Finally Published!
well
We have finally been published!
You can check it all out on the Ecology website.
or
Here are the highlights...
The photograph is of the Becancour River.
The backdrop to Woodland antics for the year we lived in Quebec.
{I miss our river}
I have to admit there's a bit of a thrill to see my name as the photographer.
(if you look at the photo on the website you can see it too)
The photograph obviously had to be cropped for the cover.
I'm a little bummed the rainbow from the original didn't survive the cut.
More importantly here's Ryan's article.
This is only the text. If you're interested in seeing the complete article with graphs and all the bells & whistles go HERE.
Incorporating temporally dynamic baselines in isotopic mixing models
Ryan J. Woodland1, Marco A. Rodríguez, Pierre Magnan, Hélène Glémet, and Gilbert Cabana
| Abstract |
|---|
Stable isotopes (particularly C and N) are widely used to make inferences regarding food web structure and the phenology of consumer diet shifts, applications that require accurate isotopic characterization of trophic resources to avoid biased inferences of feeding relationships. For example, most isotope mixing models require that endmembers be adequately represented by a single probability distribution; yet, there is mounting evidence that the isotopic composition of aquatic organisms often used as mixing model endmembers can change over periods of weeks to months. A review of the literature indicated that the δ13C values of five aquatic primary consumer taxa, commonly used as proxies of carbon production sources (i.e., trophic baselines), express seasonally dynamic cycles characterized by an oscillation between summer maxima and winter minima. Based on these results, we built a dynamic baseline mixing model that allows a growing consumer to track temporal gradients in the isotopic baselines of a food web. Simulations showed that the ability of a consumer to maintain or approach isotopic equilibrium with its diet over a realistic growth season was strongly affected by both the rate of change of the isotopic baseline and equilibration rate of the consumer. In an empirical application, mixing models of varying complexity were used to estimate the relative contribution of benthic vs. pelagic carbon sources to nine species of juvenile fish in a fluvial lake of the St. Lawrence River system (Québec, Canada). Estimates of p (proportion of carbon derived from benthic sources) derived from a static mixing model indicated broad interspecific variation in trophic niche, ranging from complete benthivory to >95% reliance on pelagic food webs. Output from the more realistic dynamic baseline mixing model increased estimated benthivory by an average of 36% among species. Taken together, our results demonstrate that failing to identify dynamic baselines when present, and (or) matching consumers with baseline taxa that possess substantially different equilibration rates can seriously bias interpretation of stable isotope data. Additionally, by providing a formalized framework that allows both resources and consumers to shift their isotopic value through time, our model demonstrates a feasible approach for incorporating temporally dynamic isotope conditions in trophic studies of higher consumers.
Key words: benthic vs. pelagic carbon, carbon isotope seasonal cycles, dynamic baseline mixing model, equilibration rate, juvenile lake fish, stable isotope, St. Lawrence River, Québec, Canada, temporal effects, trophic niche
Received: March 16, 2011; Revised: July 5, 2011; Accepted: July 19, 2011
| Introduction |
|---|
Despite the proliferation of ecological studies that have used trophic baselines, it is not clear that many of the primary consumers used as baselines in stable isotope studies actually satisfy the time-stability assumption. In aquatic ecosystems, the δ13C (ratio of heavy to light carbon isotope expressed as ‰) value of phytoplankton and periphyton is influenced by the composition and source of assimilated dissolved inorganic carbon (e.g., CO2 vs. HCO3−, atmospheric vs. respired CO2), nutrient availability (e.g., flow regime, boundary layer dynamics), algal metabolism and biomass, and fractionation kinetics (Fry and Sherr 1984, MacLeod and Barton 1998, Trudeau and Rasmussen 2003, Finlay 2004, Hill and Middleton 2006, Rasmussen and Trudeau 2007). Many of these influences are seasonally variable, resulting in dynamical δ13C patterns in aquatic primary producers (Rolff 2000, Gu et al. 2006) that can propagate to the next trophic level (i.e., primary consumers; Kline 1999, Grey et al. 2001, Nordström et al. 2009). Trophic studies in which samples are collected over limited time intervals may fail to identify such systematic seasonal shifts in the isotope value of baseline organisms (Nordström et al. 2009). Similar to aquatic ecosystems, ambient concentrations and δ13C values of atmospheric CO2 in terrestrial ecosystems can also show marked spatiotemporal variability (Buchmann et al. 1997, Flanagan and Ehleringer 1998). In addition, both environmental (e.g., soil moisture) and biological (e.g., physiology, taxonomy, phenology) factors have been shown to influence the seasonality and magnitude of δ13C discrimination during photosynthesis among terrestrial plants (e.g., Smedley et al. 1991). In terrestrial habitats where primary producers experience seasonal cycles in their δ13C values, it seems reasonable to predict that these changes would be reflected in the isotopic composition of small terrestrial consumers (e.g., herbivorous insects) via trophic mechanisms. Although our focus is on aquatic ecosystems in this paper, the same potential pitfalls exist in terrestrial habitats that display temporally variable isotopic conditions among trophic resources at the base of food webs.
