Ecology

CORRESPONDENCE
22 February 2022

Apply Singapore Index on Cities’ Biodiversity at scale

Lena Chan

 ORCID: http://orcid.org/0000-0001-7930-7678

0
,

Kenneth Er

 ORCID: http://orcid.org/0000-0003-4485-7260

1
&

Elizabeth Maruma Mrema

2

Lena Chan

National Parks Board, Singapore Botanic Gardens, Singapore.

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Kenneth Er

National Parks Board, Singapore Botanic Gardens, Singapore.

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Elizabeth Maruma Mrema

Secretariat of the Convention on Biological Diversity, Montreal, Canada.

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In the run-up to the 15th meeting of the Conference of the Parties to the Convention on Biological Diversity, the Singapore Index on Cities’ Biodiversity has been updated to align with the post-2020 global biodiversity framework to halt biodiversity loss (see Nature 601, 298; 2022) and for application at scale (see go.nature.com/3cqrknw).

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Nature 602, 578 (2022)
doi: https://doi.org/10.1038/d41586-022-00476-x

Competing Interests
The authors declare no competing interests.

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Study islands and bird dataSystematic ringing in spring on Mediterranean islands has been promoted by the Piccole Isole project since 198826. Standard methods of the project involve ringing between 16th April and 15th May attempting to include the peak of the spring passage of long-distance migrants. Ringing is performed from dawn to nightfall using a constant number of nets within ringing stations placed at stable sites located at representative habitats in each island (Supplementary Table S1). The use of tape-lures is not allowed. We have compiled ringing data for all the Spanish Mediterranean islands that have been applying this methodology, with the exception of Mallorca and Menorca where the ringing stations were located in wetlands and captured a large percentage of local birds (Fig. 2, Table 1). The nine study islands are spread along a south-west to north-east gradient and, with the exception of Columbrets, they are distributed in pairs of similar longitude but different latitudes (Fig. 2). Ringing stations have been operating over a variable number of years (5–27 years), with the maximum number of ringing stations operating at the same time occurring between 2003 and 2010. To include between-year variation on islands that started ringing campaigns more recently we used data from the years 2003–2018.Figure 2Image source: Google Earth. Data SIO, NOAA, US Navy, NGA, GEBCO. Image Landsat/Copernicus.Geographical location of studied islands in the western Mediterranean.Full size imageTable 1 Period of activity of the ringing stations located on each island between the years 1992 and 2018.Full size tableThe ringing period within each spring also varied in most islands, owing to funding or logistic limitations; thus, to reduce the possible effects on migrant composition we only used data from the standard period of the Piccole Isole project and from years that included at least one week of ringing in the fortnight of each month within this interval. This procedure excluded the use of some years for several islands, and the final number of data years for islands ranged between 5 and 16 (Table 1).We used only data for trans-Saharan nocturnal migrant passerines, which form the bulk of species ringed on Mediterranean islands during the standard period. The standard ringing period only covers the tail end of the short-distance migrants’ passage; thus, these species were excluded as their contribution to composition of migrants could vary mainly due to between-year variation in migration phenology. Diurnal migrants, like hirundinids and fringillids, also represent a small fraction of birds ringed and may use different cues to select stopover islands. In addition, some of these species nest in some of the islands studied and birds ringed could include breeding birds. To avoid the distorting effect of species that are captured accidentally in very small numbers, we considered only the species that were ringed in at least five separate years, or on five different islands, which limited the species considered to 35 (Supplementary Table S2). This led to the exclusion of just two species (Ficedula semitorquata with three individuals ringed in two islands and Locustella luscinioides with one individual ringed in Aire island). In addition, we only considered the number of ringed birds, since the proportion of recaptures varies among islands, likely reflecting variation in the duration of stopovers21, which could bias the comparison of the patterns of migrant species composition.Island descriptorsWe obtained two groups of variables describing the characteristics of the study islands (Tables 2, 3): (1) Variables related to geographical location: latitude, longitude, straight distance and minimum distance to the North African coast, minimum distance to the closest large body of land (continent or large island) in any direction and to the closest large body of land situated in a southerly angle between SW and SE. (2) Variables related to the habitat characteristics of the islands: area, maximum altitude and Normalized Difference Vegetation Index (NDVI). We estimated NDVI from Landsat 8 Images taken during the standard ringing period in the years 2015 and 2016. Pixels