Estimating trophic position in marine and estuarine food webs

Structural or binary approaches, based on presence-absence of feeding links, are the most common method of assembling food webs and form the basis of the most well explored food web models. Binary approaches to assembling feeding links are often criticized as being less powerful and accurate than flow-based methods. To test this assumption we compared binary estimates of trophic position with estimates based on stable isotope values of nitrogen (dN). For 366 species from eight marine and estuarine food webs we compared trophic position estimates based on binary (presence-absence) feeding links with estimates based on the stable isotope of nitrogen (dN). For a subset of 127 fish species in four of the webs we further compared trophic position estimates based on gut content analysis using a flow-based algorithm using data from FishBase.org with binary and dN estimates. Across all species and webs binary estimates of trophic position were strongly correlated (R1⁄4 0.644) with dN estimates. On average binary estimates differed from baseline corrected dN estimates by 2.33% for mean trophic position and 6.57% for maximum trophic position. On average the difference between binary dN estimates was 0.14 of a trophic level. For the subset of 127 fish species binary estimates performed similarly or more accurately in predicting dN values than the flow-based estimates. Binary approaches to assembling feeding links are often criticized as being less powerful and accurate than flow-based methods. Our results show a high concordance between binary and dN estimates of trophic position as well as showing that in some cases binary estimates are better predictors of dN than flow-based estimates, reaffirming the robustness of the structural approach to assembling food webs. Additional cross-validation studies in other ecosystems are necessary to determine whether our results can be generalized to terrestrial and freshwater ecosystems.


INTRODUCTION
A species trophic position, which represents a quantitative measure of its energetic interactions, is one of the most widely used descriptors of the role of species in ecological communities.Trophic position is correlated with variation in body size (Bode et al. 2006, Jennings et al. 2001, Arim et al. 2007, Arim et al. 2010, Romanuk et al. 2010), consumer-resource size ratios (Brose et al. 2006), species ranges (Mace et al. 1983, McLoughlin andFerguson 2000), interaction strengths (Wood et al. 2010) and the distributions of energy flow in food webs (Scotti et al. 2009).The maximum trophic position in an ecosystem, or food-chain length, has been shown to be related to aspects of community structure and dynamics, ecosystem processes, and bioaccumulation (Post 2002).Trophic position is determined by consumerresource links between species and the distribution of these links provides the basis for determining the topological structure of food webs (Dunne 2006).As such, trophic position is correlated with many other key food web properties, including connectance and variations in the fractions of species with different trophic roles (Vermaat et al. 2009).
Changes in food-chain length and trophic position are becoming widely used as indicators of ecosystem degradation (Pauly and Watson 2005), to assess the impact of fisheries exploitation (Pauly et al. 1998, Pauly andWatson 2005), habitat fragmentation (Layman et al. 2007), and species invasions (Vander Zanden et al. 1999).Resolving differences in trophic position are also important in studies of niche differentiation and competition (Schneider et al. 2004, Romanuk andLevings 2005), and for predicting the strength of trophic cascades (Thompson et al. 2007).
Despite the ubiquity of the use of trophic position as a variable in ecological research, few studies have attempted to cross-validate estimates of trophic position based on binary or flow-based methods or between different flow-based estimates such as between gut content analysis and stable isotope analysis.When cross-validation has been conducted between flow-based and stable isotope based estimates of trophic position, the number of comparisons typically only includes a small fraction of the species in ecosystem and while good concordance is found is some cases (see Vander Zanden et al. 1997, Harvey and Kitchell 2000, Schmidt et al. 2009) in other cases no, weak, or inconsistent relations are observed (Ribczynski et al. 2008, Franssen and Gido 2006, Dame and Christian 2008).
Flow-based methods are also time consuming, expensive, and methodologically involved.Thus, highly and evenly resolved flow-based or isotope based food webs are still exceedingly rare due to the massive effort involved in assembling these types of quantitative food webs.This leads to binary (presence-absence) food webs being the most prominent type of food web in the literature, forming the basis for the majority of published comparative analyses, theoretical models, and characterizations of food web structure (Cohen 1978, Cohen et al. 1990, Williams and Martinez 2000, Dunne 2006, Cattin et al. 2004, Vermaat et al. 2009).Still, the degree to which binary links reflect actual energy flow patterns in food webs is poorly understood.
The major criticism levied against binary food webs is that their presence or absence designation to trophic links inadequately describes the huge variability of flows among links.In the only large-scale comparative study conducted to date, spanning four highly resolved terrestrial and marine webs, binary estimates of trophic position were shown to differ by a quarter of a trophic level on average from empirically derived (e.g., gut content, observation) flow-based estimates (Williams and Martinez 2004).Thus, in general there appears to be a strong concordance between flow-based estimates of trophic position based on gut content analysis or observation and binary estimates.However, because gut content analysis and observation can bias estimates of trophic position due to limited spatial and temporal extent and the over-representation of non-assimilated materials in diet descriptions (Vander Zanden et al. 1999), a more effective test of the ability of binary webs to reflect actual trophic position is to compare binary estimates with stable isotope estimates (Williams and Martinez 2004).
Stable isotope estimates represent a temporally and spatially averaged measure of carbon and nitrogen that is actually assimilated by organisms (Schmidt et al. 2007) and thus resolve some of the methodological issues associated with the analyses of relatively episodic gut contents.Early studies on fractionation of nitrogen across trophic levels suggested an average enrichment of 3.4% with each trophic level (DeNiro andEpstein 1981, Minagawa andWada 1984).This is a result of the preferential excretion of the lighter isotope during protein synthesis (Kling et al. 1992) which enriches the 15 N of the consumer relative to its diet.Estimating trophic position based on d 15 N is complicated however by trophic and taxonomic differences in fractionation between resources and consumers (McCutchan et al. 2003), wide variability in d 15 N for basal resources across different ecosystems (Solomon et al. 2008) that requires the establishment of relevant basal baselines (Vander Zanden and Rasmussen 1999), and tissue specific fraction-ation (Hobson and Clark 1993).Despite these issues, d 15 N estimates of trophic position are widely considered the most rigorous method of determining trophic position.
In this paper, we present the results of a comparison of binary estimates of trophic position and trophic position estimates using d 15 N values for eight marine and estuarine ecosystems compiled from the primary literature.To determine whether flow-based (but non-isotope) links led to higher correlations with d 15 N estimates than binary estimates we compiled weighted estimates of trophic position from fishbase.orgfor four of the food webs for which flow-based location-specific data was available.

