Sap Flux Measurements Research Articles

DO PALM WATER USE CHARACTERISTICS EXPLAIN THE SPATIAL DISTRIBUTION OF PALMS IN THE CENTRAL AMAZON?

We studied plant water use characteristics of the tree Theobroma grandiflorum (Cupuacu, (Willd. ex Spreng.) Schum., Malvaceae) and the palm Euterpe precatoria (Acai, Mart., Arecaceae) both native to the Amazon and commonly occurring in the region. The tree species is occurring mainly in the terra firme forest whereas the palm species is restricted to the extreme habitats in stream valleys. This study was conducted in a small fruit plantation close to the city of Manaus, in the Central Amazon, Brazil. The main objective of this study was to compare water use characteristics in relation to plant structural traits. Three representative individuals of each species were equipped with Granier-type thermal dissipation probes to measure sap flux density. Water use scaled independent of species with the size of the conductive xylem area (r2=0.85). Furthermore, we found a clear species-specific scaling of water use with plant-size. Overall, palms had a 3.5-fold higher water consumption compared to trees with similar stem diameter and/or plant height. Palms transpired a mean of 1.67 mm m-2 of water per unit crown projection area per day, whereas trees transpired only 0.30 mm m-2 per day, resulting in a 5.6 times lower transpiration rate. We assume that especially the unbalanced plant height/water use ratio of the palms might be limiting the height growth due to increasing hydraulic limitations. Hence, palms are restricted to extreme habitats with higher water availability and usually do not co-occur with more efficient and taller broad leaved tree species in the terra firme forest.

Modelling canopy conductance and transpiration of fruit trees in Mediterranean areas: A simplified approach

Improving current approaches to quantify the transpiration of fruit trees is needed for water allocation purposes and to enhance the precision of water applications under full and deficit irrigation. Given that transpiration of tree crops is mainly modulated by canopy conductance (Gc) and vapour pressure deficits, we developed a functional model of tree transpiration by quantifying an average daily Gc based on radiation use efficiency and CO2 assimilation. For model calibration, an extensive experimental dataset of tree transpiration (Ep) was collected in many of the main temperate fruit tree species, namely, apricot, apple, citrus, olive, peach, pistachio, and walnut, all under non-limiting water conditions, in different orchards in Spain and California (USA). In all species, Ep was assessed by measuring sap flux with the Compensation Heat Pulse method for several months, and a transpiration coefficient (Kt) was calculated as the ratio of measured Ep to the reference evapotranspiration. For three deciduous species (apricot, peach and walnut) Kt showed maximum values close to 1, a value which stayed more or less constant throughout the summer in peach and walnut. The maximum Kt values were measured in pistachio (1.14) while they only reached 0.35 in olive and citrus trees. In the latter two species, Kt varied seasonally between 0.2 and 0.6 depending on the weather. The average Gc in July was high for apple, walnut, peach and pistachio (range 0.240–0.365molm−2s−1) and low for olive and orange (range 0.074–0.100molm−2s−1). The calibrated model outputs were compared against measured Ep data, suggesting the satisfactory performance of a functional model for Ep calculation that should improve the precision of current empirical approaches followed to compute fruit tree water requirements.

Leaf and Soil-plant Hydraulic Processes in the Transpiration of Tropical Forest

In order to reveal the control of tree transpiration by the leaf ecophysiological traits and the hydraulic processes from the soil to leaves, transpiration rates of the tree species in tropical seasonal forests were monitored and modeled using independently measured leaf photosynthetic traits. Stand-level transpiration rate was modeled for rubber trees in a plantation and alien and native species in a community forest using a multilayer biophysical model that couples the energy balance and leaf ecophysiological processes. Model simulation was carried out on the assumption that leaf gas exchange was not limited by the hydraulic processes from the root to the leaves, while transpiration rates, which were independently monitored using sap flux measurements, were influenced both by the seasonal trends in leaf ecophysiological traits and the hydraulic processes. The modeled transpiration rate (Emodel) successfully captured the diurnal trend of the in situ measured one (Esap) in most rainy seasons in rubber plantation and in dry season in community forests, suggesting the absence of hydraulic limitation in soil-plant continuum. The decoupling between the Emodel and Esap was observed in mid dry season in rubber plantation and in a native species of the community forest. The daily-scale Emodel overestimated Esap by 20-40%, mainly due to the midday depression of Esap. On the other hand, in an alien eucalyptus species in community forest, overestimate of Emodel was observed in mid rainy season, suggesting the failure of water uptake by the roots under flooding conditions. The seasonal decreases in daily Esap matched the timing of the water transport limitation of soil-plant continuum. Under lowered Esap conditions, as high Emodel as other seasons was observed in each species but could not be met due to the water supply, suggesting the leaf ecophysiological traits oriented for high leaf water demand and their imbalance with the seasonally decreasing water supply capacity. In conclusion, seasonal trends in transpiration rate were strongly characterized by the limitation in the process of soil-plant water transport, rather than the seasonal trends in the leaf ecophysiological traits.