containing shoreline were excluded and the average NDVI was calculated for the rest of the pixels.Table 2 Variables describing the characteristics of the islands that included the ringing stations studied.Full size tableTable 3 Values of the island descriptors (see Table 2) and two measures of temporal variability of migrant composition in each island: average local contribution of each island to beta diversity (LCBD) and beta diversity for each island (BDTi).Full size tableContinental abundance dataAbundance estimates for western Europe were obtained from the European Red List of Birds27. We used the mean of the minimum and maximum number of pairs estimated for the 27 EU Member States as a measure of continental abundance (Supplementary Table S2).Data analysisAll analyses were done using R 3.6.128. We built a matrix of island-year x species containing the number of individuals of each selected species ringed in the study period in each island and year. Average number of individuals of each species ringed at each island was calculated and was used (log-transformed) as a dependent variable in a linear model with continental abundance (log-transformed), island and their interaction as predictors. This model was simplified using AICc as criteria to identify the best model.To analyze variation of species composition, the matrix of island-year x species was transformed using the chord transformation29 with the function decostand in the vegan package30.Using the function beta.div of the adespatial package31 we calculated beta diversity, including temporal and between-island variability (BDI,T), as the total variance of the aforementioned transformed matrix (BDTotal in29), which varies between 0 and 1 when chord distance is used. Considering that yijk is the chord transformed abundance of the species j in the island i and year k and (overline{{y }_{j}}) is the mean for species j in all islands and years altogether, then:$${SS}_{Total}=sum_{i=1}^{n}sum_{j=1}^{p}{sum_{k=1}^{q}{({y}_{ijk}-{overline{y} }_{j})}^{2}}$$$$BD_{I,T} = , SS_{Total} /left( {N – 1} right)$$where N is the total number of samples. The function beta.div also provides an estimation of contribution of localities (LCBD) and species (SCBD) to beta diversity (Table 3). Yearly LCBD (log transformed because of skewed distribution) of each island were averaged and compared between islands using ANOVA and a post-hoc Tukey test.We partitioned the above sum of squares in several ways. First, we calculated a beta diversity that considered only between-island variability, excluding temporal variability (BDI), by averaging the chord transformed abundances of each species j in each island along study years (({overline{y} }_{ij})) and applying the same procedure, but using the number of studied islands (n):$${SS}_{I}=sum_{i=1}^{n}sum_{j=1}^{p}{{({overline{y} }_{ij}-{overline{y} }_{j})}^{2}}$$$$BD_{I} = SS_{I} /left( {n – 1} right)$$Second, we calculated a beta diversity due to inter-annual variation of migrant composition within islands (BDT) as:$${SS}_{Temp}=sum_{i=1}^{n}sum_{j=1}^{p}{sum_{k=1}^{q}{({y}_{ijk}-{overline{y} }_{ij})}^{2}}$$$$BD_{T} = SS_{Temp} /left( {Y – n} right)$$where Y is the total number of study years and n is the number of studied islands (9). We also calculated a temporal beta diversity for each island i (BDTi) as the sum of squares due to variation within the island divided by the number of the island study years (Yi) minus 1:$${SS}_{Temp,i}=sum_{j=1}^{p}sum_{k=1}^{q}{({y}_{ijk}-{overline{y} }_{ij})}^{2}$$$$BD_{Ti} = SS_{Temp,i} /left( {Y_{i} – 1} right)$$Differences in temporal variability between islands could be due to different predominance of species that are more or less variable between years. To check this, we calculated Spearman’s rank correlation between the percentage of captures of each species in the total ringed on each island and BDTi and LCDB indices, for species present on all islands.We tested for the existence of differences between islands in migrant species composition using Permutational Multivariate Analysis of Variance (PERMANOVA) using the function adonis2 in the vegan package. We performed a multivariate test of homogeneity of variances using the betadisper function (vegan package) with the adjustment for small sample bias, to test if temporal variability in species composition differed between islands. We made post-hoc comparisons between islands with False Discovery Rate (FDR) correction using the function pairwise.perm.manova of the package RVAideMemoire32.To identify gradients in migrant species composition and the island characteristics that were associated with them, we employed Redundancy Analysis using the rda function (vegan package). We used the chord transformed matrix of species x island-year as a response matrix. We used two explanatory matrices, one including variables of geographical location and the other the variables related to habitat characteristics of the islands. We evaluated the relative importance of each group of variables to explain migrant species composition by performing a variation partitioning analysis, using the varpart function (vegan package). For that analysis, we followed the steps and R scripts recommended in33.Variables describing island characteristics were transformed using natural logarithms and collinearity within each group was evaluated with variance inflation factor (VIF)34. All the habitat variables presented VIF  More

