1
Supplementary Methods:
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Assumptions of Nb and Ne estimators
3
There are assumptions associated with every method of estimating Ne and deviations from these
4
assumptions may introduce a severe bias in Ne calculations if left unaddressed. The first common
5
assumption is that no mutation or selection is present in our genetic markers. Bias introduced from
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mutation rate is unlikely to be substantial considering the short time interval of our study and influence of
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selection appears to be minimal due to the general adherence of the microsatellite loci to HWE. Another
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crucial assumption for most Ne estimators is that the assumption of closed population with no further
9
subdivision or structure. We ensured that no further population structure exists through a number of
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STRUCTURE analyses, though the resulting information did show some gene flow between the two
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populations. The LDNe method of estimating Nb is expected to be robust to migration rate lower than
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10% (Waples and England 2011), but additional steps were taken to reduce bias from this violation of
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assumption. Putative immigrants from each population were removed for all methods with the exception
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of the maximum likelihood method (MLNe), in which immigration is specifically considered for the
15
estimation of Ne.
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Most methods of estimating Ne also assume a stable population size, which may be violated for
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our study species. Splittail population numbers are driven by availability of floodplain habitat critical for
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spawning, which in turn depend on the amount of precipitation (Moyle et al. 2004). This reliance on
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precipitation may produce natural variability in the population size of the species. However, this
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presumed life history is based upon information on the Central Valley splittail population that has greater
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access to floodplain spawning habitat. Given the limited floodplain availability and comparatively low
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annual freshwater outflow within the Petaluma and Napa Rivers (Feyrer et al. 2005; Feyrer et al. 2007), it
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is unlikely that the life history of the San Pablo Bay splittail population would be identical to that of the
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Central Valley population (Moyle et al. 2004).
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The last major assumption of many Ne estimators is the assumption of discrete generations.
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Treating overlapping generations as discrete can introduce significant bias (Waples and Yokota 2007;
1
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Luikart et al. 2010) and we attempt to address this bias in a couple of ways. First, single-sample Ne
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estimators (i.e., LDNe) can be applied to individuals randomly sampled from a single cohort in a
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population with overlapping generations, providing an estimate of the effective number of breeders (Nb)
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that produced the cohort (Waples 2005). A second approach is to use the temporal method and allow for
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ample time to elapse between two sampling periods. Once several generations have passed between the
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two sampling points, signal from genetic drift should become stronger relative to the overlapping
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generation bias (Palstra and Ruzzante 2008). Although a method to incorporate age-structure effects for
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species with overlapping generations exists, it requires detailed demographic information lacking for less
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well-studied species such as splittail (Jorde and Ryman 1995).
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When using temporal estimators, Waples and Yokota (2007) recommended using samples spaced
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apart by ~3-5 generations or more to reduce overlapping generation bias. Unfortunately, otolith and scale
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analyses on adult splittail collected in the San Pablo Bay (Hobbs, unpublished data) suggested a
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moderately long generation interval for the species (~4.4 years) and indicating that ~2 generations have
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passed between our two sampling periods. Waples and Yokota (2007) observed that for species with Type
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2 or Type 3 survivorship (higher mortality among juveniles, increased survivorship in older individuals),
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sampling of newborns without sufficient time gap results in a downwardly biased estimate. Based on this
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information and our understanding of the splittail’s life history (Moyle et al. 2004), a slight downward
44
bias may be expected in our temporal Ne estimates.
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46
References:
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Feyrer F, Sommer TR, Baxter RD (2005) Spatial-temporal distribution and habitat associations of age-0
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49
splittail in the lower San Francisco Estuary watershed. Copeia 1:159–168.
Feyrer F, Sommer T, Hobbs J (2007) Living in a dynamic environment: Variability in life history traits of
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age-0 splittail in tributaries of San Francisco Bay. Trans Am Fish Soc 136:1393–1405. doi:
51
10.1577/T06-253.1
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Jorde PE, Ryman N (1995) Temporal allele frequency change and estimation of effective size in
populations with overlapping generations. Genetics 139:1077–1090.
Luikart G, Ryman N, Tallmon DA, et al. (2010) Estimation of census and effective population sizes: the
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increasing usefulness of DNA-based approaches. Conserv Genet 11:355–373. doi: 10.1007/s10592-
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010-0050-7
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Moyle PB, Baxter RD, Sommer T, et al. (2004) Biology and population dynamics of Sacramento splittail
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(Pogonichthys macrolepidotus) in the San Francisco Estuary : A review. San Francisco Estuary &
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Watershed Science 2:Article 3.
