LeMaRns: A Length-based Multi-species analysis by numerical simulation in R.

Fish stocks interact through predation and competition for resources, yet stocks are typically managed independently on a stock-by-stock basis. The need to take account of multi-species interactions is widely acknowledged. However, examples of the application of multi-species models to support management decisions are limited as they are often seen as too complex and lacking transparency. Thus there is a need for simple and transparent methods to address stock interactions in a way that supports managers. Here we introduce LeMaRns, a new R-package of a general length-structured fish community model, LeMans, that characterises fishing using fleets that can have different gears and species catch preferences. We describe the model, package implementation, and give three examples of use: determination of multi-species reference points; modelling of mixed-fishery interactions; and examination of the response of community indicators to dynamical changes in fleet effort within a mixed-fishery. LeMaRns offers a diverse array of options for parameterisation. This, along with the speed, comprehensive documentation, and open source nature of the package makes LeMans newly accessible, transparent, and easy to use, which we hope will lead to increased uptake by the fisheries management community.

Introduction

In fisheries management, fish stocks are typically managed on a stock-by-stock basis, with most assessment models having a single-species focus that does not explicitly model interactions between stocks. Single-species models are useful for assessing the current state of a stock and making short-term forecasts as you only need information regarding the stock in question. However, these models assume that inter-stock interactions (predation and competition for resources) are either fixed or vary only in a simple way with time, and so on longer timescales their use becomes increasingly problematic. Multi-species models that explicitly represent some or all of these interactions are generally more suited to making predictions as the timescale of interest increases [1]. As a result, a large number of multi-species models have been developed. The models take various approaches: statistical models, such as the Stochastic Multi-Species model (SMS) [2], are similar to age-structured single-species assessment models; biomass dynamic models, such as surplus-production models [3], describe the dynamics of bulk biomass; while mechanistic models, such as Ecopath [4], attempt to describe the processes that lead to the emergent system based on ecological theory. For a discussion regarding the relative merits of single and multi-species approaches see [1].

Size-based multi-species models are a class of mechanistic models [5] that, in contrast to single-species models, explicitly take account of foodweb interactions. In marine ecosystems size is often a key trait [6]. By representing many processes, including fishing, natural mortality, and predation as a function of length, it is possible to reproduce many aspects of the community dynamics (such as the tendency of diet to change with increasing predator size; [7]) with a relatively small number of parameters and a modest requirement for data in model set up. This makes the framework particularly suitable for use in data-limited fisheries. However, size-based multi-species models lack uptake by both managers and fisheries scientists due to the perceived complexity and lack of transparency of the models [8].

Here we introduce the new LeMaRns R-package, within which we implement a general length-structured fish community model, LeMans (Length-based Multi-species analysis by numerical simulation) [9, 10], that can be adapted to any marine ecosystem with only a modest amount of data. The speed, increased functionality, comprehensive documentation, diverse array of parameterisation, and open source nature of the package makes LeMans newly accessible to model developers and general users alike. We hope this will lead to increased user uptake and novel model development by the fisheries community.

In this paper we give a brief overview of the LeMaRns model, we describe how the package works and we provide three applications of LeMaRns. The code for these applications can be found in S1 File. We conclude with a discussion regarding future work.

Model overview

The LeMans model framework was originally developed by [9] to represent the Georges Bank fish community, but was subsequently adapted for use in the North Sea by [10-14].

LeMans is well suited for use whenever there is a need for multi-species or mixed-fisheries analysis but where there is insufficient data to support the use of more complicated models, such Atlantis [15]. The model has been used to assess the impact of mixed-fisheries [12, 13], evaluate the effect of harvest control rules [14], and as part of a multi-model ensemble along with other multi-species models [16]. LeMans models fish length because a) it is generally easier to measure than weight in the field [17], and b) fisheries selectivity is normally characterised in terms of length [18] and is thus more straightforward to relate to the parameterisation of mixed-fisheries.

The model has no spatial dependency and describes the dynamics of multiple species in n discrete length classes through time. A year in the model is subdivided into a number of equal time steps of length δt. Spatial information can be included in the model implicitly via the predator-prey interaction matrix (e.g. [19]).

