Guillaume Helbecque
email: guillaume.helbecque@univ-lille.fr

Jan Gmys

Tiago Carneiro

Nouredine Melab

Pascal Bouvry

A

Keywords: Chapel, MPI, Multi-core, OpenMP, Parallel computing, Productivityawareness

come

INTRODUCTION

Nowadays, we observe a dramatic increase in complexity, diversity and scale of High Performance Computing (HPC) environments. According to the TOP500 bi-annual ranking of the most powerful systems [14], modern supercomputers are increasingly large (millions of cores) and heterogeneous (CPU-GPU). On the other hand, HPC applications and algorithms also tend to be more and more sophisticated. Actually, in order to benefit from the parallelism provided at different levels of the hardware, hybrid hierarchical parallelism is recommended. This is a reason why there is an increased research interest in software development productivity in HPC [START_REF] Faulk | Measuring HPC productivity[END_REF][START_REF] Kepner | HPC Productivity: An Overarching View[END_REF]. Different programming models/languages, runtimes and libraries need to be used together to efficiently exploit all levels of parallelism. As a consequence, to deal with such complexity, efforts towards productivity are crucial for harnessing the processing power of modern supercomputers.

To this end, the DARPA High Productivity Computing System (HPCS) program represents an effort for creating high-productivity languages for the next generation of supercomputers [START_REF] Lusk | Languages for High-Productivity Computing: the DARPA HPCS Language Project[END_REF]. Among these languages, Chapel stands out, as it is competitive to both C+OpenMP and MPI+X in terms of performance and scalability [START_REF] Chamberlain | Chapel comes of age: Making scalable programming productive[END_REF].

The recent arrival of this language raises the question of its competitiveness with well-established conventional parallel programming environments. For this purpose, this paper provides a comparison point between Chapel and the widely adopted OpenMP and MPI+X parallel programming libraries. The focus is put on the parallel computation of the Mandelbrot set. This embarrassingly parallel application allows massive parallelism, while facing irregular workload.

In this paper, we illustrate the main parallel features of Chapel, MPI and OpenMP using the Mandelbrot test case. Six implementations are proposed using Chapel, C+OpenMP, C+MPI with different communication models (two-sided blocking and non-blocking, onesided), and a hybrid one, combining C+MPI and OpenMP. Chapel as well as its default tasking layer demonstrate high performance in shared-memory context. Moreover, in distributed-memory environment, it presents similar performance to hybrid MPI+OpenMP, even though we did not explore other features, such as the distributed iterators.

The remainder of the paper is structured as follows. Section 2 presents related works. Section 3 defines the Mandelbrot set computation. Section 4 provides an overview of each parallel programming environment and describes the corresponding implementations. Experimental results are reported in Section 5. Finally, we draw the conclusions in Section 6 and outline some future works.

RELATED WORKS

In various domains, empirical studies compare different parallel programming environments for a typical problem in the respective field of research. In [START_REF] Parenteau | Development of Parallel CFD Applications with the Chapel Programming Language[END_REF], Parenteau et al. develop Chapel-based alternatives for two CFD applications. These were compared to conventional MPI-based algorithms, and the competitiveness of Chapel is highlighted. In [START_REF] Gmys | A comparative study of high-productivity high-performance programming languages for parallel metaheuristics[END_REF], Gmys et al. are dealing with three productivity-aware languages (Chapel, Julia and Python) to solve the 3D Quadratic Assignment Problem parallel metaheuristic on a multi-core shared-memory computer. The comparison is done in terms of performance, scalability and productivity. Moreover, related works in the context of irregular applications (like Branch-and-Bound tree-search algorithms) show that it is possible to achieve parallel efficiency and performance, but also high productivity, by using the Chapel language [START_REF] Carneiro | Towards ultra-scale Branch-and-Bound using a high-productivity language[END_REF].

The parallel Mandelbrot set computation is a well-studied problem. Some authors use this test-case to describe how the fundamentals of task parallel programming are dealt with different efficient parallel environments, like Chapel, OpenMP, X10, OpenCL, etc [START_REF] Khaldi | Task Parallelism and Data Distribution: An Overview of Explicit Parallel Programming Languages[END_REF]. However, the latter focus on illustrating the fundamentals of task parallel programming without performing a performance analysis. Another study conducts performance evaluation on shared-memory architecture using MPI and OpenMP [START_REF] Gomez | MPI vs OpenMP: A case study on parallel generation of Mandelbrot set[END_REF], but doesn't include PGASbased environments.

Our paper aims at providing a useful data point using sharedand distributed-memory multi-core systems for supercomputer programmers. The well-known parallel Mandelbrot set computation is chosen because it is a complete application (not a microbenchmark kernel) that allows easy decomposition into a large number of irregular subproblems, while retaining a relative simplicity. The latter allows us to illustrate the programming effort in each environment by short but complete code snippets and thereby provide to the reader a sense of "productivity", which is a hard-to-evaluate and necessarily somewhat subjective measure.

MANDELBROT SET COMPUTATION

In this paper, we consider the parallel computation of the Mandelbrot set as a test-case. It is defined as the set of complex numbers 𝑐 = 𝑎 + 𝑖𝑏 ∈ C such that the sequence (𝑧 𝑛 ) 𝑛 ∈N ⊂ C defined by

𝑧 0 = 0, 𝑧 𝑛+1 = 𝑧 2 𝑛 + 𝑐, (1)
remains bounded in C (see Figure 1). In practice, we can prove that a point 𝑐 of the complex plan belongs to the Mandelbrot set if and only if

|𝑧 𝑛 | ≤ 2, ∀𝑛 ∈ N.
𝐼 (𝑎, 𝑏) = 1 𝑁 min 𝑛=0,...,𝑁 {𝑛 : |𝑧 𝑛 | > 2}, (2)
where 𝑁 ∈ N is an arbitrary maximum number of allowed iterations. This well-known parallel application allows to illustrate the main parallel features and to investigate the parallel efficiency of the programming environments considered in this paper. As we can see in Algorithm 1, the nested for-loops can be easily and massively parallelized due to the independence of each pixel. The granularity of the application (amount of work performed per pixel/line of the image) can be controlled by adjusting the maximum number of iterations 𝑁 . However, one has to deal with the irregular workload resulting from the drastically different amount of work performed per pixel (see Figure 2).

The parallelization of Algorithm 1 is thus based on a domain decomposition. In order to preserve the relative simplicity of the implementation, the decomposition is assumed only along the lines, i.e. only the first for-loop in Algorithm 1 (line 13) is parallelized. Moreover, in order to achieve some workload regularization, lines are mapped to processing elements in round-robin fashion. For comparison purposes, we require that the computation is deterministic. It means that the domain decomposition is done statically and we know in advance which thread computes which lines.

PARALLEL PROGRAMMING ENVIRONMENTS

This section presents the studied parallel programming environments and highlights their main features. Six parallel implementations of the Mandelbrot set computation are described using Chapel, OpenMP, MPI with different communication models (twosided blocking and non-blocking, one-sided), and a hybrid one, combining MPI and OpenMP.

OpenMP

The OpenMP API (Open Multi-Processing Application Programming Interface) [START_REF]OpenMP API[END_REF] OpenMP directives are added to the code using the #pragma preprocessor mechanism. The most common way to introduce parallelism is the omp parallel directive which creates a parallel region where concurrent threads execute the same code. The omp for work sharing directive allows to distribute iterations of a for-loop among threads. Several clauses can be employed to modify the behavior of the work sharing construct, for instance whether loop iterations are distributed using a static scheduling (Master-Worker model) or a dynamic one (Work-Pool model). Round-robin static distribution of lines onto threads is achieved by the schedule(static,1) clause, where the parameter 1 represents the chunk size. Another important point is that OpenMP relies on a fork-join model, where a set of threads is created entering a parallel region (fork), and is destroyed at the end (join). This model thus implies implicit synchronization mechanisms. A more complete documentation of OpenMP is available in [START_REF]OpenMP API[END_REF].

The OpenMP parallel Mandelbrot generation is described in Algorithm 2. One can see that parallelization is achieved through a minimal and incremental modification of the sequential code (addition of line 2). The composite omp parallel for directive is added in order to distribute the iterations of the first for-loop (line 3) onto threads.

Chapel

Chapel (Cascade High Productivity Language) [START_REF] Chapel | The Chapel Parallel Programming Language[END_REF] is an open-source high-productivity and high-performance programming language that follows the Partitioned Global Address Space (PGAS) programming model. Chapel allows shared-and distributed-memory executions, and runs on top of the GASNet one-sided communication and active message library. Furthermore, as Chapel belongs to the PGAS class of languages, the application has a global memory addressing space, and each segment of this space is assigned to a different locale [START_REF] Almasi | PGAS (partitioned global address space) languages[END_REF]. In turn, a locale refers to a unit of the machine resources that can store variables and run Chapel tasks, which is similar to an MPI process. It is also worth to say that the language supports object-oriented design and C or Fortran interoperability features. In Chapel, parallelism is expressed in terms of tasks, which can be run on one or several locale(s). The program is started with a single task, and parallelism is added through data or task-parallel features, such as the coforall statement, which is a parallel version of the for-loop, introducing task parallelism by creating a distinct task per loop iteration. This feature is suitable to create concurrent tasks, especially when the loop iterations are independent, like in the Mandelbrot set computation. Moreover, it is possible to explicitly control locality via the on clause that allows to migrate a task on the specified locale. The number of locales is passed to the implementation using the command line parameter -nl 𝐿, where 𝐿 is the number of locales on which the application is executed. The detailed Chapel documentation is available in [START_REF] Chapel | The Chapel Parallel Programming Language[END_REF].

