Modeling of Lake Malombe Annual Fish Landings and Catch per Unit Effort (CPUE)

Round 1

Reviewer 1 Report

This manuscript deals with the estimation of a catch per unit effort (CPUE) and biomass index for the fisheries of Lake Malombe. The authors address the problem of estimation and prediction by means of time series models known as ARIMA. From a methodological point of view, this work is simple but correct. The results are interesting from the point of view of providing information on quite unknown fisheries. The discussion must be improved.

Overall, the work is acceptable but would need significant improvements. The main aspects to be improved are as follows:

• In general, the state of the art should be improved.
• Lines 62-76. Only four references are cited in this paragraph. There is a vast literature on applications of time series models in fisheries (from Stergiou in 90’s to nowadays).
• Lines 69-70. I would not consider time series analysis as something new in fisheries.
• Line 72. …on fish catches and Catch per Unit Effort (CPUE).
• Lines 73-74. References. Why management approaches have failed?

Material and methods section

• Data collection. This section must be significantly extended. I think that is very important to know how CPUE is calculated.
• Conceptual framework of ARIMA models.
  • Line 104. Define ARIMA.
• In Fourth paragraph (no lines from the 111) authors say: ‘the non-stationary data can be modeled using log transformation to linearize the series’. This is not correct. You can use log transformation to homogenize variances but this necessary doesn't linearize the series.
• Final paragraph. What R function have you used?
• The authors are using R (probably the autoarima() function). Although they follow de procedure established by Box and Jenkins, why not test all values possibilities for p and q?

Results section

• Figure 2. What is X? Homogenize axes.
• Figure 3. I think that the quality of these graphs can be improved.
• Model selection. You must explain in material and methods how GMLE algorithm is used.
• The equations at the end of the Model Selection section are not corrects.
• The ARIMA accuracy section must be improved. For the observed period the authors should calculate different accuracy measures (see for example: Gutiérrez-Estrada et al., 2007), particularly the persistence index (Kitanidis and Bras, 1980).
• I would not extend the prediction beyond 5 years. What are your conclusions for 2032 when you see yours confidence bands?

Discussion section. This section must be re-written. Your discussion would be focused on your result.

• Second paragraph, line 5. ‘In other words,…..,this phenomenon’. You cannot conclude this from your results.
• Second paragragh, line 14-15. ‘The ARIMA….over exploited’. I’m not agree.
• Figure 6. This graph is not a result of this manuscript. Do you have permission to modify and publish it?
• Third paragraph. Re-write.
• What about the meaning (in a fishery context) of your p and q?

Conclusion section

• First new about the p, d and q value tested…
• And the ARIMA (2,2,2)?

I don’t agree with your last sentence.

Author Response

Thank you for your constructive review comments. We have carefully and tirelessly worked through the whole manuscript taking into accounts all your comments. Please attached are our responses to your comments.

Author Response File: Author Response.docx

Reviewer 2 Report

The objective of this study was to develop forecasting models of Lake Malombe. With this regard, the authors developed an arima-type of model, and I agree that this model could be a valuable tool for forecasting the dynamics of this system. However, this modeling framework can not be used to test different management scenarios. I therefore see it´s usefulness in a fisheries context to be rather small. Due to this I think the authors should rephrase a couple of sentence in the manuscript. For example, the statement:

“In other words, management approaches (co-management, command control and ecosystem-based management to fisheries) have failed due to lack of accurate predictive model in this lake. In this paper, we developed and tested a time series model as a tool for forecasting the status of Lake Malombe fish biomass and CPUE.”

can not be addressed using their modeling framework.

A follow up question is why the authors didn´t consider investigating potential effects of covariates, as for example fishing mortality? Please comment on this in the manuscript! Is it unfeasible to investigate potential effects of covariates?

Specific comments:

It is not clear which data was used. Was it a total sum of biomass of all species in the system? How was data assembled? Did you use a mean or a sum of the monthly collected data per year?

Line 59 bootstrap is not a model. It’s a technique for investigating uncertainty in model parameters.

After eq.3 log transformation does not make a non-stationary time series stationary!

Eq. 7 I think it would be more appropriate to use AICc as a model selection criteria. This information criteria has a penalty for small sample sizes. This information criteria should definitely be used here. Further, as a guideline models with information criteria differing less than 3 units are basically equally supported by the data. Therefore, it is not clear whether the assumed model is actually inferior to other fitted models!

Eq.8-9 what does the “u” refer to?

You should add greek letter to the equation after table 2!

Author Response

Many thanks for your constructive comments. We took time to work through the whole manuscript taking into consideration all your comments. The manuscript has tremendously improved after incorporating your suggestions. Please attached are our responses.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

In general, the manuscript has been improved. However, there are still issues that the authors have not addressed, mainly in the discussion section. For example:
- What does it mean that the terms autoregressive (p) and moving average (q) have a value of 0 in the case of best fit landings?
- Similarly, what is the interpretation of p=0 in the case of the best ARIMA for CPUE estimation?

On the other hand, the authors have made an important effort to show the good behaviour of their models. In this way, they have incorporated and calculated different adjustment measures (as recommended in the first review). However, there are some details that need to be corrected. For example:
- Equations 11 and 12 express absolute errors. Therefore they must be accompanied by their corresponding units (for example in Table 1).
- Equation 13 is expressed in %. Therefore the values in tables 1 and 2 are not correct.
- Equation 16 is not 'E2', it must be 'PI'.
- In Table 2, you must put E2 in place of 'E'.
- Are the results of the ARIMA model (0,1,1) in Table 2 correct?
- What is the difference between AIC and AICc? There is nothing in the material and methods section.
- Is NBIC the same as BIC?

The reference section should also be checked carefully.

Author Response

Thanks for the comments. we have extensively worked through the manuscript taking into accounts your comments.

Thanks

Author Response File: Author Response.docx