Let N be the number of individuals of the ith species in the jth length class after t−1 time steps. During each time step three processes occur: recruitment, mortality, and growth. The number of individuals after the recruitment phase of the tth time step is where R is the number of recruits of the ith species at time t. R depends on the spawning stock biomass of the ith species as well as the time step of the model. In [9] and [10] recruitment occurred in the first time step of a new year, using the a Ricker recruitment curve [20] and a hockey-stick recruitment curve [21] respectively (see S2 File pages 5-6 for more details).

The number of individuals after the mortality phase of the time step is where M1 is the background mortality, M2 is the predation mortality, and F is the fishing mortality. The background mortality, M1, is size and species dependent (see S2 File page 7 for more details). Predation mortality is size- and species-dependent. The size preference of a predator is described using a preference function based upon a log-normal distribution, whilst species preference is described using a predator-prey interaction matrix indicating who eats whom [10, 11] (see S2 File pages 4, 7-8 and 13 for more details).

Fishing mortality is constructed from the joint effect of a number of fishing gears exploiting different species with different size and targeting preferences. More specifically, the fishing mortality of the ith species in the jth length class at time step t is where e is the effort of the kth gear, for k = 1…H (the total number of gears in the fishery) and q is the catchability. The units for F are yr−1 and the units of q are F per unit effort.

The number of individuals after the growth phase, and the end of the time step, is where ϕ is the proportion of individuals of species i that leave length class j due to growth over the time step according to the von-Bertalanffy growth equation [22] (see S2 File pages 3-4 for more details). Further details of the model can be found in S2 File (pages 2-14) and in [9].

Using LeMaRns

LeMaRns is available on CRAN (https://cran.r-project.org/web/packages/LeMaRns/index.html) and GitHub (https://github.com/CefasRepRes/LeMaRns).

Data requirements

Biological data

The minimum amount of information required to set up a model using LeMaRns includes: species-specific maximum length (Linf), length at 50% maturity (Lmat), length-weight conversion parameters (e.g. W_a and W_b), the growth parameter from the specialised von Bertalanffy growth function (k) [23], and the recruitment parameters (recruit_params; see S2 File, page 5 for further details). The length-weight and life history parameters are often available from survey data, online databases (e.g. Fishbase [24]), or through ‘life history invariants’ [25, 26]. The recruitment parameters are typically harder to determine and can be thought of as ‘tuning’ parameters [6]. The fitting of these parameters is done outside of the LeMaRns. An illustrative example, based on the methods in [27], can be found in S3 File.

In addition to the required parameters described above, users may specify species-specific values for M1, background mortality (i.e. mortality not from fishing or predation), and the rate of change from immaturity to maturity, although default values are given for these. Users may also input a predator-prey interaction matrix, tau, which describes the diet information and spatial overlap of predators and prey. tau defaults to one for all predator-prey combinations, although we recommend that this is replaced with an ecosystem-specific matrix based on available diet information, spatial overlap, and/or expert judgement.

In LeMaRns there are five built-in recruitment functions: hockey-stick [21] (the default option), Ricker [20], Beverton-Holt [23], linear, or constant, as well as three background mortality functions: std_RNM (the default option), constant, and linear (see S2 File, pages 5 and 7).

The predator-prey mass ratio, the width of the predator-prey size preference, and the theoretical growth efficiency of a fish of length zero are all species-independent parameters in the current version of LeMaRns.

Fishing

LeMaRns allows mixed-fisheries analyses to be conducted through the definition of fishing gears. In the LeMans model, the fishing mortality is calculated using Eq 1. This means that the catchability, q, for the ith species in the jth length class with the kth gear must be defined for all species, length classes, and gears. The catchability is fixed in time but effort, e, can be dynamic. In LeMaRns there are three built-in functions that can be used to create catchability curves: logistic, log_gaussian, and knife-edge (see S2 File, page 8). In addition, there is an option that allows users to input their own catchabilities.

Test dataset

In LeMaRns, we provide a dataset, NS_par, for 21 species in the North Sea based on [10]. The dataset contains Linf, Lmat, W_a, W_b, k, and the recruitment parameters (a and b) for each species. We also include NS_other to represent other food. The recruitment parameters, a and b, and NS_other were calibrated to the North Sea (see S3 File for details). The predator-prey matrix (NS_tau) contains information regarding the diet of the 21 species and is based on [10]. In addition, we provide information regarding a number of fishing fleets (NS_mixed_fish), with catchability parameters (NS_eta and NS_L50) that are based on [12].