METHODS
We analyzed five marine food webs: North Eastern U.S. Shelf, Benguela Current, Adriatic Sea, Arctic sea-ice, and Antarctic sea-ice and three estuarine food webs: Chesapeake Bay, St. Marks Estuary, and Ythan Estuary.The eight webs were compiled from previously published sources (Baird and Ulanowicz 1989, Huxham et al. 1996, Yodzis 1998, Christian and Luczkovich 1999, Link 2002, Coll et al. 2008;Carscallen and Romanuk unpublished) and six have been used previously in structural analysis and tests of food web theory (Williams and Martinez 2000, Dunne et al. 2004, Coll et al. 2008, Vermaat et al. 2009).The food webs include between 29 and 239 species (Table 1).Additional details on the webs can be found in Vermaat et al. (2009), Coll et al. (2008), and Carscallen and Romanuk (unpublished).
We calculated four measures of trophic position (TP).Trophic position is a continuous measure of the relative trophic height of a species and is distinct from trophic level which describes categories of trophic modes based on integer values (e.g., herbivores have a trophic level of 2).For all eight webs we calculated two estimates of binary trophic position based on binary feeding matrices: prey-averaged trophic position (PA-TP) and short-weighted trophic position (SW-TP; Williams and Martinez 2004) and compiled d 15 N estimates of trophic position for as many species from the webs as we could find data for (see below for further details).For NE Shelf, Benguela Current, Arctic sea-ice, and Antarctic sea-ice we also calculated a non-isotope weighted measure of trophic position based on data from fishbase.org(see below for further details).
Prey-averaged TP is equal to 1 þ the mean TP of all the consumer's trophic resources: where n j is the number of prey species in the diet of species (Williams and Martinez 2004).Shortweighted trophic position was calculated as the average of the shortest TP for the species and prey-averaged TP (Williams and Martinez 2004).d 15 N values were used to determine an isotope measure of trophic position.To compile the isotope database we conducted an extensive literature review (see Supplement for values and sources).Either location-specific d 15 N values from the literature were used or, if none were available, values from nearby similar ecosystems.All previously published studies that report d 15 N for the species within the food web of interest were included.If more than one value was reported an average was used.The spatial extent of the food webs differed with some webs such Primary consumers were used as baseline organisms because their d 15 N is more representative of average trends in assimilated nitrogen from primary producers (Post 2002) due to larger body size and lifespan which contributes to decreased seasonal variability (Vander Zanden and Rasmussen 1999).In order to find the most accurate baseline value for d 15 N in an ecosystem, Vander Zanden and Rasmussen (1999) suggest using a wide range of organisms.To establish the primary consumer baseline we used every species with a SW-TP ¼ 2 in the binary matrices that we could find an accompanying d 15 N value for.The species/taxa used for d 15 N baselines are listed in the Supplement.
In order to further explore differences in baseline-corrected d 15 N and SW-TP estimates frequency distributions were analyzed across all species for each of eight webs as well as for four broad trophic groups: invertebrates, fish, birds and mammals across all eight webs (Figs. 1 and 2).
To determine whether a non-isotope but weighted estimate of trophic position using the TROPH algorithm from FishBase.orgprovided a better fit to d 15 N estimates than binary TP estimates we used four of the eight food webs for which location-specific trophic position information was available for fish on FishBase.org:Benguela, Arctic, Antarctic and NE Shelf.In FishBase, TROPH is calculated by adding one to the mean trophic position, weighted by relative abundance, of all food items consumed by a species (Froese and Pauly 2010).For a consumer species i, weighted trophic position (TROPH ) is defined as: where WTP j is the fractional trophic position of prey j, DC ij represents the fraction of j in the diet of i, and S is the total number of prey species.
Calculations of trophic position are based on diet information and food items in FishBase, which are assigned discrete trophic positions (Froese and Pauly 2010).Prey items include organisms that have been found in stomach contents or are otherwise known to be ingested by a given species.More than 800 citations have been used to support the diet information in FishBase, in addition to the verification of over 16,000 records.In FishBase, primary producers and detritus (including associated bacteria) are assigned a definitional trophic position of 1.