For consumers that are likely to display dynamic changes in isotope composition over relatively short timescales, the use of temporally invariant baseline organisms can be inappropriate. The most obvious cases are consumers with high growth or metabolic rates such as the juvenile life stage of many taxa (Hesslein et al. 1993, Herzka 2005), but can also include ectotherms occupying warm environments (e.g., McIntyre and Flecker 2006). Additionally, tissues such as liver, blood plasma, and mucus that undergo rapid turnover in isotope composition (Pinnegar and Polunin 1999, Church et al. 2009) can be used to track recent feeding patterns despite low somatic growth rates. Interpretation of isotope values from metabolically active tissues with high turnover rates presents the same conceptual problem as rapidly growing consumers if appropriate trophic baselines are shifting during the equilibration period. The potential for biased interpretation of trophic structure arising from a temporal mismatch in the equilibration time of consumer relative to the baseline organism has been discussed (Cabana and Rasmussen 1996, Syvaränta et al. 2006, Nordström et al. 2009, Hadwen et al. 2010). However, isotope mixing models capable of incorporating temporally varying baselines have not received widespread attention.
Given the widespread use of primary consumers to define baselines in trophic studies, we reviewed the literature for evidence of seasonal shifts in the isotope value of taxa commonly used as baselines. Based on the results of the meta-analysis and our own observations, we perceive a need for a modeling approach that integrates shifting baselines. To this end, we derived a two-endmember mixing model to account for consumer growth (and metabolic turnover) while allowing for shifts in the isotope endmembers through time (hereafter “dynamic baseline mixing model” or DBMM). The potential for interpretation errors when baselines are shifting is demonstrated by simulating the equilibration response of consumers with different growth rates. As an example, we use the DBMM in a Bayesian framework to analyze empirical invertebrate and juvenile fish δ13C time series data from a fluvial lake of the St. Lawrence River (Québec, Canada). Model output and an information-theoretic criterion of model performance were used to compare the DBMM and two common versions of the two-endmember mixing model (i.e., constant baseline, no-growth model; constant baseline, growth-included model).
| Methods |
|---|
Meta-analysis We reviewed the aquatic ecology literature and selected 31 studies that reported naturally occurring δ13C values in primary consumers over intervals that ranged from 1 week to 12 months between consecutive samples. Data were recorded directly from tables and text or interpolated from figures. We restricted our data collection to invertebrate herbivores to replicate the common convention of selecting these taxa as isotope baselines. Despite this constraint, there was a broad diversity of aquatic invertebrates in the analysis, including bivalves, gastropods, amphipods, zooplankton, and herbivorous insects. Study sites included lentic, lotic, estuarine, and marine systems, ranged in productivity from oligotrophic to eutrophic, and spanned subtropical to boreal climates.
Primary consumer data were standardized to a common scale by subtracting the mean δ13C value of the appropriate study from each observation. These standardized primary consumer δ13C residuals were then combined into one data set and a generalized additive model, GAM (Hastie and Tibshirani 1990), was used to identify any nonlinear trends in the combined residuals over time. The model was fit to the residuals (dependent variable) as a function of time (ordinal date, where day 1 is 1 January, as the independent variable) with a univariate smoothing spline (df = 3) and identity link function assuming a normal error distribution. We corrected for temporal juxtaposition of seasons between northern and southern hemispheres by adding 182 d to the collection day of the year (i.e., 1–365) for all studies that occurred in the southern hemisphere. We were also interested in the daily rate of change in δ13C among primary consumers indicated in each study. To examine this, we recorded the longest time interval in days between samples over which primary consumers showed a monotonic increase or decrease in each study. Samples were from different individuals of the same species collected at different times. The rate was calculated for each time series of species data (potentially several per study) as the slope determined by change in δ13C over the time interval: βC = |
|/Δtime.
|/Δtime. Dynamic baseline mixing model development Assuming resources and consumer are at isotopic equilibrium, the contribution of two diet resources with different isotope values (δX1, δX2) to the isotope value of a consumer δXcons can be estimated with a two-endmember mixing model:
where p is the proportional contribution of resource 1 and (1 − p) is the contribution of resource 2 to the consumer (Peterson and Fry 1987). In the case of a diet shift by the consumer, the equilibration of the consumer to the new diet is determined by the consumer's growth rate as well as the rate of metabolic turnover within its tissues (Hesslein et al. 1993), as follows:
where δX(t) is the isotope value of a consumer at time t, δX0 is the initial isotope value of the consumer at t = 0, δXn is the isotope value of the consumer at equilibrium with the new diet (subscript n), and k and m represent rates of instantaneous growth and metabolic turnover. As long as the isotope values of the resource endmembers are constant, consumers will approach equilibrium at a rate governed by the processes of growth and metabolism. If, however, the isotope values of the resources are shifting through time, then the ability of a consumer to approach or maintain isotopic equilibrium also depends on the rate of change of the resources.
 |
 |
Our DBMM, based on first principles, builds on the conceptual approach of previous equilibration models (e.g., Hesslein et al. 1993) and allows consumers that are changing their mass through time (gain or loss) to track a mixture of two time-varying resource endmembers (see Appendix A for a detailed derivation of the model). For our purposes, we assume that the effect of growth on equilibration rate dominates metabolic influences; therefore, we do not specify a separate metabolic parameter in the exponential rate function (e.g., m as described by Hesslein et al. 1993). The model can be easily reformulated to include a metabolic rate component if such information is available for a given situation. To relax the assumption of static resource endmembers in the DBMM, we derived a variant of the two-endmember mixing model (Eq. 1) for δXn (Eq. 2) in which the isotope values of resources δX1 and δX2 were allowed to vary as functions of time. This substitution results in a target equilibrium δXn that constantly changes in response to shifts in the resource endmembers. There are in principle no constraints on the shape of the resource δX(t) functions or growth models, which can be derived from models fit to empirical observations or based on theoretical arguments. If the consumer is growing while the isotope values of resources are changing, the contribution of the resource's value at time t to the consumer isotopic value depends on the instantaneous growth rate at t and is maximized during the period(s) of highest consumer growth rate. Therefore, the contribution of each resource to the biomass of the consumer at time t becomes a function of the time-averaged resource isotope value and consumer biomass gain from t0 to t, weighted by the total biomass accrued since t0.
