# Using balanced sampling in creel surveys Section 1. Introduction

Creel surveys provide the foundation for estimating the impact of recreational fishing (Pollock, Jones and Brown, 1994). They are conducted to estimate total catch, fishing effort, and catch rate for various species at several locations (Hoenig, Jones, Pollock, Robson and Wade, 1997). As they focus on fish of interest to recreational anglers, they provide useful information for the management and economic contribution of sport fisheries (Minnesota Department of Natural Resources, 2011).

Two methods are used to contact anglers in creel surveys, either the site access or the roving method. In site access, an agent waits at a location that the anglers must go through when they leave the site and interviews them when they depart (Robson and Jones, 1989). With the roving method the agent moves through the survey area and contacts anglers while they are fishing (United States Environmental Protection Agency, 1998). As the agent cannot be on location for the whole survey, survey sampling is used to select the periods when he will be on site, interviewing fishermen.

In practice creel surveys can face several operational constraints especially when they involve many sites as an agent can only be at one site at a given time. Accommodating all these constraints can be a real challenge when planning a survey. This paper discusses balanced sampling in this context. By framing some operational constraints as balancing equations in a multi-stage sampling design, one should be able to ensure that the sample selected meets the necessary requirements.

Balanced sampling is reviewed in Tillé (2011). A popular method to select a balanced sample is the cube method of Deville and Tillé (2004). An alternative is to select repeatedly several unbalanced samples until, by chance, a sample that approximately meets the balancing equations is drawn. This is the rejective method introduced by Hájek (1964), see also Fuller (2009) and Legg and Yu (2010). In a creel survey, the number of balancing equations is typically large. The implementation of the cube method in this context is discussed in Chauvet (2009) and Hasler and Tillé (2014). See Vallée, Ferland-Raymond, Rivest and Tillé (2015) for a recent application of these methods in the context of a forest inventory. A recent paper in this area by Chauvet, Haziza and Lesage (2015) investigates the properties of the balanced samples obtained using a rejective method.

The objectives of this paper are twofold. First, the operational constraints for a creel survey of striped bass (Morone saxatilis) carried out in the Gaspé Peninsula are presented. Then we will show how balanced sampling, implemented using the cube method, can be used to plan a survey fulfilling most of the constraints. The last section of the paper compares the rejective method to the cube method in the context of creel surveys.

In Section 2, balanced sampling is presented using either the cube method or rejective sampling. Section 3 introduces operational constraints for a creel survey and shows how they can be met using balanced sampling with the cube method. In Section 4, the cube method is compared with the rejective algorithm in the context of a resource inventory where the balancing equations only involve indicator variables. Discussions of the results are presented in the Section 5.

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