Statistical analysis
Pearson's correlation coefficients were used to assess the correlation between different estimates of trophic position.Dependent t-tests were used to determine whether there were significant differences between binary estimates of trophic position and baseline corrected d 15 N estimates (see above).Two sets of analyses were conducted.First, we assessed the correlation between binary and d 15 N estimates across all species and webs (n ¼ 366) as well as for each of the eight webs separately.Dependent t-tests were used to determine whether there were significant differv www.esajournals.orgences between binary and baseline corrected d 15 N estimates.For baseline corrected analyses d 15 N estimates were limited to consumer species with a TP . 2 as primary consumers (TP ¼ 2) were used as the baseline taxa to estimate d 15 N TP.Second, we compared estimates of TP calculated as TROPH, binary TP, and d 15 N for 127 fish species for four of the marine webs v www.esajournals.org(Shelf, Arctic, Antarctic, and Benguela).
Binary feeding matrices were also used to calculate food web properties that may have affected or confounded the relation between binary estimates of trophic position and d 15 N estimates of trophic position including: number of species (S), connectance (L/S 2 , number of links/ number of species 2 ), number of links per species (L/S), and fractions of top, intermediate, basal, and omnivore species (Table 2).To determine if differences in the fraction of species that we were able to find d 15 N values for might have accounted for differences in the strength of the correlations between binary and d 15 N TP, we determined whether there was a correlation between the fraction of species in the webs that d 15 N values were available for (i.e., completeness) and the correlation coefficients for the binary TP v. d 15 N relations for each web.To determine whether the strength of the correlation between different estimates were correlated with food web properties we assessed the correlation between the correlation coefficients of the binary TPd 15 N estimates and the number of species (S), number of links/species (L/S), connectance (C ¼ links/species 2 ), and fractions of top, intermediate, basal, and omnivore species.

RESULTS
The total number of species or nodes in the eight webs was 676.We were able to find d 15 N values for 366 or 54% of the species.We were able to find corresponding d 15 N values for more than 50% of the species in each web for all webs except for Ythan (S ¼ 45) and Antarctic for which only 35% and 45% of corresponding nitrogen isotope values were.Shelf was the most complete web, with corresponding d 15 N values for 74% of species (S ¼ 79; Table 1).Across all webs and species, the correlation for short-weighted TP and d 15 N was R ¼ 0.644 (p , 0.0001) and for prey-averaged TP and d 15 N was R ¼ 0.645 (p , 0.001, n ¼ 171; Fig. 3A, B).As there was no significant difference between the explained variability in d 15 N by short-weighed and preyaveraged trophic position and as short-weighted TP has previously been shown to more accurately reflect trophic position estimates based on gut content analysis (Williams and Martinez 2004) we used short-weighed trophic position as our

Comparison of binary and isotope analysis estimates of trophic position
The average correlation between binary TP and d 15 N across all eight webs was R ¼ 0.644 (Fig. 3A).Significant correlations between binary TP and d 15 N were observed in all webs ranging from R ¼ 0.594 in Chesapeake (p ¼ 0.007) to R ¼ 0.83 in Benguela (p , 0.0001, Fig. 4).
Mean binary TP differed from baseline corrected d 15 N TP by 2.33% across all webs and species with a TP .2, ranging from 0.1% in St. Marks to 18.11% in Benguela (Table 3; Appendix: Fig. A1).Mean binary TP differed significantly from baseline corrected d 15 N TP in Shelf (p , 0.0001), Benguela (p , 0.0001), and Antarctic (p , 0.0001; Appendix: Fig. A2).In the other five webs (Arctic, Adriatic, Ythan, St. Marks and Chesapeake) there was no significant difference between mean binary TP and mean baseline corrected d 15 N TP (p .0.05; Appendix: Fig. A2).Maximum binary TP differed from baseline corrected d 15 N TP by 5% on average, ranging from 0.58% in Ythan to 17.5% in Adriatic (Table 3).