Setting up the model

In LeMaRns a model can be set up using the LeMansParam() function. This function returns an object of class LeMans_param, which contains all of the information required to run the LeMans model. Below is an example of how to use the provided data to set up the model:

NS_params <- LeMansParam(NS_par, tau = NS_tau,

eta = NS_eta, L50 = NS_L50, other = NS_other)

The LeMansParam() function takes the parameters described in the previous section, as well as optional inputs including: n, the number of length classes (nsc, the default is 32); the boundaries of the length classes (bounds, the default depends on max(Linf)), and δt, the time step of the model in years (phi_min, the default is 0.1).

All default values, with the exception of tau, are the same as those used in [10].

Running the model

In LeMaRns a model can be run using the run_LeMans() function:

run_LeMans(NS_params)

By default, run_LeMans() uses the get_N0() function to initialise the population and is run for for 10 years with no fishing. However, users can specify their own initial population with the input N0, a feature that also allows users to extend model runs when required (see S2 File for examples).

Although gear catchability is calculated in LeMansParam(), fishing effort is an input to run_LeMans(), thus allowing effort to be dynamic. years is also an input to run_LeMans() and is used to define the number of years that the model should be run for. Below we run the model for 50 years with a constant effort of 0.25, which equates to an F of 0.25 on the length-class with highest selection, for each gear:

no_of_gears <- dim(NS_params@Qs) [3]

effort_mat <- matrix(0.25, 50, no_of_gears)

model_run <- run_LeMans(NS_params, years = 50, effort = effort_mat)

Model outputs

run_LeMans() returns an object of class LeMans_output, which contains a time series of the number of individuals in each length class for each species and time step (N), the weight caught in each length class for each species and time step (Catch), the predation mortality in each length class for each species and time step (M2), and the number of recruits of each species and time step (R).

The LeMaRns package also includes a number of built-in functions that enable users to explore the outputs of a model run in more detail. These functions can be used to calculate and plot community and species-specific total biomass and Spawning Stock Biomass (SSB), as well as several ecosystem indicators including the Large Fish Indicator (LFI), Mean Maximum Length (MML), Typical Length (TyL), and Length Quantiles (LQ). Functions also exist to calculate Catch Per Unit Effort (CPUE) and Catch Per Gear (CPG). See S2 File, page 18 for definitions of these outputs.

An example is shown in Fig 1, which is created using plot_SSB(NS_params, model_run).

Fig 1

The Spawning Stock Biomass (SSB) plotted using the plot_SSB() function.

Case studies

In this section we provide three applications of the LeMaRns package. The first example focuses on finding long-term multi-species fishing targets; the second examines the effect of different fishing scenarios on long-term stock status in a mixed-fishery; and the third example explores the effect of dynamic fishing effort in a mixed-fishery on ecosystem indicators. In the applications we assume that each species is a single stock. The code for generating these examples can be found in S1 File.

Nash equilibrium

Fish stocks are often managed by considering the fishing mortality that maximises the long-term yield, i.e. the Maximum Sustainable Yield (MSY) [28]. We can define f(F, −) as the ith stock’s long-term yield, where F is the fishing mortality of the ith stock and − are the fishing mortalities of the other stocks. Many stocks are managed on a stock-by-stock basis using single-species models. This means that , and then is commonly well defined. However, stocks often interact with one another and the fishing mortality of the jth stock affects the catch of the ith stock, i.e. We therefore need to define a multi-species MSY. One possibility is the Nash equilibrium [13], which is defined as the point at which we are unable to increase f(F, −) by changing F only, ∀i. Formally, F is a Nash equilibrium when Using LeMaRns and starting from the F values given in [12], we can find F for i = 1, …, 21. We can also find F values to compare to our F; this is not trivial as we need to define fishing mortalities for all of the species and F will be sensitive to these. Arbitrarily, we can set the fishing mortality for the other species to the values given in [12]. Fig 2 provides a comparison between F and F; they appear to be similar for the species with lower F and F, but differ more for larger values.

Fig 2

F and F calculated using the LeMans model for the 21 species.

The solid line is the 1-1 line.

In this study we arbitrarily chose to hold the fishing mortality of the other stocks at the F values given in [12]. However, if we had chosen to hold them at F, then F = F, ∀i, as F is a solution of F. This highlights the sensitivity of F to the fishing mortality on the other stocks.