Eddy-covariance observationsWe used half-hourly or hourly GPP, air temperature, VPD, SWC and incoming shortwave radiation from the recently released ICOS (Integrated Carbon Observation System)44 and the FLUXNET2015 dataset of energy, water, and carbon fluxes and meteorological data, both of which have undergone a standardized set of quality control and gap filling19. Data were already processed following a consistent and uniform processing pipeline19. This data processing pipeline mainly included: (1) thorough data quality control checks; (2) calculation of a range of friction velocity thresholds; (3) gap-filling of meteorological and flux measurements; (4) partitioning of CO2 fluxes into respiration and photosynthesis components; and (5) calculation of a correction factor for energy fluxes19. All the corrections listed were already applied to the available product19. We used incoming shortwave radiation, temperature, VPD, and SWC that were gap-filled using the marginal distribution method21. The GPP estimates from the night-time partitioning method were used for the analysis (GPP_NT_VUT_REF). SWC was measured as volumetric SWC (percentage) at different depths, varying across sites. We mainly used the surface SWC observations but deeper SWC measurements were also used when available. Data were quality controlled so that only measured and good-quality gap filled data (QC = 0 or 1) were used.Analysis of the extreme summer drought in 2018 in Europe to prove nonlinearityTo analyze the effect of summer drought in 2018 on GPP in Europe, we selected 15 sites with measurements during 2014–2018 from the ICOS dataset, representing the major ecosystems across Europe (Supplementary Table 1). Croplands were excluded due to the effect of management on the seasonal timing of ecosystem fluxes, both from crop rotation that change from year to year and from the variable timing of planting and harvesting. In croplands, the changes of GPP anomalies across different growing season could be mainly depend on crop varieties and management activities. Information of crop varieties, growing times yearly and other management data for each cropland site should be collected in future in order to fully consider and disentangle the impacts of SWC and VPD on its photosynthesis. Wetland sites were also removed because they are influenced by upstream organic matter and nutrient input, as well as fluctuating water tables. Daytime half-hourly data (7 am to 19 pm) were aggregated to daily values. At each site, the relative changes ((triangle {{{{{rm{X}}}}}})) of summer (June–July–August) GPP, SWC and VPD during 2014–2018 refer to the summer average of 2014–2018 were calculated for each year. For example, the calculation of the relative change in 2018 is shown in Eq. (1):$$triangle {{{{{rm{X}}}}}}=frac{{X}_{2018}-,{X}_{{average};{of};2014-2018}}{{X}_{{average};{of};2014-2018}}times 100 %$$
(1)
where X2018 is the mean of the daily values of (X) (GPP, SWC, or VPD) during the summer of 2018, and Xaverage of 2014–2018 is the mean of the daily values of (X) over all the summers of the 2014–2018 period. The average (triangle {{{{{rm{X}}}}}}) across a certain number of sites at each bin were used for the results in Fig. 1a.Daily time series of GPP, SWC and VPD during summer for each site were normalized (z-scores) to derive the standardized sensitivity of GPP to SWC and VPD. For each variable, the mean value across the summer of 2014–2018 was subtracted for each day at each site and then normalized by its standard deviation. At each site, we used a multiple linear regression (Eq. 2) to estimate daily GPP anomalies sensitivities to SWC and VPD anomalies across 2014–2018 and 2014–2017, respectively:$${GPP}={beta }_{1},{SWC}+{beta }_{2},{VPD}+{beta }_{3},{SWC},times {VPD}+{beta }_{4},{T}_{a}+{beta }_{5}{RAD}+b+varepsilon$$
(2)