Comparison of binary TP and baseline-corrected TP by taxonomic group
Across all webs no significant difference was observed for mean binary TP and baseline corrected d 15 N TP for invertebrates (p ¼ 0.161), mammals (p ¼ 0.782), or fish (p ¼ 0.055), however the latter was only marginally insignificant (fish binary TP ¼ 3.53, baseline corrected d 15 N TP ¼ 3.43).In contrast, mean binary trophic position was significantly greater for birds than the d 15 N estimate (binary TP ¼ 3.71, baseline corrected d 15 N TP ¼ 3.25; p ¼ 0.002).
Maximum binary TP was also higher for birds (maximum binary TP ¼ 4.7, baseline corrected maximum d 15 N TP ¼ 4.35) whereas for invertebrates and fish, maximum baseline corrected d 15 N was slightly higher than maximum binary TP (fish maximum binary TP ¼ 4.57, baseline corrected d 15 N TP ¼ 4.89; invertebrates maximum binary TP ¼ 4.01, baseline corrected d 15 N TP ¼ 4.14).The difference between maximum binary TP and baseline corrected d 15 N TP was particularly strong for mammals with maximum binary TP lower by more than a full trophic level than the baseline corrected estimate (maximum binary TP ¼ 4.74, baseline corrected d 15 N TP ¼ 5.86).
Analysis of the variance, skewness, and kurtosis of frequency distributions for the four taxonomic groups also showed a number of trends.Across all four groups variance in TP was higher for baseline corrected d 15 N TP and distributions were more peaked for binary TP (Fig. 4).Relative to baseline corrected d 15 N TP, binary TP was more positively skewed for birds and invertebrates and more negatively skewed for fish and mammals.These results suggest that while there are some taxonomic differences in the distributions of binary TP and d 15 N TP related to skewness, on average binary TP leads to lower estimates of maximum TP than d 15 N TP, and has a more truncated range, and a flatter distribution than baseline corrected d 15 N TP.

Comparing trophic position estimates for fish
For the 127 fish species that we were able to compile TROPH (weighted estimates of TP based on gut contents) values for the correlation between binary TP and d 15 N was R ¼ 0.259 (p ¼ 0.003; Appendix: Fig. A3A).A similar correlation was seen between TROPH and d 15 N with an R ¼

Effects of sampling effort and food web properties
The fraction of species in each web for which d 15 N values were reported in the literature differed across webs (Table 1).For example, for Shelf we were able to match 74% of the species in the binary web to d 15 N values from the literature, while for Ythan we were only able to match 35% of the species in the binary web with corresponding d 15 N values from the literature.To determine if differences in the fraction of species that we were able to find d 15 N values for might have accounted for differences in the strength of the relations between binary and d 15 N we determined the correlation between the fraction of species in the webs that d 15 N values were reported for with the correlation coefficients for the binary TP vs. d 15 N relations for each web.Completeness, in terms of the proportion of species in the webs that d 15 N values were available for was unrelated to the correlation between binary and d 15 N estimates of TP (p ¼ 0.805).
To determine whether aspects of the structure of the food webs affected relations between binary TP and d 15 N we compared the correlation coefficients of the binary TP vs. d 15 N relation with a number of key food web properties including species richness, number of links per species, connectance (links/species 2 ), and fractions of top, intermediate, basal species, and omnivores.Because we had only eight webs we would have needed an R value of 0.706 for a relation to be significant at p , 0.05.None of the food web properties analyzed were significantly correlated with the strength of the binary TP versus d 15 N relation.The two highest correlations were for fraction of basal species (R ¼ À0.576, p ¼ 0.13) and connectance (R ¼ 0.58, p ¼ 0.13).