Mixed-fishery

Here we explore the mixed-fishery example described in [12], which involves four idealised fishing fleets, i.e. a single species is caught by only one gear type. We investigated the risk of stock collapse under different fishing scenarios. A stock is deemed to have collapsed if its SSB falls below 10% of its unfished SSB [12, 29].

The dataset NS_mixed_fish contains information on which fleet catches which species. In this example, the selectivity of each species follows the logistic curve with catchability parameters eta and L50.

In a scenario, the effort of each of the four fishing fleets, Industrial, Otter, Beam, and Pelagic, was one of five levels, c(0,0.5,1,1.5,2), which was held constant for 50 years. We ran all possible combinations of these levels resulting in 625 different scenarios.

Fig 3 depicts the number of stocks at risk under varying levels of fishing effort for each fleet; the number of stocks at risk of collapse is mostly sensitive to the effort of the Otter and Beam fleets.

Fig 3

The effect of varying fishing effort on the number of stocks at risk of collapse.

Dynamic fishing

Here we add another fleet (Recreational) to the idealised fleets in the previous example. This fleet is set up to catch cod, haddock, herring, horse mackerel, mackerel, plaice, saithe, and whiting, with all fish exceeding the minimum landing size [30] being retained. Any fish that are discarded are assumed to have survived (following a knife-edge selectivity function). Having run the LeMans model for 50 years with no fishing, the model was run for a further 20 years with dynamical fishing effort (see Fig 4 and S2 File, page 39 for the time series of fishing effort).

Fig 4

The effort for the four fishing fleets.

The recreational fishing fleet is not shown but increases linearly from 0.1 in the first year to 0.15 in the final year.

Fig 5 depicts the MML, TyL, the LFI (40cm threshold), and the 0.1, 0.5, and 0.9 LQs in the last 20 years of the model run. The different fishing fleets seem to have a different effect on the dynamics of the indicators. MML and the LFI seem to correlate with the fishing effort of the Otter fleet, whilst TyL is additionally affected by the Pelagic fleet. The dynamics of the LQs suggest that larger fish are affected by the Otter fleet and medium sized fish by the Pelagic fleet. The smaller fish do not have a large reaction to fishing, but seem to have inter-annual variation due to spawning.

Fig 5

The effect of fishing scenario on community indicators.

This plot was created using the plot_indicators() function.

Conclusions and further work

LeMaRns provides a convenient and user friendly way to run the LeMans model, with comprehensive documentation. The package contains the required functions to explore different fishing scenarios in a mixed-fisheries multi-species model and allows for the customisation and tailoring of inputs to model specific environments, conditions, and scenarios. This, along with the low data requirements, makes LeMaRns a transparent, easy to use, and broadly applicable fisheries assessment tool that encourages model development and experimentation. Further, we hope this will lead to an increased uptake of LeMans by the fisheries management community.

Several developments are planned for future releases, including food-dependent growth and stochastic recruitment. The package is currently being used to explore the effects of harvest control rules in the North Sea and to explore seasonal effects using a similar method to [31].

R script.

The R script to run the case studies and generate the figures in the paper.

(R)

Click here for additional data file.

R package vignette.

Contains the description of the model and further explanation of the package.

(PDF)

Click here for additional data file.

An example of calibrating the model.

Contains an example of calibrating the model with robust uncertainty quantification using a Bayesian framework.

(PDF)

Click here for additional data file.

27 Aug 2019

PONE-D-19-20184

LeMaRns: a Length-based Multi-species analysis by numerical simulation in R

PLOS ONE

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Reviewer #1: General comments:

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The manuscript describes the implementation of the LeMans model as package for R, LeMaRns. It includes several examples to demonstrate how the package can be used. Most of the details on the model and its implementation are in the accompanying vignette. The paper is generally well written and the example code seems to do what it is supposed to do. I think that the manuscript is generally suitable for publication but there are some relatively small issues that I would like to see first addressed.

I appreciate that the vignette provides most of the details about the model and how to use the package. However, some more model details in the main manuscript would be good so that readers didn’t have to go digging too far to find out some of the basic model assumptions. For example, is the model single area? I assume so given the use of the predator-prey matrix for spatial overlap, i.e. a proxy for multiple areas.

Additionally, the time step of the model is not clear from reading the manuscript. For example, the equation for fishing mortality is described using time step (line 95), but the arguments for the *run_LeMans()* function includes year. Can the user determine the size of the time step? I see in the vignette that this is possible by using the *phi_min* argument but a note about this could be added to the main text.