The effects of elevated CO2 and nitrogen fertilization on stomatal conductance estimated from 11 years of scaled sap flux measurements at Duke FACE

In this study, we employ a network of thermal dissipation probes (TDPs) monitoring sap flux density to estimate leaf-specific transpiration (E(L)) and stomatal conductance (G(S)) in Pinus taeda (L.) and Liquidambar styraciflua L. exposed to +200 ppm atmospheric CO(2) levels (eCO(2)) and nitrogen fertilization. Scaling half-hourly measurements from hundreds of sensors over 11 years, we found that P. taeda in eCO(2) intermittently (49% of monthly values) decreased stomatal conductance (G(S)) relative to the control, with a mean reduction of 13% in both total E(L) and mean daytime G(S). This intermittent response was related to changes in a hydraulic allometry index (A(H)), defined as sapwood area per unit leaf area per unit canopy height, which decreased a mean of 15% with eCO(2) over the course of the study, due mostly to a mean 19% increase in leaf area (A(L)). In contrast, L. styraciflua showed a consistent (76% of monthly values) reduction in G(S) with eCO(2) with a total reduction of 32% E(L), 31% G(S) and 23% A(H) (due to increased A(L) per sapwood area). For L. styraciflua, like P. taeda, the relationship between A(H) and G(S) at reference conditions suggested a decrease in G(S) across the range of A(H). Our findings suggest an indirect structural effect of eCO(2) on G(S) in P. taeda and a direct leaf level effect in L. styraciflua. In the initial year of fertilization, P. taeda in both CO(2) treatments, as well as L. styraciflua in eCO(2), exhibited higher G(S) with N(F) than expected from shifts in A(H), suggesting a transient direct effect on G(S). Whether treatment effects on mean leaf-specific G(S) are direct or indirect, this paper highlights that long-term treatment effects on G(S) are generally reflected in A(H) as well.

Hydraulic time constants for transpiration of loblolly pine at a free-air carbon dioxide enrichment site

The impact of stored water on estimates of transpiration from scaled sap flux measurements was assessed in mature Pinus taeda (L.) at the Duke Free-Air CO(2) Enrichment (FACE) site. We used a simple hydraulic model with measurements of sap flux (J) at breast height and the base of the live crown for 26 trees over 6 months to examine the effects of elevated CO(2) (eCO(2)) and fertilization (N(F)) treatments, as well as temporal variation in soil moisture (M(()(t)())), on estimates of the hydraulic time constant (κ). At low M(()(t)()), there was little (<12%) difference in κ of different treatments. At high M(()(t)()), differences were much greater, with κ reductions of 27, 52 and 34% in eCO(2), N(F) and eCO(2) × N(F) respective to the control. Incorporating κ with these effects into the analysis of a larger data set of previous J measurements at this site (1998-2008) improved agreement between modeled and measured values in 92% of cases. However, a simplified calibration of κ that neglected treatment and soil moisture effects performed more dependably, improving agreement in 98% of cases. Incorporating κ had the effect of increasing estimates of reference stomatal conductance at 1 kPa vapor pressure deficit (VPD) and saturating photosynthetic active radiation (PAR) an average of 12-14%, while increasing estimated sensitivities to VPD and PAR. A computationally efficient hydraulic model, such as the one presented here, incorporated into a hierarchical model of stomatal conductance presents a novel approach to including hydraulic time constants in estimates of stomatal responses from long-term sap flux data sets.