Simulation We used the DBMM we have described to simulate a common situation in which the relative importance of two basal resource endmembers (hereafter “baselines”) is evaluated for one or more consumers that differ in growth rate κ. For our simulations, we have chosen to model the response of consumers to changes in baseline δ13C to maintain consistency with the carbon focus of the meta-analysis and the Lake St. Pierre data set. The result is identical for other elements (e.g., δ15N) in situations where they show similar temporal changes. Here, the δ13C of consumers was allowed to respond to changes in the δ13C of the two baselines over time t = 50 days. Consumers were assigned a κ = 0.01 or 0.06 d−1; whereas the proportion of carbon p assimilated from baseline 1 relative to baseline 2 was fixed at 0.95. The chosen values of κ are representative of plausible slow and fast growth rates that could be observed between taxa or life stages (e.g., Lake St. Pierre data set) and the duration of the simulation reflects a realistic two-month sampling interval.
In the first scenario, baselines (subscripts base1, base2) were static with intercepts separated by 5‰: δ13Cbase1 = −23‰, δ13Cbase2 = −28‰. We selected the 5‰ difference between baselines as a realistic example of alternative carbon sources in aquatic ecosystems (e.g., Vander Zanden and Rasmussen 1999, Vander Zanden and Vadeboncoeur 2002). Consumers started with δ13C values (δ13C0) equal to δ13Cbase2 at t = 0. This scenario is analogous to consumers switching to a diet characterized by a temporally stable baseline. In the second scenario, baselines were again offset by 5‰ but changed through time according to otherwise identical quadratic functions. The shapes of the baseline models were derived from empirical observations of a shifting trophic baseline from a lake environment (see Results: Lake St. Pierre data set). Consumers in the second scenario also started with δ13C0 = δ13Cbase2. This scenario replicates the trophic niche shift of the first scenario under dynamic baseline conditions. In the third scenario, baseline conditions were the same as those simulated in the second scenario, but consumers started the simulation at equilibrium with their diet (i.e., C0 = 0.95δ13Cbase1 + 0.05δ13Cbase2 = 0.95(−23‰) + 0.05(−28‰) = −23.25‰). The third scenario focuses on the effect of dynamic baselines by removing the additional complexity of a diet shift, requiring only that consumers maintain or “track” their initial diet equilibrium.
Example: Lake St. Pierre data set We used consumer data collected from Lake St. Pierre (46°12′ N, 72°49′ W; Québec, Canada) to evaluate the performance of our DBMM relative to simpler isotope mixing models. Lake St. Pierre is a large fluvial lake of the St. Lawrence River ecosystem that displays strong seasonality in temperature, hydrograph, nutrient regime, and productivity (Vis et al. 2007, Hudon and Carignan 2008; see Plate 1). Primary consumers were collected from early May to early September in 2004, 2006, and 2008 and were used to model temporal changes in the δ13C value of pelagic (i.e., phytoplankton) and benthic (i.e., periphyton) carbon sources. Filter-feeding bivalves (zebra mussels Dreissena polymorpha, eastern lamp mussels Lampsilis radiata, Barnes mussel Ellipitio complanata) were selected as baseline indicators of pelagic carbon. Two groups of grazing taxa, gastropods (Bithyniidae, Lymnaeidae, Physidae, Planorbidae, Pleuroceridae, Viviparidae) and amphipods (Gammaridae), were used as baseline indicators of periphytic carbon. Unlike the grazer taxa for which δ13C data were available as of 1 May, bivalves were not collected prior to 29 June. Therefore, data available for fitting the pelagic baseline model were limited to the months of July–September.
We selected specific age classes of nine abundant species of fish as model consumers for the Lake St. Pierre study (Appendix C). These included age-0 alewife Alosa pseudoharengus, white sucker Catostomus commersoni, mooneye Hiodon tergisus, yellow perch Perca flavescens, and walleye Sander vitreus; and age-1 banded killifish Fundulus diaphanus, pumpkinseed Lepomis gibbosus, golden shiner Notemigonus crysoleucas, and spottail shiner Notropis hudsonius. Fish were collected in the littoral zone (<2.5 m depth) by electrofishing from 21 June to 24 August 2006. Sampling occurred at 80 stations around the lake perimeter and consecutive daily sampling was deliberately alternated between shores to avoid spatiotemporal bias in habitat conditions. Each station consisted of a 20-min fishing transect of
650 m. Fish were identified and total length (TL, in mm) was recorded before release. A random subsample of each species was retained for stable isotope analysis (see Appendix C for isotope sample size by species). White muscle tissue samples of fish or whole invertebrates (discounting shells) were dried at 70°C, homogenized, and sent to the Stable Isotopes in Nature Laboratory (SINLAB; Canadian Rivers Institute, Biology Department, University of New Brunswick, Canada) for δ13C analysis.
In our model of juvenile fish in Lake St. Pierre, we did not explicitly consider terrestrial detritus as a unique carbon source. Isolating pure samples of either algae or particulate terrestrial detritus during field sampling is extremely difficult because seston (i.e., pelagic carbon source) and periphyton (i.e., benthic carbon source) contain both living and detrital organic matter components. Although it is likely that the primary consumers we selected as trophic baselines assimilated some fraction of both living and detrital carbon, we did not possess specific estimates of the δ13C signature of terrestrial detritus in Lake St. Pierre. Therefore, we have taken the approach of others (e.g., Post 2002, Vander Zanden and Vadeboncoeur 2002) by modeling the relative contribution of periphyton vs. seston without deconstructing the specific composition of the organic matter in each source. If available, such data could easily be incorporated into the DBMM parameterized for three or more potential resources (see Appendix E).
