On November 3rd Mobrand Biometrics (MBI) completed a revised computation of parameters for North Fork Stillaguamish chinook. The revision was based on review of the EDT inputs in preparation for circulating detailed results from this population, along with the Skagit, for review by the comanagers at the policy level and subsequent release to interested outside parties. There is some documentation of methods in the earlier report given to the comanagers by MBI on September 7[1].
Here I present a comparison of the values presented for productivity and capacity for the North Fork Stillaguamish summer chinook stock to see how close they came to other information available for this system. This is revised from the results in the memo I circulated on September 18th (see http://www.tulalip.nsn.us/StilComparison.htm) due to revision of the EDT results and correction of minor errors in the earlier analysis. I also explore some of the implications of these results for harvest management.
Previously I developed estimates of adult equivalent exploitation rates and adult equivalent recruitment of North Fork Stillaguamish chinook for eight brood years, 1986-1993. These were based on escapement surveys conducted by the Stillaguamish Tribe and WDFW and recoveries of coded-wire tags from the Stillaguamish Tribe’s indicator stock program.[2] (see http://www.tulalip.nsn.us/StillaguamishAnalysis.htm). The relevant results are in the following table:
Table
1. North Fork Stillaguamish
spawner/recruit data from coded-wire tag recoveries and escapement surveys.
|
|
Original |
Subsequent |
Expl. |
AEQ |
Recruits/ |
|
|
|
Br. Yr. |
Escapement |
Escapement |
Rate |
Recrut. |
Spawner |
|
|
|
1986 |
980 |
505 |
0.6647 |
1,506 |
1.54 |
|
|
|
1987 |
1,065 |
695 |
0.4562 |
1,278 |
1.20 |
|
|
|
1988 |
516 |
654 |
0.6429 |
1,831 |
3.55 |
|
|
|
1989 |
510 |
458 |
0.8199 |
2,543 |
4.99 |
|
|
|
1990 |
575 |
488 |
0.6651 |
1,457 |
2.53 |
|
|
|
1991 |
1,331 |
486 |
0.5330 |
1,041 |
0.78 |
|
|
|
1992 |
466 |
596 |
0.3789 |
960 |
2.06 |
|
|
|
1993 |
563 |
585 |
0.4978 |
1,165 |
2.07 |
|
|
|
Average |
751 |
558 |
|
1,473 |
|
|
In the above, the “original escapement” includes all chinook spawning naturally in the North Fork Stillaguamish, while the “subsequent escapement” includes the naturally-produced fish from the give brood year returning to spawn in the North Fork Stillaguamish. The estimate of AEQ recruits is this “subsequent escapement” value divided by (1 – the exploitation rate). Thus, this short data set allows us to look at the relationship between natural spawning escapement and subsequent recruits produced by those spawners.
The EDT analysis resulted in estimates of parameters of spawner-recruit relationships. In particular, estimates of recruits per spawner at low density (productivity) and adult capacity were provided. I used these to derive parameters of Beverton-Holt spawner-recruit functions, where:
R = S / (aS + b)
In the above, S is original spawners, R is subsequent recruits, and aand b are parameters derived from the EDT analysis. For each of the EDT runs, estimates of maximum adult capacity (C) and low-density productivity (P) were provided. These can be used to compute the parameters of the spawner-recruit models as follows[3]:
a = 1/C
b = 1/P
There were several analyses presented in the EDT results. The validation analysis looked at current habitat conditions and assumed a constant exploitation rate of 0.30[4] and a 15% loss of genetic fitness based on current conditions. The current conditions analysis used current habitat conditions. The PFC analyses used a set of habitat conditions in freshwater that conform to the “properly functioning conditions” defined by NMFS. There were two PFC analyses, which differed in their treatment of estuarine conditions. The PFC scenario assumed PFC conditions in freshwater and current conditions in the estuary. The PFC Plus scenario used PFC conditions in freshwater and historical conditions in the estuary. Thus, these two scenarios provide approximate lower and upper bounds on estimated production if PFC conditions are in place in freshwater. The current conditions and both PFC analyses also assumed a 15% loss in genetic fitness. The historic potential analysis used an assumption of undisturbed historic habitat conditions in freshwater and in the estuary. No loss of genetic fitness was assumed for this analysis.