DISCUSSION
Since Odum and Herald (1975) expanded the trophic level concept of Elton (1927) and Lindeman (1942) from a qualitative to a quantitative metric, the use of trophic position as a key descriptor of the functional role of species and the state of ecosystems has become firmly established (Pauly and Watson 2005).With the recent adoption of trophic position as a marine resource indictor to assess the state and sustainability of fisheries resources (Pauly and Watson 2005), its importance and use as a relevant metric of ecosystem degradation will only increase.While in some cases the value is relatively important, such as for the reduction in mean trophic position of landings over time (Pauly and Watson 2005), the accuracy of trophic position estimates remains highly contentious and is deeply intertwined with the utility of structural approaches to food web descriptions.
Although few studies have attempted to track changes in food web properties other than trophic position to quantify ecosystem degradation (but see Coll et al. 2008), a food web approach may be one of the more powerful ecological methods to describe how ecosystem structure changes as disturbance increases, and thus in predicting the consequences of disturbance to the functioning of ecosystems.A major impediment in using changes in food web The ability of structural approaches to accurately depict feeding interactions as opposed to flow-based methods such as gut content and v www.esajournals.orgstable isotope analysis has been a contentious issue in food web ecology for decades.Previous comparative analysis have shown that using the short-weighted trophic position algorithm, which uses prey-averaged trophic position and the shortest trophic position to calculate effective trophic position, binary links come within a quarter of a trophic level to quantitative values predicted from gut content analysis (Williams and Martinez 2004).Due to the inherent problems with gut content analysis, such as limited spatial and temporal extent and inclusion of nonassimilated material in diet data (Vander Zanden et al. 1999), it has been suggested that a more robust test of the ability of structural approaches should involve cross-validation of binary estimates of trophic position with stable isotope estimates based on nitrogen (Williams and Martinez 2004).
Our analysis of 366 species in eight marine and estuarine webs shows that trophic position estimates using binary (presence-absence) is strongly correlated with d 15 N estimates.Across all species and webs the correlation between binary and d 15 N was R ¼ 0.644 ranging from 0.594 to 0.83 for the different webs (Fig. 4).Binary estimates of mean trophic position differed by only 2.33% and maximum trophic position differed by only 6.57% from estimates based on baseline corrected d 15 N (Table 3).This high concordance between binary and d 15 N estimates clearly shows that a structural approach to constructing food webs can be highly effective in estimating trophic position.Our results also show that using binary links to construct a food web can be more accurate when compared to isotope estimates of trophic position using d 15 N than flow-based estimates based on gut content analysis.Our comparisons between different flow-based methods (i.e., TROPH versus d 15 N) and binary methods for 127 species of fish showed that binary estimates were either equivalent to flow-based estimates, which utilize gut content analysis to estimate trophic position, or performed better than TROPH estimates.Below we discuss the use of stable isotopes and gut content analysis in food web assembly in more detail, as well as the variation around the above averages for the eight different food webs.

Issues with using nitrogen isotopes to estimate trophic position
The use of stable isotope analysis to track energy flow between consumers and their resources has been an important technical advancement in determining the trophic ecology of species (Post 2002).Early studies on fractionation of nitrogen across trophic levels suggested an average enrichment of 3.4% with each trophic level (DeNiro andEpstein 1981, Minagawa andWada 1984).This value of 3.4% became somewhat of a sacred cow in isotope ecology as it could be used to infer the trophic position of consumers and their prey.While a 3.4% increase in d 15 N is still considered as a standard, more recent analyses have shown extensive variability in the average fractionation between resources and consumers.For example, McCutchan et al. (2003) analyzed trophic fractionation across a wide range of organisms and found that consumers with a high-protein diet were more enriched relative to their resources than consumers that were herbivorous or consumers that fed primarily on invertebrates, with an average enrichment of 2.0% 6 0.2 SE.Thus, in contrast to the global value of 3.4% with each increase in trophic level (DeNiro andEpstein 1981, Minagawa andWada 1984), the actual magnitude of enrichment depends strongly on the feeding habits of the consumer, with strict carnivores having a higher d 15 N relative to omnivores, which in turn show greater enrichment than herbivores (Kling et al. 1992).While this more detailed understanding of trophic fractionation has increased the accuracy of prediction of trophic position based on stable isotope values of nitrogen, it has also presented ecologists who use this method with a problem, as it is not possible to accurately predict the trophic position of all species in a community using 3.4% as a standard fractionation value.
The accuracy of using fractionation of d 15 N to estimate trophic position is further complicated by the wide variability that occurs in d 15 N in primary producers even in highly similar and spatially adjacent habitats (Solomon et al. 2008).Differences in the d 15 N of primary producers occurs as physical and chemical processes produce measurable differences in the stable isotope ratios of different classes of plants as they are assimilated into the tissues of higher-order consumers (Keegan andDeNiro 1988, Vander Zanden andRasmussen 1999).The consequence of this is that d 15 N values only represent a valid estimate of trophic position when compared to other species in the same system whose feeding pathway leads to the same basal compartments (i.e., phytoplankton versus aquatic plants).Thus, to use d 15 N values as estimates of trophic position it is necessary to establish an accurate baseline.Primary consumers (trophic position ¼ 2) are most often used as they do not differ as much spatially and temporally as primary producers (Vander Zanden and Rasmussen 1999).The algorithm, however, which is used to estimate trophic position, is still based on a 3.4% fractionation increase with each trophic level, thus introducing an additional source of methodological error into the estimate of trophic position even when an accurate baseline has been established.The use of isotope methods to estimate trophic position itself are also subject to potential errors due to methodological issues including differences in tissue specific fractionation (Hobson andClark 1993, Buchheister andLatour 2010) and effects of sample storage and preparation (Arrington andWinemiller 2002, Schmidt et al. 2009).

