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Climate models need to capture a full spectrum of data from forests such as the Brazilian Amazon.Credit: Florence Goisnard/AFP/Getty

Humanity’s understanding of how forests are responding to climate change is disconcertingly fragile. Take carbon fertilization, for example — the phenomenon by which plants absorb more carbon dioxide as its concentration in the atmosphere increases. This is one of the principal mechanisms by which nature has so far saved us from the worst of climate change, but there’s little understanding of its future trajectory. In fact, researchers don’t fully understand how climate change interacts with a multitude of forest processes. Complex, unsolved questions include how climate warming affects forest health; how it affects the performance of forests as a carbon sink; and whether it alters the ecosystem services that forests provide. Forests are our life-support system, and we should be more serious about taking their pulse.Six papers in this week’s Nature provide important insights into those questions. They also underline some of the challenges that must be overcome if we are to fully understand forests’ potential in the fight against climate change. These challenges are not only in the science itself, but also relate to how forest scientists collaborate, how they are funded (especially where data collection is concerned) and how they are trained.Forest science is an amalgam of disciplines. Ecologists and plant scientists measure tree growth, soil nutrients and other parameters in thousands of forest plots around the world. Physical scientists monitor factors such as forest height and above-ground forest biomass using remote-sensing data from drones or satellites. Experimental scientists investigate how forests might behave in a warming world by artificially altering factors such as temperature or carbon dioxide levels in experimental plots. Some of the data they generate are absorbed by yet another community: the modellers, who have created dynamic global vegetation models (DGVMs). These simulate how carbon and water cycles change with climate and, in turn, inform broader earth-system and climate models of the type that feed into policymaking.Different DGVMs make different predictions about how long forests will continue to absorb anthropogenic CO2. One reason for these differences is that models are sensitive to assumptions made about the processes in forests. There are many influences — including temperature, moisture, fire and nutrients — that are generally studied in isolation. Yet they interact with each other.Not all DGVMs account for the dampening effect that a lack of soil phosphorus can have on carbon fertilization, for example. Much of central and eastern Amazonia is poor in phosphorus, and research has shown that introducing phosphorus limitation into DGVMs can cut the carbon-fertilization effect1. This week, Hellen Fernanda Viana Cunha at the National Institute for Amazonian Research in Manaus, Brazil, and her colleagues report2 a powerful experimental demonstration of how the soil’s poor phosphorus content limits carbon absorption in an old-growth Amazonian forest.Models simulating the northward spread of boreal forest as temperatures rise are also missing key drivers3, according to Roman Dial at Alaska Pacific University in Anchorage and his colleagues. They report today that a white-spruce population has migrated surprisingly far north into the Arctic tundra. To explain this, it is necessary to take into account winter winds (which facilitate long-distance dispersal) along with the availability of deep snow and soil nutrients (which promote plant growth).Models are often based on a small number of ‘functional tree types’ — for example, ‘evergreen broadleaf’ or ‘evergreen needle leaf’. These are chosen as a proxy for the behaviour of the planet’s more than 60,000 known tree species. Yet ecologists are discovering that the biology of individual species matters when it comes to a tree’s response to climate change.David Bauman at the Environmental Change Institute at the University of Oxford, UK, and his co-workers reported in May that tree mortality on 24 moist tropical plots in northern Australia has doubled in the past 35 years (and life expectancy has halved), apparently owing to the increasing dryness of the air4. But that was an average of the 81 dominant tree species: mortality rates varied substantially between species, a variation that seemed to be related to the density of their wood.Peter Reich at the Institute for Global Change Biology at the University of Michigan in Ann Arbor and his colleagues now report that modest alterations in temperature and rainfall led to