We compiled age estimates and baleen plate δ13C data from 86 bowhead whales ( Balaena mysticetus L., 1758). We used previous whale age estimates based on aspartic acid racemization (AAR) and corpora counts to extend the use of δ13C data for age determination from cycle counting to a modified exponential model using annual baleen growth increments. Our approach used the growth increment data from individual whales in a nonlinear mixed effects model to assess both population-level and whale-specific growth parameters. Although age estimates from baleen-based models become less precise as the whales age, and baleen growth and length near steady state, the growth increment model shows promise in estimating ages of bowhead whales 10–13.5 m long with baleen lengths <250 cm, where other techniques are less precise or the data are scarce. Ages estimated using the growth increment data from such whales ranged from 6.4 to 19.8 years.

We used baleen lengths and age estimates from 175 whales and body lengths and age estimates from 205 whales to test which of several single- and multi-stage growth models best characterized age-specific baleen and body lengths for bowhead whales ( Balaena mysticetus L., 1758) with the goal of determining which would be best for predicting whale age based on baleen or body length. Previous age estimates were compiled from several techniques, each of which is valid over a relatively limited set of physical characteristics. The best fitting single-stage growth model was a variation of the von Bertalanffy growth model for both baleen and body length data. Based on Bayesian information criterion, the two- and three-stage versions of the von Bertalanffy model fit the data better than did the single-stage models for both baleen and body length. The best baleen length models can be used to estimate expected ages for bowhead whales with up to 300–325 cm baleen, depending on sex, which correspond to age estimates approaching 60 years. The best body length models can be used to estimate expected ages for male bowhead whales up to 14 m, and female bowheads up to 15.5 m or ages up to approximately 40 years.

Summary1. Biogeochemical tracers such as stable isotopes are often used to determine sources and pathways of organic matter through food webs, which may provide powerful indicators of environmental stress or insight into resource management issues. However, mixing models using such tracers are algebraically constrained and rarely attempted for more than two sources. This makes them of limited value for ecosystems that have numerous contributing sources. 2. We developed two complementary mixing models, SOURCE and STEP, which use linear programming techniques with multiple tracers, to estimate the dominant primary producer sources of consumers, and their diets and trophic levels, regardless of the number of sources and trophic steps. 3. SOURCE is used to estimate consumers' direct and indirect uptake of autotrophic sources and their trophic levels. STEP calculates an estimate of a consumer's diet, which may include autotrophs and/or heterotrophs. 4. The two models were tested using simulated data sets of producer and consumer tracer values and then used with published δ 13 C, δ 15 N and δ 34 S data from a study tracing organic matter flows in a saltmarsh estuary. 5. SOURCE and STEP accurately estimated flows and trophic structures in the simulations, with average errors of 0·07 -0·09 for SOURCE and 0·03 -0·05 for STEP, depending on the number of tracers used. 6. We illustrate two resultant food webs for the saltmarsh estuary showing possible interpretations of the SOURCE and STEP estimates. 7. Synthesis and applications . SOURCE and STEP can be used with stable isotope data to estimate accurately consumers' trophic levels, primary producer dependence and diets, even when the number of potential autotrophic sources or foods is larger than the number of tracers. SOURCE and STEP could be used to assess the roles played by individual species within food webs, to compare food webs across locations or over time, and to examine potential pollutant bioaccumulation in higher order consumers, among other potential applications. The  - code for both models is available at http:// staff.washington.edu/lubetkin.

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