Estimated Diversity in Empirical Libraries

Figure 3.6: Estimated diversity in pure and mixed-culture M. truncatula libraries. The sample size (n) is 2125. Library diversity was estimated at three identity thresholds. Results from two estimators, (A) ACE and (B) Chao 1, are shown. The means and standard deviations of estimated diversity were calculated from 50 resampled replicates.

Table 3.2: Estimated diversity in pure M. truncatula and mixed-culture libraries. Shown are the number of samples sequenced (N), and for three identity thresholds, observed diversity ($S_{obs}$), estimated diversity ($\hat{S}$, computed as the mean of ACE and Chao 1 estimators), and the ratio of observed to estimated diversity (q). All diversity estimators were computed from m=50 replicate samples of n=2125 sequences.

		90% identity			70% identity			50% identity
library	N	$S_{obs}$	$\hat{S}$	q	$S_{obs}$	$\hat{S}$	q	$S_{obs}$	$\hat{S}$	q
DSIR	2284	1893	10584	17.9	1798	7776	23.1	1765	8124	21.7
MHAM	3017	2487	11833	21.0	2360	9480	24.9	2311	9053	25.5
KV0	2491	2112	13240	15.9	2005	9749	20.6	1963	8797	22.3
KV3	2173	1931	14674	13.2	1839	10888	16.9	1800	9979	18.0
NF root	2142	1798	8294	21.7	1694	6349	26.7	1636	5554	29.5
NF nod	2689	2264	13860	16.3	2165	10265	21.1	2094	9081	23.1

Figure 3.7: Effect of increasing sample size on estimated diversity of four pure and mixed-culture M. truncatula libraries, at varied stringency (percent identity threshold). Means and standard deviations were computed from 50 resampled replicates. Results from two estimators, (A) ACE and (B) Chao 1, are shown.

Estimated diversity increases with stringency, the percent identity threshold (Figure 3.6 and Table 3.2). That is, the more stringent the criterion for considering two sequences redundant, the more distinct samples result. Diversity also increases with increasing sample size (Figure 3.7). Fortunately, the change in estimated diversity also decreases with increasing samples, as the estimates approach the limit of true diversity. As seen in Figure 3.4, estimated diversity approaches true diversity far more rapidly than observed diversity.

The two diversity estimators yield similar results, with slightly larger values arising when using the ACE estimator than the Chao 1 estimator (Figures 3.6 and 3.7). For subsequent discussion, we take the mean of these two estimators as estimated diversity.

Diversity in DSIR, the Phytophthora-infected library, is consistently lower than in the other libraries (Table 3.2, and Figures 3.6 and 3.7). However, diversity in axenic root library is comparable to that found in mycorrhizal and nodulated root libraries.

Comparing diversity in libraries prepared and sequenced independently from similar tissue types, we might expect the KV0 and NF root libraries to have similar diversity, as well as the KV3 and NF nod libraries. Indeed, this appears to be true in the latter case, though not in the former (Table 3.2). In both nodulating root libraries, estimated diversity is about 14,000 distinct transcripts at the 90% identity threshold, 10,500 at 70% identity, and 9500 at 50% identity. However, diversity estimates in the two axenic root libraries differ more dramatically, with the KV0 library having about 60% greater estimated diversity than the NF nod library.

What fraction of expected diversity has been sequenced? If we evaluate the ratio of observed to estimated diversity ( $q = S_{obs}/\hat{S}$), the proportion of expected total diversity already observed in each library varies from about 13% for KV3 at the 90% identity threshold, to 30% for the NF root library at the 50% identity threshold (Table 3.2).