https://orcid.org/0000-0003-4599-3491
Figures
Abstract
Organism-level bioenergetics models (OBMs) are an emerging tool for predicting consequences of climate change on organism growth in ecological systems. Global changes in ocean and atmospheric temperature may affect organisms that experience both environments, such as those living in intertidal systems. The acorn barnacle, Balanus glandula, is prevalent throughout the intertidal zone in the Eastern Pacific, and laboratory experiments demonstrate that feeding rates and metabolic costs are sensitive to temperature. We hypothesized that, based on these thermal responses, aerial and aquatic warming will decrease B. glandula growth in a field environment because of increased costs and reduced feeding. We measure environmental conditions (aerial and aquatic temperature) at three intertidal heights over two 6-month intervals and compare observed growth to growth estimates based on a Numerical Scope for Growth model. Initial work indicates that growth is less sensitive to shore height than predicted by lab-based physiological rates alone, so we estimate a compensation factor (Z) that captures non-linear changes in feeding with shore height when fitting the model to all three elevations and the two intervals. This full model predicts that, in this environment, aquatic warming will counteract increased costs of aerial warming, by virtue of increased feeding at warmer temperatures. This work advances OBMs by combining the effects of multiple decoupled thermal responses (e.g., feeding, respiration) in multiple contexts (aerial, aquatic), drawing on established model selection and “divide and conquer” techniques, and identifying sources of uncertainty in the model. This work indicates that future intertidal OBMs may benefit from an improved characterization of feeding behavior, including empirical estimates of elevation-dependent feeding compensation.
Citation: Roberts EA, Ober GT, Gilman SE (2025) Bioenergetic modeling reveals opposing effects of ocean and terrestrial warming of an intertidal crustacean, Balanus glandula. PLOS Clim 4(7): e0000540. https://doi.org/10.1371/journal.pclm.0000540
Editor: Jamie Males, PLOS Climate, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
Received: November 21, 2024; Accepted: June 18, 2025; Published: July 11, 2025
Copyright: © 2025 Roberts et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The code for the processing of raw field data, the curve fits, simulation runs, and optimization, as well as the figures and tables generated from this code for this manuscript are publicly accessible at https://doi.org/10.5281/zenodo.13731116. The physiology, field growth, and field temperature datasets used in our simulations are accessible at doi.org/10.5061/dryad.s1rn8pkk1.
Funding: This work was supported by the National Science Foundation (grant IOS-1351445 to S.E.G.) with additional support from the Keck Science Department of Claremont McKenna, Pitzer, and Scripps Colleges. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Organism-level bioenergetic models (OBMs) are emerging tools that predict species’ responses to climate change [1–3]. OBMs model an organism’s energy needs as a function of abiotic conditions, physiology, and species interactions to predict organismal growth and survival. There are several different OBM frameworks, including Scope for Growth [4], the Wisconsin fish bioenergetics model [5], Dynamic Energy Budget modeling (DEB) [6], the Metabolic Theory of Ecology [7–9], and other agent-based physiological energy budget models (ABMs) [10–12]. As mechanistic models, OBMs are better suited to predicting responses under the novel combinations of environmental conditions that will occur under climate change than simpler, correlational approaches such as species distribution models [1,11]. A successful OBM must accurately capture environmental, physiological, and behavioral processes at the appropriate temporal and spatial scales. The temperatures an organism experiences can vary over hourly, daily, seasonal, and annual timescales [13], and the choice of timescale affects model predictions [14]. Temperature, in turn, affects a wide range of physiological [15,16] and behavioral processes [17–19]. Importantly, each of these processes, such as consumption and metabolism [15], may have its own thermal dependence [11,15,20,21].
To have confidence in a model’s climate change predictions, it must be validated against empirical environmental and organismal data [11,22,23]. Model validation in more than one location or against multiple combinations of empirical conditions is essential, since models that perform well at one location or time can fail in other conditions [24,25]. Testing often reveals poor agreement between model predictions and independent data (e.g., [22]), but such tests provide an important opportunity to identify mechanistic details that can improve models [23,26]. Model validation should also include testing the sensitivity of the model to parameter uncertainty, as this can identify areas where better empirical estimates of parameters would improve model prediction [5,27,28].
Modeling decisions must be informed by the environment, or ecological niche, experienced by the study species [29]. Warming and increased frequency of marine heat waves are associated with shifts in marine communities at the land-sea interface [30,31]. Intertidal species experience two distinct thermal environments, aquatic and terrestrial, that alternate with the oscillation of tides. Individuals at higher elevations on a shore experience a shorter duration of submerged conditions, producing steep environmental gradients of temperature, desiccation and feeding opportunities (Fig 1) [18,25]. They often experience greater acute physiological stress [32,33] and decreased growth and reproduction [34,35]. Given that terrestrial and marine environments are expected to warm at different rates [36,37], an organism’s shore height will also affect its overall experience of climate change [38]. Further, individual species may differ in their sensitivity to warming in the two environments [39]. Representing such a dynamic thermal environment, where large shifts in temperature occur multiple times daily [40], and where physiology varies with medium [41], requires a model with high-resolution timesteps [25,42–45] and separate physiological dynamics in each environment (Fig 2a,b).
