increment (Id) × cross-sectional area at each depth (Cd)). Id was calculated as the difference between the depth of the sampled temperature value and the next depth in the depth resolution of the interpolated temperatures. Cd at each depth for each lake was calculated using standard, three-parameter models for estimating lake cross-sectional area based on surface area, maximum depth and mean depth67. For large lakes with temperature data at multiple locations across latitude and longitude, Cd was divided by the number of latitude–longitude bins used for each lake. Temperature values from large lakes were sampled regardless of their associated latitude–longitude bins. As a result of the volume-weighting procedure, temperature measurements were sampled in proportion to the volume of water represented by each value, with temperatures representing larger volumes being sampled more often. As a consequence of this volume-weighting procedure, the resulting temperature distributions were robust to moderate changes in the depths used for the temperature interpolation (Supplementary Fig. 1).We defined thermal non-overlap (TNO) as the symmetric difference (Ө) between the kernel density estimations of temperature values from parts a and b of the time series as a proportion of the union (∪) of both kernel density estimations, following an established method42. Conversely, we defined the thermal habitat overlap (as opposed to non-overlap) as the intersection (∩) of the kernel density estimations as a proportion of the union (∪) of both distributions. All values were converted to percentages by multiplying by 100.$${mathrm{TNO}}left( % right) = 100 times frac{{{{T}}_{{mathrm{recent}}},ominus,{{T}}_{{mathrm{baseline}}}}}{{{{T}}_{{mathrm{recent}}} cup {{T}}_{{mathrm{baseline}}}}} = 100 times left( {1 – frac{{{{T}}_{{mathrm{recent}}} cap {{T}}_{{mathrm{baseline}}}}}{{{{T}}_{{mathrm{recent}}} cup {{T}}_{{mathrm{baseline}}}}}} right)$$
(1)
We used simulations to test the sensitivity of TNO to changes in mean and s.d. of temperature. We primed these simulations with three baseline temperature distributions all with a mean of 15 °C but with varying s.d. (4, 6, 8 °C). We simulated a range of additional temperature distributions by increasing and decreasing the mean and s.d. of the baseline temperature distributions and then calculated the corresponding values of TNO. The simulated change in both mean and s.d. varied from −3 to +3 °C. We found that TNO was sensitive to changes in mean and s.d. but was slightly more sensitive to reductions in s.d. compared with increases. TNO values also depended on the baseline s.d., such that lower starting s.d. elevates values of non-overlap given an equivalent change in temperature (Extended Data Fig. 1).We also quantified null values of thermal non-overlap (TNOo) by repeating the thermal non-overlap calculations but where parts a and b were defined by randomly dividing the individual years of data into two separate groups as opposed to sequentially dividing them along the time series.$${mathrm{TNO}}_{mathrm{o}}(% ) = 100 times frac{{{{T}}_{{mathrm{random}},{{a}}},ominus,{{T}}_{{mathrm{random}},{{b}}}}}{{{{T}}_{{mathrm{random}},{{a}}} cup {{T}}_{{mathrm{random}},{{b}}}}}$$
(2)
To calculate standardized thermal non-overlap (TNOs), we subtracted TNOo from TNO thereby setting the null expectation to zero.$${mathrm{TNO}}_{mathrm{s}}left( {mathrm{% }} right) = {mathrm{TNO}} – {mathrm{TNO}}_{mathrm{o}}$$
(3)
In this case, if the temperature distributions in the recent and baseline time periods were identical, the TNOs would equal approximately zero. Values different from zero reflect a combination of random noise and long-term temperature change. All non-overlap values described in the main text and shown in Figs. 2–6 reflect values of TNOs. A comparison between raw values of TNO and TNOo can be found in Extended Data Fig. 5. Thermal non-overlap values and the null values were calculated using the ‘overlap’ function from the ‘overlapping’ package42 in the R environment for statistical computing and visualization. In the function, we set the number of equally spaced points at which the overlapping kernel density estimation is evaluated to 100 for all comparisons because it minimized the values of TNOo (we considered a range of values from 5 to 10,000).To assess the effect of seasonal habitat restrictions (Slimit) and volumetric habitat restrictions (Vlimit), we modified equations (1)–(3) by comparing temperature values only from a specified range of depths and/or days of the year. We considered a range of habitat restrictions scaled from 0 to 0.95, where 0.95 is the most restrictive (temperature values were compared from within bins equivalent to 1/20th of the available seasonal and volumetric habitat) and 0 is the least restrictive (temperature values were compared regardless of season and depth). We focused our interpretations on the unitless habitat restrictions (scaled from 0 to 0.95) instead of in units of days or m3 so that habitat restrictions could be more readily compared across lakes. Comparing a Vlimit value of 0.8 across lakes of different sizes assumes that a habitat restriction of 2 m3 in a 10 m3 lake would be comparable to a 20 m3 habitat delineation in a 200 m3 lake. The actual size of the seasonal habitat restrictions for each lake in units of days were calculated using the value of Slimit as follows:$$S = left( {mathrm{doy}}_{mathrm{max}} – {mathrm{doy}}_{mathrm{min}}right)left( {1 – S_{mathrm{limit}}} right)$$where S is the seasonal habitat restriction in units of days, doymax is the maximum day of the year of the lakes’ seasonal coverage, doymin is the minimum day of the year of the lakes’ seasonal coverage and Slimit is the seasonal habitat restriction scaled from 0 to 0.95. For example, in a lake with a seasonal coverage from day of the year 1 to day of the year 365, with an Slimit value of 0.75, we compared randomly selected temperatures from time periods a and b separately for four seasonal bins (days of the year 1–91, 92–183, 184–273 and 274–365). Similarly, the actual size of the volumetric habitat restrictions (V) for each lake in units of m3 were calculated using the value of Vlimit as follows:$$V = left( {mathrm{volume}} right) times left( {1 – V_{mathrm{limit}}} right)$$where V is the volumetric habitat restriction in units of m3, volume is the lake’s total volume and Vlimit is the volumetric habitat restriction value scaled from 0 to 0.95. For example, if a lake with a volume of 100 m3 had a Vlimit value of 0.75, we randomly selected temperature values from time periods a and b which were within four 25 m3 (100 m3 × (1 − 0.8)) bins. Volume bins were subsequently translated into sequential depth bins for the purpose of temperature value selection, making them functionally depth limits, and they are presented as such in the main text.We factorially combined a discrete series of values for Slimit and Vlimit (0, 1/2, 2/3, 5/6, 8/9, 12/13 and 19/20) to test a range of combined seasonal and volumetric habitat restrictions that do not require the overlap or truncation of bins. For reference, habitat restrictions are presented visually for hypothetical ‘Species 1’ (Slimit = 0, Vlimit = 0.8), ‘Species 2’ (Slimit = 0.8, Vlimit = 0) and ‘Species 3’ (Slimit = 0.8, Vlimit = 0.8) examples (Fig. 1). These limits reflect hypothetical restrictions in a species’ habitat due to ecological factors and approximate the habitat available for a low-light specialist phytoplankton (species 1), a spring migratory fish (species 2) and a diapausing benthic invertebrate (species 3). In Fig. 6, the species habitat restriction values for P. rubescens were Slimit = 0.74, Vlimit = 0.89 (Fig. 6).Explaining variability in thermal habitat non-overlapWe used BRT to explain lake-to-lake variability in thermal habitat change (percentage of non-overlap) while accounting for differences in the temporal coverage of each lake’s time series. The predictor variables in the BRT were the starting year of the time series, ending year of the time series, starting day of the year of the seasonal coverage, ending day of the year of the seasonal coverage, average number of sampling dates per year, linear trend (Theil–Sen slope) in the average number of sampling dates per year, linear trend (Theil–Sen slope) in the yearly extent of the time series’ seasonal coverage, lake mean depth, absolute latitude (degrees from the Equator), seasonal habitat restriction, depth habitat restriction and time series delineation. Geospatial and morphometric data for each lake is available from the previously published HydroLAKES database41. Of the available lake characteristics, we used latitude and mean depth because they were most strongly correlated to TNOs values and because they were least correlated to the other predictors in the model. We used a 100-fold cross-validation with a 70–30% split by lake (that is, 70% of lakes were used in each BRT). Model results were averaged to ensure that the patterns described therein were robust to the exclusion of some lakes. We optimized the learning rate for each BRT by iteratively running the model with smaller and smaller learning rates (from 0.8, 0.4, 0.2, 0.1, 0.05 to 0.025) until the number of trees in the model was greater than 1,000, as suggested in