8033

• UCREFRP Catalog Number: 8033
• Author: Lentsch, L. D., et al.
• Title: Endangered Fish Interim Management Objectives for the Upper Colorado River Basin Recovery And Implementation Program -Final Report.
• USFW Year: 1998.
• USFW - Doc Type: 55,
• Copyright Material: NO

Calculating Nm
' The estimates of N. were divided into three general calculations by accounting for 1) biased sex
ratio, 2) Ne/N and 3) population demographic stability. The minimum value of Ne was set at 1000
for all species and populations (Table 6). This value served as the initial value for the calculations.
Step 1. Accounting for a biased sex ratio (estimates of NO
' The following formulas were used to estimate the number of breeding individuals (Nb) required to
maintain the given Ne (1000):
N. = 4MbFb/Mb+Fb [1] (Wright 1931)
Nb = Mb + Fb [2]
where,
Mb = number of breeding males
Fb = number of breeding females
When the number of breeding individuals (Nb) equals the number of individuals contributing genes
' to the next generation (N), then N. = Nb. However, when the genetic contribution is biased by
males or females, N. is reduced by an amount depending on how much the sex ratio is biased.
That is, the greater the bias, the greater the reduction in Ne. To maintain a minimum Ne of 1000
when a species has a biased sex ratio (eg. 3: 1), Nb would be larger than N.
(ie. Nb> 1000). For
example:
Based on a 1:1 sex ratio;
Nb = 1000 then Mb = 500 and Mf= 500 and, based on equation [1],
Ne = 4(500)(500)/(500+500) = 1000
Based on a 3:1 sex ratio;
Nb = 1000 and Mb = 750 and Fb = 250 and , based on equation [1
Ne = 4(750)(250)/750 + 250 = 750
To account for the 25% loss in Ne the total number of breeding adults (Nb) must be increased.
The number of breeding adults (Nb) needed to maintain an Ne of 1000 in a population with a 3:1
sex ratio is 1330 (Table 6). That is;
Mb = 998 and Fb = 332 and, based on equation [1]
Ne = 4(998)(332)/1330 = 996 (approximately 1000)
Nb = (998+332) = 1330
' Step 2. Accounting for a less than 100% contribution by all adults (estimates of N
A constant value of 0.5 for Ne/N is being used here based on suggestions by Nunney (1995) which
is slightly higher than the average for fish in Table 3. This means that only one-half of the adults in
the population are contributing offspring. To ensure that enough individuals are available to
maintain an N. of 1000 the final value calculated in Step 1(Nb) was doubled. In this example,
' Nb 1330 and Ng= 2660 (Table 6).
16