Allometry and Individual Growth of the Temperate Pacific Sardine (Sardinops sagax) Stock in the Southern California Current System

Round 1

Reviewer 1 Report

In this study, the authors presented basic biological research on the somatic growth and the allometry of a sardine stock in temperate Pacific. This study is well performed and presented. I only have some minor issues with the presentation of the results. See below for details.

 

Minor issues:

line 67: missing model name

line 147-152: "Where ..." shouldn't start a new paragraph. Remove the indentation at the front.

line 264: "fishes" means different fish species

Table 2: the sample size n here is different from the sample size on line 264

Also, I suggest that the authors plot the results in Table 2. The results may be clearer that way.

Table 5: the difference among these models is minimal with delta AIC < 2. This indicates uncertainty in the choice of a particular growth model. The simulation approach ignores the uncertainty, and as such the best model in Table 7 may not be actually the best model for predictive purposes. I have reservations about VB being the best model based on the data at hand. All the models fitted the data pretty well.

Figure 8: Can you do a scatter plot with paths instead of time series plots? It is hard to see the pattern as is.

line 524: The said inverse and positive relationships were not supported by any statistics. Note that the p-values are all larger than 5%. Please do not overstate the results. These relations are potential, not affirmed.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Thank you to the authors for doing excellent work, including detailed methods to address uncertainties associated with growth parameter estimations. All sections of the manuscript are structured very well. However, still, I have some major concerns that the authors should explain clearly in their manuscripts and make corrections according to the following comments:

Fish populations significantly fluctuate in response to fishing and density-dependent and -independent processes. Time and space also influence fish population structure. Again, it is clear from Figure S1 that the length distributions were shifting towards the higher length classes with time. Besides, Table 9 indicates an increasing trend for both Linf and K. This may be due to management measures or environmental parameters changes. So why do the authors think using data collected more than eight years ago is still relevant?

Line 67: Correct the line.

Line 84: The authors should include a detailed fishing gear description. Was the similar nets with same mesh size used for the fishing from 2005 – 2014?

Line 104: Why do the authors think 60 or <60 is a good representation of 3509 individuals?

Line 124: Correct the sentence.

Lines 108 – 127: The description of Age determination is not complete. The authors should clearly describe the details of the sampling, preparation, and age reading criteria.

Line 187: What is the m for?

Lines 196, 202, 432, 439, 499 & 509: Cite properly.

Lines 274 – 276: “The X-axis label 115, for example, includes 111-115 mm, 130 includes 126-130 mm, and so on to the largest, 230 which includes 226-230 mm.” Remove this sentence since you already mentioned the CL is 5 mm.

Figure 4: What is the unit of the Y-axis? Is this figure for poled data?

Line 309 – 310 : "The highest frequency was observed at the age of two and three years.” – Why?

Lines 318 – 320: There is no evidence of using age-length keys. Therefore, it is not clear how the authors produced Table 3.

Figure 6: Use a different color for different models.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the authors collect extensive data on sardine length, weight and age and develop growth models for the fishery. They use an impressive variety of statistical methods, and the resulting models may be useful for managing the fishery. However, some of the statistical methods were not applied quite appropriately, and the paper would benefit from additional details in the methods section.

 

Analytical issues:

·       The comparison of four different growth models with AIC has a few issues. Importantly, it is generally excepted that models with delta-AIC <3 are essentially identical, so discussion of comparisons between the models isn’t appropriate.

·       Using simulation to increase the sample size also doesn’t seem quite appropriate. The fact that the models are essentially identical with the raw data and different with the boosted data implies that the simulated data does not match the raw data very well, so gives an incorrect impression of the population. Seeing the graph of the four models fitted to the boosted data, I was frankly shocked that there was any difference in the AIC. The four lines are so similar as to completely overlap, not indicating any difference between them.

·       The fitting of the ENSO index and other environmental characteristics was just done with a basic correlation analysis. Why not use a linear model and model selection with AIC for this too?

 

The discussion could also use additional clarity in the discussion to differentiate inter-annual growth differences from latitudinal growth differences.

 

 

 

Specific comments:

-       Line 96 – Data collection – I’d like a little more information about these monitoring programs and the fishing fleet. What size of gear is used? Is there any information about size biases associated with the gear? How frequently are samples collected? How many fish are in each sample? Are the samples evenly distributed amongst fishing boats?