previous literature68. We found that the BRT performed well in cross-validation—the correlation between predicted and observed values in the test datasets from the 100-fold cross-validation was moderate on average across models (r = 0.56, Kendall’s rank correlation; see full goodness-of-fit summary statistics in Extended Data Fig. 6). The correlation between the predicted and the observed values was high (r = 0.76, Kendall’s rank correlation) when predictions were averaged across BRT. We found minimal patterning in the model residuals when comparing the model residuals with each predictor variable used in the BRT (Extended Data Fig. 7).To calculate lake-specific mean thermal non-overlap values and facilitate comparison across lakes, we used the BRT to remove the variation in thermal non-overlap attributable to the starting year of the time series, ending year of the time series, starting day of the year of the seasonal coverage, ending day of the year of the seasonal coverage, average number of sampling dates per year, linear trend (Theil–Sen slope) in the average number of sampling dates per year and the linear trend (Theil–Sen slope) in the yearly extent of the time series’ seasonal coverage of each lake’s time series, following previously published work24. We did this by setting the values for these variables to their median and using the BRT to make a prediction for each lake with these medians as predictors, along with each lake’s observed values for mean depth, absolute latitude, seasonal habitat restriction, depth habitat restriction and time series delineation. The residuals from the BRT were then added back to the predicted values used in further analyses and plotting. The mean lake-specific thermal dissimilarities were calculated as the average across all seasonal habitat restrictions (Slimit), depth habitat restrictions (Vlimit) (0, 1/2, 2/3, 5/6, 8/9, 12/13 and 19/20) and all three time series delineations. The statistical significance of these lake-specific thermal non-overlap values was estimated on a continuous gradient and calculated using a Wilcoxon signed-rank test. In the test, we compared TNO values to TNOo values separately for each combination of time series delineation, seasonal habitat restriction and depth habitat restriction (n = 108). The average P values from these tests for each lake are shown in Supplementary Table 1.We compared thermal non-overlap values to a more widely used metric of whole-lake thermal change—whole-lake temperature trends. Whole-lake temperature trends were calculated based on the annual averages of all temperature values sampled for the pairwise thermal non-overlap calculations to maximize the comparability of the resulting temperature trends and thermal non-overlap values. Due to the temperature sampling probability being volume-weighted, the temperature trend was also indirectly volume-weighted. Temperature trends were calculated using Theil–Sen slopes applied to annual mean temperatures and the statistical significance of each trend (P value) was calculated using a bootstrapped one sample Wilcoxon signed-rank test with 1,000 repetitions. The input data for the Wilcoxon signed-rank test were the complete list of all slopes derived from all pairwise combinations of points in the time series. The number of pairwise slopes used in each repetition of the Wilcoxon signed-rank test was equal to the number of years of temperature data for each lake. Whole-lake temperature trends and thermal non-overlap values were not strongly correlated (r = 0.10, Kendall’s rank correlation coefficient; Extended Data Fig. 4). All statistics and graphics were produced in the R statistical computing environment69.Reporting SummaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

Systematic paleontologyOrder Rodentia Bowdich, 182131Family Ischyromyidae Alston, 187632Genus Asiomys Qi, 198733Asiomys dawsoni Qi, 198733Figure 3A–EMaterial. Fragment of right calcaneus (IVPP V24417), early Middle Eocene, Huheboerhe, Irdin Manha Formation, Erlian Basin, China.Description. The bone is damaged and most probably that of a juvenile as it shows loss of the tissue in the extremities of the bone such as the calcaneal tuber and calcaneal eminence, which are usually less calcified in juveniles. The bone is relatively large (Table 1), with an elongated calcaneal tuber and a relatively short body (Fig. 3A–D). The sustentaculum tali is partly damaged; it has a subcircular articulation facet, which was probably more extended craniocaudally than mediolaterally. The caudal margin of the sustentaculum tali is inclined cranially, similar to the condition seen in species A and more