where ({beta }_{i}) is the standardized sensitivity of GPP to each variable; ({T}_{a}) represents the air temperature; ({RAD}) represents the incoming shortwave radiation;(,b) represents the intercept; and (varepsilon) is the random error term. We compared estimated sensitivities with and without 2018 data to quantify the impacts of extreme drought in 2018 on GPP sensitivity to SWC (Fig. 1d) and VPD (Fig. 1e). The slope was calculated at each site and then the distribution of slopes across sites were plotted in Fig. 1d, e.Global analysis of the sensitivities of GPP to SWC and VPDFor the global analysis, instead of summer, we focused on the growing season and days when the SWC and VPD effects were most likely to control ecosystem fluxes and screen out days when other meteorological drivers were likely to have a larger influence on fluxes. Following previous studies5,8,45, for each site, we restrict our analyses to the days in which: (i) the daily average temperature >15 °C; (ii) sufficient evaporative demand existed to drive water fluxes, constrained as daily average VPD  > 0.5 kPa; (iii) high solar radiation, constrained as daily average incoming shortwave radiation >250 Wm−2.By combining ICOS and FLUXNET2015 data, at the global scale, we evaluated 67 sites with at least 300 days observations over the growing seasons for the years available (Supplementary Table 2). We excluded cropland and wetland sites for the above-mentioned reasons. These 67 sites were used to calculate the relative effects of low SWC and high VPD on GPP following the approach of ref. 5 (see below sections). For 8 sites, the ANN results failed performance criteria (the correlation between predicted GPP and observed GPP is {{VPD}}_{0}\ {beta }_{0},,{VPD}le {{VPD}}_{0}end{array}right.$$
(7)
where β0 and k are fitted parameters and VPD0 is 1 kPa48. Following Luo and Keenan48, we applied this method to a short time window (2–14 days) of Fc depending on the availability of flux measurements and assumed that every day in the same time window has the same daily Amax. We retrieved the daily Amax by implementing Eqs. (6) and (7) using the REddyProc R package (https://github.com/bgctw/REddyProc)20.Vcmax represents the activity of the primary carboxylating enzyme ribulose 1,5-bisphosphate carboxylase–oxygenase (Rubisco) as measured under light-saturated conditions. To evaluate the responses of Vcmax to SWC and VPD, we first calculated the daily internal leaf CO2 partial pressure (ci) in the middle of the day (11:00–14:00) via Fick’s Law (Eq. 8), excluding periods with low incoming shortwave radiation (0.7 at most sites. During the training process, weight and bias values were optimized using the Levenberg–Marquardt optimization58,59. The maximum number of epochs to train is 1000. An example to demonstrate the ANN training at one site was shown in Supplementary Fig. 3.At each site, ANN was run and sensitivities were calculated for all data within each SWC and VPD bin and the median value was used. For each of the five trained ANNs, one of the predictor variables was perturbed by one standard deviation (a value of 1 due to the initial input data normalization), and GPP was predicted again using the existing ANN with the predictors including the perturbed variable; this process was repeated for each predictor variable. The predicted values of GPP obtained with and without perturbation were then compared to determine the sensitivity values. The sample equation showing the calculation of the GPP sensitivity to VPD is shown in Eq. (10).$${{{{{{rm{Sensitivity}}}}}}}_{{VPD}}={median}left(,frac{{{GPP}}_{left({ANN};{VPD}+{stdev}left({VPD}right)right)}-{{GPP}}_{left({ANN};{all};{VAR}right)}}{{stdev}left({VPD}right)}right)$$
(10)
We repeated the ANN and sensitivity analyses five times and the median of these were used at each site. Across all sites, significances of the sensitivities for each bin were tested using t-tests (p  More