The implementation of the Mandelbrot written in Chapel is depicted in Algorithm 3. First of all, a coforall statement is used to create as much tasks as locales (line 2). Then, each allocated task is migrated on its associated locale (line 3). Following this, another coforall statement is used to create as much tasks as threads per locale (line 4). Finally, each task thus created computes sequentially its lines of pixels. Unlike the OpenMP implementation, the distribution of lines onto threads is done manually, by computing the corresponding indices (line 5).

MPI

MPI (Message-Passing Interface) [START_REF]Open MPI: Open Source High Performance Computing[END_REF] is a library interface specification for message-passing on shared-and distributed-memory multi-core computers. MPI is widely used in academic and industrial areas for its portability, standardization and its high performance. MPI defines a set of subroutines, usable in C or Fortran. Typically, a SPMD model is used, where a set of MPI processes, having their own exclusive address space, execute the same program.

Executing an MPI program in parallel consists in launching multiple copies of the same program on a set of specified hosts. The MPI environment can be initialized using the MPI_Init routine, enabling interprocess communications. MPI_Finalize shuts down the environment and cleans up all MPI-related state. Other process management operations like MPI_Comm_size and MPI_Comm_rank allow to query the number of MPI processes in a given MPI communicator and the rank of the calling MPI process, respectively.

Initially, the MPI standard (MPI-1) specifies a point-to-point communication model through send and receive operations. Since this latter implies both sender and receiver sides, we usually refer to this model as two-sided. Later, MPI-2 introduces new functionalities, like one-sided communications, also known as Remote Memory Access (RMA). MPI one-sided communications are limited to accessing only a specifically declared memory area on the target, called a window. Unlike with two-sided operations, the target process doesn't perform any action. The detailed MPI documentation is available in [START_REF]Open MPI: Open Source High Performance Computing[END_REF].

In the remainder of this section, four MPI implementations are described using different communication models: two-sided with blocking and non-blocking operations, one-sided, and hybrid MPI+OpenMP. Each MPI process will perform the computation of its lines, while only the master process stores the image. This implies communication of data between processes.

4.

3.1 Two-sided communications. The two main routines for MPI two-sided communications are MPI_Send and MPI_Recv. The send/receive buffers, sender/receiver ranks and data types must be explicitly specified by the programmer. Moreover, these are blocking communications involving implicit synchronizations.

The MPI parallel implementation with two-sided blocking communications is described in Algorithm 4. First, the MPI environment is initialized, and each process reads its rank and the number of MPI processes (lines 1-3), which are used to explicitly map processes onto work items (lines of the image). Each MPI process sequentially computes the lines it is assigned to (lines 4-5). Completed lines are send to the master process (rank 0) introducing synchronization points between the latter and all non-zero ranks. When the work is finished, the MPI environment is shut down and the master process writes the image to an output file (not included in time measurings).

The previous MPI algorithm represents the most basic MPI parallel implementation of the Mandelbrot set computation. However, implicit synchronization could induce communication overheads that become significant for fine-grained computations. This is why MPI also includes non-blocking operations. The most basic ones are MPI_Isend and MPI_Irecv. The use of non-blocking communications leave the user responsible for explicit synchronization, for instance by using the MPI_Waitall routine. A variant of Algorithm 4 using non-blocking communications is shown in Algorithm 5. Algorithm 6 shows a variant of the previous MPI-based algorithms using one-sided communications. Similarly, the implementation begins with the initialization steps, followed by the window creation procedure MPI_Win_create (line 4). Synchronization on the window (line 5), effectively acting as a global barrier, is required to ensure that the window is completely accessible by every process before performing any operations. The mapping of processes onto work items is identical to the previous MPI-based algorithms. The difference is that the master process is no more involved in the communications. At the end, the windows is freed with MPI_Win_free (line 13) and the MPI environment is closed.

Hybrid MPI+OpenMP.

In this last section, we focus on a hybrid MPI+OpenMP program to combine the distributed features of MPI with the multi-threaded execution model of OpenMP. The MPI environement is initialized using the MPI_Init_thread subroutine with the MPI_THREAD_FUNNELED multi-threading support, indicating that MPI calls will only be issued from the master thread of each process.

The hybrid approach is illustrated in Algorithm 7. At most one MPI process is allowed per computer node. This can be done using the --map-by ppr:1:node mapping policy. Locally to each node, the computation of lines is done in parallel using OpenMP, like in Algorithm 2 (line 4). Then, MPI is used for the inter-processes communications (lines 5-9). As lines computed per process are send to rank 0 in a single batch, we choose to deal communications with the basic two-sided blocking communication model.

EXPERIMENTAL EVALUATION

In this section, we experimentally evaluate the implementations introduced in Section 4. Section 5.1 introduces the experimental testbed, and Section 5.2 defines the experimental protocol. The performance results in shared-and distributed-memory environments are presented and analyzed in Section 5.3 and 5.4, respectively.

Experimental testbed

The experiments are carried out using the French national Grid'5000 experimental testbed. All computer nodes operate under Debian GNU/Linux 11 (bullseye), 64 bits and are equipped with 𝑡𝑤𝑜 AMD EPYC 7301 CPUs @2.20GHz (a total of 32 cores/64 threads per node) and 192 𝐺𝐵 RAM. All computer nodes are interconnected through a 25 Gbps Ethernet network Intel Ethernet Controller XXV710. The number of computer nodes in the experiments ranges from 1 to 6. Thus, up to 192 processing cores are used in the experiments. Concerning the Chapel implementation, each computer node hosts one Chapel locale. Table 1 presents the tools/libraries and optimization flags used for compiling the programs. Chapel's multi-locale code runs on top of GASNet, and the runtime should be built taking account the characteristics of the system on which the multi-locale code is supposed to run. One can see in Table 2 a summary of the runtime configurations for multi-locale execution. The UDP GASNet implementation is the one used for communication (CHPL_COMM_SUBSTRATE) along with SSH, which is responsible for getting the executables running on different locales (GASNET_PSM_SPAWNER).

Experimental protocol

For each implementation, the computation time is measured while varying the granularity, controlled by the maximum number of iterations 𝑁 , that takes its value in {100, 1000, 10000, 100000}. The image size is fixed to 1024x768 and 5120x3840 for shared-and distributed-memory experiments, respectively. For each experiment, the relative speed-up 𝑆, defined by

𝑆 (𝑝) = 𝑡 (1) 𝑡 (𝑝) , (3)
is then measured, where 𝑡 (𝑝) corresponds to the execution time using 𝑝 processing units, and 𝑡 (1) is the corresponding sequential time. The clock_gettime timer C function is used, since it is valid for all implementations (using the C interoperability in Chapel).

Experiments are performed multiple times, and the average is considered.

Results on shared-memory system

Figure 3 depicts the relative speed-up measured while varying the number of processing units from 1 to 64. Different maximum number of iterations 𝑁 are considered in order to see the effect of the granularity. Hyperthreading is allowed for the Chapel and OpenMP implementations, but the overloading of MPI processing elements is disabled (with the -nooversubscribe flag). We can see that the MPI-based implementations suffer from high parallel overheads. Indeed, for low granularity, 𝑁 = 100, the workload is not sufficiently large to counterbalance the MPI communication overheads. This is why speed-up remains bounded by 10. However, when the granularity increases, the MPI implementations are able to take advantage of parallelism to reach a high speed-up, very close to the ideal one (𝑁 = 100000). In addition, we note that the implementation based on two-sided non-blocking communications performs better than its blocking counterpart. In these experiments, no difference appears between the one-sided and the two-sided non-blocking MPI implementations. Concerning the speed-up of the OpenMP implementation, we observe the same behavior as in MPI, i.e., the application scales poorly for very fine granularity. This is explained by the fact that the fork-join model of OpenMP is costly, and need to be counterbalance by a sufficiently large workload. When 𝑁 increases, the OpenMP speed-up is getting closer to the ideal one. We also note that hyperthreading allows OpenMP to obtain good performance, although the speed-up for 64 threads is quite far from ideal. Finally, interestingly, we can see that the Chapel implementation doesn't suffer much from parallel overheads. Even with a low granularity, we note that Chapel can easily obtain a speed-up that reached 50 using hyperthreading, and scales well with the ideal speed-up when 𝑁 is growing.