varying rates of growth and survival5 for different species in southern boreal-forest trees. The species that prospered were rare.Failure to examine multiple factors simultaneously means that scientists are making findings that challenge the assumptions in models. Spring is coming earlier for temperate forests and most models assume that, by prolonging the growing season, this increases woody-stem biomass. However, observational work carried out in temperate deciduous forests by Kristina Anderson-Teixeira at the Smithsonian Conservation Biology Institute in Front Royal, Virginia, and her colleagues found no sign of this happening6.Modellers are all too aware of the need to incorporate more complexity into their models, and of the potential that increasing amounts of computing power have to assist them in this endeavour. But they need more data.Continuity problemTo obtain comprehensive, valuable data for the models, continuous, long-term observations need to be made, and that depends on the availability of long-term funding. Achieving such continuity is a problem for both remote-sensing and ground-based operations. The former can cost hundreds of millions of dollars, but the value of its long-term data sets is immense, as demonstrated by a team led by Giovanni Forzieri at the University of Florence in Italy. The authors used 20 years of satellite data to show that nearly one-quarter of the world’s intact forests have already reached their critical threshold for abrupt decline7. But even field-based data collection, which costs a pittance by comparison, struggles to achieve financial security.Important ground-based operations include the Forest Global Earth Observatory (ForestGEO), part of the Smithsonian Tropical Research Institute, which is headquartered in Washington DC. This monitors 7.5 million individual trees in plots around the world. The amount of work that goes into this monitoring is formidable. For example, at present, ForestGEO is conducting the eighth five-yearly census of a plot in Peninsular Malaysia. This involves determining the species for each of the 350,000 trees (there are some 800 species growing there) and measuring the circumference of each trunk. It will take 16 skilled people a year to measure all the trees. Delays in the provision of funding to ForestGEO have held up similar censuses at plots in countries including Papua New Guinea, Vietnam, Brunei and Ecuador.

A ForestGEO researcher making tree measurements at a forest plot in Barro Colorado Island, Panama.Credit: Jorge Aleman, STRI

The future of the plots in North Queensland, which supplied Bauman with a rare 49 years’ worth of continuous data, is uncertain. They have been monitored since the mid-1970s by the Australian public research-funding agency CSIRO — initially every two years, then, more recently, every five years. In 2019, monitoring of the plots was switched to every 50 years because of funding shortages at CSIRO, leaving scientists searching for new sources of funding.Without continuity of funding, organizations such as ForestGEO can’t equip researchers with the requisite skills or collect data over periods longer than an individual’s time in a specific post or a funder’s cycle. “We have trained people and then lost them due to job insecurity,” says Stuart Davies, who leads ForestGEO.Different groups of forest researchers are trying to address these problems. ForestGEO is coordinating the Alliance for Tropical Forest Science in an effort to make it easier to share data, and to bolster the morale and careers of the skilled technicians and scientists — many of whom live in low- and middle-income countries — who do the bulk of the data collection.But we also need more-imaginative funding mechanisms that lift long-term observational plots out of three- to five-year funding cycles. Space agencies that fund remote-sensing satellites could collaborate with other funding agencies, for example, so that earth-observation missions include a fully funded component for ground-based data collection — which is, after all, crucial for calibrating their results. Journals, too, could do more to value and incentivise the production of long-term data sets.And there is a need for more interdisciplinarity. The US Department of Energy is funding a project called NGEE–Tropics (Next-Generation Ecosystem Experiments–Tropics) in which modellers will work with empirical researchers, both observational and experimental, who study tropical forests to create a full, process-rich model of such forests. This is encouraging, and the idea could be pushed further. What is needed is an initiative that pulls the disciplines together towards a goal of building a better understanding of forest processes. Among other things, such an initiative would encourage researchers in different disciplines to take each other’s data needs into account when planning their projects.For this to work, we need to remember that the edifice of forest science relies on the long-term data that scientists wring from forests over decades. Our chances of overcoming climate change are small, but they will diminish further if we forget the basics of monitoring our home planet. More