-       Line 119 – If each fish is only aged twice, this doesn’t give a very robust estimate of precision. Also, Was the coefficient of variation calculated for the two readers? Or for the population?

-       Line 128 – I’m not an expert in the different sardine stocks, but it really surprises me that there is no overlap in the temperature at which these stocks are found. Are these truly genetically different populations? Reading reference [7], it looks like these groups have a significant amount of overlap, so such a simplistic division of stocks by temperature seems inappropriate. Temperature can be used as a “general rule of thumb”, but it should be accompanied by some caveats regarding when and how there may be exceptions. 

-       Line 173 – The formula for calculating AIC and AIC weight are pretty well established, it’s not necessary to include the formula here, a citation for the method would be fine.

-       Line 332 – All of the models have a delta-AIC of less than 2. It is generally accepted that models with a delta-AIC of less than 3 are essentially equal.

-       If the raw data had all models fitting equally, how are their differences in the bolstered data? The lines look like they totally overlap and there is no difference between them. I just don’t understand.

-       Age at length of zero (which is negative) doesn’t make much sense to me. Why report that parameter since it never occurs in nature?

-       It would be more helpful to have the different year models shown in a graph rather than just a table of parameters.

-       Line 429 – There is a lot of information in this paragraph, it would be better broken up into two paragraphs.

-       Line 435 – The authors propose differential growth rates are linked to latitudinal distribution, but the differences in growth rates reported in this study were inter-annual differences, so I’m not sure how this relates.

-       Line 471 – It’s inappropriate to say the LM was better than the VBN model in this case. They were essentially identical in fit.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors explained their reasoning behind many of their statistics, but I do not think the statistics were applied properly, particularly with the boosted data. I asked a colleague with more experience in these types of statistics for their read on it, and they supported many of my initial assertions. The paper should not be accepted without re-analysis of the data.

1. The authors on lines 211-214 claim they are using the bolstered observations to account for imbalanced sample design. 
1. A major  concern is that they assumed normality in their observations without proving normality
1. A better approach, if they have to do this, would be to randomly sample from a density distribution, not a normal distribution.
2. Regardless, I do not think this is an appropriate approach as they are artificially inflating their sample size, which has a whole host of problems, the least of which is artificial significance and artificially reduced uncertainty. 
1. At a minimum, Table 4 needs to specify that they are bolstered model results not actual data model results. Given this, they should probably not report confidence intervals around parameter estimates.
2. The bigger flaw with the models is that they are using the bolstering (resampling from simulated distributions) approach because they are worried about model accuracy. However, they have much much larger sources of uncertainty that they are ignoring: age classification, year-class effects, and sampling location
1. Age classification - they are [somewhat] arbitrarily assigning a fish age in 0.5 year increments. However, the difference between an age-1 (140mm) and age-2 (164mm) is approximately 17% of the fish's length. Therefore, incorrectly assigning the age of 1, 1.5, or 2 based on a judgement call could be artificially increasing the uncertainty in the data by upwards of 15%
2. Year-class effects - temperature is the master factor of fish bioenergetics. Similarly, bioenergetics is a function of temperature and food intake. Therefore, temperature and consumption data is a must to truly understand fish growth. Given the lack of this information, growth models can be drastically improved by simply by incorporating year-class. That is, year-class (i.e., born in 2005 v 2010) is a know piece of information that can act as a surrogate for the environmental conditions to which a fish was exposed (e.g., warm v cold years; good food v bad food). For example, a 2 year-old born in 2007 (2007 year class) lived through two years of La Niña whereas a 2 year-old born in 2010 had it's first (and most important) year of growth during a moderate El Niño. Simply accounting for year-class, therefore, is likely to drastically improve model fit. 
3. Sampling Location - As with year-class, sampling location and, therefore, the region in which the fish likely lived can drastically influence bioenergetics (i.e., food and temp). Accounting for sampling location should improve model fit
3. The data are hierarchically structured with fish observations nested within sampling location and fish observations nested within year-class. These variables, therefore, should be included in the models as random or fixed effects, but must be accounted for. 
4. Arbitrarily classifying an individual by a 0.5 year interval is a highly flawed approach. A much cleaner and simpler approach is to include brood day (i.e., calendar days since caught) as a covariate. As the authors note, they do not know when an individual hatched, but assigning a universal brood day based on the literature is far superior to arbitrarily assigning a fish a half year classification. Furthermore, including a year-class term would account for the interannual variability in brood day

