1. Fig. 4.1. The changes in a chocolate mixture that is available for eating over the course of a year. Each day, a consumer eats 1000 chocolates total, with an equal preference for light and dark chocolates. This preference matches the supply dynamic that also replaces 1000 chocolates each day, 500 lights and 500 darks. In this case, daily additions resupply the eaten chocolate so that the amount of chocolate remains constant. However, the mix gradually changes composition from only light chocolates present initially to an equal mix of light and dark chocolates by the end of the year.

2. Fig. 4.2. As Fig. 4.1, but with a change in the preferences for chocolate eaten. Here the consumer prefers light chocolates twice as much as dark chocolates, leaving more dark chocolates to accumulate by the end of the year.

3. Fig. 4.3. Oxygen dynamics in seawater during a four-day period. Black bars indicate night-time conditions when oxygen concentrations decline due to respiration and the absence of photosynthesis. In the daytime, algal photosynthesis increases oxygen concentrations faster than respiration removes oxygen, leading to increasing oxygen concentrations. Isotope compositions of oxygen increase at night due to strong fractionation during respiration, removing light oxygen and leaving heavier oxygen behind with higher   . In the daytime, photosynthesis adds back oxygen with low    = 0o/oo, so that    declines.

4. Fig. 4.4. Oxygen dynamics, continued. As Fig. 4.3, but there is stronger photosynthesis during a daytime algal bloom. Daytime oxygen isotope values decline when photosynthetic oxygen with    = 0o/oo is added.

5. Fig. 4.5. As Fig. 4.3, but oxygen dynamics in deeper waters have balanced photosynthesis and respiration during the day. Strong respiration demands at night lead to progressively lower oxygen concentrations and higher and higher    values.

6. Fig. 4.6. As Fig. 4.5, but for water near the sediment surface.    values decline during the day when photosynthetic oxygen with    = 0o/oo is added, but at night, respiration occurs without fractionation in sediments, so that    values do not change.

7. Fig. 4.7. Isotope dynamics in open systems where reactions are split or branched. In this example, a fractionation factor of  = 30o/oo always gives the difference between substrate and product  values, as discussed in the text.

8. Fig. 4.8. A simple model of oxygen dynamics in the sea. Photosynthesis adds oxygen to a central pool while respiration removes oxygen from the pool. The oxygen gains and losses are coupled in that they occur during each time step in the I Chi spreadsheet models.

9. Fig. 4.9. A generic box model with explicit representation of processes involved in input gains and output losses. The gain and loss steps are coupled in that they occur during each time interval in the I Chi spreadsheet models.

10. Fig. 4.10. Fractionation in an open system, with exact equations for fractionation in residual substrate (top line) and product (bottom line). R is the isotope ratio and  is the fractionation factor for the reaction, as defined in the text.

11. Fig. 4.11. Model results for a cow growing 400 days in a pasture, gaining 80g N each day while also losing 30g N to various forms of excretion. The net growth is 50g N each day, leading to a constant increase in cow N each day. During this growth, cow isotope values change from initial values to reflect the new pasture diet at 0o/oo. Final isotope values in the cow reflect a balance between dietary isotope values that pull values towards the 0o/oo diet values and fractionation during excretion losses that pushes isotope values of the cow up and away from the dietary values. Cow values approach the 0o/oo value of the mixed pasture diet by the end of 400 days, but are still offset 3.4o/oo higher than the diet due to fractionation operating during loss. The fractionation factor for total losses is set at  = 9o/oo in these and the remaining examples of this chapter, except for the following Fig. 4.12.

12. Fig. 4.12. As Fig. 4.11, but fractionation during loss has been changed from  = 9o/oo to  = 0o/oo (no fractionation). In this case, only diet influences isotopic compositions, and cow isotopes conform to the simple maxim, “you are what you eat”, i.e., the cow has the same isotopes as the diet.

13. Fig. 4.13. As Fig. 4.11, but the cow is growing more rapidly and losing less N every day, gaining 100g N and losing only 10g N each day. With this strong growth, cow isotopes still reflect mostly diet, even though fractionation during loss has been switched back on vs. Fig. 4.12, from 0o/oo to 9o/oo. Because there is little net loss, only 1 N atom lost per 10 N atoms gained, fractionation that occurs during loss still is not very important. The result is that cow isotopes are still close to diet isotopes.

14. Fig. 4.14. As Fig. 4.11, but now the cow is gaining and losing N at the same rate, so that there is no net growth. In this case, the 9o/oo fractionation during loss reactions plays an important role in pushing cow isotopes away from the diet isotopes. The maxim “you are what you eat” no longer applies simply, and clearly needs amendment to something like this: “you are what you eat less excrete”. Cow isotopes are 9o/oo higher than those of the diet due to the excretion losses.

15. Fig. 4.15. As Fig. 4.11, but now the cow is starving and not gaining any N, only losing N. Fractionation during loss is unchecked by new dietary inputs, and fractionation leads to higher and higher values as the cow loses more and more N.

16. Fig. 4.16. As Fig. 4.15 for the first 400 days for a starving cow, but then the cow is moved to a new clover pasture where it starts to grow again at the rate assumed in Fig. 4.11, i.e., 80g N gained from the diet and 30g N lost each day. The cow values approach the new - 2o/oo value of the clover diet by the end of 800 days, but are still offset 3.4o/oo higher than this new diet due to isotope fractionation during excretion.