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Experimental set-upFour vegetation species were selected: Spartina maritima, Salicornia europaea, Halimione portulacoides and Juncus maritimus. These species were chosen for a broad representation of the biomechanical properties and morphological characteristics of saltmarsh species42,43. Plants were collected in Cantabrian estuaries in late summer and early autumn (from early September to late October) during low tide (please refer to the “Methods” section). A total of 105 boxes were collected, of which 94 boxes were used to build a 9.05 m long and 0.58 m wide meadow in a flume (Fig. 1). Five boxes were used to directly estimate the meadow standing biomass in the field (Sample 1 in Table 1), leaving 6 extra boxes for possible contingencies.Figure 1(A) Shows a sketch of the experimental flume, where the vegetation box distribution in the 100% and 50% density cases is displayed in the two upper panels and a lateral view in the bottom panel. The green boxes indicate the vegetated area in each case. Free surface sensors are displayed by blue lines and numbers. (B) Shows the four species within the flume. From left to right: view of the Spartina sp. frontal edge, aerial view of Salicornia sp., frontal view of Juncus sp. and top view of the Halimione sp. rear edge.Full size imageTable 1 Standing biomass (g/m2) and plant height (m) for the four species.Full size tableExperiments were conducted in a flume 20.71 m long and 0.58 m wide at the University of Cantabria. The flume is equipped with a piston wave maker at its left end and a dissipation beach at the rear end. The 94 vegetation boxes used to create a meadow were introduced into the flume following the pattern shown in panel A of Fig. 1 to minimize any edge effects along the edges of the boxes. To ensure a smooth transition from the bottom of the channel to the vegetated area, two false bottoms were constructed with wood, and a thin sediment layer was glued to the wood to mimic the field roughness.Three meadow densities per species were considered. The meadow density directly determined in the field was chosen under the 100% density scenario. To consider a second meadow density, and therefore a second standing biomass value, plants were removed from half of the boxes following the pattern shown in Panel A of Fig. 1 to prevent creating preferential flow channels along the meadow. This case was considered the 50% density scenario. The study of these two biomass scenarios for each vegetation species is carried out with the aim of covering a wide range of standing biomass values, including low values that may be more representative of meadow winter conditions, thus facilitating the applicability of obtained results. Finally, a second cut was made, in which all plants were removed, resulting in the final scenario with a zero density. Plants were cut from above to avoid any damage along the meadow surface (as shown in Supplementary Fig. S2). In each cut, plants in 5 boxes along the leading edge and in 5 boxes at the center of the meadow were collected to quantify the standing biomass (Samples 2 and 3 for the first cut and Sample 4 and 5 for the second cut in Table 1). Therefore, the standing biomass could be monitored throughout the entire duration of the experiments, from the field until the second cut, when all plants were removed.Once located in the flume, the meadow was evaluated under regular and random wave conditions considering three water depths, i.e., h = 0.20, 0.30 and 0.40 m. Regular waves were generated using Stokes II-, III- and V-order and Cnoidal theories when applicable. Wave heights ranging from 0.05 to 0.15 m and wave periods varying between 1.5 and 4 s were considered. Random waves were generated using a Jonswap spectrum with a peak enhancement factor of 3.3, a significant wave height varying between 0.05 and 0.15 m and a peak wave period ranging from 1.8 to 4.8 s (please refer to Supplementary Table S1). Additionally, all wave conditions were considered under the zero-density scenario with bare soil for each species. The wave height evolution along the flume was recorded using 15 capacitive free surface gauges, as shown in Fig. 1 (please refer to Supplementary Table S2 for detailed coordinates).Meadow characteristics