Page 177 - Contributed Paper Session (CPS) - Volume 1

CPS1255 Tsung-Jen Shen et al.
æ m ö
ç ÷ k æ ö
m
ˆ
ˆ
F (m) = æ è k ø ö å f ç k - q ÷d (1-d ) m-(k-q) ,
ˆ k-q
q ç
ö æ
k
q
÷ q
ç m+ n ÷-ç m ÷ q=1 è ø
è k ø è k ø

where = ∑ =1 ( = ), = (1 − ) , (Chao et al. 2015) is the
̂
̂ − ̂

estimated relative abundance of an observed species with X = q > 0. The two
i
ˆ
ˆ
estimates l and q are numerical solutions of the following system of
nonlinear equations
ì n é ù
q
ï å f q ( 1-le -qq ) =1- f 1 ê (n -1) f 1 ú
ï q=1 n n (n -1) f + 2 f û
ë
ï
1
2
í n .
ï n q é ù å q(q -1) f q 2 f é (n -2) f ù 2
2
ï å f q ( 1-le -qq )ú = q=1 - 2 ê 2 ú
ê
ë
ï q=1 n ë û n(n -1) n(n -1) (n -2) f +3f û
î
2
3
Additionally, we also compare the proposed method with one unweighted
estimator (a naïve method) given as follows:

3. Results
One empirical species abundance data set was used and normalized (i.e.,
the abundance of each species was divided by the total number of individuals
in a given dataset) so as to create a sampling relative abundance distribution
( p , p ,… , p ) for each data set. The used data set is that the Malayan butterfly
1 2 S
data provided in Fisher et al. (1943) contained 620 species identified from 9031
individuals.
For the data set, we designated two initial sample sizes, n = 100 and 200.
We randomly sampled each of these n individuals from the entire data set to
represent observed species abundance information. Each additional (but
unsurveyed) sample was designated a size of m = 0.5 × , 1 × , 1.5 ×
and 2 × . For each combination of n and m, we independently simulated 2000
replicates. We then estimated the expected number of newly discovered rare
species (i.e., singletons, doubletons, and tripletons) in the additional sample
using the proposed Bayesian-weight estimator.
Our main findings can be concisely enumerated as follows.
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