We estimated the proportional contribution of benthic vs. pelagic carbon sources to each fish species within a Bayesian modeling framework (Appendix B). Bayesian applications of stable isotope mixing models are relatively new (i.e., Moore and Semmens 2008), but provide several advantages over traditional approaches (Semmens et al. 2009, Ward et al. 2010). The primary advantage of a Bayesian approach in this context lies in conserving the uncertainty associated with multiple linked models and using that uncertainty to inform estimates of probable distributions (i.e., posterior distributions) for output parameters (Hilborn and Mangel 1997). Additionally, prior information can be used to inform the likelihood of parameter distributions, allowing previous studies or complementary data sources to inform model output. In our model, we chose to restrict the flow of information between model components to occur in only one direction: fish growth and baseline models were only allowed to influence fish δ13C values (Appendix B). We accomplished this by allowing the parameters for species-specific growth and baseline trajectories (and their associated uncertainty) to influence the posterior distribution of p in the model component representing changes in fish δ13C over time. We selected this unidirectional model linkage to replicate the natural flow of information between the components being modeled; feedbacks between fish carbon source and growth rate are possible but were not considered in this example.
Within species, individual fish were assigned to age classes based on size at capture and the seasonal progression of length modes assessed for each species at a weekly time step. Fish lengths were transformed to mass via length–mass relationships established previously for the Laurentian Lakes region (Schneider et al. 2000). The growth parameter κ was estimated by fitting an exponential function to the mass-at-day data (Appendix A). Sample size and time intervals available for growth models ranged from N = 19–203 and time = 36–58 d among species (Appendix C). We lacked the data necessary to estimate a separate metabolic parameter m in our growth model. However, the influence of m is typically small relative to κ in fast-growing fish (Hesslein et al. 1993, Herzka 2005) although there are cases in which m dominates (e.g., Sakano et al. 2005, Buchheister and Latour 2010). Preliminary analysis (not shown) indicated that a quadratic function provided the best fit of the benthic baseline data to time. To maintain equal treatment of both baselines, a quadratic function was also used to model the pelagic baseline. When the exponential fish growth and quadratic baseline models are combined, several terms cancel (Appendix A) and the growth-weighted contributions of the benthic and pelagic baseline enter the mixing model as
where hF and hG are auxiliary functions associated with each baseline and t0 is the day at which fish isotopic equilibration is initiated. If the baselines are constant (i.e., slopes are zero) and t is set to infinity, Eq. 3 simplifies to Eq. 1.
We selected specific age classes of nine abundant species of fish as model consumers for the Lake St. Pierre study (Appendix C). These included age-0 alewife Alosa pseudoharengus, white sucker Catostomus commersoni, mooneye Hiodon tergisus, yellow perch Perca flavescens, and walleye Sander vitreus; and age-1 banded killifish Fundulus diaphanus, pumpkinseed Lepomis gibbosus, golden shiner Notemigonus crysoleucas, and spottail shiner Notropis hudsonius. Fish were collected in the littoral zone (<2.5 m depth) by electrofishing from 21 June to 24 August 2006. Sampling occurred at 80 stations around the lake perimeter and consecutive daily sampling was deliberately alternated between shores to avoid spatiotemporal bias in habitat conditions. Each station consisted of a 20-min fishing transect of
650 m. Fish were identified and total length (TL, in mm) was recorded before release. A random subsample of each species was retained for stable isotope analysis (see Appendix C for isotope sample size by species). White muscle tissue samples of fish or whole invertebrates (discounting shells) were dried at 70°C, homogenized, and sent to the Stable Isotopes in Nature Laboratory (SINLAB; Canadian Rivers Institute, Biology Department, University of New Brunswick, Canada) for δ13C analysis.In our model of juvenile fish in Lake St. Pierre, we did not explicitly consider terrestrial detritus as a unique carbon source. Isolating pure samples of either algae or particulate terrestrial detritus during field sampling is extremely difficult because seston (i.e., pelagic carbon source) and periphyton (i.e., benthic carbon source) contain both living and detrital organic matter components. Although it is likely that the primary consumers we selected as trophic baselines assimilated some fraction of both living and detrital carbon, we did not possess specific estimates of the δ13C signature of terrestrial detritus in Lake St. Pierre. Therefore, we have taken the approach of others (e.g., Post 2002, Vander Zanden and Vadeboncoeur 2002) by modeling the relative contribution of periphyton vs. seston without deconstructing the specific composition of the organic matter in each source. If available, such data could easily be incorporated into the DBMM parameterized for three or more potential resources (see Appendix E).
We estimated the proportional contribution of benthic vs. pelagic carbon sources to each fish species within a Bayesian modeling framework (Appendix B). Bayesian applications of stable isotope mixing models are relatively new (i.e., Moore and Semmens 2008), but provide several advantages over traditional approaches (Semmens et al. 2009, Ward et al. 2010). The primary advantage of a Bayesian approach in this context lies in conserving the uncertainty associated with multiple linked models and using that uncertainty to inform estimates of probable distributions (i.e., posterior distributions) for output parameters (Hilborn and Mangel 1997). Additionally, prior information can be used to inform the likelihood of parameter distributions, allowing previous studies or complementary data sources to inform model output. In our model, we chose to restrict the flow of information between model components to occur in only one direction: fish growth and baseline models were only allowed to influence fish δ13C values (Appendix B). We accomplished this by allowing the parameters for species-specific growth and baseline trajectories (and their associated uncertainty) to influence the posterior distribution of p in the model component representing changes in fish δ13C over time. We selected this unidirectional model linkage to replicate the natural flow of information between the components being modeled; feedbacks between fish carbon source and growth rate are possible but were not considered in this example.