analysisThe characteristics of the vegetation meadows were analyzed by measuring the standing biomass throughout the full duration of the experiments and by measuring the individual plant height (please refer to the “Methods” section). The mean standing biomass value obtained for each species was considered the value associated with the 100% density scenario. Then, half of the standing biomass value was considered under the 50% density scenarios since half of the boxes was randomly cut, and the standing biomass values obtained after the second cut agreed with those obtained after the first cut and in the field, as indicated in Table 1. The plant height for each species was also measured (please refer to the “Methods” section), and the resultant mean value detailed in Table 1 was considered.Wave height attenuation analysisWave height attenuation analysis was performed following previous studies reported in the literature assessing the capacity by fitting a damping coefficient6,7,35,44. The18 formulation was used for regular waves, and that of19 was used for random waves (please refer to the “Methods” section). Cases with a zero density were also considered in this analysis to quantify the influence of bare soil friction by determining the corresponding damping coefficient, ({beta }_{B}). Consequently, β was obtained in the 100% and 50% density cases and the cases without vegetation (please refer to Supplementary Tables S3, S4 and S5 to find the obtained coefficients for all cases). This allowed the determination of a new damping coefficient isolating the effect of the standing biomass, ({beta }_{SB}), following24 (please refer to the “Methods” section). Figure 2 shows an example of wave height attenuation analysis for the four species and the different densities under wave condition JS07 (Supplementary Table S1).Figure 2Analysis of wave attenuation under wave condition JS07 for Spartina sp. 100% (S100), 50% (S050) and zero density (S000); Salicornia sp. 100% (L100), 50% (L050) and zero density (L000); Juncus sp. 100% (J100), 50% (J050) and zero density (J000); and Halimione sp. 100% (H100), 50% (H050) and zero density (H000). The damping coefficients for the bare soil cases, ({beta }_{B}), are displayed in blue. The damping coefficients for the 100% and 50% density cases, (beta ), are displayed in dark and light green, respectively. The damping coefficients obtained after subtracting the dissipation obtained in the bare soil cases, ({beta }_{SB}), are displayed in black and dark gray. 95% confidence interval is shown in brackets and correlation coefficient (({rho }^{2})) for each fit is also displayed.Full size imageThe damping coefficients for the bare soil cases shown in Fig. 2, ({beta }_{B}), are consistent with the soil properties observed in the field. Spartina sp. was collected in a muddy area, whereas the other three species were collected in areas with coarser sediments and exhibited a mixture of sand and mud. For all species, wave dissipation was significantly higher under the 100% density scenario than that under the 50% density cases, as expected, highlighting the importance of the standing biomass in wave energy dissipation. It was also observed that bottom friction-induced dissipation plays a more important role for the pioneer species, i.e., Spartina sp. and Salicornia sp., than for the upper marsh species, i.e., Juncus sp. and Halimione sp., which can dissipate wave energy to a greater extent.The importance of wave parameters in the resultant wave attenuation has been highlighted by several works in the literature. Therefore, not only vegetation characteristics but also incident wave conditions determine the coastal protection capacity. Figure 3 shows a comparison of the obtained wave height attenuation due to Halimione sp. under the different wave conditions.Figure 3Analysis of wave attenuation under the different irregular wave conditions for the Halimione sp. 100% (H100) and zero-density (H000) cases. The top panel shows two cases with different h but equal Hs and Tp values (JS01 and JS08), the middle panel shows two cases with different Tp but equal h and Hs values (JS10 and JS11), and the bottom panel shows two cases with different Hs but equal h and Tp values (JS09 and JS12). 