If you have time at this stage in the project (or to do later if you are rushed now), I have a new graph option to suggest or request: plot body composition data in this way:
Y variables:
- protein mass (= proportion protein * body mass),
- ash mass (= proportion ash * body mass), and
- lipid mass (= proportion lipid * body mass)
versus
X variable: water mass (= proportion water * body mass).
Both X and Y axes should be log10.
Why?
This type of graph will help people understand (1) the strong patterns in body composition, and (2) the related differences in energy density among sizes and species of fish.
Explanation:
Plotting the components as log(mass) versus log(water mass) should produce very clear patterns, nearly straight lines, with minimal variation.
(There will be some differences between species, especially for ash. Salmonids tend to have low levels of ash. Centrarchids and Percids tend to have higher levels of ash.)
Why water mass as the X variable?
The explanation for the strong pattern is that the composition of the lipid-free mass is tightly regulated, and nearly constant for fish of a given size. The amount of water per gram of protein is tightly regulated (to keep the enzymes working correctly). The ratio changes slightly with fish size. Same for ash. The amount of storage lipid can vary widely for fish of a given lipid-free mass, as would be expected for a storage compartment that can range from full to nearly empty.
Why log-log plots?
There is a notable allometric effect influencing body composition that is apparent on the log scale. If the sampled fish differ in mass by a factor of about 3 or more, then this allometric effect becomes very noticeable.
Why log10?
Body composition data can be approximately linearized by a log(mass) transformation using either natural or common logs. But readers (or viewers of the graphs) can more easily understand the common-log transformation. For example a value of 2 for the log10(mass) means a mass of 100; a value of 3 for the log10(mass) means a mass of 1000. You can do the interpretation in your head. Not many people can do the same for the values produced by a natural log. The pattern of dots on a log-log graph will look exactly the same whether the transformation is natural or common logs; only the scale markings will differ. But it is much easier to understand the values of common (log10) logs.
Why not plot % body components versus body mass?
Plotting protein, ash, lipid as percent body mass against body mass adds noise to the relationships because (1) that does not account for the allometric (nonlinear in mass) changes in body composition, and (2) using body mass as the X variable adds noise due to the lipid, which does not participate in the strong relations among protein:water:ash. (Well, OK, structural lipid is actually part of the "lipid-free" mass, but only a very small part, maybe 1.5-2%? I'm still working on this.)
I'm happy to talk more about this. I realize it is only indirectly related to ED. But I think this is a good opportunity for learning and thinking about some of the factors underlying ED for a given size and species of fish. So I understand if there isn't time now to add this graph. But if we can use Ben's time to get it done, that would be great!
If you have time at this stage in the project (or to do later if you are rushed now), I have a new graph option to suggest or request: plot body composition data in this way:
Y variables:
versus
X variable: water mass (= proportion water * body mass).
Both X and Y axes should be log10.
Why?
This type of graph will help people understand (1) the strong patterns in body composition, and (2) the related differences in energy density among sizes and species of fish.
Explanation:
Plotting the components as log(mass) versus log(water mass) should produce very clear patterns, nearly straight lines, with minimal variation.
(There will be some differences between species, especially for ash. Salmonids tend to have low levels of ash. Centrarchids and Percids tend to have higher levels of ash.)
Why water mass as the X variable?
The explanation for the strong pattern is that the composition of the lipid-free mass is tightly regulated, and nearly constant for fish of a given size. The amount of water per gram of protein is tightly regulated (to keep the enzymes working correctly). The ratio changes slightly with fish size. Same for ash. The amount of storage lipid can vary widely for fish of a given lipid-free mass, as would be expected for a storage compartment that can range from full to nearly empty.
Why log-log plots?
There is a notable allometric effect influencing body composition that is apparent on the log scale. If the sampled fish differ in mass by a factor of about 3 or more, then this allometric effect becomes very noticeable.
Why log10?
Body composition data can be approximately linearized by a log(mass) transformation using either natural or common logs. But readers (or viewers of the graphs) can more easily understand the common-log transformation. For example a value of 2 for the log10(mass) means a mass of 100; a value of 3 for the log10(mass) means a mass of 1000. You can do the interpretation in your head. Not many people can do the same for the values produced by a natural log. The pattern of dots on a log-log graph will look exactly the same whether the transformation is natural or common logs; only the scale markings will differ. But it is much easier to understand the values of common (log10) logs.
Why not plot % body components versus body mass?
Plotting protein, ash, lipid as percent body mass against body mass adds noise to the relationships because (1) that does not account for the allometric (nonlinear in mass) changes in body composition, and (2) using body mass as the X variable adds noise due to the lipid, which does not participate in the strong relations among protein:water:ash. (Well, OK, structural lipid is actually part of the "lipid-free" mass, but only a very small part, maybe 1.5-2%? I'm still working on this.)
I'm happy to talk more about this. I realize it is only indirectly related to ED. But I think this is a good opportunity for learning and thinking about some of the factors underlying ED for a given size and species of fish. So I understand if there isn't time now to add this graph. But if we can use Ben's time to get it done, that would be great!