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Correction to: Nature Ecology & Evolution https://doi.org/10.1038/s41559-019-0970-7, published online 2 September 2019.The Journal would like to note that the authors first made contact in September 2019 to raise the concerns that follow, and the Journal apologizes both for the delay in relaying these corrections publicly and for the changed instances that prevent making corrections to the original article itself. What follows is the Author correction.In the version of this article initially published, we made several errors in our R analysis code, and in the text and figures. First, the number of species with negative net dispersal velocity (net DV) were incorrectly calculated, resulting in slight changes in Fig. 2 and Supplementary Fig. 6, and in the text. The amended figures are provided below (Figs. 1–7). Changes to the text under the ‘DVs’ subsection of Results are: “When considering the mainstem pathway, we estimate that the mobile subpopulations of 134 (old version: 124) and 185 (old version: 174) (RCP 4.5 and 8.5, respectively) species will experience dispersal deficits in at least 50% of their southern Appalachian range, whereas these estimates increase to 229 (old version: 226) and 231 (old version: 232) species for the stationary subpopulation. Slow-climate-velocity tributaries reduce the number of species experiencing dispersal deficits by 99.3% (old version: 99.2%) and 90.3% (old version: 16.9%) (RCP 4.5 and 8.5, respectively) for the mobile component and 17.9% (old version: 90.8%) and 12.1% (old version: 12.9%) for the stationary component (Fig. 2a,b).” The two large discrepancies in dispersal deficit values (90.3% vs. 16.9%; 17.9% vs. 90.8%) were solely consequences of original text errors (16.9% and 90.8% values were erroneously switched), and not differences in calculations; therefore, the results did not change.Fig. 1Figure 2, original and corrected.Full size imageFig. 2Figure 3c,d, original and corrected.Full size imageFig. 3Figure 4, original and corrected.Full size imageFig. 4Figure 5, original and corrected.Full size imageFig. 5Supplementary Figure 6, original.Full size imageFig. 5Supplementary Figure 6, corrected.Full size imageFig. 6Supplementary Figure 8, original.Full size imageFig. 6Supplementary Figure 8, corrected.Full size imageFig. 7Supplementary Figure 9, original.Full size imageFig. 7Supplementary Figure 9, corrected.Full size imageSecond, we made errors when plotting Fig. 3c,d. Boxplots of mean change in habitat suitability were plotted instead of median change as specified in the caption; further, whiskers did not include the entire range of values. The amended figure is provided below. We would like to correct associated errors in text; specific changes are: “Our ENMs estimate a median 15.1% (old version: mean 14.1%) reduction (range −42.5% to +16.6% [old version: −51.6% to +2.4%] across 233 species) in habitat suitability associated with the tributary pathway compared with only a 3.8% (old version: 1.6%) reduction (−11.0% to +12.3% [old version: −7.9% to +1.8%]) for the mainstem pathway due to differing non-temperature habitat conditions (Fig. 3a,b).”Third, we made errors when plotting Fig. 4 and Supplementary Fig. 8. Specifically, net DV values were incorrectly rescaled; one extinct species was erroneously included in the plot; and the number of species in each quadrant was counted incorrectly. The amended figures are shown below. We would like to add a sentence (“The y-axes are inverse hyperbolic sine (asinh)-transformed”) to the caption of Fig. 4 to describe the y-axis scaling in the amended figures. There were two other text errors in the caption. The phrase “Mean net DV” should have been “Median net DV,” whereas the phrase “mean habitat suitability” should have read “median change in habitat suitability.” Therefore, the corrected Fig. 4 caption should read: “Species-level mismatch between net DV and upstream habitat suitability. a–d, Median net DV of mobile (a,b) and stationary subpopulations under the RCP 8.5 scenario plotted as a function of median change in habitat suitability for mainstem (a,c) and tributary (b,d) dispersal pathways. Each point represents a species and is computed as the median response across all projected occupied reaches. Red and blue numbers correspond to the number of species in each of the four quadrants. The y-axes are inverse hyperbolic sine (asinh)-transformed. e–h, Four species highlighting the diversity in dispersal-based and habitat suitability-based vulnerability: streamline chub (e); brook trout (f); flathead catfish (g); blacknose dace (h). Credit: David Neely (e–h)”. These corrections did