than in species B (Fig. 3A). The sustentacular facet overlaps about one-half of the craniocaudal reach of the ectal facet. The groove for the ‘spring ligament’ (sensu Szalay and Decker34), which runs along the medial edge of the sustentaculum tali, is poorly pronounced. Likewise, the calcaneal groove for the tendon of the flexor fibularis muscle is shallow and poorly marked, most probably due to poor preservation. The ectal facet is relatively wide and similarly shaped as in species B (below). The peroneal process is completely damaged.Table 1 Measurements (in mm) of ischyromyid calcanei from the early middle Eocene of the Erlian Basin, Nei Mongol, China.Full size tableFigure 2Linear measurements of the calcaneus. Abbreviations: AEW, ectal facet anterior width; BL, calcaneal body length; BW, calcaneal body width; CCL, calcaneocuboid facet length; CCW, calcaneocuboid facet width; CL, calcaneus length; CMT, calcaneus maximum thickness; CW, calcaneal width; EL, ectal facet length; TEW, ectal facet total width; TL, tuber calcanei length; TT, tuber calcanei thickness; TW, tuber calcanei width; TWM, tuber calcanei width in mid-length. (Figure created in Corel Draw X4 (v.14.0.0.567) by Łucja Fostowicz-Frelik).Full size imageFigure 3Ischyromyid calcanei from the early middle Eocene of the Erlian Basin, Nei Mongol, China. (A–E), Asiomys dawsoni (IVPP V24417), right calcaneus, juvenile?; (F–K), species A (IVPP V24416), right calcaneus, adult; (L–Q), species B (IVPP V24418), right calcaneus, adult. In: A, F and L, dorsal; B, G and M, medial; C, H and N, lateral; D, I and O plantar; J and P caudal; E, K and Q, cranial views. Explanatory line drawings (right side) show important morphological features. Note sustentacular facet marked pale yellow. Scale bar equals 10 mm. (Photographs taken by Łucja Fostowicz-Frelik; drawings created in Corel Draw X4 (v.14.0.0.567) by Łucja Fostowicz-Frelik).Full size imageThe calcaneal tuber is strongly compressed, but it resembles in shape those of species A and B. A long groove for the calcaneofibular ligament is impressed on its lateral side.The anterior plantar tubercle is large and swollen, similar to that in species A, and touches the brim of the calcaneocuboid surface. The latter, only slightly damaged laterally, is round in outline, without a distinct pit, and inclined about 20–30°.Systematic remark: The fossil was associated with Asiomys dentition found in the same spot. We attribute specimen IVPP V24417 to Asiomys dawsoni, based on this fact and its distinctive size (Asiomys being the largest rodent in the assemblage). Asiomys is the only ischyromyid rodent known from the basal strata of the Irdin Manha Formation of Huheboerhe.Genus indet.Species AFigure 3F–KMaterial. Right calcaneus (IVPP V24416), early Middle Eocene, Irdin Manha Escarpment, Irdin Manha Formation, Erlian Basin, China.Description. The right almost complete calcaneus of an adult specimen is relatively large (Table 1), comparable in length to the calcaneus of a coypu (Myocastor coypus) or Asiatic brush-tailed porcupine (Atherurus macrourus). The bone has a characteristically elongated calcaneal tuber and rather short body (Fig. 3F–I). The calcaneal tuber is quite slender in comparison with the structure found in the coypu and porcupines. The shape of the bone resembles most closely the calcaneus of Paramys wortmani (see35: Fig. 12B), although in Paramys the calcaneal tuber is more compressed mediolaterally.The sustentaculum tali is large and eminent, reaching far medially and tapering, although its medial end forms a blunt edge parallel to the long axis of the bone. This medial edge also bears a well-marked but not deep groove of the calcaneonavicular (or ‘spring’) ligament (Fig. 3G). The sustentacular facet (facies articularis talaris media in Fostowicz-Frelik36: Fig. 12B2) is round, with only slight anteroposterior compression. It occupies almost the whole dorsal surface of the sustentaculum, encroaching slightly onto the calcaneal body. In that it differs from Notoparamys and Paramys wortmani, which both have a much more medially placed sustentacular facet, which does not encroach on the calcaneal body. The range of the sustentacular facet overlaps less than one-third of the ectal facet (posterior facies articularis talaris in Fostowicz-Frelik36: Fig. 12B2) on its anterior and medial sides. The calcaneal eminence is slightly longer than that in Marmota and Sciurus, in proportions closer to that of porcupines and of similar size as in Paramys wortmani. The ectal facet is wide, long, and has a distinctly helical course, even more strongly marked than in North American ischyromyids (see Rose