Following this, there is some inconsistency in how the time axes are labelled. The axes for Figures 1 and 5 are in time steps (the scale implying 10 time steps per year), whereas the axis for Figure 4 is year.

Line 105, the predator-prey matrix, NS-tau, is described as containing information regarding the diet of the species in the model. It would be good to know what kind of information this is and how users might go about getting this information for their own models.

The supplementary R script works as it is supposed to and recreates the figures in the manuscript (tested using R 3.6.1). I note that the model does run very fast (certainly quicker than the initial implementation of the mizer model used to).

Specific points

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* Line 6: “However, over longer timescales models that take account of multi-species interactions, such as predation and competition for resources are required for meaningful predictions.”

This is a strong statement. I don’t necessarily disagree with it but it would be good see to some additional exploration and justification of this point. For example, it is not always the case that multi-species models are better than single-species models for “meaningful” predictions. Multi-species models generally have higher data requirements, make more assumptions and are more difficult to parameterise than single-species models. This can result in an increase in uncertainty in the model predictions. Depending on the type of advice that is required for management it may be better to use a simple model, whose limitations are well understood, than a more complex model. Additionally, multi-species interactions may only become important when fishing mortality is relatively low, i.e. when fishing pressure is high it is the dominant source of mortality, in which case single-species models may be adequate. There are many challenges when using multi-species models, including LeMans, for example the estimation of an initial population abundance (as noted in the manuscript, which states that the provided data for the North Sea ecosystem has not been calibrated). This is simpler with a single-species model as they can often be used for stock assessment as well as projections.

I understand that the focus of the paper is not about the pros and cons of single- vs multi-species models but I think the introduction could benefit from a small discussion about when using a multi-species model might be appropriate and the kind of management advice it is able to provide, including the robustness of that advice.

* Line 8: “…several multi-species models have been developed”.

There are certainly more than several multi-species models. Do the authors mean several multi-species modelling approaches?

* Line 97: “…catch at length…”

Do the authors mean “catchability at length”?

* Line 108: “Note that due to the generalisations of the LeMans model in the LeMaRns R-package, the provided data is not calibrated to the North Sea ecosystem and is therefore used for demonstration purposes only.”

This is slightly concerning. Does this means that the implementation here is not the full LeMans model? What are these generalisations and what are the key differences between the LeMans model (as described and reviewed in references 8 – 13) and this implementation as LeMaRns? How do they impact the data in the package so that it is essentially uncalibrated?

It’s a shame that the data has not been calibrated. Some notes on how calibration could be performed would be good, rather than just pointers to references, i.e. what data is required to perform tuning?

* Line 117: Is it necessary to include the *other* argument? It isn’t described in the main text and the default value (according to the man page for LeMansParam()) is 1e12 anyway.

* Figure 1: There should be units on the y-axis for SSB.

* Figure 2: Why are the axes inverted (i.e. go from high to low)? Also, there should be units on these axes.

* Line 186: “Using a factorial design…”

It is not immediately clear what this means. I can figure it out from the attached R script but this could be expanded in the text to add clarity.

* There is a possible mistake in the package vignette. On page 13 of the vignette it says “Below we run the model for 10 years” but then the variable years is set to 50 (with a comment saying run for 10 years).

Reviewer #2: Review of PONE-D-19-20184- “LeMaRns: a Length-based Multispecies analysis by numerical simulation in R

This manuscript introduces an R version of the ecosystem model LeMans first developed by Hall et al. 2006. The authors provide a very brief introduction to the model and a few examples of ways the model can be applied. The manuscript is well written but falls very short of any actual detail. The authors have decided to push almost all of the meat of this study into the supplemental materials. Although this may be what the journal wants, as a potential end-user of the package I find it very frustrating to not have the most pertinent information in the main text. As a result, the manuscript reads more like a vignette that could be included with the package on CRAN rather than the primary literature source for the model.

The statement on lines 108 – 110 concerns me quite a bit. It sounds like it is saying that the R package can not reproduce the LeMans outputs using the same data set? If so, that is not good. If a few more parameters need to be adjusted so that it will produce the same results than they should be included. The premise of the R package is that it is a easier more transparent version of LeMans but that may not be the case it it can't reproduce the results using the same data.