not change our inferences.Fourth, there were errors in rescaling and plotting net DV values and in the calculation of quadrant percentages in Fig. 5 and Supplementary Fig. 9. The amended figures are shown below. We would like to add two sentences at the end of Fig. 5 caption to provide greater detail on plotting methods: “The y-axes of the scatterplots are inverse hyperbolic sine (asinh)-transformed. For clarity, the scatterplots show net DV values ≥ −13,000 and ≤ 130, and change in habitat suitability values ≤ 100, representing >99.5% of all observations.” There was one other text error in the caption: the phrase “mean habitat suitability” should have read “mean change in habitat suitability.” Therefore, the corrected Fig. 4 caption should read: “Community-level mismatch between net DV and upstream habitat suitability. a–d, Mean net DV of mobile (a,b) and stationary (c,d) subpopulations under the RCP 8.5 scenario plotted as a function of mean change in habitat suitability for mainstem (a,c) and tributary (b,d) dispersal pathways. Each point (scatterplot) and reach (map) is computed as the mean response for all species projected to occur within the reach. Quadrant numbers represent percentage of reaches in the quadrant. Colours associated with the upper-right quadrant correspond to ‘safe’ reaches where community members can keep pace with ISVs and habitat suitability increases. Colours associated with the lower-left quadrant correspond to ‘vulnerable’ reaches where community members cannot keep pace with ISVs and habitat suitability declines. The y-axes of the scatterplots are inverse hyperbolic sine (asinh)-transformed. For clarity, the scatterplots show net DV values ≥ −13,000 and ≤ 130, and change in habitat suitability values ≤ 100, representing >99.5% of all observations.” These corrections did not change our inferences.Fifth, there was an error in the last sentence of the “Calculating net DVs” subsection in Methods: “Last, we calculated the mean net DV for each species (species-specific DV) by averaging net DVs at all occupied reaches, as well as the community-wide net DV at each stream reach (reach-specific DV) by averaging the net DVs of all species at each reach.” This sentence should have read “Last, we calculated the median net DV for each species (species-specific DV) across all occupied reaches, as well as the mean community-wide net DV at each stream reach (reach-specific DV) by averaging the net DVs of all species at each reach.”Corrections of calculation errors yielded results that were similar to those in the original analysis whereas corrections of plotting and text errors did not affect our original inferences. Therefore, these errors did not change the overall results and conclusions of the article. We sincerely apologize for any misunderstanding and inconvenience caused by these errors. More

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Long-term acoustic data collectionPassive acoustic monitoring was conducted from November 19, 2018 to October 3, 2020, with 683 days of recording effort overall (Supplementary Table 2), using a High-frequency Acoustic Recording Package (HARP)37. The HARP was deployed in Bahía Norte, Guadalupe Island, located approximately 150 miles offshore of México’s Baja California Peninsula (Fig. 1). The HARP was bottom-mounted and deployed to a depth of approximately 1100 m, with a calibrated hydrophone suspended ~30 m above the seafloor. The same hydrophone was used for both deployments to facilitate data comparison. The omnidirectional hydrophone sensor (ITC-1042, International Transducer Corporation, Santa Barbara, CA) had an approximately flat (±3 dB) hydrophone sensitivity from 10 Hz to 100 kHz of −200 dB re V/μPa. The sensor was connected to a custom-built preamplifier board and bandpass filter. The calibrated system response was corrected for during analysis. Data were sampled continuously at a 200 kHz sampling rate with 16-bit quantization, effectively monitoring a frequency range of 10 Hz–100 kHz.Automatic detection and manual classification of beaked whale echolocation clicksBeaked whales can be acoustically identified by their echolocation clicks38. These signals are frequency-modulated (FM) upswept pulses, which appear to be species-specific and are distinguishable by their spectral and temporal features. Cuvier’s beaked whale echolocation signals are well differentiated from the acoustic signals of other beaked whale species. They are polycyclic with a characteristic FM pulse upsweep, peak frequency around 40 kHz, and uniform inter-pulse interval of about 0.4–0.5 s39,40. Additionally, Cuvier’s beaked whale FM pulses have characteristic spectral peaks at