Urban Tree Species Show the Same Hydraulic Response to Vapor Pressure Deficit across Varying Tree Size and Environmental Conditions

BackgroundThe functional convergence of tree transpiration has rarely been tested for tree species growing under urban conditions even though it is of significance to elucidate the relationship between functional convergence and species differences of urban trees for establishing sustainable urban forests in the context of forest water relations.Methodology/Principal FindingsWe measured sap flux of four urban tree species including Cedrus deodara, Zelkova schneideriana, Euonymus bungeanus and Metasequoia glyptostroboides in an urban park by using thermal dissipation probes (TDP). The concurrent microclimate conditions and soil moisture content were also measured. Our objectives were to examine 1) the influence of tree species and size on transpiration, and 2) the hydraulic control of urban trees under different environmental conditions over the transpiration in response to VPD as represented by canopy conductance. The results showed that the functional convergence between tree diameter at breast height (DBH) and tree canopy transpiration amount (E c) was not reliable to predict stand transpiration and there were species differences within same DBH class. Species differed in transpiration patterns to seasonal weather progression and soil water stress as a result of varied sensitivity to water availability. Species differences were also found in their potential maximum transpiration rate and reaction to light. However, a same theoretical hydraulic relationship between G c at VPD = 1 kPa (G cref) and the G c sensitivity to VPD (−dG c/dlnVPD) across studied species as well as under contrasting soil water and R s conditions in the urban area.Conclusions/SignificanceWe concluded that urban trees show the same hydraulic regulation over response to VPD across varying tree size and environmental conditions and thus tree transpiration could be predicted with appropriate assessment of G cref.

Environmental controls on growing-season sap flow density of Quercus serrata Thunb in a temperate deciduous forest of Korea

Sap flux density (SFD) measurements were used, in combination with morphological characteristics of trees and forest structure, to calculate whole-tree transpiration, stand transpiration (St) and mean canopy stomatal conductance (Gs). Analysis based on the relationships between the morphological characteristics of trees and whole tree water use, and on the responses of SFD and Gs to short wave radiation (RR), vapor pressure deficit (VPD) and soil water content (SWC) during drought and non-drought periods were conducted. The results showed a strong positive correlation between whole tree transpiration and both tree diameter at breast height (DBH) (<TEX>$r^2$</TEX> = 0.95, P < 0.05) and sapwood area (SA) (<TEX>$r^2$</TEX> = 0.98, P < 0.05). Relationships between SFD and DBH (<TEX>$r^2$</TEX> = 0.25), as well as SA (<TEX>$r^2$</TEX> = 0.17) were weak. Daily SFD of Quercus serrata Thunb was closely related to VPD and RR. Although operating at different time scales, RR and VPD were important interacting environmental controls of tree water use. SFD increased with increasing VPD (<1 kPa) and RR. SWC had a considerable effect on stand transpiration during the drought period. The relationships between SFD, VPD and RR were distorted when SWC dropped below 35%.

Testing transpiration controls by quantifying spatial variability along a boreal black spruce forest drainage gradient

ABSTRACTOne of the biggest challenges in predicting ecohydrologic fluxes is scaling from easily measured variables to more difficult, often emergent patterns and processes. This is especially true in spatially heterogeneous systems such as black spruce (Picea mariana)‐dominated boreal forests containing excessive and low soil moisture conditions. Traditional hypotheses suggest that transpiration is controlled by hydraulic responses to vapor pressure deficit (D) and soil moisture; however, these may potentially be misinformed because of omission of soil drainage gradients. Thus, we predict that 1) spatial heterogeneity in tree transpiration along a soil drainage gradient is positively correlated withD, 2) sap flux (JS) and leaf‐level transpiration (EL) are higher and whole‐tree transpiration (EC) lower in the poorly drained than well‐drained stands, and 3) spatial heterogeneity ofECis regulated primarily by tree‐related covariates such as sapwood and leaf area and secondarily by environmental covariates including peat and moss depth. With the use of 122 black spruce sap flux measurements, the range of autocorrelation (inverse of spatial variation) decreased from 20 m at lowD(&lt;0.7 kPa) to 2 m at middayDvalues (&gt;0.9 kPa).JSandELwere significantly greater andECless in poorly drained than well‐drained stands; controlled primarily by tree‐related covariates (sapwood and leaf area) representing long‐term growth conditions and secondarily by soil moisture and spatially sampledDreflecting shorter‐term environmental variation. Quantification of spatial heterogeneity informs predictive models of the distance at which homogeneity can no longer be assumed and will improve mechanistic predictions of transpiration at multiple spatial scales. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Sapflow+: a four‐needle heat‐pulse sap flow sensor enabling nonempirical sap flux density and water content measurements