and Chinnery35: Fig. 12A). It is, however, inclined more strongly mediolaterally than in Notoparamys and Paramys, and faces strongly medially. On the dorsal side of the calcaneal eminence, posterolateral to the ectal facet, there is a flattened rough area (finely pitted), marking the place of attachment of the lateral collateral ligaments binding the distal fibula and the astragalus with the calcaneus and stabilizing the astragalocalcaneal joint.A calcaneal body is short and stocky with poorly marked tendon ridges at the dorsal surface. A large peroneal process is partly damaged at its lateral margin. The process is placed closer to the cuboid surface than the sustentaculum tali. The position of the sustentaculum tali and the proportions of the calcaneal body of specimen IVPP V24416 resemble rather closely the calcaneus of Paramys wortmani (see35).The calcaneal tuber is not ‘pinched’ at its dorsal side but moderately compressed, thus there is no coracoid ridge posterior to the ectal facet. At the lateral side of the tuber, there is a long groove for the calcaneofibular ligament running askew, towards the dorsal surface of the calcaneal tuber. The groove for the calcaneofibular ligament is more weakly expressed than in the North American paramyines and arboreal sciurids, but similar to that of Marmota.The caudal surface of the calcaneal tuber is subcircular (only slightly more extended dorsoplantarly than mediolaterally, see Fig. 3 and Table 1). The groove for the calcaneal tendon (= Achilles tendon) is deep and placed asymmetrically at the surface (Fig. 3J). Also, the medial process of the calcaneal tuber is much better developed and extending medially.The plantar surface of the bone is almost straight with a delicate flexure cranially to a well-developed plantar heel process (Fig. 3G). The anterior plantar tubercle is relatively large, swollen, but shifted medially, towards the sustentaculum tali. It is placed very close to the cuboid surface, almost touching its margin; such location and the medial shifting resembles the condition in some ground squirrels, e.g., Cynomys (see Fostowicz-Frelik et al.8: Fig. 3D–F). The anterior plantar tubercle is also somewhat flattened and inclined medially and forms a well-marked calcaneal groove for the tendon of the flexor fibularis muscle.The calcaneocuboid articular surface is semicircular, slightly wider mediolaterally than long dorsoplantarly, which distinguishes species A from Marmota and paramyines (see35). It is almost transversally positioned, not inclined, as in most of the rodent taxa (coypu and porcupines included), and gently concave; it is also confluent and level with the cuboid pit, forming one round surface at the cranial end of the bone.Genus indet.Species BFigure 3L–QMaterial Right calcaneus (IVPP V24418), early Middle Eocene, Daoteyin Obo, Irdin Manha Formation, Erlian Basin, China.Description The bone is complete, slightly larger than in species A (Table 1), matching in length the calcaneus of the coypu. Its overall structure is very similar to the calcaneus of Paramys (either P. wortmani or P. taurus, see Rose and Chinnery35: Fig. 12B, C). It has a long and strong calcaneal tuber and a relatively strong but short calcaneal body (Fig. 3L). The tuber is more compressed mediolaterally than in species A; thus, the caudal surface of the tuber is extended more dorsoplantarly than mediolaterally (Fig. 3P). The attachment for the calcaneal tendon forms a rounded concavity at the caudal side of the tuber, and is more horizontally and symmetrically located at the surface than in species A. The lateral surface of the calcaneal tuber bears a marked scar from the calcaneofibular ligament, although the scar is convex, not concave as in species A and in other compared taxa (e.g., Cynomys).The sustentaculum tali is large and round; it is located relatively close to the calcaneal body, not extending as far medially as in the North American paramyines (see35). It is slightly longer anteroposteriorly and located more caudally (closer to the ectal facet) than in species A. Thus, the sustentacular surface overlaps ca. one-half of the cranial part of the ectal facet. The medial edge of the sustentacular shelf bears a deep groove for the ‘spring ligament’.The ectal facet is large, equally wide throughout its length, long and helical, although its course is straighter along the proximodistal direction than in species A. The ectal surface faces mediodorsally, with a slightly weaker medial component than in species A. The dorsal surface of the tuber, just caudal to the ectal facet, is not typically ‘pinched’ into a sagittally oriented crest, but it