Comparing binary and d 15 N estimates of trophic position
Given the above cautions regarding the interpretation of d 15 N estimates of trophic position, stable isotope analysis of nitrogen is still widely considered to be the most accurate method of estimating trophic position, particularly in experimental settings.The assembly of structural food webs is fraught with many of the same potential errors as flow-based methods based on isotopes including the decisions involved in determining spatial and temporal extent, node resolution, and the inclusion or exclusion of detail for changes in diet sources during ontogeny, among others.Despite these caveats, our analysis shows that structural approaches are not only highly accurate in estimating trophic position based on d 15 N but also that the deviations in predicted trophic position are relatively minor given differences between webs in spatial and temporal extent and resolution.
Differences in binary versus d 15 N estimates averaged 2.33% for mean trophic position and 6.57% for maximum trophic position across all 366 species and ranged from 0.1% to 18.11% for mean trophic position and from 2.49% to 15.9% for maximum trophic position across webs (Table 3).On average the difference between binary and d 15 N estimates was 0.14 of trophic level.This difference is smaller than the mean difference of 0.25 of a trophic level in an earlier comparison of binary and flow-based estimates based on gut content analysis (Williams and Martinez 2004) suggesting that the earlier analysis underestimated the accuracy of binary measures of trophic position.
The correlation between binary and d 15 N estimates was highest in Benguela with an R ¼ 0.83 and was lowest in Chesapeake with an R ¼ 0.594 (Fig. 4).It is important to note that we found no significant relations between any of the food web properties and the strength of the correlation between binary and d 15 N estimates.However, given that we only used eight webs in these analyses, the lack of any significant correlation with food web properties should be approached with caution.
It was initially expected that the correlation between binary and d 15 N estimates would be lowest in estuarine webs due to multiple source pathways of primary producers that differed strongly in d 15 N (e.g., aquatic plants, phytoplankton, macroalgae).There was no consistent effect of broad habitat types such as marine versus estuarine on the strength of the relation.Additional studies spanning more habitat types are necessary to determine whether structural approaches show higher correlations with isotope estimates in different habitat types and whether multiple source pathways such as exist in estuaries might result less concordant results between different estimates of trophic position.Only minor differences were observed for binary TP and baseline corrected d 15 N TP among invertebrates, fish, birds, and mammals.In general, binary TP under-predicts maximum TP relative to d 15 N TP, has a more truncated range, and a flatter distribution than baseline corrected d 15 N TP.Under-prediction of maximum trophic position was observed for fish, mammals, and invertebrates while binary TP over-predicted maximum trophic position for birds relative to baseline corrected d 15 N TP.This under-prediction is due in part to the shortweighted trophic level algorithm which calculates TP as the average of the shortest TP for the species v www.esajournals.organd prey-averaged TP, which tends to have a bias towards shorter chain lengths, thus reducing the probability of species being given a higher trophic position estimate (Williams and Martinez 2004).Under-prediction of maximum values may also be due to the lack of inclusion of species in webs that have relatively high trophic positions but are lumped together into trophic groups that on average have lower trophic positions.For example, predatory invertebrates such as jellyfish are listed in many marine food webs as trophic level¼ 2 (e.g., Adriatic food web).Likewise, the exclusion of parasites from binary food webs, particularly for highly parasitized species such as fish would lower the trophic position of fish predators.It is likely that the reduction in the range of binary TP values relative to baseline corrected values is also partially due to the lack of high resolution of invertebrates.Binary TP values also showed more peakedness than baseline corrected values, indicating a bias toward average values.
The primary taxonomic difference observed was for skewness, with binary TP estimates being more positively skewed for birds and invertebrates and more negatively skewed for fish and mammals, relative to baseline corrected d 15 N TP.These differences in skewness could be due to a number of methodological issues.First, d 15 N for birds and invertebrates likely captures a greater range of food resources than binary links.In particular heterotrophic bacteria are generally not included in binary food webs and when they are, they are often treated as a autotrophic basal node.Similarly, birds often prey on parasites, and the exclusion of parasites from binary webs likely lowers the trophic position estimates for birds.For fish and mammals in contrast binary TP was more negatively skewed relative to baseline corrected d 15 N TP.As organisms typically receive more energy from lower trophic levels than higher trophic levels, binary TP may over-predict trophic position, particularly for omnivores.
Perhaps the most fundamental issue concerning feeding and d 15 N estimates of TP is the definition of a feeding interaction and the distinction between the effect of the consumer on its resources and the effect of the resources on the consumer.For example, the former may have little to do with what the consumer assimilates.The resource mortality, inflicted by the consumer, is most directly related to the biomass or number of individuals lost in the act of feeding.However, how much the consumer grows or reproduces due to feeding is more directly related to how much of the resource species is assimilated.While this distinction may only alter TP estimates a small fraction of a level in most cases analyzed here, other cases may lead to a discrepancy of more than a full trophic level, with ruminants being the clearest example.While ruminants typically consume plant matter, the rich and multi-trophic position microbial gut flora that feeds directly and indirectly on the moist and masticated vegetation forms a substantial and protein enriched fraction of the ruminant's diet (Callewaert and Michiels 2010).Similarly, when a decomposer consumes dead plant matter, the communities of bacteria and fungi growing on that plant matter can also form a substantial diet fraction (Callewaert and Michiels 2010).While we only touch on these issues here, future work may do well to reconsider the definition of feeding and distinguish consumption TP from assimilation TP rather than conflating them as is standard in discussions and analyses of TP.