Author Response

Response to Reviewer 3 (fishes-1841648) – Round 2

Dear Reviewer,

We sincerely thank you for thoroughly reviewing our manuscript and providing us with very helpful comments and suggestions that are intended to help us improve our manuscript. However, we want to point out that it was impossible for us to address your main comment noted in the review report, that is, that the paper should not be accepted without re-analysing the data, and you proposed a different approach than the one we used in our manuscript. Our responses to your comments (highlighted in bold blue) point by point are presented below:

 

Comments and Suggestions for Authors

The authors explained their reasoning behind many of their statistics, but I do not think the statistics were applied properly, particularly with the boosted data. I asked a colleague with more experience in these types of statistics for their read on it, and they supported many of my initial assertions. The paper should not be accepted without re-analysis of the data.

Thank you very much for your observations and suggestions. Our responses to your comments are in bold blue.

1. The authors on lines 211-214 claim they are using the bolstered observations to account for imbalanced sample design. 

1. A major  concern is that they assumed normality in their observations without proving normality

In this work, the normality tests were performed, and the results indicated that the data of most of the age groups conformed to a normal distribution. On this basis, we assumed that all age groups fitted to normal distribution.

 

1. A better approach, if they have to do this, would be to randomly sample from a density distribution, not a normal distribution.

There was no need to do what you mentioned because the data did fit to normal distribution.

 

1. Regardless, I do not think this is an appropriate approach as they are artificiallyinflating their sample size, which has a whole host of problems, the least of which is artificial significance and artificially reduced uncertainty.

As noted in the Methods Section, these are not all new data, that is, in those cases where there were less than 500 data, the approach allowed generating the missing data to complete 500. In the case of the group of 2.0 and 3.0 years of age that had more than 500 data (1,090 and 640 data points, respectively), only 500 data were randomly selected to represent those two age groups. This is an approach that is considered statistically valid (Bolser et al. 2018 [52] and Scherrer et al. 2021[53]). It is also pertinent to note that if we only stick to the statistical result, we could end up (as has been pointed out in Bolser et al. 2018 [52] and Scherrer et al. 2021[53]) with results that biologically do not adequately represent the growth of the Pacific sardine. In this sense, we expand the paragraph of the "Sensitivity analysis" subsection a bit, to include what we noted above.

  

1. At a minimum, Table 4 needs to specify that they are bolstered model results not actual data model results. Given this, they should probably not report confidence intervals around parameter estimates.

It is possible that there would not have been a correct reading of the table, since the results presented in Table 4 are the results obtained with the original data (raw data). The results obtained with the bolstered data are those presented in Table 6 and Table 7, and in the headings of these tables, it is specified that they are the results obtained with the raw data bolstered.

 

1. The bigger flaw with the models is that they are using the bolstering (resampling from simulated distributions) approach because they are worried about model accuracy. However, they have much much larger sources of uncertainty that they are ignoring: age classification, year-class effects, and sampling location

We agree with you that there are several other sources of uncertainty, and we are not really ignoring those aspects (they are noted in the Discussion), it is simply that this is not the approach that we are using in this work, and really an analysis with that approach by itself it would be another research work, which we intend to carry out in the near future.

 

1. Age classification- they are [somewhat] arbitrarily assigning a fish age in 0.5 year increments. However, the difference between an age-1 (140mm) and age-2 (164mm) is approximately 17% of the fish's length. Therefore, incorrectly assigning the age of 1, 1.5, or 2 based on a judgement call could be artificially increasing the uncertainty in the data by upwards of 15%

Regarding age assignment in 0.5-year age groups, it is also considered a valid approach for age determination, i.e. age can be calculated with a resolution of one year or half year depending of the life-span of the species and the possibility of discriminating between opaque and translucent edges (Carbonara and Follesa 2019). In the case of the Pacific sardine, this is a species that is short-lived, on the other hand, the otoliths of this species are relatively easy to read and therefore discriminate the opaque and translucent edges quite reliably. Therefore, we believe that the half-year approach can be considered acceptable for this species.