In order to investigate the high performance of Chapel compared to the other implementations, we suggest to measure the computation time when fixing 𝑁 = 1. In accordance with Algorithm 1, it represents the minimum valid value of 𝑁 for which the workload for each pixel is negligible, almost zero, and thus the computation time reflects the parallel overheads. Experiments are performed fifty times, and the average is considered.

These results are depicted in Figure 4. Firstly, concerning the MPI-based implementations, we can see that for two-sided communications, the computation time is slightly increasing with the number of processing cores, and we note that the removal of implicit synchronizations through non-blocking operations allows a minor gain. Moreover, we observe that the MPI one-sided approach is more expensive than others, due to the fact that this model requires the creation of a window, in addition to communication and synchronization mechanisms. Secondly, we observe also that the OpenMP computation time is growing with 𝑁 . We note that OpenMP is faster than all MPI-based implementation, except when using hyperthreading. Finally, we observe that Chapel is consistently faster than all others. Interestingly, the computation time is decaying with the number of processing units. This behavior can partly explain the very good Chapel performance in the shared-memory multi-core experiments of Figure 3, whatever the granularity. The Chapel 𝑞𝑡ℎ𝑟𝑒𝑎𝑑𝑠 default tasking layer, that provides a lightweight implementation of Chapel tasking as well as an optimized implementation of synchronization variables, is thus very appropriate, and allows high performance [START_REF] Wheeler | The Chapel Tasking Layer Over Qthreads[END_REF][START_REF] Wheeler | Qthreads: An API for programming with millions of lightweight threads[END_REF].

Results on distributed-memory system

In this section, the parallel speed-up is observed while varying the number of processing units from 1 to 192. MPI processes overloading and hyperthreading are not allowed. The hybrid MPI+OpenMP implementation uses 1, 2, 3, 4, and 6 MPI process(es) with 32 threads each. Communications are performed by process 0. The results are presented in Figure 5.

Firstly, when considering low granularity, 𝑁 = 100, all implementations suffer from high parallel overheads. Each speed-up associated to MPI-based implementation remains bounded by 20. This is also true for the hybrid MPI+OpenMP program. Actually, the OpenMP parallelism cannot counterbalance the MPI overheads generated by the distribution of work onto computer nodes. Regarding Chapel, we observe an almost ideal speed-up for 32 processing units, since it implies only one locale. Indeed, we have seen in the previous section that Chapel is particularly efficient in single locale execution. However, when considering multi-locale executions (more than 32 cores), the performance dramatically drops. When 𝑁 is growing, each implementation scales well, since the parallel overheads are counterbalance by the workload. The distributed-memory experiments allow to better see the differences between the MPI-based implementations. The two-sided blocking communication model is outperformed by its counterparts, whatever the granularity. Moreover, we note for this application that the one-sided communication model is not as good as the two-sided non-blocking one. Actually, it can be explain by the fact that tasks are independent, and thus few inter-process communications occur. The hybrid MPI+OpenMP program is as good or better than all others, whatever the value of 𝑁 . In addition, we observe that for high granularity (𝑁 = 100000 for example), Chapel is able to compete with the hybrid program. The number of processing units varies from 2 to 64 (hyperthreading enabled for Chapel and OpenMP)

As we did in the previous section, we investigate the communication overheads in the distributed-memory experiments by fixing 𝑁 = 1. Again, experiments are performed fifty times, and the average is considered.

The results are depicted in Figure 6. First of all, we can see that for two-sided MPI, the communication overheads for both blocking and non-blocking communication models are approximately the same. Moreover, we note a light increase when the number of processing units growths. For one-sided MPI, this last observation is also true. The higher the number of processing units, the higher the communication overheads. However, compared to two-sided MPI, the latter are 2 times higher for 96 and 128 processing units, and almost 6 times higher for 192. Like in the shared-memory experiments, it can be attributed to the window management, that requires creation, communication and synchronization mechanisms. Concerning the hybrid MPI+OpenMP approach, we can see that the overheads remain constant, whatever the number of processing units. This can be justified by the fact that only one MPI process is allowed per computer nodes. Finally, we note that the communication overheads of Chapel in our distributed-memory experiments are high. Indeed, from 3 computers nodes (96 processing units), overheads are 10 to 21 times higher than the ones observe using the hybrid model. Chapel may suffer from the fact that our cluster is not equipped with high-performance network between nodes. This last observation can explain the poor performance of Chapel in distributed-memory when 𝑁 is low (see Figure 5).

CONCLUSION

In this paper, we have compared the Chapel high-productivity programming language to the well-established conventional parallel programming libraries OpenMP and MPI+X, in terms of performance. Shared-and distributed-memory multi-core experiments were conducted on a cluster composed of 192 processing cores, using the French national testbed Grid'5000.

In this work, the embarrassingly parallel computation of the Mandelbrot set was chosen as a test-case for its high degree of parallelism and its irregular workload. This study represents a good comparison element between Chapel and its OpenMP and MPI counterparts. However, this study should be extended to more complicated problems, involving dependent tasks, and thus more communication between processing units.

Chapel outperforms its counterparts in shared-memory context. This may be explain by its 𝑞𝑡ℎ𝑟𝑒𝑎𝑑𝑠 default tasking layer that provides a lightweight implementation of Chapel tasking as well as an optimized implementation of synchronization variables. Moreover, in distributed-memory environment, Chapel competes with hybrid MPI+OpenMP, even though its 𝑞𝑡ℎ𝑟𝑒𝑎𝑑𝑠 tasking layer seems to suffer from the lack of high-performance network of the cluster.

Finally, we plan to investigate the use of Chapel and other highproductivity languages for more complex applications, in particular irregular ones (such as tree-search algorithms). Another important aspect is GPU programming support. Although there exist two modules that facilitate GPU programming in Chapel (GPUIterator and GPUAPI), they are not yet mature.

ACKNOWLEDGEMENT

Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted

Figure 1 :Algorithm 1 : 3 𝑛 = 0; 4 while 𝑥 2 + 5 𝑡 = 𝑥; 6 𝑥 = 𝑥 2 - 7 𝑦 = 2𝑡𝑦 + 𝑏; 8 𝑛

 1134256278 Figure 1: Monochrome Mandelbrot set.

9 end 10 𝐼 15 Compute_pixel

 91015 (𝑎, 𝑏) = 𝑛/𝑁 ; 11 end 12 function Compute_image() : 13 for 𝑎 = 0 to 𝑛𝑏_𝑙𝑖𝑛𝑒𝑠 do 14 for 𝑏 = 0 to 𝑛𝑏_𝑐𝑜𝑙𝑢𝑚𝑛𝑠 do

Figure 2 :Algorithm 2 : 2 # 3 for 𝑎 = 0 to 𝑛𝑏_𝑙𝑖𝑛𝑒𝑠 do 4 for 𝑏 = 0 to 𝑛𝑏_𝑐𝑜𝑙𝑢𝑚𝑛𝑠 do 5 Compute_pixel

 222345 Figure 2: Computation time per line of pixels for an image of size 1024x768 and 𝑁 = 1000, on AMD EPYC 7301 CPU @2.20GHz.

Algorithm 3 :

 3 Pseudo Chapel parallel implementation of the Mandelbrot set computation 1 function Compute_image_chpl() : 2 coforall 𝑙𝑜𝑐 = 0 to 𝑛𝑏_𝑙𝑜𝑐𝑎𝑙𝑒𝑠 do 3 on loc do 4 coforall 𝑟𝑎𝑛𝑘 = 0 to 𝑛𝑏_𝑡𝑎𝑠𝑘𝑠 do 5 for 𝑎 = 𝑙𝑜𝑐.𝑖𝑑 + 𝑟𝑎𝑛𝑘 * 𝑛𝑏_𝑙𝑜𝑐𝑎𝑙𝑒𝑠 to 𝑛𝑏_𝑐𝑜𝑙𝑢𝑚𝑛𝑠 by 𝑛𝑏_𝑡𝑎𝑠𝑘𝑠 * 𝑛𝑏_𝑙𝑜𝑐𝑎𝑙𝑒𝑠 do 6 for 𝑏 = 0 to 𝑛𝑏_𝑐𝑜𝑙𝑢𝑚𝑛𝑠 do 7 Compute_pixel(𝑎, 𝑏);

Algorithm 4 : 5 Compute_line

 45 Pseudo MPI parallel implementation of the Mandelbrot set computation with two-sided blocking communications 1 MPI_Init(); 2 MPI_Comm_size(𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒); 3 MPI_Comm_rank(𝑟𝑎𝑛𝑘); 4 for 𝑙 = 𝑟𝑎𝑛𝑘 to 𝑛𝑏_𝑙𝑖𝑛𝑒𝑠 by 𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒 do