A) Abiotic conditions vary with the duration of low tide exposure at each shore height in the intertidal zone. B) Violin plot of daily time emerged (exposed to air) at the three different experimental shore heights representing the low, mid, and upper intertidal zones. The percent of time emerged is calculated at each tidal elevation as the percent of 15-minute timepoints per day in which the water level is greater than the elevation of the experimental plots over the course of a year.
Intertidal animals alternate between submergence under water (A) and emergence in air (B), each with a distinct set of physiological conditions and processes. These can be captured in a Numerical Scope for Growth model (C), if timesteps are high enough resolution to capture the tidal fluctuations.
Scope for Growth (SFG) models are a class of OBMs that predict organismal growth and reproduction by quantifying the effects of environmental conditions and size-scaling relationships on physiology [4,46–49]. While SFG models were originally designed to calculate energetics and growth from mean conditions over long (e.g., annual) intervals, more recently, Numerical SFG (“NSFG”, Fig 2C) models have been developed to capture shorter time steps [50,51]. The shorter timesteps allow for energy fluxes to change allometrically as organisms grow [51]. A central advantage of SFG and NSFG models is their use of empirically-derived thermal sensitives [5,46], rather than assuming a specific theoretically-derived relationship between temperature and physiology [6,7]. This allows for separate physiologies in air and water (e.g., [49]) and for separate thermal sensitives of energy demand and energy acquisition. The latter is not a central focus in some OBM modeling frameworks (e.g., [6], but see [50–52]), despite strong empirical evidence for its need when describing thermal relationships [20,53,54]. Further, SFG and NSFG models allows for more straightforward sensitivity analyses and model skill assessment than is typically needed for more complex modeling frameworks whose parameters may not be independent from one another [27,55].
Here we develop an intertidal OBM model of the barnacle, Balanus glandula, using a hybrid of NSFG and other modeling approaches. This sessile crustacean is native to the Pacific coast of North America (Mexico to Alaska) [56] with a wide vertical distribution [57]. We model the growth of B. glandula across an environmental gradient, shore height. We first develop this model from empirical studies of B. glandula growth and physiology. We then validate the model with two six month field observations of barnacle growth at three shore heights. Our objectives are to (1) build the OBM model for B. glandula and test it across an environmental gradient, (2) test the sensitivity of the model’s predictions to parameter uncertainty, and (3) predict the effects of future warming of air and water temperatures on B. glandula’s SFG across its vertical range.
Methods
The traditional Scope for Growth model
Scope for Growth (SFG) models [58,59] convert physiological rates into energy flux equivalents and use the following equation:
Where C is the total consumption of energy from food, P is the production of both somatic and gonadal tissues, and R is the energy expenditure measured in terms of respiration, often expressed as J per unit of time. Additional energy is lost in the excretion of nitrogen waste (U) and feces (F). We assumed U was zero because Wu and Levings [49] found very little energy lost to nitrogen waste excretion in B. glandula. The production of tissue (P) may then be estimated as the difference between energy assimilated from the food (A = C – F) and energy expenditure via respiration (R):
This estimate (P) is known as the Scope for Growth (SFG). While this ’static’ SFG estimate is calculated for an animal of a certain size over a period of time (e.g., hour, day, year), numerical modeling approaches allow net fluxes to be calculated as a function of ‘dynamic’ changes in the environment and size at a higher temporal resolution [6,12,60].
The Numerical Scope for Growth model
We built a NSFG model (Table 1) in which energy fluxes (i.e., feeding and respiration, J hr-1) were calculated every 15 minutes. The energy flux estimates were then used to calculate a daily net SFG and change in body size (Fig 2) [51]. We estimated daily SFG as the difference between energy assimilated from food and respiration costs within each day:
Daily SFG was used to calculate barnacle opercular length (Lday) over the course of each 6-month experiment. First, we calculated the daily mass at the start of the following day (Mday+1) as the prior day’s mass plus the change in mass (Mday). We calculated
Mday by dividing the SFGday by the energy density of barnacle tissue (ED, J/ mg AFDW, Table 1) multiplied by 1.4 to incorporate overhead costs of new tissue growth [6].
Daily length (mm) was then calculated as a function of mass estimated from B. glandula from the same location in the Pacific Northwest, by solving for L in the following equation (<3mm opercular length, n = 9, Palmer 1980):
15-minute energy flux calculations
We modeled the temperature and size-dependence of ingestion and respiration separately for immersion and emersion periods. All fluxes followed the same general function, b(T, L):
where x refers to a specific energy flux in either an air or water medium: ingestion (bI) or respiration (bR_AER, bR_Recov, bR_AQ), and i refers to the 15-minute interval. T is the temperature, L is the body size (operculum length, mm), d is an allometric length-scaling exponent, and ax and cx are constants for the individual flux equations, fit from laboratory data (Table 1). We fit four separate flux equations (Ingestion, Aquatic Respiration, Aerial Respiration, Aerial Recovery, Table 1) to laboratory collected data (S1 Text) [61]. The size scaling parameters (d) were sourced from the published literature (Table 1, S1 Text). Exponential temperature scaling equations were selected (eq. 6) after first comparing the fit of 5 different thermal scaling equations to the laboratory-collected data (S1 Text) [65].