95% confidence interval is shown in brackets and correlation coefficient (({rho }^{2})) for each fit is also displayed.Full size imageThe top panel in Fig. 3 shows two cases where Hs and Tp are equal, i.e., JS01 and JS08 in Supplementary Table S1, and two water depths are considered, namely, h = 0.2 and 0.3 m. As can be observed, wave damping is higher for the smallest water depth, where most of the water column is covered by vegetation since the mean vegetation height for Halimione sp. reaches 0.187 m (Table 1). The importance of the water depth with respect to the plant height in terms of wave height attenuation has been reported by several authors44,45,46 who have highlighted this aspect based on the submergence ratio, i.e., the plant height divided by the water depth, revealing higher attenuation at lower submergence ratios on a consistent basis. Bottom friction attenuation is also higher for the smallest water depth, as expected.The middle panel of Fig. 3 shows two cases with equal h and Hs but different Tp values, namely, JS10 and JS11 in Supplementary Table S1. Wave height attenuation is higher for the shortest wave period, as well as the damping produced by bottom friction. This is in line with previous studies, such as35 and44, who conducted experiments involving simulated and real saltmarshes, respectively. Finally, the bottom panel of Fig. 3 shows two cases with different Hs but equal h and Tp values, i.e., JS09 and JS12 in Supplementary Table S1. As widely reported in the literature, e.g.,7,47,48, wave height attenuation increases with the wave height, as shown in the bottom panel of Fig. 3. Bottom friction also increases with the wave height, as expected.A set of damping coefficients was obtained via the 288 tests conducted in the laboratory, 144 tests involving regular waves and 144 tests involving random waves. Additionally, in all cases, the damping coefficient considering the isolated effect of the standing biomass, ({beta }_{SB}), was determined. The relationship of these damping coefficients to the measured standing biomass is explored in the next section with the aim of establishing a new relationship to estimate the wave damping effect of the different saltmarsh species based on the standing biomass, without the need for data fitting.Wave damping coefficient as a function of the standing biomassThe mean standing biomass obtained for the different species, Table 1, is considered here to analyze the relationship with the wave damping coefficients obtained by fitting18 formulation to wave heights measured along the meadow for regular waves and19 formulation for random waves. The plant height was highly variable among the different species (Table 1), ranging from 0.170 m for Spartina sp. to 0.714 m for Juncus sp. Then, some species were submerged at all tested water depths, while other species remained above water in all tests. In the latter cases, there remained a portion of each plant above the water level, thus not contributing to wave attenuation. To consider the actual interaction between the standing biomass and flow conditions and assuming a uniform vertical distribution, the effective standing biomass, (ESB), can be defined as follows:$$ESB=DryWeight*frac{minleft{{h}_{v},hright}}{{h}_{v}}$$
(1)
where (DryWeight) denotes the measured dry weight for each species (g/m2), ({h}_{v}) is the mean plant height and (h) is the water depth. Additionally, in the submerged cases, the same (ESB) value will impact flow differently depending on the submergence ratio, (SR), as defined in Eq. (2). To consider this effect, the standing biomass ratio, (SBR) in Eq. (3), can be defined as follows:$$SR=frac{{h}_{v}}{h}, ;;where ;; SR=1 ;;for ;;{h}_{v} >h$$
(2)
$$SBR=ESB*SR$$
(3)
Figure 4 shows the relationship between (SBR) and the measured wave damping coefficient, (beta ). The results for regular and random waves are displayed for each water depth, and a linear fit was found under each condition.Figure 4Wave damping coefficient, (beta ), as a function of the standing biomass ratio, (SBR), under all regular (left panels) and random (right panels) wave conditions. Each panel shows the wave trains assessed at each water depth, h = 0.20, 0.30 and 0.40 m. The results for the 100% density case are marked with circles and those for the 50% density case are marked with squares. The linear fitting results obtained under each wave condition are also displayed.Full size imageUnder each wave condition, a linear fitting relationship between (beta ) and (SBR) was obtained for the eight (SBR) values, as shown in Fig. 4. For similar (SBR) values, the highest (beta ) values were consistently obtained at the smallest water depth, highlighting the notable influence of this parameter on the obtained wave attenuation. Following previous works, such as those of24 and25, who considered the vegetation submerged solid volume fraction to estimate the resulting wave attenuation and established a common relationship for different water depths, the volumetric standing biomass, (VSB), can be defined as follows:$$VSB= SBR*frac{1}{h}$$
(4)
