Tutorial example upright=1.5|Tutorial illustration of isotope dilution analysis with fish counting in lakes Isotope dilution can be effectively explained using mark and recapture method from biology - a method commonly used in ecology to estimate the population sizeof fish . Isotope dilution can be likened to Lincoln-Petersen method. Assume that the number of fish in a pond is to be determined. Five labeled fish are added to the pond during the first visit (nB = 5). On the second visit,  a number of fish is captured and one observes that the ratio of native-to-labeled is 10:1. From here, we can estimate the original number of fish in the pond, nA : This is a simplified view of isotope dilution yet it illustrates the salient features of isotope dilution . A more complex situation arises when the distinction between labeled and unlabeled fish becomes fuzzy. This can occur, for example, when the lake already contains a small number of labeled fish from the previous field experiments . In such situation, the following expression can be employed: where  RA is the ratio of the native-to-labeled fish in the lake , RB is the ratio of the native-to-labeled fish in the lot of nB marked fish which are added to the pond, and RAB is the ratio of the native-to-labeled fish captured during the second visit.
Tutorial example upright=1.5|Tutorial illustration of isotope dilution analysis with fish counting in lakes Isotope dilution is analogous to the mark and recapture method , commonly used in ecology to estimate population size . For instance, consider the determination of the number of fish (nA) in a lake. For the purpose of this example, assume all fish native to the lake are blue. On their first visit to the lake, an ecologist adds five yellow fish (nB = 5). On their second visit, the ecologist captures a number of fish according to a sampling plan and observes that the ratio of blue-to-yellow (i.e. native-to-marked) fish is 10:1. The number of fish native to the lake can be calculated using the following equation : This is a simplified view of isotope dilution but it illustrates the method's salient features . A more complex situation arises when the distinction between marked and unmarked fish becomes fuzzy. This can occur, for example, when the lake already contains a small number of marked fish from previous field experiments ; and vice versa, where the amount of marked fish added contains a small number of unmarked fish. In a laboratory setting, an unknown (the "lake") may contain a quantity of a compound that is naturally present in dominant ("blue") and lesser ("yellow") isotopic forms. A standard that is enriched with the lesser isotopic form may then be added to the unknown, which can be subsequently analyzed. Keeping to the fish analogy, the following expression can be employed: where , as indicated above, nA and nB represent the number of fish in the lake and the number of fish added to the lake, respectively; RA is the ratio of the native-to-marked fish in the lake prior to the addition of marked fish; RB is the ratio of the native-to-marked fish in the amount of marked fish added to the lake; finally, RAB is the ratio of the native-to-marked fish captured during the second visit.
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