Another small editorial note, I wonder why the title of the package is LeMaRns, which stands for a Length-based Multi-species analysis by numerical simulation in R. Why not LeMansR? Not only is LeMansR easier to say it makes it obvious that it is an R version of LeMans and not a completely different model.

Other detailed notes:

Line 40 – 41 – claim that LeMans is less complicated than Ecopath or Atlantis. It is true that it is less complicated than Atlantis but Ecopath does not require length data, stock-recruitment relationships, or catchability information.

Line 66 – 69 – I don't think this is necessary to describe the model unless stepping through all of the code. A simple mention tht it is available of CRAN in the introduction should be sufficient.

Line 75 – Are you using the specialized or general k form of the von Bertalanffy growth equation (See Essington et al. 2001 CJFAS 58(11): 2129-2138)?

Line 85 – States that users may input a predator-prey matrix. Is there a default if they do not?

Line 96 – Effort and catchability need to be applied to a biomass or number which I assume is the Lj but the way it is written is not clear. Also, should the catchability term be specific to the length group so qkij instead of qik?

Line 102 – A better sub-heading would be “Test Data Set”

Line 103 – While I'm sure the test data is in a data frame that is probably too technical and should just be referred to as the data set instead. It would also be helpful to flesh out why the test data set is included.

Line 121 – What are the default values based on?

Lines 122 – 125 – Which is the default and why?

Line 139 – I'm guilty of this as well but it is bade form to use the same name for a variable as an argument (e.g. effort = effort).

Line 177 – 178 – Is this an expected result based on other Nash equilibrium studies?

Line 213 – I'm not sure that this manuscript is as transparent as the authors intended. Other than calculations for Nash equilibrium there are no equations.

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Reviewer #1: Yes: Finlay Scott

Reviewer #2: Yes: Sean M. Lucey

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10 Oct 2019

See attached document

Submitted filename: Reviewer_resp.pdf

Click here for additional data file.

26 Nov 2019

PONE-D-19-20184R1

LeMaRns: a Length-based Multi-species analysis by numerical simulation in R

PLOS ONE

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Reviewers' comments:

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Reviewer #2: Yes

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Reviewer #1: (No Response)

Reviewer #2: Review of PONE-D-19-20184-R1 “LeMaRns: a Length-based Multispecies analysis by numerical simulation in R

This is a revision of the manuscript that introduces an R version of the ecosystem model LeMans. The authors have done a good job addressing my major concerns from the first review. My biggest concern was the inability of the package to recreate a published version of the LeMans model but that has been resolved. I would still prefer to see more meat of the package in the main text rather than as supplemental but see the type of article the authors are going for.

I do have a few minor editorial comments:

Abstract – final sentence says “...leading to increase uptake by fisheries management community”. This is an optimistic statement that should say “we hope will lead to...”. Which is how the authors say it in the main text (Line 36)

Line 63 – Can you provide a citation for how spatial information is included implicitly?

Line 78 – States that predation mortality is size- and species-dependent. I think there is a term missing from M2. Right now there is only a i (species), j (length), and t (time). Nothing for predator or predator size.

Fishing mortality equation has a number but none of the other equations do.

Line 122 – delete “(the default option is hockey-stick)” as it is already stated earlier in the sentence.

Line 148 – It is unclear how NS_other has been calibrated to represent other food. I understand that this was how the authors dealt with my concern over LeMaRns not recreating a published version but this needs further explaination.

Line 170 – The statement about the model is run for 10 years with no fishing can be confusing. Better to note that the default parameters are 10 years and 0 fishing effort.

Line 179 – What is the units for effort? Is this relative effort?

Conclusion – The authors should add a paragraph echoing the end of the abstract/ intro to tie everything together.

**********

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Reviewer #1: Yes: Finlay Scott

Reviewer #2: Yes: Sean M. Lucey

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

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18 Dec 2019

See attached pdf

Submitted filename: reviewer_resp.pdf

Click here for additional data file.

30 Dec 2019

LeMaRns: a Length-based Multi-species analysis by numerical simulation in R

PONE-D-19-20184R2

Dear Dr. Spence,

We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.

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With kind regards,

Athanassios C. Tsikliras

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

8 Jan 2020

PONE-D-19-20184R2

LeMaRns: a Length-based Multi-species analysis by numerical simulation in R

Dear Dr. Spence:

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