**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 Li be the length of actual effort spent in the i-th transect and Yi denotes the number of individuals detected in the i-th *

*transect. We now assume that Yi* is a random variable having a Poisson distribution Po(λ*Li*), 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*

*L*

### λ

### ω

=### =

## ∑

, (1)where ω*i is a weight to the observed encounter rate in the i-th trackline. The weights *ω*i (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( )λ*Y* should be minimized

The resultant estimator based on the conditions above is given by

4

1

### ˆ( )

*i*

*i*
*i* *i*

*Y*

*Y*

*L*

### λ

### ω

=### =

## ∑

### =

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

**RESULTS **

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

### ˆ

### λ

### =

and its standard error, the standard deviation of ˆ( )λ*Y* , 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

**Fictitious Article **

**Appendix A **

The unbiasedness condition implies

ˆ( ) 0

*E*_{}λ *Y* =>_{} λ *for all*λ

⇔

The variance of ˆ( )λ*Y* is expressed as

ˆ( )

*V*_{}λ *Y* =_{}