Comparisons between gut content, binary, and d 15 N estimates of trophic position
In contrast to the lack of cross-validation studies focusing on structural versus d 15 N estimates of trophic position, a number of studies have attempted to cross-validate flow-based estimates based on gut content analysis with isotope estimates of trophic position.Vander Zanden et al. (1997) found an r 2 ¼ 0.78 between gut content and d 15 N estimates for eight pelagic fish species in 36 lakes in Ontario and Quebec, and Nilsen et al. (2008) reported an r 2 ¼ 0.72 for 65 taxa in Sorfjord, a high-latitude fjord.Correlations between flow-based and isotope-based estimates of trophic position are not, however, always as high or as consistent as is in the above studies.For example, in salt marsh ponds, Dame and Christian (2008) reported differences in mean trophic positions ranging from 0.12 to 0.53 for four different ponds with one of the four ponds showing no significant relation between flowbased and isotope estimates despite the same model specification.In stream fish, Ribczynski et al. (2008) reported high concordance between gut content and d 15 N estimates for omnivorous fish but large differences between gut content (TP range ¼ 3.5-3.7)and d 15 N estimates (TP range ¼ 2.5-4.1) for predatory fish.Likewise, Franssen and Gido (2006) found only weak relations between gut content and d 15 N estimates for stream fish in Kansas and no significant differences in d 15 N estimates across algivore/detritivore, omnivore, and insectivore functional groups.
Estimates of trophic position in FishBase using the TROPH routine have been previously shown to correlate closely with estimates based on stable isotope ratios (Kline and Pauly 1998).For example, Kline and Pauly (1998) showed an R ¼ 0.986 for flow-based and d 15 N estimates for seven functional groups in Prince William Sound, Alaska.We were able to cross-validate estimates of trophic position using TROPH, binary TP, and d 15 N estimates for 127 fish in the Benguela (n ¼ 9), Shelf (n ¼ 26), Arctic (n ¼ 44) and Antarctic (n ¼ 48).In our direct comparisons of gut content, binary, and d 15 N estimates, binary estimates showed similar concordance with d 15 N estimates as gut content based estimates (Appendix: Fig. A3A, B).In the Benguela and Arctic webs, the correlation between binary TP and d 15 N was significant while the correlation between TROPH and d 15 N TP was not (Fig. 5A, B).Thus, in contrast to the generally accepted view that flowbased methods such as gut content analysis should be more accurate at predicting d 15 N estimates of trophic position than binary approaches, our results actually suggest the opposite may be correct in some cases.
There are a number of possible explanations for the greater concordance of binary and d 15 N estimates than between gut content and d 15 N estimates.In one of the most comprehensive explorations of seasonal effects on trophic level in fishes, Karachle and Stergiou (2008) have shown that trophic level of 59 fishes differed by 0.45 6 0.04 SE of a trophic level on average seasonally ranging from no change to a change of 1.48.The fraction of species that changed more than one functional trophic group seasonally ranged from 27.3 to 38.9% depending on the number of seasons included in the analysis, and 8.5% of the species changed by more than one functional group.The seasonal changes in trophic position due to seasonal diet variability observed by Karachle and Stergiou (2008) were greater than the differences in trophic position we observed between binary and d 15 N estimates, suggesting that snapshot gut content analysis can significantly bias estimates of trophic position.Thus, while it seems counterintuitive, flow-based methods such as gut content analysis may actually be more inaccurate due to restricted temporal and spatial sampling as well as errors in species identification and counting than binary methods which typically focus on assembling spatially and temporally averaged meta-webs for ecosystems (Dunne 2006).