• To our knowledge, to date, no nonempirical method exists to measure reverse, low or high sap flux density. Moreover, existing sap flow methods require destructive wood core measurements to determine sapwood water content, necessary to convert heat velocity to sap flux density, not only damaging the tree, but also neglecting seasonal variability in sapwood water content. • Here, we present a nonempirical heat-pulse-based method and coupled sensor which measure temperature changes around a linear heater in both axial and tangential directions after application of a heat pulse. By fitting the correct heat conduction-convection equation to the measured temperature profiles, the heat velocity and water content of the sapwood can be determined. • An identifiability analysis and validation tests on artificial and real stem segments of European beech (Fagus sylvatica L.) confirm the applicability of the method, leading to accurate determinations of heat velocity, water content and hence sap flux density. • The proposed method enables sap flux density measurements to be made across the entire natural occurring sap flux density range of woody plants. Moreover, the water content during low flows can be determined accurately, enabling a correct conversion from heat velocity to sap flux density without destructive core measurements.

Crown conductance in dwarf, medium, and tall pitch pines in the Long Island Pine Plains

The New York Pine Plains are a unique ecosystem with normal statured and a dwarfed variety of pitch pines (Pinus rigida Mill.). Growing interspersed with the dwarf pines are trees of intermediate height and features. Several hypotheses have been put forward as to why some of the trees are dwarfed, but none have been substantiated. In this study, we tested whether dwarf or medium trees are hydraulically limited compared to normally growing trees. Granier style sap flux sensors were installed in three to six trees of each tree type and sap flux was measured in early August 2004. Sap flux measurements were scaled to crown stomatal conductance using leaf area to sapwood area ratios for each tree. Contrary to expectation, dwarf and medium stature trees had very low leaf area to sapwood area ratios, but high crown stomatal conductances compared to normal trees. Analyses of leaf area, ring widths, and crown stomatal conductance indicate that differences between normal, and dwarf and medium pines are not due to hydraulic limitation, but that stunted growth may be due to other causes.

EFFECTS OF THINNING ON TRANSPIRATION BY RIPARIAN BUFFER TREES IN RESPONSE TO ADVECTION AND SOLAR RADIATION

EFFECTS OF THINNING ON TRANSPIRATION BY RIPARIAN BUFFER TREES IN RESPONSE TO ADVECTION AND SOLAR RADIATION

A MARIOTTE-BASED VERIFICATION SYSTEM FOR HEAT-BASED SAP FLOW SENSORS

Determination of the accuracy of commonly used techniques for measuring sap flux density in trees often presents a challenge. We therefore designed and built a verification system for heat-based sap flow sensors typically used at stem level. In the laboratory, a Mariotte's bottle device was used to maintain a constant flow rate of water through freshly cut stem segments of American beech (Fagus grandifolia Ehrh.). This verification system was used to determine the accuracy of three heat-based sap flux density techniques: heat pulse velocity, thermal dissipation and heat field deformation. All three techniques substantially underestimated sap flux density when compared against gravimetric measurements. On average the actual sap flux density was underestimated by 35% using heat pulse velocity, 46% using heat field deformation and 60% using thermal dissipation. These differences were consistent across sap flux densities ranging from 5 to 80 cm(3) cm(-2) h(-1). Field measurements supported the relative sensor performance observed in the laboratory. Applying a sensor-specific correction factor based on the laboratory test to the field data produced similar estimates of sap flux density from all three techniques. We concluded that a species-specific calibration is therefore necessary when using any of these techniques to insure that accurate estimates of sap flux density are obtained, at least until a physical basis for error correction can be proposed.

Simple models for stomatal conductance derived from a process model: cross‐validation against sap flux data

Representation of stomatal physiology in models of plant-atmosphere gas exchange is minimal, and direct application of process-based models is limited by difficulty of parameter estimation. We derived simple models of stomatal conductance from a recent process-based model, and cross-validated them against measurements of sap flux (176-365 d in length) in 36 individual trees of two age classes for two Eucalyptus species across seven sites in the mountains of southeastern Australia. The derived models - which are driven by irradiance and evaporative demand and have two to four parameters that represent sums and products of biophysical parameters in the process model - reproduced a median 83-89% of observed variance in half-hourly and diurnally averaged sap flux, and performed similarly whether fitted using a random sample of all data or using 1 month of data from spring or autumn. Our simple models are an advance in predicting plant water use because their parameters are transparently related to reduced processes and properties, enabling easy accommodation of improved knowledge about how those parameters respond to environmental change and differ among species.