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We showed that the new metabolic rate relation13 can be directly linked to the total energy consumed in a lifespan if a constant number ({mathrm{N}}_{mathrm{r}}) of respiration cycles per lifespan is conjectured, and a corrected relation for the total energy consumed in a lifespan was found [Eq. (1)] that can explain the origin of variations in the ‘rate of living’ theory2,5 and unify them into a single formulation. It is important to note that Eq. (1) is a direct consequence of combining the two empirical relations mentioned (the new metabolic rate relation and the relation of the total number ({mathrm{N}}_{mathrm{r}}) of respiration cycles per lifespan) and is not an assumption (based on the lifespan energy expenditure per gram) as in the traditional ‘rate of living’ theory2,5. We test the validity and accuracy of the predicted relation [Eq. (1)] for the total energy consumed in a lifespan with (sim 300) species representing different classes of living organisms, and we find that the relation has an average scatter of only 0.3 dex, with 95% of the organisms having departures of less than a factor of (pi) from the relation, despite the difference of (sim 20) orders of magnitude in body mass.Successful testing of predictions is crucial in any proposed theory according to Popper’s deductive method of falsification (27), which is the criterion for identifying a successful scientific theory. Therefore, the success of the predicted Eq. (1) that is displayed in Fig. 1 implies that the corrected metabolic rate relation13 has passed an initial test. This prediction also reduces any possible interclass variation in the relation, which has been considered the most persuasive evidence against the ‘rate of living’ theory, to only a geometrical factor and strongly supports the conjectured invariant number ({mathrm{N}}_{mathrm{r}} sim 10^8) of respiration cycles per lifespan in all living organisms.Invariant quantities in physics traditionally reflect fundamental underlying constraints, a principle that has also been applied recently to life sciences such as ecology21,22. Figure 2 indicates the fact that, for a given temperature, the total lifespan energy consumption per gram per ‘generalized beat’ (({mathrm{N}}_{{mathrm{b}}}^{mathrm{G}} equiv mathrm{a} {mathrm{N}}_{{mathrm{r}}} = {mathrm{a}} ,1.62 times 10^8)) is remarkably constant (around ({mathrm{E}}_{2019})), a result that is also in agreement with previous expectations based on (lifespan) basal oxygen consumption at the molecular level38. This supports the idea that the overall energetics during the lifespan are the same for all the organisms studied, as it is predetermined by the basic energetics of respiration, and therefore, Rubner’s original picture is shown to be valid without systematic exceptions but in a more general form. Moreover, since the value determined from Fig. 2 is remarkably similar to ({mathrm{E}}_{2019} {mathrm{N}}_{mathrm{r}}), it can be considered an independent determination of ({mathrm{E}}_{2019}), suggesting that ({mathrm{E}}_{2019}) is a candidate for being a universal constant and not just a fitting parameter from the corrected metabolic relation13.In addition, we showed here that the invariant total lifespan energy consumption per gram per ‘generalized beat’ comes directly from the existence of another invariant, the approximately constant total number ({mathrm{N}}_{mathrm{r}} sim 10^8) of respiration cycles per lifetime, effectively converting the ‘generalized beat’ into the characteristic clock during the lifespan. Therefore, the exact physical relation between (oxidative) free radical damage and the origin of aging is most likely related to the striking existence of a constant total number of respiration cycles ({mathrm{N}}_{{mathrm{r}}}) over the lifetime of all organisms, which predetermines the extension of life. Moreover, the