approximately 17 and 23 kHz.Beaked whale FM pulses were detected in the HARP data with an automated method using the MATLAB-based (Mathworks, Natick, MA) custom software program Triton (https://github.com/MarineBioAcousticsRC/Triton) and other MATLAB custom routines. After all potential echolocation signals were identified with a Teager–Kaiser energy detector41,42, an expert system discriminated between delphinid clicks and beaked whale FM pulses. A decision about presence or absence of beaked whale signals was based on detections within a 75 s segment. Only segments with more than seven detections were used in further analysis. All echolocation signals with a peak and center frequency below 32 and 25 kHz, respectively, a duration less than 355 μs, and a sweep rate of More

The theoretical modelThe model presented here builds on a recently developed metabolic theory based on biochemical kinetics. It describes a non-linear relationship between plant metabolic rate per unit of dry mass (Bs, nmol g−1 s−1), such as light-saturated photosynthetic rates and dark respiration rates, plant water content (S, g g−1), and temperature (in degrees K)19,20, i.e.$${B}_{{{{{{rm{s}}}}}}}={g}_{1}{e}^{{k}_{1}S/left({K}_{1}+Sright)}{e}^{-E/{kT}}$$
(1)
where g1 is a normalisation constant, k1 represents the maximum increase in specific metabolic rates due to changes in water content (i.e. from dehydrated to fully hydrated), K1 represents the water content when the mean reaction rate of cellular metabolism reaches one-half of its maximum, E is the activation energy, and k is Boltzmann’s constant. In this model S is defined on a dry mass basis (i.e. the ratio of plant water mass to plant dry mass) to broaden its range and better reflect the proportional changes in the amount of water in plant tissues20. Full details of the model’s assumptions can be found in the Methods and Huang et al.19,20. The model was tested and shown to hold true for a broad range of species and for whole plants and above- and belowground organs20. Here, we first applied the model to describe the quantitative effects of dry mass-based LWC (the ratio of leaf water mass to leaf dry mass) and temperature on the light-saturated leaf photosynthetic rate per unit of dry mass or leaf photosynthetic capacity (Ps, nmol CO2 g−1 s−1), which can be expressed as$${{{{{rm{ln}}}}}}left({P}_{{{mbox{s}}}}right)={{{{{rm{ln}}}}}}left(frac{{P}_{{{{{{rm{L}}}}}}}}{{M}_{{{{{{rm{L}}}}}}}}right)={{{{{rm{ln}}}}}}left({g}_{1}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}-frac{E}{{kT}},$$
(2)
where PL is the light-saturated whole-leaf photosynthetic rate (nmol s−1). Equation 2 indicates that the log-transformed temperature-corrected Ps (i.e. Pscor) should increase with LWC, following Michaelis-Menten type hyperbolic response, i.e.$${{{{{rm{ln}}}}}}left({P}_{{{mbox{scor}}}}right)={{{{{rm{ln}}}}}}left({P}_{{{{{{rm{s}}}}}}}{e}^{E/{kT}}right)={{{{{rm{ln}}}}}}left({g}_{1}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}.$$
(3)
Rearranging Eq. (2) shows that the temperature- and LWC-corrected whole-leaf photosynthetic rate (i.e. PLcor) should scale isometrically with ML, i.e.$${P}_{{{mbox{Lcor}}}}={P}_{{{{{{rm{L}}}}}}}{e}^{-{k}_{1}cdot {{{{{rm{LWC}}}}}}/left({K}_{1}+{{{{{rm{LWC}}}}}}right)}{e}^{E/{kT}}={g}_{1}{M}_{{{{{{rm{L}}}}}}}.$$
(4)
In this study, we refer to the temperature or water content correction as moving the temperature term ((frac{E}{{kT}})) or water content term ((frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}})) to the left-hand side of the model, an approach that has been commonly used in previous studies28.Following previous studies29,30,31, we assume that PL is proportional to AL, i.e. ({P}_{L}propto {A}_{L})because leaf area directly determines the light interception capacity1. Therefore, the quantitative relationship between SLA and LWC and temperature can be described as$${{{{{{mathrm{ln}}}}}}}left({{mbox{SLA}}}right)={{{{{{mathrm{ln}}}}}}}left(frac{{A}_{{{{{{rm{L}}}}}}}}{{M}_{{{{{{rm{L}}}}}}}}right)={{{{{{mathrm{ln}}}}}}}left({g}_{2}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}-frac{E}{{kT}},$$
(5)
where g2 is another normalisation constant. Given that leaf area is a direct indicator of leaf photosynthetic capacity and that both traits reflect the long-term adaptation of plants to environmental change3,13, k1 in Eqs. (2) and (5) represent the maximum increase in mass-specific leaf photosynthetic capacity due to changes in water content. Since the temperature has a direct effect on the metabolic rates32 and productivity of ecosystems33, it is reasonable to assume that temperature can affect SLA globally34,35. Therefore, in this context T denotes the mean growing-season temperature (in degrees K), as SLA might be more responsive to long-term changes in temperature. Equation (5) predicts that SLA should increase with both LWC and the growing-season temperature. Rearranging Eq. (5) yields$${{{{{{mathrm{ln}}}}}}}left({{mbox{SL}}}{{{mbox{A}}}}_{{{mbox{cor}}}}right)={{{{{{mathrm{ln}}}}}}}left({{mbox{SLA}}}{e}^{E/{kT}}right)={{{{{{mathrm{ln}}}}}}}left({g}_{2}right)+frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}},$$