Improving sap flux density measurements by correctly determining thermal diffusivity, differentiating between bound and unbound water

Several heat-based sap flow methods, such as the heat field deformation method and the heat ratio method, include the thermal diffusivity D of the sapwood as a crucial parameter. Despite its importance, little attention has been paid to determine D in a plant physiological context. Therefore, D is mostly set as a constant, calculated during zero flow conditions or from a method of mixtures, taking into account wood density and moisture content. In this latter method, however, the meaning of the moisture content is misinterpreted, making it theoretically incorrect for D calculations in sapwood. A correction to this method, which includes the correct application of the moisture content, is proposed. This correction was tested for European and American beech and Eucalyptus caliginosa Blakely & McKie. Depending on the dry wood density and moisture content, the original approach over- or underestimates D and, hence, sap flux density by 10% and more.

Sap flux density measurements based on the heat field deformation method

Accurate measurements of whole tree water use are needed in many scientific disciplines such as hydrology, ecophysiology, ecology, forestry, agronomy and climatology. Several techniques based on heat dissipation have been developed for this purpose. One of the latest developed techniques is the heat field deformation (HFD) method, which relies on continuous heating and the combination of a symmetrical and an asymmetrical temperature measurement. However, thus far the development of this method has not been fully described in the scientific literature. An understanding of its underlying principles is nevertheless essential to fully exploit the potential of this method as well as to better understand the results. This paper therefore structures the existing, but dispersed, data on the HFD method and explains its evolution from an initial ratio of temperature differences proportional to vapor pressure deficit to a fully operational and practically applicable sap flux density measurement system. It stresses the importance of HFD as a method that is capable of measuring low, high and reverse flows without necessitating zero flow conditions and on several sapwood depths to establish a radial profile. The combination of these features has not been included yet in other heat-based sap flow measurement systems, making the HFD method unique of its kind.

Use of the correct heat conduction–convection equation as basis for heat-pulse sap flow methods in anisotropic wood

Heat-pulse methods to determine sap flux density in trees are founded on the theory of heat conduction and heat convection in an isotropic medium. However, sapwood is clearly anisotropic, implying a difference in thermal conductivity along and across the grain, and hence necessitates the theory for an anisotropic medium. This difference in thermal conductivities, which can be up to 50%, is, however, not taken into account in the key equation leading to the currently available heat-pulse methods. Despite this major flaw, the methods remain theoretically correct as they are based on derivations of the key equation, ruling out any anisotropic aspects. The importance of specifying the thermal characteristics of the sapwood according to axial, tangential or radial direction is revealed as well as referring to and using the proper anisotropic theory in order to avoid confusion and misinterpretation of thermal properties when dealing with sap flux density measurements or erroneous results when modelling heat transport in sapwood.

Bayesian analysis of canopy transpiration models: A test of posterior parameter means against measurements

Summary Big-leaf models of transpiration are based on the hypothesis that structural heterogeneity within forest canopies can be ignored at stand or larger scales. However, the adoption of big-leaf models is de facto rather than de jure , as forests are never structurally or functionally homogeneous. We tested big-leaf models both with and without modification to include canopy gaps, in a heterogeneous quaking aspen stand having a range of canopy densities. Leaf area index ( L ) and canopy closure were obtained from biometric data, stomatal conductance parameters were obtained from sap flux measurements, while leaf gas exchange data provided photosynthetic parameters. We then rigorously tested model-data consistency by incrementally starving the models of these measured parameters and using Bayesian Markov Chain Monte Carlo simulation to retrieve the withheld parameters. Model acceptability was quantified with Deviance Information Criterion (DIC), which penalized model accuracy by the number of retrieved parameters. Big-leaf models overestimated canopy transpiration with increasing error as canopy density declined, but models that included gaps had minimal error regardless of canopy density. When models used measured L the other parameters were retrieved with minimal bias. This showed that simple canopy models could predict transpiration in data scarce regions where only L was measured. Models that had L withheld had the lowest DIC values suggesting that they were the most acceptable models. However, these models failed to retrieve unbiased parameter estimates indicating a mismatch between model structure and data. By quantifying model structure and data requirements this new approach to evaluating model-data fusion has advanced the understanding of canopy transpiration.