Within species, individual fish were assigned to age classes based on size at capture and the seasonal progression of length modes assessed for each species at a weekly time step. Fish lengths were transformed to mass via length–mass relationships established previously for the Laurentian Lakes region (Schneider et al. 2000). The growth parameter κ was estimated by fitting an exponential function to the mass-at-day data (Appendix A). Sample size and time intervals available for growth models ranged from N = 19–203 and time = 36–58 d among species (Appendix C). We lacked the data necessary to estimate a separate metabolic parameter m in our growth model. However, the influence of m is typically small relative to κ in fast-growing fish (Hesslein et al. 1993, Herzka 2005) although there are cases in which m dominates (e.g., Sakano et al. 2005, Buchheister and Latour 2010). Preliminary analysis (not shown) indicated that a quadratic function provided the best fit of the benthic baseline data to time. To maintain equal treatment of both baselines, a quadratic function was also used to model the pelagic baseline. When the exponential fish growth and quadratic baseline models are combined, several terms cancel (Appendix A) and the growth-weighted contributions of the benthic and pelagic baseline enter the mixing model as
 |
To examine the effect of explicitly modeling shifting baselines in our Lake St. Pierre data set, we modeled p for each fish species using three progressively more complex mixing model variants. In the first model (Model 1), each baseline was represented as a stationary distribution and fish growth was not considered. In Model 2, baselines were again assumed constant, but fish growth was included in the estimation of p. Model 3 (i.e., the DBMM) included both shifting baselines and fish growth in estimates of p. Model formulations 1 and 2 are representative of the approaches taken in most trophic isotope models published to date: consumers are assumed to either exist in a state of equilibrium with their diet (or representative baseline) or to be equilibrating to stable endmembers separated by a gradient. We used the Deviance Information Criterion, DIC (Spiegelhalter et al. 2002) to compare the adequacy of Models 1, 2, and 3. The DIC is one of a family of information-theoretic criteria that are used to assess the relative goodness of fit among alternative statistical models while penalizing models for increased parameterization (Spiegelhalter et al. 2002). Bayesian modeling was conducted on the open-source OpenBUGS platform (available online)2 simulation models were run in the R programming environment, and modal length progression was analyzed with FiSAT II (available online).3 All other statistical analyses were performed with SAS 9.2.
| Results |
|---|
Meta-analysis When plotted together, the primary consumer residuals (N = 264) collected from the literature suggested a curvilinear relationship between primary consumer δ13C and ordinal date (Fig. 1A). The GAM verified a significant nonlinear trend in the data (analysis of deviance χ2 = 45.53, P < 0.001) with a predicted curve that increased from spring to summer (enrichment) followed by a decrease (depletion) at the transition from summer to autumn. The standardized mean (0) fell outside the 95% curvewise confidence intervals around the predicted curve during the summer maximum and local spring and fall/winter minima, supporting the interpretation of a significant, dynamical seasonal cycle.
In the studies included (Appendix D), Δtime spanned 5 days (Lake Ontario: zooplankton) to 223 days (Australian billabong: bivalves, gastropods) (Fig. 1B), and
ranged from 0.21‰ (San Francisco Bay: bivalve) to 19.5‰ (Hiji River: zooplankton). The
values were generally higher when data were collected 3–6 months apart across a sequential seasonal transition (e.g., spring–summer, summer–fall) or the summer–winter transition. Rates of change in primary consumer δ13C, βC, were evenly distributed between −0.23‰ per day and 0.20‰ per day. Absolute values of βC ranged from <0.01‰ to 0.23‰ per day, with a mean |βC| = 0.05‰ ± 0.04‰ per day (mean ± SD). Taxon-specific mean |βC| decreased with increasing average body size, from 0.07‰ ± 0.05‰ per day (zooplankton) to 0.02‰ ± 0.01‰ per day (bivalves; Table 1). Maximum |βC| values coincided with sampling across short time intervals, from <1 to 2 months, and were collected at or very close to seasonal transitions.