We calculated energy assimilation (Ai) at each time point from the ingestion flux (bI,i),
Where pmax is the maximum ingestion rate (J 15-minutes-1 mg-1), and bI,i is the ingestion of the organism as a function of Ti and Li (eq. 6). Food availability (, unitless), is a Holling’s Type II functional response where Fi is chlorophyll concentration at time i, a proxy of food availability, and FH is the chlorophyll concentration at half of the maximum ingestion rate [6].
Additional modifications for an intertidal species
Additional modifications of the NSFG model were needed to accurately reflect intertidal dynamics. First, we used separate energy demand equations during immersion and emersion that reflected their differing thermal sensitivities. We further calculated the metabolic cost of aerial exposure (bR_AER) as the sum of measured respiration during emersion (bR_EXP) plus additional recovery costs (“oxygen debt”) upon resubmersion (bR_REC) [61,66]. Daily energy demand values were then calculated as a daily sum of the 15-minute timesteps:
where WLi is the water level at timestep i and elev is the elevation or height on the shore of the modeled barnacles.
Second, assimilation was calculated under immersion using Eq. 7, but during emersion assimilation was considered to be negligeable. Daily assimilation values (Ad) were then determined from the summation of assimilation estimates at 15-minute timestep:
Last, we added a tidal compensation term Sz (Table 1) to this assimilation flux to allow for greater rates of consumption at higher shore heights. Here S is the proportion of time submerged over the entire period of the model. Without this term, the model would assume energy intake declines linearly as a function of submergence times at higher shore heights. Yet many intertidal species [34,67,68], including B. glandula [69] compensate for reduced submergence with greater feeding activity and/or larger feeding structures. Initial model runs without this term severely underestimated growth at higher shore heights and overestimated growth at lower shore heights.
Observational study site
Field temperatures and barnacle growth were recorded on a Southwest-facing rock wall at the University of Washington’s Friday Harbor Laboratories Biological Preserve (FHL), San Juan Island, WA (48°32’45.1” N, 123° 0’ 39.2” W) in the Salish Sea. This region is characterized by mixed semi-diurnal tides, and experiences its greatest low tide temperatures in the summer, when daytime low tides are most common [57]. Local water temperatures average ~10°C annually [61].
Biological observations
Thirty-three 13.5 cm x 13.5 cm photoquadrats were established along the rock wall as part of a larger study of B. glandula growth across multiple latitudes. At each of three shore heights (1.20m, 1.55m, and 1.97m + MLLW), we spaced eleven quadrats in a horizontal row approximately 1.5 m long. The three heights spanned the upper and lower limits of B. glandula on the wall. We photographed each quadrat in February 2018, August 2018, and March 2019. At each time point, a PentaxK50 digital SLR camera was placed 16 cm above the quadrat. The opercular length of B. glandula was measured as the maximum operculum diameter on the digital images using ImageJ (v.1.5) [70]. Growth was calculated as the change in opercular length between each pair of time points. All analyses were restricted to the smallest barnacles (1.5mm – 3mm initial opercular length) to maximize our ability to detect growth and to ensure that we used an independent set of barnacles for each growth period.
Environmental observations
To estimate barnacle body temperature during both emersion and immersion, three temperature dataloggers (Onset Hobo TidbiT v1 and v2) were deployed within each shore height and recorded temperature every 15-min from February 2018 – March 2019. Temperature loggers were attached to the rock face within individual quadrats using z-spar epoxy. We averaged the replicate loggers within a shore height to reduce the effect of thermal microhabitat variation [71]. Tidal elevation was determined by comparing seawater temperature and 6-minute tide gauge data (National Buoy Data Center Station FRDW1–9449880, NOAA National Ocean Service, ndbc.noaa.gov/station_page.php?station = frdw1) to the 15-minute temperature logger data. Weekly averages of seawater chlorophyll fluorescence were calculated from the Padilla Bay Gong Site, WA (48° 33’ 26.9“ N, 122° 34’ 19.2” W) and used as a proxy of food availability (YSI EXO-2 sonde, Chl g/L, NERRS CDMO PDBGSWQ, 2017–2020, [72]).
Energy flux parameters
We used laboratory-collected data [49,61] to fit the energy flux equations bR_AQ(T, L), bR_EXP(T, L), and bR_REC(T, L) bI(T, L) (eq. 6, S1 Text, data available at doi.org/10.5061/dryad.s1rn8pkk1). Given that these studies were performed over a narrow range of body sizes, the size-scaling exponents dAQ, dAER, and dI were derived separately from equations reported by Wu and Levings [49] for B. glandula. For energy demand, we converted the laboratory-measured respiration rates to joules by multiplying by 0.457 J μmol O2 L-1 [61,73,74].