What we can comment on in relation to the second part of the paragraph of your comments is that, if the one-year approach is used for a short-lived species, when assigning the age to a specimen it could have an uncertainty of more-less one year, whereas that with the approach we use it would be plus-minus 0.5 years, which would apparently indicate that there would be greater uncertainty with the one-year approach because this is a short-lived species.

 

1. Year-class effects - temperature is the master factor of fish bioenergetics. Similarly, bioenergetics is a function of temperature and food intake. Therefore, temperature and consumption data is a must to truly understand fish growth. Given the lack of this information, growth models can be drastically improved by simply by incorporating year-class. That is, year-class (i.e., born in 2005 v 2010) is a know piece of information that can act as a surrogate for the environmental conditions to which a fish was exposed (e.g., warm v cold years; good food v bad food). For example, a 2 year-old born in 2007 (2007 year class) lived through two years of La Niña whereas a 2 year-old born in 2010 had it's first (and most important) year of growth during a moderate El Niño. Simply accounting for year-class, therefore, is likely to drastically improve model fit.

Indeed, there are approaches with random or mixed effects models (random and fixed) to explore their effects on growth determination (for example, Cope and Punt 2007; Thorson and Minte-Vera 2014; Lee and Punt 2016). However, several studies have found that the effect of the cohort (or year class) has a smaller effect on growth compared to the effect of the year, so it is not as linear as the simple fact of considering the year-class will drastically improve the fit of the model.

So, doing what you mention would be different and new research work with respect to what we want and are presenting to the consideration of the journal Fishes.

In the manuscript, towards the end of the Discussion we noted that, once we have the complete time series (of age readings) between the year 2000 and 2021, approaches such as the ones you suggest can be addressed.

 

1. Sampling Location - As with year-class, sampling location and, therefore, the region in which the fish likely lived can drasticallyinfluence bioenergetics (i.e., food and temp). Accounting for sampling location should improve model fit

Indeed, there are approaches with random or mixed effects models (random and fixed) to explore their effects on growth determination (for example, Cope and Punt 2007; Thorson and Minte-Vera 2014; Lee and Punt 2016). Considering the results that have been obtained in different works that have included various types of factors, it is not so linear that the simple fact of taking into account this or that factor will drastically improve the fit of the model.

So, doing what you mention would be different and new research work with respect to what we want and are presenting to the consideration of the journal Fishes.

In the manuscript, towards the end of the Discussion we noted that, once we have the complete time series (of age readings) between the year 2000 and 2021, approaches such as the ones you suggest can be addressed.

 

1. The data are hierarchically structured with fish observations nested within sampling location and fish observations nested within year-class. These variables, therefore, should be included in the models as random or fixed effects, but must be accounted for.

Indeed, there are approaches with random or mixed effects models (random and fixed) to explore their effects on growth determination (for example, Cope and Punt 2007; Thorson and Minte-Vera 2014; Lee and Punt 2016). However, several studies have found that the effect of the cohort (or year class) has a smaller effect on growth compared to the effect of the year, so it is not as linear as the simple fact of considering the year-class will drastically improve the fit of the model.

So, doing what you mention would be different and new research work with respect to what we want and are presenting to the consideration of the journal Fishes.

In the manuscript, towards the end of the Discussion we noted that, once we have the complete time series (of age readings) between the year 2000 and 2021, approaches such as the ones you suggest can be addressed.

 

1. Arbitrarily classifying an individual by a 0.5 year interval is a highly flawed approach. A much cleaner and simpler approach is to include brood day (i.e., calendar days since caught) as a covariate. As the authors note, they do not know when an individual hatched, but assigning a universal brood day based on the literature is far superior to arbitrarily assigning a fish a half year classification. Furthermore, including a year-class term would account for the interannual variability in brood day.

