Page 415 - Contributed Paper Session (CPS) - Volume 6

CPS2007 Jai-Hua Yen et al.
species. However, when species identity error occurs, , may not be equal
to species. When the -th species is misidentified and other species are
not misidentified to the - th species, -th species is not recorded. After that,
we have the equations:
( ,0 ) = ∫ × × (1 − )() ≈ × ̅ × (1 − ), (1)
and
−1

( , ) = − ∑ [( 0)] ≈ − ∫ × (1 − ) ()
=
=1 − 1

̅×
≈ − × ̅ × (1 − − ) −1 . (2)
By solving those two equations, we have the estimate of ̅ and r which are
denoted by ̅ ̂ and ̂.
Second, the sampled observed, singleton, and doubleton richness should
be adjusted after sampling in the plot. The true observed, singleton, and
doubleton richness are denoted by , , and , respectively. The sampled
1
2
observed, singleton, and doubleton richness without adjustment are denoted
by , , , and , respectively. When species identity error occurs, the
1
2
sampled observed richness is formed by the observed species which do not
misidentified and observed species which misidentified as species do not exist
in the plot. Thus, we have the expected sampled observed richness:
( , ) ≈ { [(1 − ) + × (1 − )]}.
Next, we have the expected observed richness adjustment:

,
, = 1−̅ ̂ ×̂ (3)
When species identity error occurs, the possibilities of sampled singleton
species are as follows: (1) singleton species which do not misidentified, and
other species would not be misidentified as the singleton species at the same
time, and (2) singleton species which misidentified as species do not exist in
the plot, and other species would not be misidentified as the singleton species
at the same time. Thus, we have the expected sampled singleton richness:
−1

( ) ≈ { [(1 − ) + × (1 − )] × (1 − ) }
1
1

− 1
≈ { [(1 − ) + × (1 − )] × (− × )}.
1
Similarly, when species identity error occurs, the possibilities of sampled
doubleton species are as follows: (1) doubleton species which do not
misidentified, and other species would not be misidentified as the singleton
species at the same time, (2) doubleton species which misidentified as species
do not exist in the plot, and other species would not be misidentified as the
singleton species at the same time, and (3) when a singleton species
misidentified to a singleton species, the doubleton richness increases by one
unit, and other species would not be misidentified as the doubleton species

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