is, nevertheless, more mediolaterally compressed than in the species A, similar to Marmota.The calcaneal body forms about one-third of the bone length. Its dorsal surface is carved by deep longitudinal marks indicating the position of the extensor digitorum brevis muscle (Fig. 3). A middle-size peroneal process is located cranially at the calcaneal body. It is strong and long anteroposteriorly, reaching almost the edge of the calcaneocuboid surface. Its lateral edge shows a deep groove for the tendon of the peroneus longus muscle, while its dorsal surface forms a groove for the peroneus brevis muscle tendon (Fig. 3). Species B differs from the ground squirrels in the shape and location of the peroneal process, which is less extended laterally in species B than e.g., in marmots, although it is relatively much larger than in the coypu and porcupines.The anterior plantar tubercle looks less swollen than in species A; it is located at the very margin of the calcaneocuboid surface and as in species A is shifted medially (Fig. 3O, Q). The calcaneocuboid surface is slightly inclined (ca. 25°) anteromedially, which distinguishes the bone from species A, Marmota, and Notoparamys, which all have the calcaneocuboid facet almost transversal and perpendicular to the long axis of the calcaneus. In this respect, the calcaneocuboid surface resembles more closely the calcaneus of Paramys taurus (Rose and Chinnery35: Fig. 12C). The calcaneocuboid surface is almost round, slightly wider mediolaterally, resembling that of species A. A relatively small calcaneal pit (extending only to a half of the anterior plantar tubercle base, see Fig. 3Q), smaller but deeper than in species A, forms a shallow sink at the medial side of the surface, cranially to the sustentaculum tali.PCA analysisA Principal Component Analysis (PCA) was performed based on 14 measurements of the calcaneus. The analysis included the calcaneal measurements of five ischyromyid species (two described here as species A and B, and three comparative species from North America) and 16 extant large rodent species (Supplementary Table S1). The extant taxa represent six basic types of locomotor adaptations found in rodents: ambulatorial (terrestrial generalists), amphibious (swimming), arboreal (tree climbing), cursorial (four-pedal runners), ricochetal (bipedal jumpers), and semi-fossorial (burrowing).Principal Components 1 and 2 (PC1 and PC2) represent 87.48% and 5.75% of the variance, respectively, whereas Principal Components 3–4 represent further 4% of the variance (Supplementary Table S2). All the variables are positively correlated with PC1 and their loadings are very balanced (Fig. 4). Thus, it implies that the PC1 represents a proxy for the size of the bone. PC2 is most strongly correlated with the length of the calcaneal body, BL (-0.86) and more weakly correlated with the width of the cuboid facet (CCW) and anterior width of the ectal facet (AEW), 0.31 and 0.21, respectively (Fig. 4). The correlation with the length of the calcaneal body is an especially important factor for estimating an animal’s vertical jumping ability; the species with elongated calcaneal bodies are generally better jumpers (see8,36). The strong negative correlation of the length of the calcaneal body in the second component is illustrated by grouping the species with a strong jumping locomotor repertoire (e.g., squirrels and chinchillas) towards the left side of the plot (Fig. 4). Incidentally, this phenomenon does not concern the calcanei of ricochetal species (see the position of Pedetes versus that of Sciurus and Chinchilla: Fig. 4), where the mechanics of a jump are differently realized, and the stabilisation and relative stiffness of the ankle joint plays the most important role (thus, the calcaneal body and calcaneal tuber are more similar in size).Figure 4Principal component analysis of 14 metric parameters of rodent calcanei. The morphospace including paramyid calcanei from Nei Mongol in yellow circle. Lines connecting all data points represent a minimum spanning tree (MST) based on a Euclidean distance matrix. The loadings of the Components 1 and 2 shown at the corresponding axes. Strictly fossil taxa marked in red and pink, extant in black. (Figure created in Corel Draw X4 (v.14.0.0.567) by Łucja Fostowicz-Frelik).Full size imageIn the plot of PC1 against PC2, ischyromyids do not cluster together. Instead, the PCA morphospace is divided into two (or even three) broad groups of ischyromyid locomotor adaptations: the ambulatorial species and those with more pronounced jumping or cursorial ability. Chinese taxa fall among typically large ambulatorial rodents, such