(6)
which predicts that the log-transformed temperature-corrected SLA (i.e. SLAcor) should increase with LWC following Michaelis-Menten dynamics. Likewise, by moving (frac{{k}_{1}cdot {{{{{rm{LWC}}}}}}}{{K}_{1}+{{{{{rm{LWC}}}}}}}) and (frac{E}{{kT}}) to the left-hand side and ML to the right-hand side of Eq. (5), we observe that the temperature- and LWC-corrected leaf area (i.e. ALcor) should scale isometrically with leaf mass, i.e.$${A}_{{{mbox{Lcor}}}}={A}_{{{{{{rm{L}}}}}}}{e}^{-{k}_{1}cdot {{{{{rm{LWC}}}}}}/left({K}_{1}+{{{{{rm{LWC}}}}}}right)}{e}^{E/{kT}}={g}_{2}{M}_{{{{{{rm{L}}}}}}}.$$
(7)
We note that the scaling of PLcor and ALcor with respect to ML will reveal how LWC mediates the scaling exponent of leaf trait relationships.Effects of LWC and temperature on leaf trait scalingThe numerical value of the exponent for the PL versus AL scaling relationship calculated from the empirical data was 0.99 (Supplementary Fig. 1; 95% CI = 0.95 and 1.02, r2 = 0.87), strongly supporting the model assumption that PL scales isometrically with AL. We then examined the effect of LWC on leaf trait scaling. The numerical value of the scaling exponent for the PL versus ML relationship was 0.95 (Fig. 2a; 95% CI = 0.92 and 0.99, r2 = 0.83). The non-linear relationship between Pscor and LWC described by Eq. (3) was supported by the empirical data (Fig. 2b; Supplementary Table 1). The non-linear model (Eq. 3) also had a lower Akaike’s Information Criterion score than the simple linear model between log-transformed Pscor and LWC (i.e. 793.5 versus 1988.8). After LWC and temperature were corrected (see Eq. 4), the numerical value of the scaling exponent became 0.97 (Fig. 2c; 95% CI = 0.94 and 1.01, r2 = 0.85), which was statistically indistinguishable from 1.0 (P  > 0.05), as predicted by the model. Likewise, the numerical value of the exponent (i.e. α) for the AL versus ML scaling relationship was 1.02 (Fig. 2d; 95% CI = 1.02 and 1.03, r2 = 0.92). Additional analyses using the pooled dataset showed that log-transformed SLA increased with LWC following Michaelis-Menten dynamics, as predicted by Eq. (6) (Fig. 2e; Supplementary Table 1). After the effects of LWC and temperature were accounted for (using Eq. 7), the numerical value of α became 1.01 (Fig. 2f; 95% CI = 1.00 and 1.01, r2 = 0.95). Thus, both of the scaling exponents numerically converged onto 1.0 once LWC and temperature were corrected. In addition, an inspection of the locally weighted smoothing (LOWESS) curves showed that the curvature in both scaling relationships was reduced after the effects of LWC and temperature were corrected, as predicted by the model (Fig. 2).Fig. 2: The quantitative effects of dry mass-based leaf water content (LWC) on leaf photosynthesis and SLA.a Scaling of leaf photosynthetic rate (PL, nmol s−1) with leaf dry mass (ML, g). b Non-linear fit to the relationship between temperature-corrected mass-specific leaf photosynthetic rate (Pscor, nmol g−1 s−1) and LWC (g g−1) based on Eq. (3). c Scaling of temperature- and LWC-corrected leaf photosynthetic rate (PLcor, nmol s−1) with ML (g). d Scaling of leaf area (AL, cm2) with leaf dry mass (ML, g). e Non-linear fit to the relationship between temperature-corrected specific leaf area (SLAcor, cm2 g−1) and LWC based on Eq. (6). f Scaling of temperature- and LWC-corrected leaf area (ALcor, cm2) with leaf dry mass (ML, g). Data with LWC greater than 25 were not shown in panel e for a better visualisation. LOWESS curves (blue lines) and 95% confidence intervals are shown.Full size imageThe results presented here show that temperature and LWC quantitatively correlate with other leaf traits, such as Ps and SLA (or LMA), as predicted by the model. The increases in Ps and SLA attenuate with increasing LWC (Fig. 2b, e), indicating that leaf water availability sets a constraint on the maximum Ps and SLA that leaves can reach. It has long been recognised that SLA is closely correlated with leaf growth rate and metabolic activity14,36,37. Therefore, it is reasonable to also expect that SLA, as well as Ps, will be quantitatively affected by LWC, which can change as a function of developmental status (such as leaf maturation and the accumulation of