Regarding age assignment in 0.5-year age groups, it is also considered a valid approach for age determination, i.e. age can be calculated with a resolution of one year or half year depending of the life-span of the species and the possibility of discriminating between opaque and translucent edges (Carbonara and Follesa 2019). In the case of the Pacific sardine, this is a species that is short-lived, on the other hand, the otoliths of this species are relatively easy to read and therefore discriminate the opaque and translucent edges quite reliably. Therefore, we believe that the half-year approach can be considered acceptable for this species.

It was noted that there is arbitrariness and flaws in using a half-year approach and that a much cleaner and simpler approach is to assign a hatch day. However, from our point of view, making the assumption that all individuals of this species hatch on a given day of the year, when we know that this is a species that has partial reproduction and an extended reproductive period that can last up to six months, also has a lot of subjectivity and uncertainty, which could add or subtract one year to an individual's age if the date-of-birth approach is used, which is subjective and uncertain. That criterion could result in changes in accuracy and precision of ±1.0 years, while with our approach it would be ±0.5 years.

 

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

The authors still have not adequately addressed several of my previous comments. Specifically:

1. They still refer to the Logistic model as being the "best" fit for the raw data, despite all the models being within a delta-AIC of 3 from each other. Furthermore, all the models ended up with essentially identical curves (based on figure 7), so the discussion of the sensitivity of the analysis to sampling biases is confusing. If all the models resulted in the same curve, they should provide identical Log-Likelihood, with the only difference in AIC coming from the number of parameters. So the discussion that says the logistic model had "null plausibility", is inappropriate. The way the authors describe the differences in AIC needs to be re-worked throughout the paper. 

2. While they explain that they tested the data for normality in their response to reviewers, no mention of it is made in the paper. Furthermore, they frequenly cite Schrerrer et al as one of the sources for their method, but Schrerrer et al. says that   "It was not possible to simulate new observations without making assumptions about growth parameters because the growth observed in each individual between marking and recapture events is an essential input to growth increment approaches, so a synthetic dataset was constructed through hierarchical resampling of the original OTP data." Using resampling of the original data would be a better method. At a minimum, they need to describe how they tested the dataset for normality.  

3. A hierarchical model structure would be more appropriate for this analysis. The authors described reasons why they did not do this in the response to reviewers, but there were no changes made to the paper to describe their reasoning.  Explanations should be included, or (ideally) the analysis should be re-run with a hierarchical model structure. 

Author Response

Dear Reviewer,

We sincerely thank you for thoroughly reviewing our manuscript and providing us with very helpful comments and suggestions that are intended to help us improve our manuscript. Our responses to your comments (highlighted in bold blue) point by point are presented below:

 

Comments and Suggestions for Authors

The authors still have not adequately addressed several of my previous comments. Specifically:

1. They still refer to the Logistic model as being the "best" fit for the raw data, despite all the models being within a delta-AIC of 3 from each other. Furthermore, all the models ended up with essentially identical curves (based on figure 7), so the discussion of the sensitivity of the analysis to sampling biases is confusing. If all the models resulted in the same curve, they should provide identical Log-Likelihood, with the only difference in AIC coming from the number of parameters. So the discussion that says the logistic model had "null plausibility", is inappropriate. The way the authors describe the differences in AIC needs to be re-worked throughout the paper.

- Thank you very much. We agree with you that the fit for the raw data was very similar, with delta values ​​< 2. We modified some paragraphs a bit to read as follows:

Lines 355-364:

“The values ​​of the growth parameters with their 95% CI for each model adjusted to the raw data ​​are presented in Table 4. Estimated ​​of L_∞ varied between 207.4 mm and 216.3 mm SL, while the ​​k estimated varied between 0.372 and 0.586 year^-1, with the lowest value estimated for VBM and highest values ​​estimated for the other models (Table 4). The estimated values ​​for AICi, Δi, and WAIC_i of each evaluated model are presented in Table 5. All the compared models have a value of Δ < 2, while the WAIC varied between 13.47% and 34.61%, which indicates that all models are substantially supported by the data. This would indicate that although LM was marginally better than GM, VBM and SM, there was not clearly "winner" model. It is shown in Figure S3 (Supplementary Material) that the growth models produced similar asymptotic growth patterns.”