Model fitting
We used a two-step optimization method to estimate three model parameters (pmax, z, FH) on independent subtidal and intertidal datasets. First, we determined the maximum assimilation rate pmax by fitting the model to observed B. glandula growth over 5 weeks in subtidal conditions, using data from Nishizaki and Carrington [64]. Environmental chlorophyll data (μg/L) was used as a proxy of food availability. To account for a lag in growth, we used average chlorophyll values that started and ended 2 weeks prior to this growth interval (6.9μg/L) [75].
Second, we estimated the feeding compensation parameter (z) and the feeding half saturation coefficient (FH) by fitting the full model to the 291 intertidal barnacle growth measurements across the three elevations and two-time intervals (n = 10–107 growth measurements per elevation and timepoint combination). In this step, weekly averages of environmental chlorophyll data (μg/L) were used as a proxy of food availability (S3 Fig).
For both optimizations, the growth of individuals from the photo quadrats was compared with model predictions of growth. Final length was determined from the numerical model. The initial length of each replicate sample (Linit) was the initial length of each barnacle from the photo quadrat. The model estimated length (Lday) each day based on SFG, iterating for each day of the 6-month dataset. The predicted growth
Lpred was calculated for each replicate barnacle as the difference between the final (Lfinal) and initial lengths (Linit). We solved for the values of pmax, z, and
that gave the lowest negative log likelihood of the data given the model, optimizing for the sum of
for all barnacle growth measurements.
Statistical and numerical analysis
All statistical analyses and numerical modeling were performed in R (v4.0) and RStudio (v1.3) [76], and data visualization used the ggplot2 package [77]. The model optimization minimized the sum of the negative log likelihoods (NLLs) of the data given the model for each tidal elevations and season. NLL estimations assumed a normal distribution. A bounded BFGS algorithm was used for the maximum likelihood estimation (optimParallel function [78]). The hessian matrix was used to estimate approximate standard error of the parameters.
Sensitivity analysis
The sensitivity analysis of the NSFG model was modified from the individual parameter perturbation (IPP) approach (e.g., [5]). Rather than determining the sensitivity to a percentage change in the absolute value of each parameter, we determined the sensitivity to a change of one standard error (±1 SE) in each parameter value [79]. This method was used to capture the sensitivity of the model relative to a realistic range of uncertainty in parameters values [80] rather than a fixed percentage of the mean. The standard error of each parameter value was determined from either the published literature or from our empirical parameter fits (Table 1). A sensitivity of 1.5 indicates that a change in the parameter by 1 SE causes a resulting change in the SFG by 50%.
Climate change estimation
The effect of ocean and aerial warming on cumulative SFG (J) was determined over each 6-month interval for a barnacle of an initial size of 2.2 mm at each elevation. Seawater and/or aerial warming was estimated by adding a discrete integer value from 0 to 2°C (seawater) and/or 0–4°C (aerial warming) to every 15-minute observation of estimated body temperature during immersion and emersion. We chose these ranges because they encompassed the range of abiotic warming expected in the Salish Sea in the year 2095 relative to 2000 under the Representative Concentration Pathway 8.5 emissions scenario (RCP8.5) [36].
Results
Environmental and biological observations
Weekly averaged chlorophyll ranged from 0 to 18 μg/ L and was highest in June (S3 Fig). Measured water temperatures at the field site ranged from 5°C to 17°C, and aerial low tide temperatures ranged from -3°C to 31°C. Aerial exposure occurred 72% of the year at the highest elevation, 48% at the mid elevation, and 33% at the lowest elevation (Fig 1b, 3a-c, 4a-c). The low shore height experienced consistently cooler aerial temperatures than the other two shore heights (Fig 3d-f, 4d-f). However, the mid shore was often warmer at low tide than the high shore, due to a rock overhang that shaded some of the high shore quadrats. Generally, the warmest aerial temperatures (up to 31°C) occurred in late-summer (August), while the coldest (< 0°C) were in mid-winter (February).
A-C) Proportion of the day submerged and food availability (f) in the low, middle, and upper intertidal zone during the first interval. D-F) Mean daily temperature during aerial (solid purple line) and aquatic (solid blue line) conditions and daily 75% quantile of temperature (dotted red line). G-I) Daily physiological intake (dark green), aerial cost (purple), and aquatic cost (blue) of a barnacle of 2mm initial operculum length. The aerial cost includes both aerial exposure and aerial recovery costs. J-L) Daily and cumulative Scope for Growth of a representative barnacle of ~2mm.
See Fig 3 for details.
Small barnacles (mean initial size 2.2 mm) grew 0.5 to 0.8 mm in operculum length over 6 months depending on the time interval and shore height (Fig 5, x-axis). Individuals in the low intertidal tended to grow 34 and 40% more than those the upper intertidal in intervals 1 and 2, respectively (S1 Fig), but this difference was not statistically significant (S1 Table). The narrow range in mean growth rates contrasted with the large range in time submerged across the three shore heights (Fig 1b).