Algorithm 5 : 5 Compute_lineAlgorithm 6 : 7 Compute_line

 5567 Pseudo MPI parallel implementation of the Mandelbrot set computation with two-sided non-blocking communications 1 MPI_Init(); 2 MPI_Comm_size(𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒); 3 MPI_Comm_rank(𝑟𝑎𝑛𝑘); 4 for 𝑙 = 𝑟𝑎𝑛𝑘 to 𝑛𝑏_𝑙𝑖𝑛𝑒𝑠 by 𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒 do .2 One-sided communications. When dealing with one-sided communications, the main calls are MPI_Put to send data to the window of another process, MPI_Get to fetch data from the window of another process, and MPI_Accumulate to update data by combining the existing data and the data sent. Moreover, like in two-sided non-blocking operations, explicit synchronizations are required. It can be achieved via the MPI_Fence routine. Pseudo MPI parallel implementation of the Mandelbrot set computation with one-sided communications 1 MPI_Init(); 2 MPI_Comm_size(𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒); 3 MPI_Comm_rank(𝑟𝑎𝑛𝑘); 4 MPI_Win_create(𝑤𝑖𝑛); 5 MPI_Fence(); 6 for 𝑙 = 𝑟𝑎𝑛𝑘 to 𝑛𝑏_𝑙𝑖𝑛𝑒𝑠 by 𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒 do

Algorithm 7 : 6 MPI_Send

 76 Pseudo MPI+OpenMP parallel implementation of the Mandelbrot set computation 1 MPI_Init_thread(MPI_THREAD_FUNNELED); 2 MPI_Comm_size(𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒); 3 MPI_Comm_rank(𝑟𝑎𝑛𝑘); 4 Compute_image_omp(𝑟𝑎𝑛𝑘,𝑐𝑜𝑚𝑚𝑠𝑖𝑧𝑒); 5 if rank ≠ 0 then

Figure 3 :

 3 Figure 3: Speed-up achieved by all five shared-memory implementations. The number of processing units varies from 1 to 64 (hyperthreading enabled for Chapel and OpenMP). Results are for different maximum number of iterations 𝑁 .

Figure 4 :

 4 Figure 4: Computational overhead measured by all five shared-memory implementations when considering 𝑁 = 1.The number of processing units varies from 2 to 64 (hyperthreading enabled forChapel and OpenMP)

  𝑏) ∈ Ω the algorithm determines the smallest integer 𝑛 required for observing divergence of (𝑧 𝑛 ) 𝑛 ∈N . Then the luminous intensity 𝐼 of pixel (𝑎, 𝑏) is defined as

This observation directly yields a simple "escape time" algorithm shown in Algorithm 1. Considering a bounded domain Ω (hereafter called image) uniformly cut into pixels. For each pixel (𝑎,

Table 1 :

 1 Summary of the tools/libraries and optimization flags used for compilation and execution.

	Tools/libraries	Version
	C compiler 𝑔𝑐𝑐	10.2.1
	Open MPI	4.1.0
	OpenMP	4.5
	Chapel	1.25.0
	C optimization flag	-O2
	Chapel optimization flag --fast

Table 2 :

 2 Summary of the Chapel environment configuration for multi-locale execution.

	Variable	Value
	CHPL_RT_NUM_THREADS_PER_LOCALE	64
	CHPL_TARGET_CPU	𝑛𝑎𝑡𝑖𝑣𝑒
	CHPL_HOST_PLATFORM	𝑙𝑖𝑛𝑢𝑥64
	CHPL_LLVM	𝑛𝑜𝑛𝑒
	CHPL_COMM	𝑔𝑎𝑠𝑛𝑒𝑡
	CHPL_COMM_SUBSTRATE	𝑢𝑑𝑝
	GASNET_PSM_SPAWNER	𝑠𝑠ℎ

by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).


Valéria Marques Lemos

Henrique Cabral
email: henrique.cabral@inrae.fr.

Stephanie Pasquaud
email: spasquaud@fc.ul.pt.

João Paes

Occurrence and abundance of young mullet Mugil liza (Teleostei: Mugilidae) in the surf zone along the southern coast of Brazil

Keywords: mullet, nursery areas, southern Brazil, surf zone, estuary, recruitment lisas, zonas de cría, Sur del Brasil, zona de oleaje, estuarios, reclutamiento

The southern population of Mugil liza is distributed from Argentina (47°S) to the state of São Paulo, Brazil (23°S). Young mullets use the estuaries as nursery grounds, and prior to recruitment into estuaries they use the surf zone as a temporary habitat. Based on 12 consecutive months of sampling, this study used generalized linear models (GLM) to analyse the relationships between environmental variables and the presence and relative abundance of young mullets in the surf zone adjacent to six major estuaries in southern Brazil (between 29°S and 33°S). Young mullets were present in all seasons over the sampling period, but the probability of occurrence was higher in winter and was associated with low temperatures. The water temperature alone explained more than half of the total deviance of the GLM models for presence (23%) and abundance (21%) of young mullets in the surf zone. Site 2 (Rio Grande) had lower temperatures in the colder months, the highest probability of occurrence of all collection sites and the greatest abundance (n=3402) of young M. liza, which represented 52% of the total of individuals (n=6493) caught among the six sites sampled.

pre-juvenile stage ends at approximately 13 mm TL and involves a change from predaceous to iliophagous (detritivorous) feeding habits [START_REF] Martin | Development of fishes of the Mid-Atlantic Bight[END_REF]Drewry 1978, Vieira 1991). Young mullets, which first appear in small schools along the coasts and in the estuaries, measure 18 to 28 mm in length (Vieira 1991, González-Castro and[START_REF] González-Castro | Sexuality and reproduction of Mugilidae[END_REF]. In the coastal area of the state of Rio Grande do Sul, young mullets are frequently present and abundant in the surf zone throughout the year [START_REF] Ramos | Composição específica e abundância de peixes de zonas rasas dos cinco estuários do Rio Grande do Sul, Brasil[END_REF]Vieira 2001, Rodrigues et al. 2015), which is also the case on the coast of Argentina [START_REF] Acha | Estudio anatômico-ecologico de la lisa (Mugil liza) durante su primer año de vida[END_REF][START_REF] Castellini | Juveniles recruitment and daily growth of the southern stock of Mugil liza (Actinopterygii; Fam. Mugilidae): new evidence for the current life-history model[END_REF]. However, in the northern area of the southern population (state of São Paulo) [START_REF] Mai | Microsatellite variation and genetic structuring in Mugil liza (Teleostei: Mugilidae) populations from Argentina and Brazil[END_REF], the presence of young mullets in the surf zone occurs shortly after the reproductive period, and individuals are less abundant or absent in the surf zone during the remaining months of the year [START_REF] Favero | Juvenile fish use of the shallow zone of beaches of the Cananéia -Iguape coastal system, southeastern Brazil[END_REF]. It seems that there is a clinal decrease in surf zone occurrence from the northern to the southern limits of the southern population.

Surf zones of sandy beaches are important recruitment and nursery zones and migratory paths to other nearshore habitats (Strydom 2003, McLachlan and[START_REF] Mclachlan | The Ecology of Sandy Shores[END_REF]. Larvae and juvenile of estuary-dependent marine fishes move from offshore spawning grounds (initially passively but later by active migration) to surf zones [START_REF] Boehlert | Roles of behavioral and physical factors in larval and juvenile fish recruitment to estuarine nursery areas[END_REF]. Despite the available information on recruitment of young fishes into estuaries worldwide, there is a paucity of information describing the factors driving the recruitment process [START_REF] Strydom | Occurrence of larval and early juvenile fishes in the surf zone adjacent to two intermittently open estuaries, South Africa[END_REF]. The aim of the present study was to compare the abundance of young M. liza (≤30 mm TL) in the adjacent surf zones of six estuaries between 28.5°S and 33.7°S in southern Brazil and to determine which environmental variables are related to their occurrence and abundance.

MATERIALS AND METHODS

Study area

The study area encompassed the coastal surf zone of southern Brazil from Laguna, Santa Catarina state (29°S, 48°W), to Chuí, Rio Grande do Sul state (34°S, 53°W) (Fig. 1). These coastal areas are characterized by sandy beaches exposed to wave action with a wide dissipative to intermediate surf zone [START_REF] Calliari | Variabilidade das praias oceânicas entre Cassino e Chuí[END_REF]. Tidal oscillations along the southern Brazilian coast are defined by their low amplitude, with an average tidal amplitude of 0.47 m and minimal influence on estuarine circulation [START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF]).

The regional climate is temperate with well-defined seasons and is under the control of the South Atlantic anticyclone high-pressure centre. The latitudinal movement of the anticyclone centre and the passage of polar frontal systems influence and modify the seasonal cycle of the climate [START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF]). These systems are responsible for dominant winds from the northeast quadrant (NE, mean speed 5 m s -1 ) throughout the year and winds from the southwest quadrant (SW, mean speed 8 m s -1 ) during the passage of polar frontal systems, which are common during

INTRODUCTION

Estuaries and coastal lagoons are considered highly productive areas and are important refuge and nursery zones for several fish species with high economic and/or environmental value [START_REF] Boehlert | Roles of behavioral and physical factors in larval and juvenile fish recruitment to estuarine nursery areas[END_REF]. Migratory marine species spawn in offshore waters, regularly enter estuaries in substantial numbers, particularly as juveniles, and use the nearshore marine waters as an alternative habitat [START_REF] Boehlert | Roles of behavioral and physical factors in larval and juvenile fish recruitment to estuarine nursery areas[END_REF]. In southern Brazil, juveniles of many commercially and recreationally important fish species (Micropogonias furnieri [Desmarest, 1823], Brevoortia pectinata [Jenyns, 1842], Pogonias courbina [Linnaeus, 1766] and Mugil liza Valenciennes, 1836) use the estuarine areas as nurseries [START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF][START_REF] Mai | Coastal zone use and migratory behavior of the southern population of Mugil liza in Brazil[END_REF].