(VSB) is expressed in units of g/m3, which is the weight per unit volume. Exploring the relationship of (beta ) with this new parameter, it was found that the results for the three water depths could be fitted with a single linear relationship, as shown in Fig. 5. However, despite the linear trend observed in Fig. 5, notable data scatter was observed for each (VSB) value. Each of these groups corresponds to a certain water depth and (SBR) value, which were determined under different wave heights and wave periods.Figure 5Wave damping coefficient, (beta ), as a function of the volumetric standing biomass, (VSB), under all regular (top panel) and random (bottom panel) wave conditions. The obtained linear fitting results are displayed in both panels. 95% confidence interval is shown in brackets and correlation coefficient (({rho }^{2})) for each fit is also displayed.Full size imageFinally, to account for the characteristics of the incident wave conditions, including the wave height and period, two nondimensional parameters were considered. The first parameter, considering the wave height, is the relative wave height, defined as the ratio of the incident wave height to the water depth, (H/h). Previous studies have highlighted the importance of this parameter in the resultant wave attenuation (e.g.24,44). Under random wave conditions, the considered wave height is ({H}_{rms}), according to wave attenuation analysis. The second parameter, considering the effect of the different wave periods and the importance of the number of wave lengths inside the vegetation length49, is the relative meadow length, defined as the ratio of the meadow length to the wave length, ({L}_{v}/L). To ensure consistency with the above wave attenuation analysis, in which the wave damping amount per unit length was obtained, the unit meadow length was considered here. Thus, the hydraulic standing biomass, (HSB), can be defined as:$$HSB=VSB*frac{H}{h}*frac{{L}_{v}}{L}$$
(5)
Figure 6 shows the relationship obtained between (beta ) and this new variable under all regular and random conditions following the linear fitting relationship of (beta =A*HSB+B), where (A) and (B) are fitting constants with units of (g/m2)−1 and m−1, respectively.Figure 6Wave damping coefficient, (beta ), as a function of the hydraulic standing biomass, (HSB), under all regular (top panel) and random (bottom panel) wave conditions. Both panels show linear fitting results obtained without considering the saturation point, indicated by the black solid line, and those obtained considering the saturation point, indicated by the gray solid line. The black dashed line indicates the saturation point. 95% confidence interval is shown in brackets and correlation coefficient (({rho }^{2})) for each fit is also displayed.Full size imageThe linear fitting results obtained between (beta ) and (HSB) under regular and random wave conditions are shown in Fig. 6 as solid black lines and expressed as Eqs. (6) and (7), respectively, where values between brackets are the 95% confidence interval for each coefficient.$$beta =9.206cdot {10}^{-4} left(9.006cdot {10}^{-5}right)*HSB+0.103 (0.021)$$
(6)
$$beta =1.192 cdot {10}^{-3} left(9.124 cdot {10}^{-5}right)*HSB+0.071 (0.016)$$
(7)
The inclusion of incident wave condition characteristics reduces the resulting data scatter, highlighting the role of the wave height and period in the obtained wave attenuation, as described in the previous section. An interesting aspect observed in Fig. 6 is that the four cases with the highest wave damping coefficients yielded similar values for the different (HSB) values. Under regular wave conditions, the mean (beta ) value for these four cases is 0.76, and under random wave conditions, the value reaches 0.68. This may indicate that the damping coefficient has reached its maximum value and no longer increases with increasing (HSB) value. To analyze this aspect in more detail, the wave height evolution measured for the four tests in which (beta ) reaches its maximum value are plotted (as shown in Supplementary Fig. S3). These tests correspond to Halimione sp. with a density of 100% and the shallowest water depth, h = 0.20 m. This species achieved the highest standing biomass value among the species considered in these experiments, and for h = 0.20 m, almost the entire water column was covered by vegetation. For these tests, a notable wave height attenuation was observed, where the wave height strongly decayed along the first 5 m of vegetation, and the wave height entirely dissipated along the last 4 m (as shown in Supplementary Fig. S3). The wave damping equation cannot suitably reproduce the strong wave decay within this few meters. Then, an almost constant wave damping coefficient value is reached under the different considered wave conditions, and a saturation regime is observed, in which the wave height beyond the meadow can be assumed to be negligible. To consider this phenomenon, a two-section fitting relationship is proposed, as shown in Fig. 6. The value of the saturation damping coefficient, chosen as the mean value of the four cases analyzed, is plotted as a dashed gray line, and a linear fit is obtained for the remaining data. The two-section fitting relationship is expressed in Eqs. (8) and (9) for both regular and random waves, respectively, where values between brackets are the 95% confidence interval for each coefficient.