as the coypu (Myocastor) and porcupines (Atherurus and Hystrix). Closest to them there is the North American ischyromyid Quadratomus, which is somewhat shifted towards the cursorial species and can be thus distinguished as differently specialized (more cursorial). Two other North American ischyromyids, Ischyromys and Reithroparamys, are grouped with Chinchilla and Ondatra, respectively, which may imply some jumping and slightly scansorial locomotor adaptations for Ischyromys and those of typical agile generalist species for Reithroparamys.Although the sample is limited, the results of the PCA analysis point to general differences in the structure of the calcaneus, and thus, locomotor specialisation, between Asian and North American ischyromyid species. Moreover, Asian species seem to differ less from each other than the North American ones do, reflecting the overall greater species diversity and coverage of a wider niche spectrum of the North American ischyromyids.Functional and paleoecological implicationsThe studied calcanei add to our knowledge on the functional aspects of locomotion of ischyromyid rodents. Proximal tarsal morphology has been recently used to interpret the locomotor behavior of some extinct rodents (see e.g.,8,37,38,39). In the scheme of locomotor categories of Samuels and Van Valkenburgh40, attributions proposed for early ischyromyids fit into generally terrestrial41, arboreal42 or a mixture of those two35.A relatively short calcaneal body, widely spread sustentaculum tali, and a large peroneal process observed in most ischyromyid species (including these studied herein) indicate rather poor cursoriality. Instead, their ankle joint structure allows for a large freedom of foot movements in different planes. A medially extended sustentaculum tali together with a long and helically twisted ectal facet indicate a large degree of sliding between the calcaneus and astragalus along their articular facets, which makes possible a great degree of foot torsion resulting in foot eversion and inversion. This effect is further enhanced by an extended calcaneocuboid facet that is gently concave and oriented perpendicularly to the long axis of the calcaneus in species A.Such adaptations are helpful for both clinging to branches and adjusting to uneven or inclined substrate during climbing. A great degree of freedom of movement may be helpful also during burrowing, when the hind legs are used to push forward loose soil out of a burrow or an animal is forced to maintain a crouched posture, when it digs with its forelegs and head. Nevertheless, as much as the calcaneal structure may suggest some burrowing ability in ischyromyids (see Rose and Chinnery35), the rest of the postcranial skeleton known from the more complete specimens of North American representatives41 does not support fossorial adaptations. In particular, a long tail in the pre-Oligocene North American (see e.g., Paramys or Reithroparamys in Wood41: figs. 8 and 44, respectively) suggests some arboreal adaptations or at least occasional climbing, as such a tail greatly enhances balancing on uneven terrain. In contrast, typically fossorial mammals have reduced tails43.The overall morphology of dental and mandibular remains16,18 of Asian ischyromyids is similar to that of their North American counterparts16,19. As complete or even partial postcranial skeletons are unknown for the Asian ischyromyids, we can surmise their general locomotor adaptations based on calcaneal morphology which, although not in striking contrast with their North American counterparts, shows some differences.Overall, the calcaneal morphology of Chinese ischyromyids is closest to that of ground squirrels and especially porcupines (both Atherurus and Hystrix) and the coypu; the similarity to the last one is supported also by the PCA analysis. The calcaneal morphology and proportions may therefore reflect their locomotion behavior as generalized terrestrials, with a somewhat limited ability to climb (a rare but observed behavior in Hystrix) and to dig burrows (as does Atherurus43). A transverse and gently concave calcaneocuboid facet of species A facilitates foot rotation along the long axis, useful on an uneven, rocky terrain or while traversing branches, when an animal needs a flexible foot for a better grip (see Chester et al.44). On the other hand, the lack of both a characteristically bent calcaneal tuber and posteriorly located peroneal process in all ischyromyids (except for Notoparamys, see Rose and Chinnery35) argues against the arboreal adaptations characteristic of tree squirrels. More

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