relation ({mathrm{t}}_{{mathrm{life}}} = mathrm{N}_{mathrm{r}}/mathrm{f}_{{{mathrm{resp}}}}) quantifies the ideas of oxidative damage by the respiratory metabolism, which are motivated mainly by biomedical considerations, into a simple mathematical form that could be included in a broader life-history framework; this is needed to produce testable predictions for the ‘free-radical’ hypothesis in the life-history context28. Future theoretical and experimental studies that investigate the exact link between the constant number ({mathrm{N}}_{mathrm{r}} sim 10^8) of respiration cycles per lifespan and the production rates of free radicals (or alternatively, other byproducts of metabolism) should shed light on the origin of aging and the physical cause of natural mortality.Although this relation ({mathrm{t}}_{{mathrm{life}}} = mathrm{N}_{mathrm{r}}/mathrm{f}_{{mathrm{resp}}}) has only been empirically examined for mammalian vertebrates, in terms of heartbeats per lifetime, there is evidence to believe that the relative constancy of the number of respiration cycles per lifetime is more widely distributed in the animal kingdom. For example, a reptile such as the Galapagos tortoise with a life expectancy of 177 years and a respiration rate of 3 breaths/min has (2.8 times 10^8) breaths per lifetime29, which is within a factor of 2 of the value determined for mammals. A more different case is that of birds, which have more heartbeats/lifetime by a factor of 330; this difference is reduced to a factor of 1.5 in terms of breaths/lifetime ((mathrm{N}_{mathrm{r}} = mathrm{N}_{mathrm{b}}/{mathrm{a}}), with (hbox {a}=9) for birds and 4.5 for mammals; 17). Among fish, the average number of heartbeats/lifetime tends to be an order of magnitude less than that in mammals ((mathrm{N}_{mathrm{b}} = 7.3 times 10^8);16), for example, (mathrm{N}_{mathrm{b}} = 6.7 times 10^7) for trout31, but in such cases, the parameter a can be as low as 0.5 (i.e., a heart frequency lower than the respiratory frequency; 32), again implying a similar ({mathrm{N}}_{mathrm{r}} ,(= mathrm{N}_{mathrm{b}}/{mathrm{a}} = 1.3 times 10^8)). A more extreme difference in terms of heartbeats is the tiny Daphnia, which uses up to (1.7 times 10^7) heartbeats (at 25 C) in a short lifespan of 30 days33. Simple invertebrates, such as Daphnia, do not have a complex respiratory system with lungs and obtain oxygen for respiration through diffusion, but a “breath frequency” can be estimated from its respiration rate ((sim mu {mathrm{l}} {mathrm{O}}_2 hbox {hr}^{-1});34) divided by ({mathrm{E}}_{2019} M) (with ({mathrm{M}} sim 100 mu {mathrm{g}});35), giving ({mathrm{N}}_{mathrm{r}} = 1.5 times 10^8) respiration cycles per lifetime. In summary, a difference of two orders of magnitude in total heartbeats (between Daphnia and birds) is reduced to less than a factor of 2 in breaths per lifetime, further supporting that all organisms seem to live for the same span in units of respiration cycles (({mathrm{N}}_{mathrm{r}} sim 10^8)).It has also been suggested that an analogous invariant originates at the molecular level23, the number of ATP turnovers of the molecular respiratory complexes per cell in a lifetime, which, from an energy conservation model that extends metabolism to intracellular levels, is estimated to be (sim 1.5 times 10^{16})23. A similar number can be determined by taking into account that human cells require the synthase of approximately 100 moles of ATP daily, equivalent to (7 times 10^{20}) molecules per second. For (sim 3 times 10^{13}) cells in the human body and for a respiration rate of 15 breaths per minute, this gives (sim 9 times 10^{7}) ATP molecules synthesized per cell per breath, which for the invariant total number ({mathrm{N}}_{mathrm{r}}) of respiration cycles per lifetime found in this work, rises to the same number of (sim 1.5 times 10^{16}) ATP turnovers in a lifetime per