 

Lines 380-384:

“… Table 6 shows the parameters estimate for the four models adjusted to the raw data bolstered, including their 95% CI. Estimated ​​of L_∞ varied between 207.9 mm and 217.1 mm SL, while the ​​k estimated varied between 0.372 and 0.586 year^-1, with the lowest value estimated for SM and VBM and highest values ​​estimated for LM and GM…”

 

Lines 400-405:

“In Table 7, the estimated values ​​for AICi, Δi and WAICi to the bolstered raw data for each evaluated model are presented. Only VBM y SM models have a value of Δ < 2, while the WAIC was 60.92% and 38.28%, which indicates that these two models are substantially supported by the data. This would indicate that VBM described the bolstered raw data by simulated values best. The LM and GM received no support from the Δ o WAIC (Table 7).”

2. While they explain that they tested the data for normality in their response to reviewers, no mention of it is made in the paper. Furthermore, they frequenly cite Schrerrer et al as one of the sources for their method, but Schrerrer et al. says that   "It was not possible to simulate new observations without making assumptions about growth parameters because the growth observed in each individual between marking and recapture events is an essential input to growth increment approaches, so a synthetic dataset was constructed through hierarchical resampling of the original OTP data." Using resampling of the original data would be a better method. At a minimum, they need to describe how they tested the dataset for normality. 

- Thank you for your comments and suggestions. We have added the requested description in "Sensitivity analysis" subsection (lines 226-227) and we have also added a paragraph in Results section (lines 370-372).

3. A hierarchical model structure would be more appropriate for this analysis. The authors described reasons why they did not do this in the response to reviewers, but there were no changes made to the paper to describe their reasoning.  Explanations should be included, or (ideally) the analysis should be re-run with a hierarchical model structure.

- Thank you for your comments and recommendations. We have added a paragraph at the end of the Discussion section, which reads as follows:

“Finally, it is important to point out that growth can also be approached using random or mixed effects models (random and fixed), with which the effects that different intrinsic and extrinsic covariates have on the estimation of growth and its variability have been explored [79,81,82,83,84,85,86]. On the other hand, it has been noted that integrated mixed-effects models could reduce bias in growth model parameters versus non-integrated [87], but that this line of research has not yet fully explored the performance of integrated mixed-effects models to simultaneously estimate unknown ages, growth model parameters, and derived variables. In this context, for this species there is an open route in which the growth of the different Pacific sardine stocks that inhabit the California Current and the Gulf of California can be explored.”

 

Author Response File: Author Response.pdf

Round 4

Reviewer 3 Report

The authors still say that one model is "better" or "marginally better" than another model when they are within a delta-AIC of 2. This is not appropriate. 

Author Response

Dear Reviewer,

We sincerely thank you for thoroughly reviewing our manuscript and providing us with very helpful comments and suggestions that are intended to help us improve our manuscript. Our responses to your comments (highlighted in bold blue) point by point are presented below:

 

Comments and Suggestions for Authors

The authors still say that one model is "better" or "marginally better" than another model when they are within a delta-AIC of 2. This is not appropriate. 

- Thank you for your comments. We modified some paragraphs a bit, in the Results section, to read as shown below; while in the Discussion section, at line 534, we changed the word "best" to "feasible", and at line 535, we changed "better" to "suitable".

Lines 355-363:

“The values ​​of the growth parameters with their 95% CI for each model adjusted to the raw data ​​are presented in Table 4. Estimated ​​of L_∞ varied between 207.4 mm and 216.3 mm SL, while the ​​k estimated varied between 0.372 and 0.586 year^-1, with the lowest value estimated for VBM and highest values ​​estimated for the other models (Table 4). The estimated values ​​for AICi, Δi, and WAIC_i of each evaluated model are presented in Table 5. All the compared models have a value of Δ < 2, while the WAIC varied between 13.47% and 34.61%, which indicates that all models are substantially supported by the data. It is shown in Figure S3 (Supplementary Material) that the growth models produced similar asymptotic growth patterns.”

 

Lines 399-403:

“In Table 7, the estimated values ​​for AICi, Δi and WAICi to the bolstered raw data for each evaluated model are presented. Only VBM y SM models have a value of Δ < 2, while the WAIC was 60.92% and 38.28%, which indicates that these two models are substantially supported by the data. The LM and GM received no support from the Δ o WAIC (Table 7).”

Author Response File: Author Response.pdf