ranged from 0.21‰ (San Francisco Bay: bivalve) to 19.5‰ (Hiji River: zooplankton). The values were generally higher when data were collected 3–6 months apart across a sequential seasonal transition (e.g., spring–summer, summer–fall) or the summer–winter transition. Rates of change in primary consumer δ13C, βC, were evenly distributed between −0.23‰ per day and 0.20‰ per day. Absolute values of βC ranged from <0.01‰ to 0.23‰ per day, with a mean |βC| = 0.05‰ ± 0.04‰ per day (mean ± SD). Taxon-specific mean |βC| decreased with increasing average body size, from 0.07‰ ± 0.05‰ per day (zooplankton) to 0.02‰ ± 0.01‰ per day (bivalves; Table 1). Maximum |βC| values coincided with sampling across short time intervals, from <1 to 2 months, and were collected at or very close to seasonal transitions. Simulation results
Results from scenario 1 (diet switch, constant baselines) showed that under stable baseline conditions, δ13C of the fast-growing consumer (κ = 0.06 d−1) was −23.6‰ by day50, 97% of the target δ13Cbase1 value of −23.0‰ (Fig. 2A). Conversely, the slow-growing consumer (κ = 0.01 d−1) failed to reach 40% of the δ13Cbase1 value by day50. When dynamic baselines were included in scenario 2 (diet switch, dynamic baselines), the consumer with κ = 0.06 d−1 equilibrated to −21.3‰ or 85% of the δ13Cbase1 value of −20.6‰ at day50 (Fig. 2B). Despite assimilating 95% of its carbon from δ13Cbase1, the slow-growing consumer fell below the trajectory of δ13Cbase2 and finished the simulation 0.18‰ depleted relative to δ13Cbase2 at day50. Consumers that started the simulation at equilibrium with their target δ13Cbase (scenario 3: diet tracking, dynamic baselines) immediately became depleted in δ13C value relative to their diet (Fig. 2C). The equilibration curves of the fast- and slow-growing consumers showed inflection points at day23 and day39, corresponding to depletion of 1.13‰ (fast growth) and 2.23‰ (slow growth) relative to the tracked baseline. By the end of the simulation, the fast- and slow-growing consumers ended scenario 3 at 90% and 57% of δ13Cbase1, respectively. In all scenarios, consumers failed to reach complete equilibrium with their diet by day50 of the simulations, despite constant growth rates. Contrasting the results from scenario 1 to those of scenario 2 and 3 illustrates the compounding effect that dynamic baselines can have on a consumer's ability to equilibrate to its diet.
Example: Lake St. Pierre data set Grazing primary consumers (benthic δ13C baseline) from Lake St. Pierre showed a strong seasonal enrichment, increasing from a predicted δ13C of −34.86‰ ± 2.80‰ (mean with 95% credible interval) on 1 May to −20.50‰ ± 0.63‰ by 1 August (Fig. 3A). There was evidence of depletion by the end of the benthic time series on 6 September, suggesting a curvilinear relationship similar to that identified in the meta-analysis. Within the available sampling interval, filter-feeding primary consumers (pelagic δ13C baseline) did not display the strong seasonality or enrichment trend of the benthic data; predicted δ13C values declined slightly from −25.95‰ ± 0.77‰ at the start of the time series (29 June) to −26.29‰ ± 0.80‰ at the end (28 August). Without data from May and early June, it was impossible to determine if the pelagic baseline in Lake St. Pierre experienced the spring-to-summer enrichment we observed in the benthic baseline.
Among the fish species included in the Lake St. Pierre study, estimates of p ranged from 0.05 to 1.0 (Fig. 4). Within species, results displayed three general patterns of increasing discrepancy in p estimates among models. For alewife, white sucker, yellow perch, and spottail shiner, all three models yielded similarly high estimates of p (0.8–1.0) despite differences in the width of 95% credible intervals. The observed δ13C values for these species either started more enriched or rapidly became more enriched than the benthic baseline for the modeled time interval, forcing estimates of p to be high regardless of whether the baselines were considered static or dynamic. For alewife and spottail shiner, estimates of p were uniformly high across the three models (Fig. 4). This differed from the mooneye and walleye results, in which p estimates from Model 1 (0.6–0.65) were notably lower than the other models (0.9–0.98; Fig. 4) and estimated δ13C trajectories from Model 3 showed close agreement with the trends in the observed data (Fig. 5). For the remaining three species (i.e., banded killifish, pumpkinseed, and golden shiner), estimates of p from Model 1 were 57–95% lower than estimates from Models 2 and 3. The large discrepancy between models for these species was due to relatively depleted δ13C values for most of the time series followed by an enrichment trend that coincided with the slowing of the benthic δ13C rate of change as the baseline approached the late-summer inflection point (e.g., banded killifish; Fig. 5). These species consisted only of age-1 individuals and included three of the four slowest observed growth rates (Appendix C).
Among the fish species included in the Lake St. Pierre study, estimates of p ranged from 0.05 to 1.0 (Fig. 4). Within species, results displayed three general patterns of increasing discrepancy in p estimates among models. For alewife, white sucker, yellow perch, and spottail shiner, all three models yielded similarly high estimates of p (
0.8–1.0) despite differences in the width of 95% credible intervals. The observed δ13C values for these species either started more enriched or rapidly became more enriched than the benthic baseline for the modeled time interval, forcing estimates of p to be high regardless of whether the baselines were considered static or dynamic. For alewife and spottail shiner, estimates of p were uniformly high across the three models (Fig. 4). This differed from the mooneye and walleye results, in which p estimates from Model 1 (0.6–0.65) were notably lower than the other models (0.9–0.98; Fig. 4) and estimated δ13C trajectories from Model 3 showed close agreement with the trends in the observed data (Fig. 5). For the remaining three species (i.e., banded killifish, pumpkinseed, and golden shiner), estimates of p from Model 1 were 57–95% lower than estimates from Models 2 and 3. The large discrepancy between models for these species was due to relatively depleted δ13C values for most of the time series followed by an enrichment trend that coincided with the slowing of the benthic δ13C rate of change as the baseline approached the late-summer inflection point (e.g., banded killifish; Fig. 5). These species consisted only of age-1 individuals and included three of the four slowest observed growth rates (Appendix C).Model selection criterion (DIC, reported as ΔDIC; see Table 2 for details) values for Model 3 were lower than Model 1 for all fish species and lower than Model 2 for eight of the nine species (Table 2). The additional complexity of Model 3 was supported by the data for all species except mooneye. Differences between Model 2 and Model 3 were more subtle because estimates of p and DIC values were often similar. Still, 95% credible intervals around p were narrower for seven of nine species, with mooneye and walleye the exceptions (Fig. 4). Together, the lower DIC values and narrower credible intervals for Model 3 relative to Model 2 support the selection of Model 3 as the best model.