cell, showing the equivalence between both invariants and linking ({mathrm{N}}_{mathrm{r}}) to the energetics of respiratory complexes at the cellular level.The excellent agreement between the predicted relation [Eq. (1)] and the data across all types of organisms emphasizes the fact that lifespan indeed depends on multiple factors (B, a, M, T & (mathrm{T}_{mathrm{a}})) and strongly supports the methodology presented in this work of multifactorial testing, as shown in Fig. 1, since quantities in life sciences generally suffer from a confounding variable problem. An example of this problem, illustrated by individually testing each of the relevant factors, is given in24, which for a large (and noisy) sample test for ({mathrm{t}}_{{{mathrm{life}}}} propto 1/B) shows no clear correlation. From Eq. (1), it is clear that in an uncontrolled experiment, the dependence on the rest of the parameters (M, a, T, & ({mathrm{T}}_{mathrm{a}})) might eliminate the dependence on the metabolic rate B (in fact, this may be for the same reason that Rubner’s work7 focused on the mass-specific metabolic rate B/M instead of B). This work24 finds only a residual inverse dependence of ({mathrm{t}}_{{mathrm{life}}}) on the ambient temperature ({mathrm{T}}_{{mathrm{a}}}) for ectotherms, which is expected according to Eq. (1) (Big (mathrm{t}_{{mathrm{life}}} propto {mathrm{exp}}Big ({small frac{mathrm{E}_{mathrm{a}}}{mathrm{k} {mathrm{T}}_{mathrm{a}}}}Big ) Big )).Finally, the empirical support in favor of Eq. (1) allows us to perform several estimations regarding how much the energy consumption will vary with changing physical conditions on Earth. For example, computing by how much the energy consumption will vary in biomass performing aerobic respiration as the Earth’s temperature increases is relevant in the current context of possible global warming. This is given by the factor ({mathrm{exp}}Big [{small frac{mathrm{E}_{mathrm{a}}}{{mathrm{k}}} Big (frac{1}{ {mathrm{T}}}} – {small frac{1}{ {mathrm{T}}+1}}Big ) Big ]), which for an activation energy of ({mathrm{E}}_{mathrm{a}} = 0.63 ,hbox {eV}) and a temperature of (30^{circ }hbox {C}) implies an increase of 8.3% in energy consumption per 1 degree increase in the average Earth temperature. This result can be straightforwardly applied in ectotherms since their body temperatures adapt to the environmental temperature (({mathrm{T}}={mathrm{T}}_{mathrm{a}})), but its implications for endothermic organisms are less clear. Another relevant estimation is to compute by how much B({mathrm{t}}_{{mathrm{life}}})/M would vary from Eq. (1) (i.e., the difference between Figs. 2 and 3) as a function of body temperature (T) and the ratio of heart rate to respiratory rate ((mathrm{a}= mathrm{f}_{mathrm{H}}/ {mathrm{f}}_{{mathrm{resp}}})). Variations in B({mathrm{t}}_{{mathrm{life}}})/M are relevant since this is a key quantity in the estimation of the energy allocation to fitness, which aims to explain in terms of trade offs the so-called ‘Equal Fitness Paradigm’39 that concerns why most organisms in the biosphere are more or less equally fit, other than the diversity seen in the size, form and function of living organisms on Earth.In the near future, our plan is to generate a (metabolic) theory starting from the new metabolic rate relation13 by assuming that it is the controlling rate in ecology in order to explain a variety of ecological phenomena in a similar fashion as the metabolic theory of ecology18 does using Kleiber’s law. A first step in this direction looks very promising40, as it can show that ontogenetic growth can be described by a universal growth curve without the aid of fitting parameters, can explain the origin of several ‘Life History Invariants’21 and can show how the heart rate may actually set several biological times (i.e., lifespan and generation time) and even some ecological rates (i.e., The Malthusian parameter). More