The Lebranche mullet, Mugil liza (Teleostei, Mugilidae), occurs from the Gulf of Mexico to the coast of Argentina. Using the mitochondrial control region, [START_REF] Heras | Shaken not stirred: A molecular contribution to the systematics of genus Mugil (Teleostei, Mugilidae)[END_REF] described two highly divergent M. liza populations: a northern population, which is distributed from Cuba to the state of Rio de Janeiro, Brazil, and a southern population, which is distributed from Rio Grande do Sul, Brazil, to Argentina. [START_REF] Mai | Microsatellite variation and genetic structuring in Mugil liza (Teleostei: Mugilidae) populations from Argentina and Brazil[END_REF] and [START_REF] Lemos | Stock identification of tainha (Mugil liza) by analyzing stable carbon and oxygen isotopes in otoliths[END_REF] showed that the southern population encompasses the Rio Grande do Sul state and actually ranges from the state of São Paulo in southeastern Brazil (23°S) to Argentina.

Mugil liza is commercially exploited in Argentina by a small-scale fishery that operates mainly in Samborombón Bay. Commercial catches were between 5.4 and 78.8 t from 2000 to 2010, with a maximum capture of 194.0 t in 2004 [START_REF] Castellini | Juveniles recruitment and daily growth of the southern stock of Mugil liza (Actinopterygii; Fam. Mugilidae): new evidence for the current life-history model[END_REF]). In the southern states of Brazil (Rio Grande do Sul, Santa Catarina and Paraná) and São Paulo, the M. liza southern population fishery is a very important resource [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF], 2016[START_REF] De Abreu-Mota | Resilience thinking applied to fisheries management: perspectives for the mullet fishery in Southern-Southeastern Brazil[END_REF], with a maximum reported capture of 13600 t in 2007 (de [START_REF] De Abreu-Mota | Resilience thinking applied to fisheries management: perspectives for the mullet fishery in Southern-Southeastern Brazil[END_REF]). The Patos Lagoon estuary, located in the state of Rio Grande do Sul, is considered the main M. liza nursery area in Brazil [START_REF] Herbst | Local ecological knowledge of fishers about the life cycle and temporal patterns in the migration of mullet (Mugil liza) in Southern Brazil[END_REF]Hanazaki 2014, de Abreu-Mota et al. 2018).

The southern population of M. liza performs an annual reproductive migration from Argentina, Uruguay and estuaries of southern Brazil, especially the Patos Lagoon estuary, to offshore spawning areas located on the Brazilian coast between northern Santa Catarina and Paraná (28°-26°S) [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF][START_REF] Lemos | Tracking the southern Brazilian schools of Mugil liza during reproductive migration using VMS of purse seiners[END_REF]. Mugil liza is a single spawner and spawning occurs between May and July at temperatures of 19°C to 21°C in offshore waters [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF]. According to the life cycle model proposed by [START_REF] Vieira | Juvenile mullets (Pisces: Mugilidae) in the Estuary of Lagoa dos Patos, RS, Brazil[END_REF], M. liza larvae and early juveniles are neustonic and are carried, mainly by wind-driven currents, from offshore waters to the coast, where they concentrate in surf zones prior to recruitment to estuarine environments. This use of the coastal zone and migratory behaviour characterize M. liza as a marine estuarine-dependent species [START_REF] Mai | Coastal zone use and migratory behavior of the southern population of Mugil liza in Brazil[END_REF]. [START_REF] Martin | Development of fishes of the Mid-Atlantic Bight[END_REF] recognized a pre-juvenile stage for mullets starting at 11 mm total length (TL), and the transformation from the larval to the 1) Chuí Creek, Rio Grande do Sul (RS), Brazil, is located on the border between Brazil and Uruguay. The Chuí Creek drainage basin has an area of approximately 340 km 2 and an estuarine area of 0.5 km 2 [START_REF] Ramos | Composição específica e abundância de peixes de zonas rasas dos cinco estuários do Rio Grande do Sul, Brasil[END_REF]. Chuí Creek arises in an area of wetlands and runs almost parallel to the coast in a southerly direction for approximately 66 km until it reaches the Atlantic Ocean. Chuí Creek has suffered from anthropic modifications over time, including the change in its original course, the use of its fresh water and the construction of a pair of jetties (1500 m long) in the late 1970s to demarcate the border between Brazil and Uruguay. At low flow, the the winter. The mean annual rainfall (1200-1500 mm) is related to the pattern and frequency of these systems and to the effects of the El Niño-Southern Oscillation cycle [START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF].

The complex hydrographic system of the coastal plain in southern Brazil includes several lagoons and estuaries. Our study area encompassed six estuarine systems: 1) Chuí Creek (33.73°S), 2) the Patos Lagoon estuary (32.20°S), 3) the Peixe Lagoon (31.15°S), 4) the Tramandaí-Armazém Lagoon complex (29.98°S), 5) the Mampituba River (29.32°S), and 6) the Imaruí-Mirim-Santo Antônio Lagoon complex (28.49°S) (Fig. 1, Table 1). small freshwater lakes. The Peixe Lagoon covers approximately 43 km 2 with a depth ranging from 0.3 to 2 m, and the lagoon has an intermittent opening to the ocean [START_REF] Schwarzbold | Gênese e Morfologia das Lagoas Costeiras do Rio Grande do Sul-Brasil[END_REF].

4) The Tramandaí-Armazém Lagoon complex is located in Tramandaí, RS. The Tramandaí River Basin has an area of 3145 km² and the Tramandaí River is the primary effluent. From the estuary area (29°55'S to 30°00'S and 50°06'W to 50°11'W), the connection with the Atlantic Ocean is via a narrow, short channel (55 m) that is stabilized by a single jetty along the left margin. The amplitude of the astronomical tide in this region is low (0.3 m) [START_REF] Lira | Nota prévia sobre o comportamento da cunha salina no Estuário de Tramandaí RS[END_REF].

5) The Mampituba River is located in Torres, RS, and Passo de Torres, Santa Catarina. The hydrographic basin of the Mampituba River (29°11' to 29°26'S and 49°42' to 50°12'W) has an area of 1224 km 2 that empties into the Atlantic Ocean. The Mampituba River is small (62 km long) and has an average flow of 19 m 3 s -1 . The average depth is 4 m and the mouth is stabilized by a pair of jetties (north jetty, 100 m and south jetty, 260 m). The tidal pattern is microtidal and is primarily governed by the wind regime [START_REF] D'aquino | Caracterização oceanográfica e do transporte de sedimentos em suspensão no estuário do Rio Mampituba[END_REF].

6) The Imaruí-Mirim-Santo Antônio Lagoon complex is located in Laguna, Santa Catarina. The lagoon system has an area of approximately 220 km 2 and has the Tubarão River as its main tributary. The communication between the lagoon system and the ocean oc-stream has a maximum width of 100 m and a depth ranging between 1.5 and 3 m. The amplitude of the astronomical tide is low (0.5 m) and the wind regime determines the saltwater flow into the system (Hartmann and Pereira 2001).

2) The Patos Lagoon estuary is located in Rio Grande, RS. The Patos Lagoon, with a total area of ~10000 km 2 (draining a large hydrological basin of 200000 km 2 ), is one of the largest choked coastal lagoons in the world. It extends for 270 km along the coastline of southern Brazil. It was formed by multiple sand barrier complexes and can be divided into biological units. The estuarine region, with a total area of 900 km 2 (approximately 10% of the lagoon) is characterized by large shallow areas (<2 m deep). The estuary is connected to the South Atlantic via a 20 km channel (0.5-3000 m in width), and the mouth is stabilized by a pair of jetties. Owing to its morphological characteristics and the proximity of an amphidromic point, the tides in the region have low amplitude (mean 0.4 m). The wind patterns and precipitation in the watershed determine the salinity regime in the estuary [START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF].

3) The Peixe Lagoon is located in Mostardas, RS. It is situated in the narrow sandy strip between the Patos Lagoon and the Atlantic Ocean and was recognized as a National Park in 1986. It has an area of 34000 ha, including not only the Peixe Lagoon but also surrounding ecosystems such as beaches and dissimilarity matrix of calculating the Euclidean distances.

The relationships between the abundance of young mullets and the selected environmental variables were evaluated using generalized linear models (GLMs). Prior to the statistical analysis, a pairwise correlation matrix was constructed using Spearman's rank corre-curs through a fixed bar in the Santo Antônio Lagoon that is approximately 200 m wide and 1200 m long. The tide is of low amplitude, and hydrodynamics are primarily governed by the wind [START_REF] Pimenta | A faixa costeira meridional de Santa Catarina[END_REF].