| Discussion |
|---|
Temporal variability at the base of food webs Considering the widely divergent habitats and latitudes of the study locations included in the literature review, the generality of the spring-to-summer enrichment of primary consumer taxa is striking. An analysis of the various processes responsible for this pattern is beyond the scope of this study, but the most parsimonious explanation is that seasonal cycles in autotroph δ13C are propagated to the next trophic level. If autotrophic δ13C patterns are primarily responsible for changes in primary consumer values, then seasonal oscillations in primary consumers should be amplified in systems with greater fluctuations in the underlying autotrophic value. This would include eutrophic ecosystems with large intra-annual fluctuations in P/R (production/respiration), water bodies with seasonally dependent flow regimes, or ecosystems that receive large pulses of nutrient subsidies. In addition to trophic effects, seasonal changes in body content (Post et al. 2007), condition (Hobson et al. 1993), or species composition (e.g., zooplankton communities; Grey et al. 2001) could explain some of the temporal variability that we documented in primary consumer δ13C from the literature.
The amplitude and prevalence of primary consumers' δ13C cycles have important implications for the design of trophic studies and the interpretation of food web structure. First, they provide compelling evidence that temporal trends in trophic resources should be assessed prior to the application of isotope mixing models (Post 2002, Syvaränta et al. 2006). Consistent linear or curvilinear temporal trends were not limited to small-bodied consumers (e.g., zooplankton, amphipods), but included larger taxa such as bivalves and gastropods (e.g., Lake St. Pierre study) that are often specifically selected as long-term integrators of autotrophic isotope conditions. As a corollary, intra-annual time series of resource data are necessary to identify and, if necessary, model changes in isotopic conditions. Another important point is that collection of resource and consumer samples must be contemporaneous; Nordström et al. (2009) recently noted that seasonal differences of macroinvertebrates in some studies were higher than the default fractionation values of 0–1‰ (δ13C) typically used to define trophic structure. In fact, 69% of the values that we identified in the meta-analysis were >1‰ (37% were >2‰) and 44% of the βC values exceeded 0.04‰ per day (or 1.2‰ per month).
1.2‰ per month). Static vs. dynamic baselines: when does it matter? Some of the strongest implicit assumptions that enter trophic applications of isotope mixing models involve temporal equilibria. Most previous mixing models assume either that consumers express isotopic values proportional to their diet, or that isotope ratios of resources are constant across timescales relevant to consumers, or that both of these conditions hold (Peterson and Fry 1987, Post 2002, Jardine et al. 2006). Still, many animals migrate, undergo trophic niche shifts, forage opportunistically on intermittently available prey resources, or exhibit any range of behaviors that could lead to temporary disequilibrium with their diet. We have shown that failure to account for both consumer equilibration dynamics and, if present, temporal changes in the resource value will lead to erroneous conclusions regarding diet composition. This is particularly true if the consumer is considered to be at dietary equilibrium at the time of collection (Gratton and Forbes 2006). For example, naive calculations of p during our simulation study show that violations of the consumer equilibrium assumption can yield errors up to 115% (not shown). Interannual trends in baseline value pose similar problems in long-term studies of food web changes (Solomon et al. 2008b) and customizing our modeling approach to integrate such multiyear patterns (either singly or linked with a intra-annual model) would be relatively straightforward.
Our results indicate that the potential error arising from equilibrium estimates of p under dynamic baseline conditions increases as the consumer equilibration rate declines relative to the rate of baseline change. In some instances, this could lead to consumers with isotope values outside the bounds of the contemporaneously “available” resource pool despite a diet composed entirely of local resources (e.g., scenario 2 in our simulation study). This scenario is not unrealistic. For example, many fish species transition from relatively δ13C-depleted pelagic food webs to δ13C-enriched benthic food webs following the larva–juvenile transformation. The timing of this transition varies, but occurs during late spring or early summer for many temperate fishes (Scott and Crossman 1973, Able and Fahay 1998), the same period over which we observed the highest rates of change among primary consumers in the meta-analysis and Lake St. Pierre study.
Patterns indicative of this type of pelagic–benthic niche shift are apparent in the empirical age-0 fish data from Lake St. Pierre, consistent with what is known of the life history for most of these species (Scott and Crossman 1973). Similar to the age-0 fish, age-1 fish also displayed depleted δ13C values in mid-June, despite enrichment trends throughout the summer and estimates of p > 0.8. For these individuals, the bulk of recent growth would have occurred in the current spring and previous fall (Perga and Gerdeaux 2005, Gagné and Rodríguez 2008), seasons that we have identified as having depleted benthic carbon values relative to summer conditions. Legacy isotope values associated with recent feeding on seasonally depleted benthic baselines could explain the initially low δ13C values of the age-1 fish.
Our results indicate that the potential error arising from equilibrium estimates of p under dynamic baseline conditions increases as the consumer equilibration rate declines relative to the rate of baseline change. In some instances, this could lead to consumers with isotope values outside the bounds of the contemporaneously “available” resource pool despite a diet composed entirely of local resources (e.g., scenario 2 in our simulation study). This scenario is not unrealistic. For example, many fish species transition from relatively δ13C-depleted pelagic food webs to δ13C-enriched benthic food webs following the larva–juvenile transformation. The timing of this transition varies, but occurs during late spring or early summer for many temperate fishes (Scott and Crossman 1973, Able and Fahay 1998), the same period over which we observed the highest rates of change among primary consumers in the meta-analysis and Lake St. Pierre study.