The relationship between predicted growth and observed growth in mm at the three elevations (low – blue, mid – orange, upper – grey) in interval 1 (closed circles) and interval 2 (open circles, means ± SE).
Model fit
Predictions from the NSFG model matched mean observed growth fairly well (R2 = 0.76), with the largest model discrepancies in the low intertidal during interval 1, which had the fewest samples (Fig 5). There was also a large amount of inter-individual variation in growth within each time point and shore height, and individual growth was not well predicted by the SFG model (R2 = 0.07, data not shown). Representative trajectories of energy fluxes in aerial and aquatic conditions over the course of a day for each elevation are shown in S2 Fig.
Parameter estimation
Based on the subtidal analysis, we found pmax, the size-dependent maximum assimilation rate was 2.0 ± 0.1 J 15-min-1 normalized per mg of tissue (AFDW, Table 1). The chlorophyll half-saturation coefficient, fit on the intertidal growth data, was low (FH = 0.13 ± 0.04 μg Chl/ L), relative to the observed chlorophyll concentrations. Consequently, the model predicted feeding and ingestion (f) to remain over 80% of the maximum ingestion rate throughout the study (S3 Fig, Fig 3a-c, Fig 4a-c). The feeding compensation exponent, z, was estimated as 1.16 ± 0.04, which corresponds to a three-fold increase in feeding activity for barnacles at the high shore height compared to those at the low shore height (Table 1, Fig 6).
Estimated feeding activity in the upper (square), mid (circle), low (triangle) tidal elevations as a function of the proportion of time submerged over each 6-month interval (interval 1 – open symbols, interval 2 – closed symbols). Feeding activity at each elevation is calculated as an exponential function of the proportion of time submerged (S) over the full 6-month interval, y = Sz (z = 1.16 + 0.04, mean + SE, Table 1).
Daily energy fluxes and predicted Scope for Growth
Daily energy intake and costs followed the daily patterns in submergence time. On days with more time emerged aerial costs increased, while feeding and aquatic costs increased on days with more time submerged. As barnacles grew over each 6-month period, all energy fluxes increased (Fig 3D–I, 4D-I). Interestingly, barnacles in the low intertidal exhibited the greatest energy intake even after including feeding compensation in the model (Fig 7, S4 Fig). For animals at higher shore heights, the decreased time in aquatic conditions yielded a decrease in immersion costs and an increase in emersion costs (Fig 7). Overall, predicted SFG increased over time across all elevations. Interestingly, except for the low shore (Fig 3J, 4J), SFG was not monotonic with time. In the upper intertidal, the cumulative SFG initially decreased in September, a period of low submergence durations and warm aerial temperatures, before increasing later in the interval (Fig 4L).
The distribution of cumulative weekly intake (green), aquatic cost (blue) and aerial cost (purple) over interval 1 (A) and interval 2 (B). Aerial cost is the sum of exposure and recovery costs.
Model sensitivity to parameter estimates
The individual parameter perturbation (IPP) found that the SFG (J) was most sensitive to uncertainty in the temperature parameters for feeding, followed by aerial and aquatic respiration (Fig 8). Increasing the feeding coefficient (cI) and feeding temperature exponent (aI) by each parameter’s empirical standard error (SE) had the largest effect on predicted SFG. A one SE increase in cI resulted in a 300% increase in SFG, while a one SE increase in aI led to a 260% increase in SFG. Increasing the aquatic and aerial respiration coefficients (aR_aq and aR_aer) by one SE caused a ~ 80% decrease in SFG. In contrast, SFG was minimally sensitive to changes in the energy density parameter (ED, J mg-1) and in the size scaling parameters for all energy fluxes (dI dR aq, dR aer). Within aerial respiration, SFG was also more sensitive to the exposure parameter uncertainty (aR EXP, cR EXP) compared to the recovery parameter uncertainty (aR REC, cR REC). Finally, the variability of the SFG estimate due to the variability in initial body size was 40% (population SE, PopSE, Fig 8).
The sensitivities are for the SFG of a representative barnacle in the mid elevations in interval 1 (Feb – Aug), and the PopSE is the population uncertainty among the barnacles in the middle elevation. See Table 1 for parameter definitions.
Warming body temperatures and SFG
Warming body temperatures during emersion decreased SFG, by 10–30% per 1°C increase, depending on the shore height and time interval, while warming during immersion increased SFG by 15–40% per 1°C (Fig 9). For example, in the mid shore, a 2°C increase in aerial body temperatures resulted in a 30–50% reduction in SFG, while a 2° C increase during immersion increased SFG by 40–60%. Thus, when body temperatures warmed similar amounts in air and water there was almost no change in SFG.
In scenarios that remained below 2°C warming, SFG remained high in the low shore sites (>70 J), with only a 17–23% decrease in SFG due to warming aerial body temperatures. Both the cost of aerial warming and the benefit of warming during immersion were greater in the upper intertidal, where 4°C aerial warming alone caused the SFG prediction to drop to near or below 0 (-7 to 12J). However, when that aerial warming was combined with 2°C aquatic warming, the high shore SFG remained above 0, and within 30–50% of the present day SFG prediction.