Fish sampling and environmental variables

The fish were collected monthly between June 2011 and May 2012 in the surf zones adjacent to the mouths of the six estuaries (Fig. 1). Two marine surf zone sampling points, starting at 500 m from the jetties and spaced 1 to 6 km apart from each other, were selected at each site (Fig. 1). At each of the 12 sampling points we collected five samples monthly. Each beach seine sample was conducted perpendicular to the beach at a depth of 1.5 m. The beach seine net was 9 m long and 1.5 m high with a 13 mm knot-to-knot mesh in the wings and a 5 mm knot-to-knot mesh in the 3 m central section. Each haul covered an area of approximately 120 m 2 . The fish caught were held on ice and subsequently processed in the laboratory. Mullet abundance was calculated as the catch per unit effort (CPUE), i.e. the total number of individuals per haul.

Water temperature (°C) and salinity were recorded monthly at each sampling point using a digital multiparameter probe. The salinity was measured using the Practical Salinity Scale (PSU). The water transparency was measured using a Secchi disc (cm). Additionally, the estuarine area (the area, km 2 ) and mouth width (width, km) of each of the six estuaries, the distance of each sampling point from the mouth of the adjoining estuary (distance, km), and the distance from each sampling point to the M. liza theoretical spawning area as defined by [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF] (distance to the spawning area, km) were also included in the analyses. Tides, estuarine area and width were obtained from the literature (Table 1); the other distances were determined using the ArcMap 10.0 tool.

This study was conducted in accordance with the recommendations of the Brazilian Ministry of the Environment (MMA), and all data collection and fish handling were endorsed by the Permanent Licence for Collection of Zoological Material (Number: 10125-2) granted to JPV since September 2007. There was no experimentation in the present work.

Data analysis

A one-way ANOVA was performed to test temporal differences in environmental variables among sites and differences in mullet abundance between sampling points at each site. This analysis was also used to test the significances of differences in abundance of mullets ≤30 mm TL and mullets >30 mm TL between sites. Temporal differences in abundance of mullets ≤30 mm TL (CPUE) between sites (six levels) and months (12 levels) of the year were tested by a two-way ANO-VA. Tukey post hoc tests were conducted to evaluate the paired comparisons that were significantly different. We used a non-metric multidimensional scaling (nMDS) plot to visualize the environmental factors and potential differences between sampling sites, from sites; 1) Chuí, 3) Mostardas, 4) Tramandaí, 5) Passo de Torres, and 6) Laguna (ANOVA, F=10.73, p>0.05). Among the 12 sampling points, only points 3 and 4 (Site 2, Rio Grande) showed significant differences in mullet abundance (ANOVA, F=14.15; p<0.05).

The size distribution of the M. liza individuals varied between 12 mm and 126 mm TL. Individuals 30 mm TL were more abundant than larger individuals (TL>30 mm) at all sites (ANOVA, F=13.050, p<0.05) (Fig. 4). At all sites, the total number of individuals from classes 15 to 30 (≤30 mm TL) represented more than 96% of all mullets collected, with the exception of Site 3 (Mostardas), where they represented 77% (Table 2). Individuals in size class 15 mm TL (10 to 15 mm TL) occurred occasionally at Chuí (Site 1), Tramandaí (Site 4) and Laguna (Site 6), but individuals from size class 25 mm TL were the modal length at all sampling sites (Table 2). Mullets ≤30 mm TL occurred in all 12 months sampled at Sites 2 and 4 and were present among 9 to 11 of all months sampled at the other sampling sites (Table 2).

The best model for presence/absence of young mullets (i.e. lower AIC) included three significant variables (site, month and water temperature). Those variables explained 33.5% of the total deviance of the model. The water temperature alone explained more than half of the total deviance (23%) (Table 3). Young mullets were present in all seasons, but the probability of occurrence was higher in winter (May to July) and was associated with low temperatures (Fig. 5A,B). The highest probability of occurrence of young mullets was observed at Site 2 (Rio Grande) (Fig. 5C). The best GLM for the abundance data of M. liza included three explanatory variables, sampling site, month and water temperature (Table 3), and explained 39% of the total deviance of the model. Similar to the GLM model for presence/absence, the abundance GLM model showed that water temperature was responsible for more than half of the explained deviance (21%). Young mullets were observed in the surf zone in all months, and abundance was a positive observed in a preliminary analysis (p<0.05), and an interaction term between the month and the sampling point was therefore included in all models.

The best model was selected according to the method described by [START_REF] Rodrigues | Assessing surf zone fish assemblage variability in southern Brazil[END_REF]. The drop1 function was used to compare the full model with the reduced model, from which the interaction was eliminated using the chi-squared test. Stepwise selection was used to select the variables included in the final models and to rank them from most to least significant. All models were tested for overdispersion. The best final combination of variables was selected using the chi-squared test, the Akaike information criterion (AIC) and graphical residual analysis. The final model included only the significant variables. For each model, the relative contribution of each variable to the model was evaluated by comparing the percent deviance explained. A significance level of 0.05 was adopted for all statistical procedures, and all statistical procedures were performed using R software (R Development Core Team 2013).

RESULTS

Significant differences in salinity (ANOVA, F=22.69; p<0.05), temperature (ANOVA, F=10.74; p<0.05) and water transparency (ANOVA, F=19.06 p<0.05) were observed between sites and months over the study period (Fig. 2). The mean values of seawater surface temperature differed among the six sampling sites but showed seasonal fluctuations with a clear annual cycle: they declined steadily from April to August (monthly average 21°C-13.5°C), and thereafter the monthly average temperature increased to 18.5°C by September (Fig. 2A). Site 2 (Rio Grande) had higher temperatures in the warmer months and lower temperatures in the colder months. Site 6 (Laguna) had lower temperatures in the warmer months (Fig. 2A). Salinity showed no seasonal pattern (Fig. 2B). The lowest salinity values were recorded at Sites 5 (Passo de Torres) and 6 (Laguna) (the lowest salinity value was recorded in August at Site 5). The highest salinities were found from May to July (Fig. 2B). Significant differences were observed among sampling sites for water transparency, and sampling Site 6 (Laguna) showed the highest water transparency values in January, February, June, September and November (Fig. 2C). The nMDS plot was used to compare the similarity in the environmental factors of sampling sites. It is possible to observe three groups in the nMDS plot: Site 1 (Chuí), separated from the other sites; Sites 2 (Rio Grande) and 3 (Mostardas); and Sites 4 (Tramandaí), 5 (Passo de Torres) and 6 (Laguna) (Fig. 3).

A total of 6493 M. liza individuals were captured (Table 2). Significant differences in the number of individuals captured per beach seine sample (CPUE) were observed between the collection sites. Rio Grande (Site 2) had the highest abundance of M. liza (CPUE=26.4 individuals/haul; ANOVA, F=4.98, p<0.05), representing more than 52% of the total of individuals caught at the six collection sites. No significant differences in abundance were observed among the remaining posed a model for the early life history of M. liza in southern Brazil, suggesting that young individuals use the surf zone temporarily after the larval neustonic life stages and before recruitment to the estuarine environment. Young mullets remain present throughout the year in the surf zone over the entire sampling area. The surf zone is therefore an important environment for young mullets, and long periods in these areas could provide better opportunities for young mullets to find and penetrate estuaries.

relationship of temperature (Fig. 5D,E). Mullet abundance was highest at Site 2 (Rio Grande) (Fig. 5F).

DISCUSSION

Surf zone habitats form a productive ecosystem, serving important functions as nursery areas, major fishery zones and migratory pathways. The importance of this area for species dependent on the estuary has long been known [START_REF] Whitfield | Ichthyoplankton in a southern African surf zone: nursery area for the postlarvae of estuarine associated fish species?[END_REF]. [START_REF] Vieira | Juvenile mullets (Pisces: Mugilidae) in the Estuary of Lagoa dos Patos, RS, Brazil[END_REF] pro- the Tramandaí-Armazém Lagoon Complex and Chuí Creek [START_REF] Figueiredo | Sedimentologia e suas implicações na morfodinâmica das praias adjacentes às desembocaduras da linha de costa do Rio Grande do Sul[END_REF]. Although water salinity and transparency were not important factors in explaining the occurrence and availability of young M. liza throughout the study area, the sediment input via estuarine discharge can be an important factor for explaining the greater abundance and occurrence of young mullet near the mouth of Patos Lagoon.

The best models for presence/absence and for abundance of young mullets demonstrate that temperature was the factor that most contributed to the explanation of variance. However, temperature showed a negative relationship with the occurrence and a positive relationship with the abundance of young mullet in the study area. Young mullets were present in all seasons, but the probability of presence was higher in winter (May to July) and was associated with low temperatures. This can be explained by the reproductive migration of M. liza, which occurs at the end of the austral autumn and the beginning of the austral winter (from April to July), and the occurrence of one peak spawning in June between northern Santa Catarina and Paraná (26°S) [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF]. Similar to the GLM model for presence/absence, the GLM model for abundance showed that the water temperature was responsible for more than half of the explained deviance, but mullet abundance was positively associated with temperature. The abundance of young mullets remained at the same level over a wide temperature range, between 16°C and 24°C.