$$beta =left{begin{array}{ll}1.020 cdot {10}^{-3}left(1.112 cdot {10}^{-4}right)*HSB+0.088 ; (0.020) \ 0.758; (0.027)end{array}right. begin{array}{l} ;;0 < HSB < 659\ ;; HSB > 659end{array}$$
(8)
$$beta =left{begin{array}{l}1.310cdot {10}^{-3}left(1.232cdot {10}^{-4}right)*HSB+0.059; (0.017) \ 0.684 ;(0.066)end{array}right. begin{array}{l};;0474end{array}$$
(9)
All damping coefficients considered in the previous analysis were obtained without subtracting any additional source of dissipation such as bottom and wall friction. Previous works, such as24, highlighted the high importance of considering any other sources of wave dissipation besides the effect of vegetation elements when quantifying the wave height attenuation capacity. In this case, the flume walls were made of glass, and the friction induced by these walls could be considered negligible. However, bottom friction could be significant, as observed in tests run after removing all vegetation stems. Then, the wave damping coefficient obtained after subtracting the bottom friction contribution, ({beta }_{SB}), is studied here. Figure 7 shows the relationship obtained between this damping coefficient, ({beta }_{SB}), and hydraulic standing biomass, (HSB).Figure 7Wave damping coefficient, ({beta }_{SB}), as a function of the hydraulic standing biomass, (HSB), under all regular (top panel) and random (bottom panel) wave conditions. Both panels show linear fitting results obtained without considering the saturation point, indicated by the black solid line, and those obtained considering the saturation point, indicated by the gray solid line. The black dashed line indicates the saturation point. 95% confidence interval is shown in brackets and correlation coefficient (({rho }^{2})) for each fit is also displayed.Full size imageA linear relationship was also obtained for ({beta }_{SB}), revealing correlation coefficients similar to those obtained when analyzing (beta ). The obtained linear relationships under regular and random wave conditions are expressed as Eqs. (10) and (11), respectively, where values between brackets are the 95% confidence interval for each coefficient. A two-section fitting relationship, Eqs. (12) and (13), was also included considering the saturation regime obtained in the Halimione sp. 100% density and h = 0.20 m cases with a ({beta }_{SB}=) 0.69 and 0.63 under regular and random wave conditions, respectively.$${beta }_{SB}=1.051*{10}^{-3} left(7.063cdot {10}^{-5}right)*HSB$$
(10)
$${beta }_{SB}=1.296*{10}^{-3} left(6.894cdot {10}^{-5}right)*HSB$$
(11)
$${beta }_{SB}=left{begin{array}{l}1.151cdot {10}^{-3} left(7.445cdot {10}^{-5}right)*HSB \ 0.685 ;(0.047)end{array}right. begin{array}{l} ;; 0599end{array}$$
(12)
$${beta }_{SB}=left{begin{array}{l}1.396cdot {10}^{-3}left(7.919cdot {10}^{-5}right)*HSB \ 0.631 ;left(0.055right)end{array}right. begin{array}{l};; 0451end{array}$$
(13)
As can be noted, the ({beta }_{SB}) values are significantly lower than those obtained for (beta ), especially in the shallowest water depth cases where bottom friction is the highest, as discussed above. The estimation of (beta ) and ({beta }_{SB}) allows two possible approaches to determine the wave damping effect of a saltmarsh. The first approach, based on (beta ), includes wave damping induced by the combined effect of vegetation and bottom friction. Therefore, the consideration of (beta ) in analytical or numerical analysis could provide the total dissipation induced by the species under study, and sediment characteristics are not necessary for analysis. Considering that saltmarsh species grow in muddy to sandy environments and that the major contribution to the obtained wave attenuation is associated with vegetation, this approach may be the best option if soil properties are not thoroughly characterized.The second approach relies on the definition of ({beta }_{SB}). In this case, the wave damping contributions of vegetation drag and bottom friction are separated. Then, ({beta }_{SB}) can be used in cases where the effect of both momentum sinks can be separately evaluated. To quantify the wave damping contribution of vegetation drag only, ({beta }_{SB}) can be used, and then, the additional friction due to the bottom effect can be added considering the soil properties in each case. This second approach assumes a linear sum of both momentum sinks and could be applicable when soil properties are thoroughly characterized. More