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Palstra FP, Ruzzante DE (2008) Genetic estimates of contemporary effective population size: what can
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they tell us about the importance of genetic stochasticity for wild population persistence? Mol Ecol
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17:3428–3447. doi: 10.1111/j.1365-294X.2008.03842.x
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Waples RS (2005) Genetic estimates of contemporary effective population size: to what time periods do
the estimates apply? Mol Ecol 14:3335–3352. doi: 10.1111/j.1365-294X.2005.02673.x
Waples RS, England PR (2011) Estimating contemporary effective population size on the basis of linkage
disequilibrium in the face of migration. Genetics 189:633–644. doi: 10.1534/genetics.111.132233
Waples RS, Yokota M (2007) Temporal estimates of effective population size in species with overlapping
generations. Genetics 175:219–233. doi: 10.1534/genetics.106.065300
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Fig. S1 Mean estimated Ln Pr(X|K) values from STRUCTURE K inference analysis of the full data set.
Vertical lines denote standard deviation. Out of K= 1-8, K= 2 has the highest mean value.
1
2
3
4
Mean of estimated Ln probability of data
-84000
80
-85000
-86000
-87000
-88000
-89000
-90000
-91000
81
82
83
84
85
86
87
88
89
90
4
K
5
6
7
8
91
92
93
Fig. S2 Mean estimated Ln Pr(X|K) values from STRUCTURE K inference analysis of 2011 San Pablo
Bay (Petaluma and Napa Rivers) collection. Vertical lines denote standard deviation. Out of K= 1-8, K= 2
has the highest mean value.
1
2
3
4
Mean of estimated Ln probability of data
-21000
94
-21500
-22000
-22500
-23000
-23500
-24000
-24500
-25000
95
96
97
98
99
100
101
102
103
5
K
5
6
7
8
104
105
106
Fig. S3 Mean estimated Ln Pr(X|K) values from STRUCTURE K inference analysis of 2012 San Pablo
Bay (Petaluma and Napa Rivers) collection. Vertical lines denote standard deviation. Out of K= 1-8, K= 1
has the highest mean value.
1
2
3
4
Mean of estimated Ln probability of data
-21000
107
-21500
-22000
-22500
-23000
-23500
-24000
-24500
-25000
108
109
110
111
112
113
114
115
116
6
K
5
6
7
8
117
118
119
Fig. S4 Mean estimated Ln Pr(X|K) values from STRUCTURE K inference analysis of 2011 Central
Valley collection. Vertical lines denote standard deviation. Out of K= 1-8, K= 1 has the highest mean
value.
1
2
3
4
Mean of estimated Ln probability of data
-17000
120
-17500
-18000
-18500
-19000
-19500
121
122
123
124
125
126
127
128
129
7
K
5
6
7
8
130
131
132
Fig. S5 Mean estimated Ln Pr(X|K) values from STRUCTURE K inference analysis of all individuals
assigned to the San Pablo Bay population. Vertical lines denote standard deviation. Out of K= 1-8, K= 1
has the highest mean value.
1
2
3
4
Mean of estimated Ln probability of data
-40000
133
-40500
-41000
-41500
-42000
-42500
-43000
134
135
136
137
138
139
140
141
142
8
K
5
6
7
8
143
144
145
Fig. S6 Mean estimated Ln Pr(X|K) values from STRUCTURE K inference analysis of all individuals
assigned to the Central Valley population. Vertical lines denote standard deviation. Out of K= 1-8, K= 1
has the highest mean value.
1
2
3
4
Mean of estimated Ln probability of data
-43000
-44000
-45000
-46000
-47000
-48000
-49000
-50000
-51000
146
-52000
147
148
149
150
151
152
153
154
155
9
K
5
6
7
8
156
157
Fig. S7 ΔK values, calculated as ΔK = m|L′′(K)|/s[L(K)], from K inference analysis of the 2011 San Pablo
Bay (Petaluma and Napa Rivers) collection.
2
3
K
4
450
400
350
300
ΔK
250
200
150
100
50
158
0
159
160
161
162
163
164
165
166
167
168
169
10
5
6
7
170
Fig. S8 ΔK values, calculated as ΔK = m|L′′(K)|/s[L(K)], from K inference analysis of the full dataset.
2
3
K
4
3000
2500
2000
ΔK 1500
1000
500
171
0
11
5
6
7