Coast Coho Adult Diversity Inference Design
The Ricker PVA model used in the ODFW coho assessment and the TRT persistence assessment was used to assess this
criterion. The loss rate of heterozygosity for coastal coho populations was forecast using a long known relationship between
a theoretical population size and the rate at which heterozygosity is lost. This relationship developed in the early in the 20th
century and as described by Wright (1969), can be described by the following equation:
?H = (-1/2Ne)(100%) (11)
where ?H = the expected amount of genetic variation lost in one generation (expressed percent of heterozygosity lost), and
Ne is the number of adults in a population, where each member has equal probability of contributing offspring to the next
generation (expressed as the effective population size). Based upon this equation the value for Ne necessary to retain 95%
of the genetic variation after a certain number of generations (t = generations) can be expressed as:
Ne = 1/[2(1 – 0.95(1/t))] (12)
To solve the calculation of Ne in Equation 12 for coho, a value for the number of generations (t) expected for a coho
population over a period of 100 years (the reference time period) is required. Although coho salmon spawn primarily at age
3, some precocious males (jacks) from each brood spawn at age 2. The proportion of jacks appears to vary among coastal
populations, with stream populations averaging about 6% and lake populations averaging about 22% (ODFW, unpublished
data). The result is that average age at maturity for stream populations is 2.94 years (34.01 generations in 100 years). And
for lake populations, is 2.78 years (35.97 generations in 100 years). Therefore, substituting these values for t into Equation
12, a Ne of 332 and 351 is obtained for stream and lake populations, respectively. So in other words if these values for Ne
are obtained, no more than 5% of the population’s heterozygosity will be lost over a period of 100 years.
An ‘ideal’ population represented by Ne is assumed to have a pattern of offspring per parent across all parents that follow a
poisson distribution characterized by a ratio of Vk/K ˜ 1. With salmonid populations, apparently having a ratio that is much
greater than 1 (for example 2.77 in the studies discussed above), there is a need to adjust Ne calculations to account for this
difference. As described by Hartl (2000), the ratio of VK/K can be used to adjust the calculation of Ne for unequal
probabilities of reproductive success using the following equation
Ne = 2N/[1 + (VK/K)] (13)
The net result of the overlapping generation adjustment and the adjustment for unequal reproductive contribution among
families (Equation 13) is the following:
Ne = (0.53N)(1-0.60) = 0.212N (14)
It is interesting that this level of reduction (Ne = 0.212N) is within the range of values suggested for salmonids by Allendorf et
al. (1997) (Ne = 0.20N) and by McElhaney et al. (2000) (Ne = 0.30). Spawner abundance estimates for salmon are typically
collected on an annual basis. However, for a species with overlapping generations (such as salmon) the value for N, such as
in Equation 14, needs to incorporate the fact that each year’s spawning population is comprised of individuals from different
year classes. Waples (1990) demonstrated that for Pacific salmon this problem of overlapping generations can be
accounted for in the calculation of Ne using the relationship described below.
Ne = g (Nb) (15)
Where g = the average age at maturity for the species and Nb is the harmonic mean of annual counts of spawners for the
entire data set. As previously discussed the average age at maturity was g = 2.78 years for lake populations (i.e., Siltcoos,
Tahkenitch, and Tenmile) and g = 2.94 years for all other populations (stream populations). The harmonic mean of annual
spawner counts (Nb in Equation 15) is calculated from:
Nb = 1 / (1/t)( ? (1/Ni) ) (16)
Where t = number of years counted and Ni = number of spawners counted for each year. It should also be noted that using
a harmonic mean to characterize spawner abundance essentially gives greater weight to the smaller numbers in the data
set. This approach is generally accepted as a way to incorporate the errors that will occur in estimating Ne if population
abundance fluctuates widely, as is frequently the case for coho salmon. Finally, bringing together the previous adjustments
described by Equation 14 for estimating Ne with those of Equation 15 to account for overlapping generations yields the
following equation:
Ne = 0.212 g (Nb) (17)
Substituting the average maturity age for lake populations (g = 2.78) and stream population (g = 2.94), Equation 17 can be
simplified to: Ne = 0.589Nb (18) for lake populations and for stream populations,
Ne = 0.623Nb (19)
Ne values were computed as the Ne that must be achieved to retain at least 97.5% (conversely, losing no more than 2.5%)
of the population’s heterozygosity over a 100-year time period.
Equations 18 and 19 can be used to calculate Ne values directly from an easily measurable quantity – annual spawner
abundance, expressed as a harmonic mean over several years. These equations can also be rearranged such that given a
desired Ne; the harmonic mean necessary to achieve this Ne can be calculated.
The value for the abundance threshold for the diversity criterion was conservatively established by averaging the critical Nb
values for the lake and stream populations and rounding this number upward. The output from the population viability model
was used to estimate the harmonic mean for a period of time 100 years into the future. Mechanically, a harmonic mean of
the spawner escapements was computed for each 100- year trial of the viability model. After all of the trials were completed
(generally there were 3,000 trials per model run), the average of the harmonic means for the individual trials was
determined.
Evaluation Threshold
To pass the diversity criterion the average of the harmonic means had to be greater than 1200.
References
Chilcote, M., T. Nickelson and K. Moore. 2005. Oregon Coastal Coho Assessment Part 2: Viability Criteria and Status
Assessment of Oregon Coastal Coho. Oregon Department of Fish and Wildlife, Salem, OR.
Hartl, D.L. 2000. A Primer of Population Genetics. Sinauer Associates, Inc.
Allendorf, F.W., D. Bayles, D.L. Bottom, K.P. Currens, C.A. Frissell, D. Hankin, J.A. Lichatowich, W. Nehlsen, P. Trotter, and
T.H. Williams. 1997. Prioritizing Pacific salmon stocks for conservation. Cons. Biol. 11:140-152.
McElhany, P., M.H.Ruckelshaus, M.J.Ford, T.C. Wainwright, and E.P. Bjorkstedt. 2000. Viable salmonid populations and the
recovery of evolutionarily significant units. U.S. Department of Commerce, NOAA Technical Memorandum
NMFSNWFSC- 42. 156p.
Waples, R.S. 2002. Effective size of fluctuating salmon populations. Gen. 161:783-791.