Given Caprinae life history and plausible combinations of mean recruitment and adult female survivorship, we evaluated population persistence and estimated population MVP. The values describing adult female survivorship and recruitment, plus the variability we employed match values found in other populations of Caprinae. We do not pool data across different Caprinae populations or species. Our approach and results directly inform the conservation and management of many Caprinae, especially those for which the acquisition of demographic data remains beyond reach.Our work embodies the characteristics of a high-quality PVA: clear objectives, appropriate demographic data, model structure matching species life histories, stochasticity, examination of extinction probability, appropriate time interval, use of mean values and associated variability6. As with most ecological models, the quest for more data remains problematic, not debilitating, and is addressed by creatively and aptly using existing information to generate meaningful results3.Wildlife agencies generate lamb:adult female ratios from Caprinae surveys, recognizing that yearlings can be mistaken for adult females, causing miscounts. Excluding yearlings from the ratio’s denominator assumes that no miscounts are occurring, yet an unknown and inconsistent number of yearlings remain in the adult female category across survey events. For these reasons, surveyors of other species, like Dall’s sheep and caribou, pool counts of yearlings and adult females, generating lamb:“adult female-like” ratios instead15,23,24,25.Managers of Caprinae populations can follow these precedents and produce lamb:(adult female + yearling) ratios. Consistency would help standardize methods for building comparisons and meta-analyses across populations of Caprinae, while reducing variability across surveys due to differing techniques.Typically, metrics like elasticity (proportional) and sensitivity (additive) describe the influences of demographic parameters on population growth13,14,22,26. For Caprinae, when adult female survivorship is 0.90 and recruitment 0.30, the elasticity in survivorship and recruitment are 0.61 (90% CIs 0.40–0.75) and 0.24 (90% CIs 0.13–0.40) respectively (elasticity in young adult survivorship is 0.16 (90% CIs 0.12–0.21). For ungulates in general, the elasticity values for survival tend to be higher than those for recruitment27. Our results match this pattern, as the elasticity results indicate that a change in adult survival has a 2.5 times greater effect on λ than an equivalent change in recruitment. Relatedly, other theoretical work reports that demographic parameters with more temporal variability have lower elasticities, indicating less impact on population fitness (e.g.28,29).Our work centers on applications. Since most management actions affect these demographic parameters simultaneously, at issue is the practicality (e.g. feasibility and affordability) of management to increase these parameters, and understanding how such changes could impact λ. For example, imagine a population with mean recruitment of 0.30 and adult survival 0.85, with a biologist interested in increasing recruitment or adult female survival to acquire λ ≥ 1. The answer is to increase either value by 0.02 (Fig. 1, Supplementary Data S1). Similarly, one can set a λ target and determine the amount of recruitment and adult female survival necessary for acquiring it (Fig. 1, Supplementary Data S1).Minimum abundance targetA minimum population of 50 adult females meets the persistence criteria, given intermediate levels of recruitment and survival producing λ ~ 1 (Table 2). The risk of population collapse wanes as populations increase above the minimum threshold (Table 2; Fig. 1). For example, a population of ~ 100 adult females always meets persistence criteria (Table 2). Populations of adult females should be somewhat larger than 50 when modest declines (λ ~ 0.97) are suspected, providing a cushion to address the causes of decline, and mitigate further reductions.Translocation of 5 adult females during each of 5 years, or 10 in each of 3 years, requires a starting abundance of 70 adult females for the population to maintain the persistence criteria, never reach a lower confidence interval of 0, and for the population to return to the starting population size within 30 years. If managers mistakenly target a population having  More

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