Ok, I'm trying again.
This is a calculation to take into account a few facts about fish growth. I need to be able to figure out an average daily change in length (daily delta L, or DDL). I weight the fish at P1, then again at P2 (weight and length can be readily interchanged using the condition factor, so I measure weight, but that's a standin for length). The DDL can be calculated as:
DDL = DW/Interval
where DW is the change in length over the time period between P1 and P2 and Interval is the number of days between P1 and P2. That ones pretty simple.
Now, if I were to move more fish into the location with a different length, the calculation becomes:
DDL = DW/((Interval * F1) + (I2 * F2))
where:
DW is the total change in the length over the interval.
Interval is the number of days between P1 and P2.
F1 is the fraction of the total fish that were already in the location.
I2 is the number of days from the time more were moved in to P2.
F2 is the fraction of the total fish that were moved into the location.
The point of this is to figure out how much daily growth there was in the location over the interval when the addition of larger or smaller fish is taken out. Those larger or smaller fish can be assumed to grow at the same rate once they are added to the same location. This calculation is pretty straightforward, too, and seems like it should work for multiple moves into the location.
Now, to complicate things:
At some point during the interval, the feeding strategy could be changed, which would result in a change in the growth rate. If there are no fish being moved into or out of the location, then a DDL can be calculated for the time prior to the change and a different DDL can be calculated for the time after the change. The two equations for these two DDL are:
DDL1 = DW / (D1 + (R/D2))
DDL2 = DW / ((R * D1) + D2)
Where:
DW = Change in length over the total interval.
D1 = Number of days from the start of the interval to the date of the change in feeding strategy.
D2 = Number of days from the change in strategy to the end of the total interval.
R = The ratio of the desired growth rate for the first part to the desired growth rate of the second part.
To explain R a bit more, there is an expected growth rate, which is the point of feeding. The change in the strategy would switch to a different expected growth rate. R would be the first expected growth rate over the second expected growth rate. If the feeding rate remains the same, the ratio is 1. A value greater than 1 means that the change was a decrease in the feeding while a value less than 1 would mean that the feeding rate increased.
This calculation works well, but only if no fish are moved into the location. The problem I'm having is combining the two calculations. If the rate of feeding is increased, then R will be less than 1 and the fish should grow faster after the feeding change. However, if larger fish were added to the location after the feeding change, then the average size of the fish will increase anyways. The DW value will be larger, in this case, not due solely to increased growth, but due partially to increased growth and partially to adding larger fish.
So, I have a calculation for adding fish and a calculation for changing feeding, but I'm not sure how to figure out the growth before and after the feeding change if fish are added either before or after the feeding change.
This is a calculation to take into account a few facts about fish growth. I need to be able to figure out an average daily change in length (daily delta L, or DDL). I weight the fish at P1, then again at P2 (weight and length can be readily interchanged using the condition factor, so I measure weight, but that's a standin for length). The DDL can be calculated as:
DDL = DW/Interval
where DW is the change in length over the time period between P1 and P2 and Interval is the number of days between P1 and P2. That ones pretty simple.
Now, if I were to move more fish into the location with a different length, the calculation becomes:
DDL = DW/((Interval * F1) + (I2 * F2))
where:
DW is the total change in the length over the interval.
Interval is the number of days between P1 and P2.
F1 is the fraction of the total fish that were already in the location.
I2 is the number of days from the time more were moved in to P2.
F2 is the fraction of the total fish that were moved into the location.
The point of this is to figure out how much daily growth there was in the location over the interval when the addition of larger or smaller fish is taken out. Those larger or smaller fish can be assumed to grow at the same rate once they are added to the same location. This calculation is pretty straightforward, too, and seems like it should work for multiple moves into the location.
Now, to complicate things:
At some point during the interval, the feeding strategy could be changed, which would result in a change in the growth rate. If there are no fish being moved into or out of the location, then a DDL can be calculated for the time prior to the change and a different DDL can be calculated for the time after the change. The two equations for these two DDL are:
DDL1 = DW / (D1 + (R/D2))
DDL2 = DW / ((R * D1) + D2)
Where:
DW = Change in length over the total interval.
D1 = Number of days from the start of the interval to the date of the change in feeding strategy.
D2 = Number of days from the change in strategy to the end of the total interval.
R = The ratio of the desired growth rate for the first part to the desired growth rate of the second part.
To explain R a bit more, there is an expected growth rate, which is the point of feeding. The change in the strategy would switch to a different expected growth rate. R would be the first expected growth rate over the second expected growth rate. If the feeding rate remains the same, the ratio is 1. A value greater than 1 means that the change was a decrease in the feeding while a value less than 1 would mean that the feeding rate increased.
This calculation works well, but only if no fish are moved into the location. The problem I'm having is combining the two calculations. If the rate of feeding is increased, then R will be less than 1 and the fish should grow faster after the feeding change. However, if larger fish were added to the location after the feeding change, then the average size of the fish will increase anyways. The DW value will be larger, in this case, not due solely to increased growth, but due partially to increased growth and partially to adding larger fish.
So, I have a calculation for adding fish and a calculation for changing feeding, but I'm not sure how to figure out the growth before and after the feeding change if fish are added either before or after the feeding change.