Discussion
Successfully predicting the effects of warming temperatures from climate change on species requires building physiologically accurate, field-tested models of organismal responses to warming temperatures [1,81]. Here we developed a Numerical Scope for Growth (NSFG) model for the intertidal barnacle Balanus glandula and used it to predict the effects of warming body temperature during high and low tide. The model explained 76% of the variability in growth across the three intertidal shore heights and two time periods, after adding a new parameter for feeding compensation. We found that increasing body temperatures during immersion buffered the negative effects of increased air temperatures at low tide. Specifically, higher aquatic body temperatures increased growth by increasing feeding rates during immersion more than they increased energy costs, while warming aerial body temperatures reduced growth by increasing costs without changing feeding. The NSFG model demonstrated a new method for developing and testing OBMs that used high resolution timesteps, independent curve fits for different energy fluxes, and estimated one parameter, rather than many, with an independent subtidal growth dataset [11]. However, our findings are contingent on the accuracy of the laboratory-measured parameters for feeding and energy demand. Our sensitivity analysis showed that lab-based predictions of growth were greatly influenced by the uncertainty in the relationship between temperature and feeding (S5 Fig, S1 Text). Finally, this work highlights the importance of model testing and sensitivity analyses to identify information gaps and form new hypotheses that can improve future models.
Warming body temperatures and barnacle SFG
Our model suggests that B. glandula will respond very differently to warming body temperatures at high and low tide. Warming during submersion enhanced growth while warming during emersion reduced growth (Fig 9). When submerged, the energetic costs of warming were offset by larger gains in energy intake. In contrast, emersion warming could only influence costs. A similar pattern has been observed in laboratory experiments with Nucella ostrina, a whelk from from the same region [39,82]. This effect was greatest on the low shore, where Scope for Growth increased with warming as long as the magnitude of aerial warming did not exceed aquatic warming (Fig 9E,F). In contrast, warming on the high shore only led to increased growth when aquatic warming was greater than aerial warming (Fig 9A,B). Interestingly, shore height also influenced the relationship between SFG and aerial warming, as the same amount of aerial warming depressed SFG more on the high than the mid shore, even though the mid-shore had warmer emersion temperatures overall.
Importantly, terrestrial rates of warming are predicted to exceed marine warming, a phenomenon known as the “land-sea warming contrast” [83]. In the Salish Sea, average air temperatures are predicted to increase by 3.5°C by 2095 under RCP 8.5, more than double the predicted sea surface temperatures warming of 1.57°C [36,37]. At this 2:1 warming ratio of emersion to immersion, our model predicts up to a 40–70% decrease in SFG at the higher elevation, and a 10–40% decrease in SFG at the lower elevation, depending on the time interval.
These results suggest that the negative effects of climate warming are likely to be greatest on the high shore. If this is the case, B. glandula could experience a vertical contraction of its upper limit, due to negative Scope for Growth (Figs. 3,4) [84], even as individuals lower on the shore continue to thrive. Indeed, Harley [30] has already documented an average 40 cm drop in the upper vertical limit of B. glandula over 50 years at 20 sites within the Salish Sea. However, the relationship between survival and energetics is complex because of the time-dependence and complexity of energy homeostasis (reviewed by [85,86]). This makes it difficult to predict survival based on energetics alone [85,86]. These vertical range contractions could also be driven by changes in the frequency of acute lethal events [87] or changes in other low tide stressors, such as desiccation [88], rather than a sustained negative Scope for Growth. Further, our study animals were 2–3mm opercular length, but individuals at earlier life stages (e.g., in the days following settlement) could be more susceptible to abiotic stressors at high elevations [89]. Additional research is needed to determine the relative importance of these different mechanisms of stress, including interactions, to intertidal species distributions. It is also worth noting that, while intertidal animals will experience the full amount of aquatic warming during immersion periods, body temperature warming is often much less than the full amount of abiotic aerial warming because of differences in heat transfer (e.g., heat budgets) in air vs. water [38,90]. This is because emersion body temperatures are greatly influenced by the time of day and duration of aerial exposure, which is modulated by the tides [91]. If barnacle body temperatures during emersion warm more slowly than air temperatures, barnacles will be less negatively impacted than we predict here [38]. Accurate predictions of barnacle body temperature warming at low tide will require detailed biophysical modeling [38,81], and could also incorporate biomimetic temperature loggers [38].
Intertidal organisms in the Salish Sea, including B. glandula, occupy a unique thermal niche. In this region, B. glandula experience some of the coldest immersion temperatures anywhere in its geographic range and some of the warmest emersion body temperatures [92]. It is unclear how generalizable the benefits of warming aquatic temperatures observed here are to other populations of B. glandula or to other intertidal species. Experimental studies of other Northeastern Pacific intertidal species, have found an increase in feeding rates under warming water temperatures for some snails [82,93,94], seastars [93] and barnacles [39], but increases in feeding do not always translate into increased growth [93]. Moreover, different populations of a species can vary in their response to temperature [94]. The relationship between growth and temperature can also be influenced by species interactions, such as non-lethal predator effects on prey [39,95]. Further, species that regularly experience temperatures near and above their thermal feeding optima, or that live in environments in which temperature modulates local biogeochemistry may be especially vulnerable to the combined effects of aerial and water warming [96]. Thus, while some intertidal species may experience the benefits of warming water temperatures under specific conditions, those conditions may be idiosyncratic to specific populations and/or ecological situations.