Patterns indicative of this type of pelagic–benthic niche shift are apparent in the empirical age-0 fish data from Lake St. Pierre, consistent with what is known of the life history for most of these species (Scott and Crossman 1973). Similar to the age-0 fish, age-1 fish also displayed depleted δ13C values in mid-June, despite enrichment trends throughout the summer and estimates of p > 0.8. For these individuals, the bulk of recent growth would have occurred in the current spring and previous fall (Perga and Gerdeaux 2005, Gagné and Rodríguez 2008), seasons that we have identified as having depleted benthic carbon values relative to summer conditions. Legacy isotope values associated with recent feeding on seasonally depleted benthic baselines could explain the initially low δ13C values of the age-1 fish.
Our results show that the presence of dynamic baselines is particularly relevant to consumers with relatively high equilibration rates. We specifically chose to bracket the growth rates that we observed across age classes in fish from Lake St. Pierre (Appendix C) to provide an empirical grounding for our simulation values. In addition to young fish, κ values of 0.01 d−1 and 0.06 d−1 overlap with feasible growth rates for a variety of aquatic ectotherms (e.g., mayfly larvae, Humpesch 1979; crayfish, Pratten 1980; amphipods, Sutcliffe et al. 1981; turtles, Brown et al. 1994; bivalves, Dubois et al. 2007), as well as tissue-specific turnover rates of fish blood, liver, and mucus (MacAvoy et al. 2001, 2006, MacNeil et al. 2006, Church et al. 2009, Logan and Lutcavage 2010). Tissues that have relatively high metabolic turnover rates provide a mechanism for studying trophic ecology of large or slow-growing animals at temporal resolutions that would be impossible from analysis of muscle alone. The same potential for errors associated with shifting baselines exists when interpreting data from these tissues and care must be taken to identify an appropriate baseline and account for temporal gradients if present.
Recommendations
1. Temporal changes.—When designing a study, it is imperative that the potential for temporal changes in basal food web components be considered. Sampling of baseline organisms at approximately equal intervals throughout the study period allows for detection of complex temporal trends and is a generally robust sampling strategy, although a minimum of three temporally staggered samples over the time period of interest would allow a nonlinear trend in the baseline to be modeled if present. For example, if the isotope value of the baseline is dynamical with an annual period, such as we observed in the meta-analysis for δ13C, sampling during nonconsecutive seasons (e.g., spring and autumn) would fail to capture the true functional relationship of the baseline over time and may fail to identify any change at all. Conducting pilot studies or collecting baseline samples during the season directly preceding the primary collection period (in addition to the primary collection period) should provide a reasonable indicator of the presence or absence of temporal changes in the isotope value(s) of basal consumers.
2. Consumer equilibration rate.—When the isotope value of resources is changing, estimates of consumer equilibration rate are necessary to model time-specific contributions of resources to a consumer's isotope value. Careful selection of an appropriate trophic baseline can minimize potential errors associated with “mismatches” of equilibration rates between consumers and baselines (Table 3). Under shifting baseline conditions, the error induced by a temporal lag between a consumer's isotopic value and its contemporaneous diet will increase as the disparity in equilibration rate between consumer and baseline increases. Simple calculations based on realistic κ and βC values show that such mismatches can yield differences of 6‰ between consumer and diet after a 100-day equilibration period (Table 3). We have focused on trophic baselines and two-endmember mixing models, yet the same potential errors underlie violations of consumer and resource equilibrium assumptions when using probability-based diet reconstructions with multiple prey resources (Phillips et al. 2005, Moore and Semmens 2008, Ward et al. 2010).
3. Metabolic turnover.—Finally, our model emphasizes somatic growth, yet metabolic turnover plays a dominant role in the isotopic equilibration rate of certain consumers or tissue types. Although a number of studies have identified consistent differences in the relative importance of metabolism across groups (e.g., age class, tissue type), very few have examined the interaction between environmental conditions and the magnitude of the metabolic rate component. Research into the effects of temperature, oxygen stress, and other factors that influence the metabolic component of isotopic equilibration rates will increase both the explanatory and predictive power of mixing models and thereby facilitate complementary approaches to isotope-based food web modeling (e.g., bioenergetic; Harvey and Kitchell 2000).
| Acknowledgments |
|---|
We thank A. Cattaneo, C. Hudon, M. Bertrand, M. Léveillé, and A. Paris for field and lab assistance. Chantal Vis provided valuable information on the Lake St.-Pierre ecosystem. The manuscript benefited greatly from comments by two anonymous reviewers. This research was supported by grants from the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT), the Natural Sciences and Engineering Research Council of Canada (NSERC), and Université du Québec à Trois-Rivières.
Did you catch all that?
A huge congratulations to my main squeeze.
We're all so proud of you baby.
xo
Woodland Morning News:
* Fiona jumped into bed with us.
Fiona: Mom you know how we have a lot of bacteria in our mouths in the morning?
Half asleep Me: uh huh.
Fiona: Your bacteria smells really bad this morning.
* Mornings are crazy around here. Making breakfast (almost always pancakes), cutting up fruit and veggies for lunches, getting myself and the kids showered & dressed plus reading books. Throw in the mix that Ry is hustling about getting ready for work, helping me out where he can. It has to be the most stressful part of the day. This morning we made it through all of this only to find out that today is Labor Day in Australia... there is no school today. Lucky for me I get to spend the entire day with my monkeys.
* Fiona is getting the last installment of her birthday gifts tonight. Baby chicks! {from Grandma & Grandpa} We're all so excited. I'll post pictures asap.
Wishing you a brilliant day!
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