Juveniles of M. liza have been observed to remain in the surf zone for long periods in southern Brazil and Argentina [START_REF] Acha | Estudio anatômico-ecologico de la lisa (Mugil liza) durante su primer año de vida[END_REF][START_REF] Vieira | Juvenile mullets (Pisces: Mugilidae) in the Estuary of Lagoa dos Patos, RS, Brazil[END_REF][START_REF] Castellini | Juveniles recruitment and daily growth of the southern stock of Mugil liza (Actinopterygii; Fam. Mugilidae): new evidence for the current life-history model[END_REF]). The specific size at which the mullets start to appear in surf zones and enter estuaries varies between authors (González-Castro and Minos 2016). In the present study, we observed that individuals smaller than 15 mm TL occur occasionally throughout the study area. However, individuals ≤30 mm TL represented more than 96% of all mullets collected (with the exception of Site 3, where they represented 77%) and were present in the surf zone at least 9 of the 12 months of the year. This result is in accordance with [START_REF] Vieira | Juvenile mullets (Pisces: Mugilidae) in the Estuary of Lagoa dos Patos, RS, Brazil[END_REF], who demonstrated that after reaching approximately 20 mm TL, the young M. liza gradually migrate to the bottom in the surf zone and begin to feed on benthic organisms

The recruitment to estuaries of species that spawn at sea has two major phases [START_REF] Boehlert | Roles of behavioral and physical factors in larval and juvenile fish recruitment to estuarine nursery areas[END_REF]. The first is the arrival at and movement through the coastal zone. This phase is associated with physical factors responsible for the passive transport of organisms, such as tides, oceanographic fronts and coastal currents [START_REF] Boehlert | Roles of behavioral and physical factors in larval and juvenile fish recruitment to estuarine nursery areas[END_REF]. The longshore currents in the study region follow the seasonal wind pattern. Strong winds from the south and southwest predominate between April and August (especially during the passage of cold fronts), causing strong currents towards the northeast [START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF]. The importance of this wind pattern for the reproductive migration of adult individuals is already known [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF]). However, during most of the year (September to March), there is a predominance of northeast winds and coastal currents with low intensity but high frequency towards the southwest [START_REF] Tozzi | Morfodinâmica da praia do Cassino[END_REF]. These coastal currents can be important for the transport of young mullets along the coast towards the south.

The second phase of recruitment to estuaries is the aggregation of individuals near estuary mouths [START_REF] Boehlert | Roles of behavioral and physical factors in larval and juvenile fish recruitment to estuarine nursery areas[END_REF]. Many of important commercial fish species recruit in estuaries, presumably in response to certain olfactory cues transported into the marine environment from either estuarine or freshwater sources [START_REF] Wasserman | The importance of estuary head waters as nursery areas for young estuary-and marine-spawned fishes in temperate South Africa[END_REF]. A strong aggregation of juvenile mugilids was observed in response to the presence of estuarine discharges in surf zones [START_REF] Strydom | Occurrence of larval and early juvenile fishes in the surf zone adjacent to two intermittently open estuaries, South Africa[END_REF]. In southern Brazil, [START_REF] Rodrigues | Assessing surf zone fish assemblage variability in southern Brazil[END_REF] observed a positive effect of the weaker morphodynamics and the occurrence of an estuarine plume at the beach on the abundance of M. liza juveniles in the surf zone. Several environmental and ecological attributes were assessed in the present study to explain the occurrence and abundance of young mullets in the surf zone, and the abundance near the Patos Lagoon estuary mouth (Site 2) was significantly higher than that at the other sites sampled. The Patos Lagoon is the largest estuary in the study area, and the plume is related to the size of the drainage basin and the high discharge of the lagoon, which are important factors for the high sediment input into the adjacent coastal zone [START_REF] Figueiredo | Sedimentologia e suas implicações na morfodinâmica das praias adjacentes às desembocaduras da linha de costa do Rio Grande do Sul[END_REF]. In contrast, the sediment input via estuarine discharge was not significant at the beaches adjacent to the Mampituba River, In summary, the results of our study demonstrate that the probability of occurrence of young M. liza throughout the sampling area is higher in winter (May to July) and associated with low temperatures; however, young mullets remain present throughout the year in the surf zone over the entire sampling area. Site 2, adjacent to the Patos Lagoon estuary, had the highest probability of occurrence of all collection sites and the greatest abundance (n=3402) of young M. liza, which represented 52% of the total of individuals (n=6493) caught among the six sites sampled. Although other estuaries along the southern Brazilian coast are also used by mullets as nursery grounds [START_REF] Ramos | Composição específica e abundância de peixes de zonas rasas dos cinco estuários do Rio Grande do Sul, Brasil[END_REF][START_REF] Loebmann | Distribuição espacial e abundância das assembléias de peixes no Parque Nacional da Lagoa do Peixe, Rio Grande do Sul, Brasil[END_REF][START_REF] Favero | Juvenile fish use of the shallow zone of beaches of the Cananéia -Iguape coastal system, southeastern Brazil[END_REF], our results indicate that the Patos Lagoon estuary can be considered the largest nursery area for the southern population of M. liza, and corroborate the perception of local fishermen that Patos Lagoon is the largest nursery area for M. liza [START_REF] Herbst | Local ecological knowledge of fishers about the life cycle and temporal patterns in the migration of mullet (Mugil liza) in Southern Brazil[END_REF]. Comparative studies between surf zone and estuary growth rates, based on daily increment growth in otoliths, morphological development and changes in feeding habits in the M. liza ontogeny, should be performed to support some of the hypotheses raised in this work. and mineral particles. At this stage, individuals occupy the surf zone before recruitment to the estuarine environment [START_REF] Vieira | Juvenile mullets (Pisces: Mugilidae) in the Estuary of Lagoa dos Patos, RS, Brazil[END_REF].

From the larvae to juvenile stage, the feeding habits change from zooplanktophagous to iliophagous [START_REF] Acha | Estudio anatômico-ecologico de la lisa (Mugil liza) durante su primer año de vida[END_REF][START_REF] Vieira | Juvenile mullets (Pisces: Mugilidae) in the Estuary of Lagoa dos Patos, RS, Brazil[END_REF]. The surf zone occurrence of young mullets appears to be less important at beaches with strong morphodynamics, and in this situation the change in feeding habits seems to occur inside the estuaries [START_REF] Blaber | The feeding ecology of juvenile mullet (Mugilidae) in southeast African estuaries[END_REF]. The coastal zone in our study area is characterized by an extensive dissipative beach (Calliari andKlein 1995, Ramos and[START_REF] Ramos | Composição específica e abundância de peixes de zonas rasas dos cinco estuários do Rio Grande do Sul, Brasil[END_REF], and at dissipative beaches the transition between feeding habits may occur slowly and in the surf zone [START_REF] Blaber | Factors affecting the distribution of juvenile estuarine and in shore fish[END_REF]. Considering that M. liza in southern Brazil show only one peak of spawning in June and young mullets occur year-round, it is possible that the young mullets that remained in the surf zone exhibited a lower growth rate than those that were already recruited to the estuary. Thus, long periods in the surf zone could provide better opportunities for young mullets to find and penetrate estuaries, but this would imply lower growth rates. However, comparative studies with different salinities (surf zone and estuarine areas) must be performed to analyse the available information on the biology and physiology of the young stages of M. liza. [START_REF] Acha | Estudio anatômico-ecologico de la lisa (Mugil liza) durante su primer año de vida[END_REF] and [START_REF] Castellini | Juveniles recruitment and daily growth of the southern stock of Mugil liza (Actinopterygii; Fam. Mugilidae): new evidence for the current life-history model[END_REF] also reported young mullets along the Argentinian coast throughout the year. González-Castro et al. ( 2011) described a strong reproductive period in the austral winter (April-May), similar to that reported for southern Brazil, and a second period in the austral summer (November-December), which was not observed by [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF] in southern Brazil. Those two periods of reproduction were used by [START_REF] Castellini | Juveniles recruitment and daily growth of the southern stock of Mugil liza (Actinopterygii; Fam. Mugilidae): new evidence for the current life-history model[END_REF] to explain the occurrence of young mullets with a minimum size of between 19 and 33 mm SL along the Argentinian coast throughout the year. However, [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF] reviewed and described the reproductive biology of M. liza in southern Brazil and showed that the peak in the gonadosomatic index (IG) values for females caught in marine waters (by industrial purse seine fisheries) occurred in June (mean±sd IG♀=11.5±3.1) and was closely related to the presence of hyaline oocytes. The gonadosomatic index values for fish caught in Argentina are lower (4 to 6) according to [START_REF] González-Castro | Studies on reproduction of the mullet Mugil platanus Günther, 1880 (Actinopterygii, Mugilidae) from the Mar Chiquita coastal lagoon, Argentina: similarities and differences with related species[END_REF], who did not identify the presence of hyaline oocytes. The hydration phase during final maturation appears to be important in the production of pelagic (buoyant) mullet eggs, and the presence of hyaline oocytes has been associated with high salinity and sea surface temperatures of 19 to 21°C [START_REF] Lemos | Migration and reproductive biology of Mugil liza (Teleostei : Mugilidae) in south Brazil[END_REF]. Recently, [START_REF] Morado | Local ecological knowledge indicates: There is another breeding period in the summer for the mullet Mugil liza in a Brazilian tropical bay[END_REF] describes a second breeding period in the summer for the mullet M. liza in a Brazilian tropical bay (Sepetiba Bay coast of the State of Rio de Janeiro). The summer spawning was not foreseen in the biological literature for this place, but the local ecological knowledge of artisanal fishermen associated this spawning season with a possible resident population [START_REF] Morado | Local ecological knowledge indicates: There is another breeding period in the summer for the mullet Mugil liza in a Brazilian tropical bay[END_REF]. More studies must be carried out to support the hypothesis of a local summer spawning event in southern Brazil.