Advantages and limitations of our numerical scope for growth approach
One of the central challenges of modeling organismal responses to climate change is designing models that capture physiology and environmental conditions at appropriate levels of detail [40,81]. A multitude of organism-level bioenergetic models have been proposed [4–6,9]. We used a hybrid modeling approach that combined a short time-step Numerical Scope for Growth model with elements of several other approaches (Fig 2, Table 1). Our OBM model estimated growth daily, which is a much shorter timestep than traditional SFG models, and relied on temperature data at an even shorter timestep (15 minutes) to accurately capture the dynamic tidal environment of B. glandula. The model also incorporated key ideas from DEB models, including a nonlinear function of feeding rate relative to food concentration [6,51] and a 40% overhead cost for growth [6].
One major difference among OBM frameworks is the number of distinct thermal sensitivities incorporated into the model for different aspects of an organism’s physiology, such as consumption and energy demand, despite a growing consensus that they exhibit different thermal sensitives [11,20,54]. At one extreme, all thermal sensitivities in DEB and MTE are often modeled with a single equation derived from theoretical principles [6,7], and only some applications of these models allow individual parameters to vary by physiological process (e.g., [9,25]). In contrast, incorporating unique thermal sensitivity equations for more than one distinct process is fundamental to building fish bioenergetics and SFG models [5,46]. We fit four distinct curves: feeding, aquatic energy demand, aerial energy demand, and aerial recovery (oxygen debt). In fitting thermal sensitivity equations to empirical data, there are a wide range of curves to choose from [8,97,98]. We used an information theory approach to compare 5 representative curve formulations (S1 Text, including Table A, B in S1 Text). In fitting the curves, we drew on empirical datasets that contained a wide range of temperatures, well beyond what this species currently experiences (aerial: 5–38°C, aquatic: 5–26°C), to ensure the model would be relevant for novel environmental conditions [11].
Divide and conquer strategies integrate sub-model simulations with top-level simulation experiments with the aim of assessing research questions with more valid and realistic simulations [11,99]. Many bioenergetics models include sub-model growth simulations within the preparatory stage [26,100,101]. Importantly, we used a sub-model growth simulation to estimate two parameters, only one of which was then integrated into the top-level model. Specifically, this sub-model simulation was an independent dataset of barnacle growth in a subtidal environment (no immergence). This sub-model simulation was used to estimate maximum assimilation rate pmax. Then, the top-level experiment investigated whether the model predicted growth across three tidal elevations and two time periods. When this model failed to converge, we tested a new quantitative hypothesis, that feeding varied exponentially with tidal elevation, and we then tested this against all three tidal elevations and two time periods. This strategy allowed us to use one parameter (z) to account for the discrepancy between predicted growth based on the model vs. observed growth. This approach assumes that the three parameters, pmax, z, and FH, are sufficient to explain growth, but other biological processes and factors (e.g., microclimate [38], flow, composition of food available, e.g., POM vs. plankton [64]) could play a role in barnacles ecophysiology and be incorporated and tested in future models.
Within a statistical model, only some parameters have scientific interest. In such models, “nuisance parameters” address random mechanisms, and variability resulting from them, but have no intrinsic value in themselves [102]. The half-saturation coefficient is used in NSFG and DEB models [6,51], and allows for saturation of feeding at high food densities which is more realistic [103,104]. Here, the half saturation coefficient for feeding (FH) was estimated once, independently for each of the sub model and top level model. In DEB models, this coefficient is calculated for each location separately [6]. This method of validation in place of independent model testing is difficult to avoid since this variable is associated with food quality and is difficult to characterize empirically [6], and may vary by location [24,25]. In our study, the three shore heights were within a meter of one another. While it’s plausible that food quality may have varied across the 6-month experiment, this work makes strategic use of a system in which a similar food quality across space is a reasonable assumption. The half-saturation coefficient value (Table 1) constrained feeding to ~80–100% of the maximum feeding rate throughout the entire year (Fig 3a-c). Rather than considering this value as corresponding to some intrinsic value of food quality, perhaps this number is best considered a nuisance parameter that constrains the influence of the food metric on intake. In this study, a low FH limited the influence of monthly chlorophyll on food availability (S3 Fig). Finally, we used chlorophyll fluorescence as a proxy for food availability, but more direct measurements of food sources (e.g., POM, plankton species, etc. [64]) could improve our understanding of the effect of food supply on growth.