CONCLUSION
More stable isotope data is needed to determine how broadly our results can be extrapolated.There was often less data available for primary producers and invertebrates than for vertebrates, thus having representative samples across taxonomic and functional groups is needed to determine whether there are differences in the ability of binary estimates to predict d 15 N estimates across specific taxonomic and functional groups.The availability of isotope data for marine and estuarine species was also much greater than for freshwater or terrestrial species, which is why we limited our analysis to marine and estuarine webs.Despite these caveats, our analysis represents a robust comparison of binary, other flow-based, and isotope estimates of trophic position for marine and estuarine ecosystems.Our results clearly show that binary estimates of trophic position show high concordance to isotope based methods and most surprisingly are more accurate than flow-based method such as gut content analysis.

Fig. 1 .
Fig. 1.Frequency distributions of binary (SW-TP) and baseline corrected trophic position estimates for all eight webs: St. Marks estuary, Ythan estuary, NE shelf, Benguela current, Adriatic sea, Chesapeake bay, Arctic sea-ice, and Antarctic sea-ice.Normal distribution curves are represented by the solid black line (binary estimates) and dotted line (baseline corrected).

Fig. 2 .
Fig. 2. Frequency distributions of binary (SW-TP) and baseline corrected trophic position estimates of four broad taxanomic groups, including mammals, birds, fish, and invertebrates, across all eight webs.Normal distribution curves are represented by the solid black line (binary estimates) and dotted line (baseline corrected).
0.285 (p ¼ 0.001; Appendix: Fig. A3B).Binary TP and TROPH were correlated with an R ¼ 0.462 (p , 0.0001; Appendix: Fig A3C).Arctic and Benguela were the only webs to show a significant correlation between binary TP and d 15 N (p ¼ 0.024, p ¼ 0.022, Fig. 5A).No significant correlation was observed between TROPH and d 15 N estimates for any of the webs.Correlations

Fig. 3 .
Fig. 3. d 15 N values versus binary trophic position estimates based on (A) short-weighted trophic position (SW-TP) and (B) prey-averaged trophic position (PA-TP) for across all webs and species (n ¼ 366) in eight marine and estuarine food webs.Shown are the CI (60.95) and line of best fit (black).

Fig. 4 .
Fig. 4. d 15 N values versus binary trophic position estimates (based on the short-weighted trophic level algorithm) for all eight webs: St. Marks estuary, Ythan estuary, NE shelf, Benguela current, Adriatic sea, Chesapeake bay, Arctic sea-ice, and Antarctic sea-ice.Shown are the CI (60.95) and line of best fit (black).

Fig. 5 .
Fig. 5. Comparison of flow-based and binary estimates of trophic position.(A) d 15 N values versus binary trophic position (SW-TP) estimates for 127 species of fish in Shelf, Benguela, Arctic and Antarctic.(B) d 15 N values versus TROPH estimates from FishBase.org.c) relation between TROPH and binary trophic position estimates (SW-TP).Shown are the CI (60.95) and line of best fit (black).Fine black dotted line represents a perfect correspondance between SW-TP and TROPH estimates of trophic position.Data points above the line have a higher TROPH estimate of trophic position in comparison to SW-TP, whereas species below the line have a higher SW-TP estimate of trophic position in comparison to TROPH.
Fig. A2.Comparison of baseline corrected (BC-TP) and binary estimates (SW-TP) of trophic position for individual webs: St. Marks estuary, Ythan estuary, NE shelf, Benguela current, Adriatic sea, Chesapeake bay, Arctic sea-ice, and Antarctic sea-ice.Shown are the CI (60.95) and line of best fit (black).

Fig. A3 .
Fig. A3.Separate comparisons of flow-based and binary estimates of trophic position for each of the four webs used in the analyses.(A) d 15 N values versus binary trophic position (SW-TP), (B) d 15 N values versus TROPH estimates from FishBase.org,(C) relation between TROPH and binary trophic position estimates (SW-TP).Shown are the CI (60.95) and line of best fit (black).

Table 1 .
Summary of characteristics of each of the eight marine and estuarine webs: name of web, reference, habitat (marine or estuarine), number of species/taxa in the web, number of location specific d 15 N values, completeness (fraction of species/taxa for which d 15 N values were available, R, and p-value.

Table 2 .
Food web properties calculated based on binary feeding links for each web showing number of links/ species (L/S), connectance (link/species 2 ), and the fraction that is top, intermediate, basal, and omnivores.

Table 3 .
Differences in trophic position based on d 15 N values and binary trophic position (SW-TP) estimates across all webs and species with TP . 2 and for each of the eight marine and estuarine webs.Shown are means, maximum, SDs, and percentage difference.