Differences in water use between mature and post-fire regrowth stands of subalpine Eucalyptus delegatensis R. Baker

We estimated plot level water use from sap flux measurements over a 9-month period, in post-fire regrowth and mature plots of Eucalyptus delegatensis R. Baker (Alpine ash) in high elevation catchments near Falls Creek, Victoria, Australia, seven years after a major stand-replacing bushfire. Water use was more than double (460±100mmyear−1 more) in regrowth as compared to mature plots, whereas sap flux was similar between age classes. This difference in water use reflected 72% greater sapwood area index and 35% greater leaf area index in regrowth than in mature plots. A small part of the difference in water use can be attributed to nocturnal transpiration, which was greater in regrowth than in mature plots (10.3±0.8% vs 7.3±0.8% of diel totals). As evaporative demand was 41% greater in mature than in regrowth plots, these data suggest mean transpiration rate and stomatal conductance per unit leaf area were approximately 1.6 and 2.3 times greater, respectively, in the regrowth. However, mid-day leaf water potential and photosynthetic capacity were similar in both age classes. Evaporative demand was the primary environmental driver of water use in all cases, whereas soil moisture was not a strong driver of either water use or canopy conductance (estimated as sap flux/evaporative demand). Together, our results suggest (a) stand water use rapidly recovers after fire in these high elevation forests and quickly surpasses rates in mature stands, confirming projections by Kuczera (1987) for lower-elevation Mountain Ash (E. regnans) forests and highlighting the potential impact of tree water use on water yield in the first decade of forest regeneration after fires, and (b) stomatal conductance and sapwood area/leaf area ratio are both less in tall, older Alpine ash trees, whereas leaf water status and photosynthetic capacity appear to be sustained – consistent with predictions from optimisation theory but not Pipe-Model Theory.

Plant water-use efficiency as a metric of urban ecosystem services

Trees in urban ecosystems are valued for shade and cooling effects, reduction of CO2 emissions and pollution, and aesthetics, among other benefits. However, in arid and semiarid regions, urban trees must be maintained through supplemental irrigation. In these regions it is desirable to identify tree species that are especially efficient in the balance between water loss and carbon uptake. We used a common-garden approach to compare water-use efficiency (WUE) at leaf and tree scales for commonly planted, nonnative tree species in the Los Angeles Basin (California, USA), in order to evaluate WUE as a metric of the trade-off between water use and growth in urban trees. Leaf-level gas exchange, sap flux density, leaf δ13C, and stem growth measurements were conducted on eight species within the Los Angeles County Arboretum: Brachychiton discolor, B. populneus, Eucalyptus grandis, Ficus microcarpa, Jacaranda chelonia, Gleditsia triacanthos, Lagerstroemia indica, and Koelreuteria paniculata. We found species wit...

Nocturnal water loss in mature subalpine Eucalyptus delegatensis tall open forests and adjacent E. pauciflora woodlands.

We measured sap flux (S) and environmental variables in four monospecific stands of alpine ash (Eucalyptus delegatensis R. Baker, AA) and snowgum (E. pauciflora Sieb. ex Spreng., SG) in Australia's Victorian Alps. Nocturnal S was 11.8 ± 0.8% of diel totals. We separated transpiration (E) and refilling components of S using a novel modeling approach based on refilling time constants. The nocturnal fraction of diel water loss (fn) averaged 8.6 ± 0.6% for AA and 9.8 ± 1.7% for SG; fn differed among sites but not species. Evaporative demand (D) was the strongest driver of nocturnal E (En). The ratio En/D (Gn) was positively correlated to soil moisture in most cases, whereas correlations between wind speed and Gn varied widely in sign and strength. Our results suggest (1) the large, mature trees at our subalpine sites have greater fn than the few Australian native tree species that have been studied at lower elevations, (2) AA and SG exhibit similar fn despite very different size and life history, and (3) fn may differ substantially among sites, so future work should be replicated across differing sites. Our novel approach to quantifying fn can be applied to S measurements obtained by any method.