lignified tissues) and transiently as a function of evapotranspiration. LWC is also a reflection of species-specific adaptation to environmental conditions in different biomes. Nevertheless, our model, as well as the empirical data used to test it, reveal a broad and statistically robust correlation between critical leaf functional traits and leaf tissue water content. However, the observed variations in Pscor (Fig. 2b) suggest that in addition to temperature and LWC, other factors (e.g. plant phylogeny and soil fertility) may also affect leaf photosynthetic capacity, which is not accounted for in our model and should be critically examined in future research.Leaf area-mass scaling among different groupsThe numerical value of α varied across different plant growth forms, ecosystems, and latitudinal zones (Fig. 3 and Supplementary Table 2). In particular, the leaf area versus mass scaling relationship showed a clear pattern along a latitudinal gradient (Fig. 3c and Supplementary Table 2). The numerical value of α decreased from 1.10 in boreal regions (95% CI = 1.08 and 1.12, r2 = 0.91) to 1.00 in temperate regions (95% CI = 0.99 and 1.01, r2 = 0.91), and to 0.94 in tropical regions (95% CI = 0.92 and 0.95, r2 = 0.91). However, after correcting for the effects of LWC and temperature, as predicted, α converged onto 1.0 across all different groupings, and the r2 values of the scaling relationships also increased (Fig. 3 and Supplementary Table 2).Fig. 3: The exponents of leaf area-mass scaling with and without temperature and LWC corrections among different groups.a Comparison of scaling exponents among plant growth forms (n = 1688, 491, 1097, and 832 for forbs, graminoids, shrubs, and trees, respectively). b Comparison of scaling exponents among ecosystem types (n = 97, 1367, 1285, 1271, and 114 for deserts, forests, grasslands, tundra, and wetlands, respectively). c Comparison of scaling exponents among different latitudinal zones (n = 1111, 2113, and 910 for tropical, temperate, and boreal zones, respectively). Error bars indicate 95% confidence intervals.Full size imageOur analyses show that LWC also affects the numerical values of the exponents of leaf trait scaling relationships, which helps to explain why different works sometimes report significant differences in the exponents governing these relationships8,10. In particular, the numerical values of the scaling exponent governing the leaf area versus mass scaling relationship differ among different plant growth forms, ecosystems, and latitudinal zones (Fig. 3 and Supplementary Table 2), indicating that no invariant “scaling exponent” (i.e. α) holds true for the leaf area-mass scaling relationship. For example, in our dataset, α is significantly smaller than 1.0 in tropical regions (i.e. in keeping with a “diminishing returns” relationship in leaf area with respect to increasing leaf mass), close to 1.0 in temperate regions (i.e. a break-even relationship), and significantly larger than 1.0 in boreal regions (i.e. an “increasing returns” relationship). This shift in α along a latitudinal gradient may be associated with the different strategies to cope with variations in water availability, e.g. the high evapotranspiration rates in tropical regions may constrain increases in leaf area with increasing leaf mass, therefore resulting in diminishing returns, whereas, in boreal regions, the reduced water stress may enable plants to maximise leaf area to achieve relatively high photosynthetic capacities. Despite the variability in the numerical values of scaling exponents across different groups, the degree of curvature in these scaling relationships is reduced, and exponents converge onto unity after the effects of LWC and temperature are accounted for (Fig. 3), as predicted by the model (Eq. 7). This finding indicates that the variations in the exponent can, at least partially, be ascribed to the effects of LWC on SLA and the relative rate of increase in leaf area versus leaf mass. It is noteworthy that the numerical value of the scaling exponent for the PL versus ML relationship is also very close to 1.0, indicating the relatively weak effects of temperature and LWC on leaf photosynthesis-mass scaling. This may be partially attributed to the relatively limited number of data with concurrent LWC measurements and the adaptation of leaf traits to long-term temperature changes (see below for detailed discussion). Nevertheless, more measurements on LWC and leaf photosynthetic rates are needed to further test how LWC mediates leaf photosynthesis-mass scaling.Given that LWC was weakly correlated with ML (Supplementary Fig. 2, log-log slope = −0.01, 95% CI = −0.02 and 0, r2  More