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Fictitious Article

Estimating the encounter rate of XXX dolphins in the YYY Bay using a line transect method

Taro Kaiyo and Hanako Kagaku

Tokyo University of Marine Science and Technology

Abstract

… INTRODUCTION

It has been widely recognized….(omission)

MATERIALS and METHODS Data

A line transect survey was conducted using the Suisan-maru from May 22nd to 25th in 2013 to collect the information on the encounter rate of the XXX dolphins in the YYY Bay. A total of four transects were allocated in the study area and the vessel traversed along the predetermined tracklines (see Fig 1). Table 1 summarizes the data obtained through this survey.

Figure 1. The predetermined tracklines for …..

Table 1. Summary of data obtained by the survey

Estimation method

Let L_i be the length of actual effort spent in the i-th transect and Y_i denotes the number of individuals detected in the i-th transect. We now assume that Y_i is a random variable having a Poisson distribution Po(_λL_i), where the parameter _λ has a specific meaning of encounter rate of dolphins per nautical mile. For estimating the parameter of interest _λ, we propose the following type of estimator,

4

1

ˆ( ) _i ⁱ

i _i

Y Y

λ ω

=

_∑

where _ωi is a weight to the observed encounter rate in the i-th trackline. The weights _ωi (i=1,2,3,4) were determined by the two criteria:

1) The estimator ˆ( )_λ Y should be unbiased 2) The variance of ˆ( )_λY should be minimized

The resultant estimator based on the conditions above is given by

4

1

ˆ( ) _i ⁱ

i i

Y Y

λ ω

=

_∑

The derivation of Equation (2) is shown in Appendix A.

RESULTS

The estimate of the encounter rate _λ per n.mile was given by

λ

and its standard error, the standard deviation of ˆ( )_λY , was assessed as

. .( ) ˆˆ ( )

s e _{λ =} V  _{ λ} Y  _{ =}

DISCUSSION

In this paper ……(omission)

Trackline Actual effort (n.mile)

# individuals detected

1 50 2

2 40 0

3 60 5

4 50 3

Fictitious Article

Appendix A

The unbiasedness condition implies

ˆ( ) 0

E_λ Y _{ => λ} for all_λ

⇔

The variance of ˆ( )_λY is expressed as ˆ( )

V_λ Y _{ =}

To find the weights minimizing the variance, the partial derivatives with respect to _ωi’s are calculated.