### The IFU Biomass Measurement: The Base Unit of the Fishsheet

For those wondering what biomass is and how the Fishsheets calculate biomass.

Biomass, for the purposes of HMF, is the quantity or mass of a biological entity that produces a biological effect. In other words, biomass is a calculation that tries to assess the proportional impact of an animal or plant using or approximating one or more of its physical properties. Nearly all stocking guidelines address biomass, but they differ from the Fishsheets in how they measure biomass. Most common stocking rules measure biomass using length; most rules assume that the biological impact of a fish is proportional to its length. Using length alone means that a fish that is twice as long as another fish will have twice the biomass of the other fish, but this is not necessarily true. Consider the following diagram:

If two fish have the same body proportions, then their difference in biomass will be more accurately assessed by taking all of their basic dimensions into consideration. Consequently, a fish that is two times longer than its counterpart will also be two times wider and two times higher, a net effect of having eight times more biomass. To account for this multi-dimensional view of biomass, the Fishsheets originally cubed the length of each fish that was entered into them and compared that displacement to a standard displacement. The basic formula looked something like the following:

Biomass = A*A*A = A^3 Where A is the adult length of the fish in question.

These new units were called IFUs (Ideal Fish Units) and could account for a much greater range of fish sizes than other stocking rules in that they required no transition to switch between large and small fish. Some of the common stocking rules have different sections based on the length of the fish. These sections require the aquarist to use different computations depending on the length of the fish. IFUs, contrarily, require no such adjustment as the proportionality difference is implicitly accounted for.

Nonetheless, the above cubic relationship proved inaccurate for very small fish and very large fish. Why? The impact of a fish on its environment depends on more than just a dimensional comparision. Other factors include the unique proportions of each fish and on the oxygen needs of each fish. Account for each species' unique habits requires the use of a family-specific coefficient (f), but accounting for oxygen use requires a little bit of abstraction:

Volumetric Biomass = f*A*A*A = f*A^3
Surface Area Available for Oxygen Absorbtion = F*A*A = F*A^2

Surface Area per Volume = F*A^2/(f*A^3) = (F/f)*(1/A)
Surface Area per Volume Applied to Volumetric Biomass = (F/f)*(1/A)*f*A^3 = F*A^2

Comparing the the two means of measuring biomass it becomes evident why the old IFU calculation did not work well for very small fish or very large fish: Compared to the new formula, the old formula was way too small for little fish and much too large for bigger fish. Now the Fishsheets use the more moderate F*A^2 calculation. This new hypothesis that compares oxygen requirements is called the SAVI adjustment (Surface Area and Volume Integration).

Nonetheless, there is a question that does occassionally come up: What about the metabolism of young fish? For instance, a young Silver Dollar and a full-grown  Black Skirt Tetra are similar in size, shape, and habits, but does their similarities in size and species negate that one is much younger than the other? No, the Silver Dollar will have a greater biological impact because its metabolism will be higher. It is still growing and will require more food, oxygen, and space than its aged cousin. Most of the new fishsheets do address the current size of the fish but may use a variety of equations to do so.

Currently, the Fishsheets use species-specific biomass measures that are as follows (adjustments are made for male/female, etc):