Tidal compensation and sensitivity of the SFG estimate to feeding
One surprising result of our model was that it failed to capture growth across the tidal gradient unless we allowed feeding rate to vary with shore height. Most intertidal animals can only feed while submerged so that a shorter submergence time should shorten the time for feeding. Yet, growth differences across tidal elevation were not directly proportional to submergence time. B. glandula at the higher elevations were submerged ~60% less than those in the lower elevation, but their growth was only 30% less than that in the low elevation and this difference was not statistically significant (S2 Fig, S1 Table). Intertidal animals can compensate for reduced submersion by either increasing feeding rates or conserving energy [34,105–107]. While not all intertidal species exhibit tidal compensation [105], 1.5 to 10-fold increases in feeding rates with elevation have been reported in Balanus species [68,69]. We found a 3-fold increase in feeding activity across B. glandula’s vertical range, which is comparable to the 6-fold increase reported by Horn et al. [69] for a central California population of B. glandula. Other factors, such as energy conservation at high elevations [34], species interactions [108], or hydrodynamics [64] could also modulate relationships between submergence time and feeding activity. The need for a tidal compensation parameter highlights the importance of strategically field-testing models across multiple environments or populations [11]. A model based on only laboratory data or tested in only one environment would not have identified the need for tidal compensation.
The sensitivity analysis also identified that the SFG was most sensitive to the uncertainty in the feeding energy flux equation. Specifically, increasing the feeding coefficient by its SE increased SFG by ~3-fold. Feeding rates are highly variable and challenging to characterize given effects of particle selection, food quality, uptake of nutrients, current velocity [64], as well as the hiding behaviors [68] and passive vs. active feeding behaviors [69] described above. This work suggests that future lab-based growth models may be improved by focusing on more accurately characterizing feeding behavior.
Model sensitivity to parameter uncertainty
One advantage of Scope for Growth models over other OBMs is that they have a simpler structure so model uncertainty is easier to evaluate and interpret [27,28]. We used a variation on Individual Parameter Perturbation [5,80], in which we tested the model sensitivity to parameter uncertainty. This method allowed for realistic estimates of uncertainty that are scaled based on parameter uncertainty rather than the magnitude of the parameter. When parameter sensitivity is calculated in bioenergetics models, it is often based a nominal 10% change in each parameter value to investigate sensitivity to each value [5,109]. A nominal 10% change in a parameter value is sensitive to the units (e.g., °C vs. K), and may not be biologically relevant. Here, we estimated the error around each parameter (SE) or obtained its SE from the literature, and perturbed each parameter with this uncertainty [79]. This method may be most appropriate for NSFG models and other models with simple structures that meet two criteria; first, there is little to no information about the shape of the priors necessary for Bayesian analyses [27], and second, the uncertainty of individual parameters is estimated separately from independent datasets such that newer multi-tier parameter estimation methods are not required to characterize parameter uncertainty [110].
Conclusions
This study presents an OBM to describe physiological consequences of changing aerial and atmospheric temperatures on a rocky intertidal crustacean. We found that warming of aerial and aquatic temperatures had opposite effects on the growth of the intertidal barnacle Balanus glandula. The high sensitivity of the model to the relationship between temperature and feeding suggests that factors affecting clearance rates, feeding, and assimilation may have a large impact on growth and distribution. Our OBM applied standardized statistical methods to physiological energy budgets, incorporating high-resolution environmental data and a suite of physiological lab-derived data. The process of field testing models is necessary to build effective predictive models that forecast the effect of climate change on marine species [11]. Such models are needed to adjust marine species management and conservation efforts to dynamic and changing environmental conditions [10,12].
Supporting information
S1 Text. Supporting information on data collection and model development.
Collection of aquatic respiration and feeding rate data, oxygen debt calculation, AIC intercomparison of TPCs, and final energy flux equations.
https://doi.org/10.1371/journal.pclm.0000540.s001
(PDF)
S1 Table. Summary of ANCOVA of the effect of elevation and initial opercular length on barnacle growth.
https://doi.org/10.1371/journal.pclm.0000540.s002
(PDF)
S1 Fig. The relationship between elevation and growth.
https://doi.org/10.1371/journal.pclm.0000540.s003
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S2 Fig. Representative temperatures and estimated physiological rates over one day.
https://doi.org/10.1371/journal.pclm.0000540.s004
(PDF)
S3 Fig. Timeseries of estimated food availability.
https://doi.org/10.1371/journal.pclm.0000540.s005
(PDF)
S4 Fig. Intake calculated with and without feeding compensation.
https://doi.org/10.1371/journal.pclm.0000540.s006
(PDF)
S5 Fig. Thermal performance curves used in model.
https://doi.org/10.1371/journal.pclm.0000540.s007
(PDF)
Acknowledgments
We thank R. Rognstad, E. Hazelton, E. Carrington and M. Nishizaki for generously sharing data and providing other help. We also thank A.Gleekel, S. Malik, E. Ueland, S. Ueland, K.Roberts, E. Kovachevich, and S. Martin for their contributions to the photoquadrat dataset. Finally, special thanks to E. Pousse, E. Munroe, W. King, and R. Cerrato for feedback and insightful discussions that improved the quality of this manuscript.
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