The unit of fishing effort can be measured in different ways in recreational fishing: number of hooks in the water per unit of time, number of fishing trips per unit of time, number of fishermen per unit of time, etc. It depends on the characteristics of the fishery, and on the facilities available to take the data.

But I think the question and what you have put into the development of it, generates a bit of noise. The original question is: how to measure the fishing pressure in recreational fishing? But what you are taking forward is to indirectly assess the status of the fish population through the CPUE, and you use this response variable (CPUE) as a measure of the action of the fishing pressure.

They are two different issues that answer different questions:

1) Do you want to know if there is any other way to measure the response of the exploited fish population?

2) Or do you want to know how to measure the fishing pressure?

You must be clear that what you do with the CPUE is to mask the fishing pressure in the fishing effort unit. And I think the question that remains is whether the response of the fish population is adequate to assess, in the particular case of the fishery you study, the fishing pressure.

I would like to recommend to you to get in contact with the working group of Robert Arlinghaus - they have a lot of experience in measuring fishing pressure in recreational fishing. You should have a look under https://www.igb-berlin.de/en/profile/robert-arlinghaus

I suggest adding “length of visit per angler” to your formula and I think you may have all you need (get this by survey on site, survey cards, sample of anglers, etc) depending on what you want to do with the index results. The reason I suggest this is that if the population of target catachable species/sizes is high to start with, the length of visit to reach a “limit” per angler may be short (less pressure), but as populations of target species/sizes decrease, anglers may/will extend the length of visit (more pressure). If the target size/species is already low in abundance and anglers generally stay an entire day per visit regardless of fish abundance, then your current formula for pressure may be all you need to give a reasonable rough relative index, depending on what you want to do with that index. A simple way to compute CPUE is all you need if all you need is a simple solution.

IT depends on what you mean by "pressure". Do you mean fishing mortality? Or do you mean fishing effort? What you measured as CPUE is usually looked at as an index of relative abundance, so we look at the trend of CPUE over time.

For pressure in terms of effort, it seems that the trend in number of anglers per unit of time would show that. However, for fishing mortality, the definition by Baranov is Fishing Mortality (F) is defined as F = catch/ (average stock size over a year or other period). F can also be defined as F = q* effort, where q is the catchability coefficient, meaning the fraction of a fish stock caught by one unit of effort. If you can find a copy, I recommend W. F. Ricker. 1975. Computation and Interpretation of Biological Stats of Fish Populations., or Quinn and Deriso. 1999, who have a good coverage of CPUE theory. To see the trend in F, use relative F, defined as Relative F = catch(kill, really) / CPUE, where CPUE can be any measure of relative abundance. As you can see relative F will convert to the trend in fishing effort, which is correct.

Desmond makes a good point. I just assumed you meant effort. What you mean by "pressure" makes a difference as he addresses quite well.