MBI completed runs using both low marine survival and high marine survival assumptions. The low marine survival assumption was designed to reflect conditions prevailing for Puget Sound chinook in recent years (the past decade or so). The high marine survival assumption was for a marine survival approximately twice the low marine survival. In all of the following, I have used results from the North Fork Stillaguamish for the low marine survival assumption only.
The following table shows the productivity and capacity estimates from the most recent EDT runs, along with the corresponding estimates of the parameters of the Beverton-Holt models.
Table 2. Productivity and capacity factors computed from EDT (MBI November 3, 2000) and Beverton-Holt spawner-recruit parameters computed from these.
|
|
EDT Run |
||||
|
Parameter |
Validation |
Current |
PFC |
PFC Plus |
Historic |
|
P |
3.2 |
4.0 |
8.5 |
10.6 |
16.9 |
|
C |
1,633 |
2,483 |
9,792 |
13,957 |
22,170 |
|
Equil. Abund. |
1,114 |
1,859 |
8,646 |
12,635 |
20,857 |
|
The following are computed from the above : |
|
|
|
||
|
a |
.000612 |
.000403 |
.000102 |
.0000716 |
.0000451 |
|
b |
.31746 |
.25126 |
.11710 |
.094697 |
.059242 |
|
|
|
|
|
|
|
The following figure shows the spawner-recruit curves from the validation run compared with the observed values for spawning escapement (of natural origin fish). The upper curve is based on the validation parameters provided by MBI and the Beverton-Holt spawner/recruit relationship implied by those parameters. The lower curve (gray) is an adjusted version of the validation curve, taking onto account the fact that the average observed exploitation rate was 0.5823, not the 0.30 used by MBI in computing the validation parameters[5].
Visual examination of the adjusted validation run curve indicates a very good fit of the observed data for brood years 1986 through 1993 with the theoretical curve (as adjusted for the observed average exploitation rate) provided by MBI.
The following figure compares the observed relationship of recruits to spawners with the Beverton-Holt curve based on the parameters from the current conditions analysis.
Again, the diamonds represent values computed for the 8 brood years examined, only, in this case the y-axis represents total adult equivalent recruitment rather than escapement of natural origin spawners. Again, visually, the fit of the theoretical curve to the observed data appears to be very good, although the variance of the observed data around the theoretical curve appears to be greater than that about the adjusted validation curve. These deviations could be due to 1) a high degree of variability in marine survival during the 1986-1996 period, 2) errors in estimating the adult equivalent recruitment values from the observed coded-wire data, 3) a difference in the form of the actual spawner-recruit curve from the assumed Beverton-Holt, or 4) error in the productivity and capacity parameters computed by EDT. Undoubtedly, all of these factors contribute to the differences between the observed data and the theoretical curve. I have listed the sources of potential error in what I believe is the order of their contribution to the total error (from highest to lowest). Overall, based on the limited available production data, I think the EDT results appear to very accurately reflect current condition for chinook salmon in the North Fork Stillaguamish.
In order to be able to visualize the difference between “current conditions”, “PFC”, “PFC Plus”, and “historic” conditions, I graphed the spawner-recruit curves implied by each of these EDT runs.
The following graph compares the Beverton-Holt curves implied by the four runs (along with the 8 observed values). I have written “PFC” in the area between the “PFC” and “PFC Plus” runs, indicating that this may be a zone within which the comanagers recovery goal for this population will lie.
Clearly the PFC and Historic EDT runs indicate much higher potential production of chinook from this system than we have observed in recent years. The only data available to help answer the important question of whether these much higher production levels have ever been observed or are even theoretically possible are summarized in an analysis of historical population status provided in the technical background document for a Stillaguamish chinook recovery plan[6]. These analyses suggest that the escapement of chinook to the Stillaguamish may have been in the 12,000 –13,000 range in the 1930s, been as high as 10,000 in the 1950s-1960s, and averaged 7,000 in the late 1960s. These values are all well above the averages for 1986-1993 (Table 1), even given the fact that the North Fork population only represents 50% - 75% of the total Stillaguamish chinook population.