Fig. 1 .

 1 Fig. 1. -Map of the six sampling sites: Site 1, Chuí; Site 2, Rio Grande; Site 3, Mostardas; Site 4, Tramandaí; Site 5, Passo de Torres; and Site 6, Laguna. Numbers (1 to 12) represent sampling points where beach seine samples were obtained.

Fig. 2 .

 2 Fig. 2. -Temporal fluctuations in environmental variables (A) surface water temperature; (B) salinity; (C) transparency, of each sampling site: Site 1, Chuí; Site 2, Rio Grande; Site 3, Mostardas; Site 4, Tramandaí; Site 5, Passo de Torres; and Site 6, Laguna. Error bars=standard error of the mean.

Fig. 3 .

 3 Fig. 3. -Non-metric multidimensional scaling (nMDS) ordination plot based on Euclidean distances matrix illustrating differences among sampling sites. Site 1, Chuí; Site 2, Rio Grande; Site 3, Mostardas; Site 4, Tramandaí; Site 5, Passo de Torres; and Site 6, Laguna. Stress of analysis=0.084.

Fig. 4 .

 4 Fig. 4. -Mugil liza juvenile abundance (Log (CPUE+1)) among the collection sites: Site 1, Chuí; Site 2, Rio Grande; Site 3, Mostardas; Site 4, Tramandaí; Site 5, Passo de Torres; and Site 6, Laguna. Error bars, standard error of the mean; TL, total length (mm).

Fig. 5 .

 5 Fig. 5. -Relations between significant variables in the GLM models and mullet occurrence and abundance. Prediction of occurrence: (A) temperature, (B) month and (C) sampling site. Prediction of abundance (CPUE): (D) temperature, (E) month and (F ) sampling site. Site 1, Chuí; Site 2, Rio Grande; Site 3, Mostardas; Site 4, Tramandaí; Site 5, Passo de Torres; and Site 6, Laguna.

Table 1 .

 1 -Summary of environmental variables used in the Mugil liza occurrence and abundance models.

	Site	Lat.-Long.	Estuarine area (km 2 )	number Sampling point	Tide	mouth (km) Distance from estuary	Salinity	Temperature (°C) Transparency (cm)
							min -max mean ± sd	min -max	mean ± sd	min -max	mean ± sd
	1. Chuí	33.73°S, 53.36°W	0.3 a	1 2	0.6 e	0.3 1.4	24.0-30.3 28.1±1.7 13.2-28.0 19.8±4.6 10-50 33.6±13 26.4-30.1 28.5±1.2 14.9-26.0 20.0±4.0 10-100 39.0±23
	2. Rio Grande	32.20°S, 52.17°W	971.0 a	3 4	0.47 f	8.8 0.7	15.8-32.6 28.5±4.5 12.0-28.0 20.3±4.4 10-60 30.0±16 17.3-33.0 28.1±4.6 11.4-28.5 20.1±4.5 10-100 40.3±23
	3. Mostardas	31.15°S, 50.80°W	45.0 b	5 6	0.45 g	13 13.9	29.0-36.4 32.0±2.6 14.9-26.0 20.2±3.1 15-60 31.0±17 29.1-37.5 32.4±2.8 15.2-25.7 20.3±3.4 10-70 34.0±18
	4. Tramandaí	29.98°S, 50.12°W	30.0 a	7 8	0.3 h	3.6 0.4	25.2-36.7 30.9±3.0 15.4-24.8 20.6±2.7 0-100 44.6±30 22.6-36.9 30.8±3.8 15.4-25.0 21.0±2.6 15-70 45.8±14
	5. P. Torres	29.32°S, 49.71°W	0.5 c	9 10	0.5 i	0.2 0.8	6.4-37.8 23.4±9.3 16.6-26.0 20.7±2.9 20-60 40.3±13 15.5-38.2 29.8±5.0 15.0-23.5 20.1±3.0 0-45 29.1±14
	6. Laguna	28.49°S, 48.76°W	184.0 d	11 12	0.6 j	0.3 2.2	28.0-36.8 32.5±2.3 16.1-23.0 19.1±2.3 35-100 71.9±24 25.2-37.4 31.9±3.2 16.3-23.0 19.1±2.3 30-100 64.6±25

Estuarine area and mouth width obtained from the literature were a

[START_REF] Ramos | Composição específica e abundância de peixes de zonas rasas dos cinco estuários do Rio Grande do Sul, Brasil[END_REF]

, b

[START_REF] Loebmann | Distribuição espacial e abundância das assembléias de peixes no Parque Nacional da Lagoa do Peixe, Rio Grande do Sul, Brasil[END_REF]

and d (Fonseca and Netto 2006); the rest were calculated with the ArcMap tool (c). Tides were obtained from the literature: e

[START_REF] Hartmann | Arroio Chuí: influencia antrópica na manutenção de um ambiente estuarino. Uberlândia[END_REF]

, f

[START_REF] Seeliger | Os Ecossistemas Costeiro e Marinho do Extremo Sul do Brasil[END_REF]

, g

[START_REF] Schwarzbold | Gênese e Morfologia das Lagoas Costeiras do Rio Grande do Sul-Brasil[END_REF]

, h

[START_REF] Lira | Nota prévia sobre o comportamento da cunha salina no Estuário de Tramandaí RS[END_REF]), i (D'Aquino et al. 2011

) and j

[START_REF] Pimenta | A faixa costeira meridional de Santa Catarina[END_REF]

).

Table 2

 2

					Frequency of occurrence FO (%) / size classes (mm TL)
	Site	Total captured (n)	Total length (mm)	TL ≤ 30 mm	TL > 30 TL mm		Monthly Frequency of occurrence FO (%)
			min -max	mean ± sd	15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 >100 TL ≤ 30 mm
	1. Chuí	456 20 -51 26.8 ± 4.6 0.4 38.9 49.5 9.5 0.2 0.5 0.3 0.7				75.0
	2. Rio Grande 3402 20 -67 28.6 ± 6.8	9.8 77.8 10.0 1.0 0.7 0.3 0.2 0.1	0.1 0.1		100.0
	3. Mostardas	624	24 -103	28.3 ± 10.0	4.3 58.5 13.7 8.2 6.6 2.3 2.3 0.6 1.3 1.1		0.6	83.3
	4. Tramandaí	286	22 -109	29.8 ± 14.4 0.3 19.2 69.2 8.0 0.3 0.7 1.0		0.3	0.7	100.0
	5. P. Torres	391	22 -126	30.6 ± 15.2	18.4 70.1 7.4 1.5 1.0 0.8	0.3 0.3		0.3	83.3
	6. Laguna	1334 12 -82 31.1 ± 12.6 0.5 20.6 72.3 4.4 0.8 0.3 0.3 0.1 0.1 0.2	0.2 0.2 0.1		91.6
	Total	6493	12 -126	29.0 ± 10.9

. -Total number and total length (TL in mm) range of Mugil liza sampled and percentage frequency of the size classes at each study site. The sampling effort was the same at all sites.

Table 3 .

 3 -Analyses of deviances for the best generalized linear model obtained to explain the occurrence and abundance of the mullet Mugil liza. AIC, Akaike information criterion; Res. Dev., residual deviance; Dev. Expl., deviance explained in percentage; Sig.

	, significance; *,

ACKNOWLEDGEMENTS

The authors thank the National Council for Scientific and Technological Development (CNPq), the Coordination for the Improvement of Higher Education Personnel (CAPES), the Brazilian Long-Term Ecological Research Programme (PELD-EL-PA) and the Institute of Oceanography (IO-FURG). This work benefited from financial support provided by the CNPq (Proces. No. 406563/2012-8), the PELD (CNPq/PELD 34/2012 and CNPq/Capes/ FAPs/BC-Fundo Newton 15/2016) and the CAPES (process A101/2013). VML currently has a postdoctoral fellowship from the CAPES (Proces. No. 88887.461550/2019-00) and JPV has received a grant from the CNPq (process 482236/2011-6).