Using the theoretical spawner-recruit relationships from EDT, it is possible to compute surplus production, or the amount of recruitment exceeding the escapement, for each level of escapement for each spawner-recruit curve. The following graph shows the relationship of surplus production to escapement for each set of habitat conditions in the EDT analysis.
The surplus production represents the “harvestable amount”, and, under traditional fixed-goal escapement management, we would choose as the goal that level of escapement for which the harvestable amount is maximized. The following table shows the relationships between the escapement that maximizes harvest [Esc(MSH)], the maximum harvest [MSH], and the exploitation rate at that level of escapement and harvest [ER(MSH)] for each of the theoretical curves.
Table 3. MSH escapement, MSH, and MSH exploitation rates at each scenario of habitat conditions (low marine survival assumption).
|
Scenario |
Esc(MSH) |
MSH |
ER(MSH) |
|
Current |
625 |
618 |
50% |
|
PFC |
2,200 |
4,237 |
66% |
|
PFC Plus |
3,000 |
6,689 |
69% |
|
Historic |
4,100 |
12,691 |
76% |
These results show that, if this system were rebuilt to PFC conditions, both the amount of harvest and the rate of harvest could increase, with the increase in the amount of harvest being as much as ten-fold. Importantly, even with MSH harvest rates in place, the magnitude of the spawning escapement would increase by nearly a factor of five going from current conditions to PFC Plus. And this is all under the low marine survival assumption.
Finally, it is interesting to look at the implications of different production scenarios under fixed exploitation rate management. The following graph shows the relationship between the spawning escapement and the equilibrium exploitation rate at that escapement for each scenario. In other words, under conditions of constant freshwater production, marine survival, and exploitation rate, the graphs show the exploitation rate that would maintain the escapement at the constant level indicated on the x-axis.
If the Beverton-Holt spawner-recruit relationship holds, and conditions are constant, the equilibrium escapement resulting from fishing at a constant exploitation rate can be determined from the graph. The following table shows the equilibrium escapement levels that would result from given exploitation rates for each scenario of habitat conditions.
Table 4. Equilibrium escapement at fixed exploitation rates (ER).
|
ER |
"Current" |
"PFC" |
"PFC Plus" |
"Historic" |
|
0% |
1,900 |
8,600 |
12,600 |
20,900 |
|
10% |
1,600 |
7,650 |
11,300 |
18,800 |
|
20% |
1,350 |
6,700 |
9,900 |
16,600 |
|
30% |
1,125 |
5,700 |
8,500 |
14,300 |
|
40% |
875 |
4,700 |
7,100 |
12,000 |
|
50% |
625 |
3,750 |
5,700 |
9,800 |
|
60% |
375 |
2,800 |
4,300 |
7,600 |
|
70% |
125 |
1,800 |
2,900 |
5,300 |
In the above table, the equilibrium escapement under 0% ER corresponds to the equilibrium stock size for each scenario provided by MBI. It is interesting to note that the average “subsequent escapement” from Table 1 for current conditions (558) is close to, but slightly higher than, the equilibrium escapement for the average exploitation rate observed for brood years 1986-1993. According to the above table, even if exploitation rates were reduced as low as 10%, the average escapement to the North Fork Stillaguamish under current conditions would be approximately 1,600. On the other hand, if exploitation rates remained as high as 60%, improved habitat conditions would lead to escapements in the 3,000-4,000 range.
Based on the comparison of the validation and current conditions runs with known data for brood years 1986-1993, the EDT model, using a low marine survival assumption, appears to have done a reasonably good job of reflecting the overall production pattern of chinook from the North Fork Stillaguamish. It is difficult to validate the model for PFC or historic conditions, since we have little data from times when those conditions prevailed in the system. However, the limited estimates of historic production that we do have indicate that escapements and run sizes much higher than recently observed in the Stillaguamish system may have been reality in the 1930s and as recently as the 1960s.
Besides providing a means to evaluate the accuracy of the EDT results, the above analysis also illustrates the relative contributions that harvest management and habitat improvement can make to future production and harvest. We can also use this approach to show what our recovery goals for a population may mean in terms of future harvest opportunity when the populations reach a recovered condition and compare the future potential harvest with the harvest levels realized under today’s conditions.