Martinson-Stokes-Scarnecchia April 15 2008 Edited in red by stokes
Effects of North Pacific climatic-oceanic regimes, body size, and salmon abundance on the
growth of sockeye salmon, 1925-1998
Ellen C Martinson, John H Helle, Dennis L Scarnecchia, and Houston H Stokes
Ellen C Martinson, Alaska Fisheries Science Center, National Marine Fisheries Service,
NOAA, 17109 Point Lena Loop Road, Juneau, Alaska 99801, USA. ellen.martinson@noaa.gov.
tel. (907) 789-6604. fax. (907) 789-6094. Corresponding Author.
John H Helle, Alaska Fisheries Science Center, National Marine Fisheries Service, NOAA,
17109 Point Lena Loop Road, Juneau, Alaska 99801, USA. jack.helle@noaa.gov. tel. (907) 7896038. fax. (907) 789-6094.
Dennis L Scarnecchia, Department of Fish and Wildlife Resources, University of Idaho,
Moscow, Idaho 83844, USA. scar@uidaho.edu. tel. (208) 885-5984. fax. (208) 885-5534.
Houston H Stokes, Department of Economics, University of Chicago, 601 S. Morgan Street
Chicago, Illinois 60607, USA. hhstokes@uic.edu. tel. (312) 996-0971. fax. (312) 996-3344.
Abstract: To investigate how marine growth and the relationship between marine growth
and sockeye salmon abundances was influenced by climate regimes and shifts, body size at the
start of the growing season, and abundances of sockeye salmon we used multivariate adaptive
regression spline threshold modeling for a 75 year time series from 1924 to 1998. Marine growth
during the juvenile, immature, and maturing life stage was estimated from increments on scales
of adult sockeye salmon that returned to spawn at Karluk River and Lake on Kodiak Island,
Alaska. Intra-specific density-dependent growth was inferred from inverse relationships between
growth and sockeye salmon abundance and occurred in all marine life stages, during the cool
regime, at lower abundance levels, and at smaller body sizes at the start of the juvenile life stage.
A positive relationship between immature growth and sockeye salmon abundances and reduced
density-dependent relationship in juvenile and maturing growth during the warm regimes that
favored the survival of Alaska salmon indicate that processes influencing the survival of Pacific
salmon in the Central North Pacific Ocean are reflected in the scale growth of sockeye salmon.
We question whether a scenario of a shift to a cold regime or extreme warm regime at higher
population abundances could drastically reduce the marine growth of salmon and increase
competition for resources.
Keywords: sockeye salmon, growth, density-dependent, regime
INTRODUCTION
In the last quarter of the twentieth century, considerable research was conducted to
assess the effects of variations in climatic and oceanic factors on production and yield of
salmonid fishes. Although studies earlier in the century had focused on dominant freshwater
factors (Neave 1949, Shapovalov & Taft 1954), evidence from numerous studies suggested that
broad climatic and oceanic factors had been inadequately considered (Ricker 1976). In the later
part of the century, yield and survival rates of Pacific salmon (Oncorhynchus spp.) were also
linked to fluctuations in the regional and basin-scale variations in climate and oceanic
conditions (Royal & Tully 1961, Cushing 1971, Scarnecchia 1981, Beamish 1993, Mueter et
al. 2005). Climatic and oceanic variations have also been associated with fluctuations in
Atlantic salmon abundance and catches in Iceland (Scarnecchia 1984, Scarnecchia et al. 1988),
Ireland (Boylan & Adams 2006), Norway and Scotland (Friedland et al. 2000).
During the twentieth century, climatic and oceanic conditions in the North Pacific
underwent large fluctuations, with two distinct warm regimes (1925-46 and 1977-98) and a
cool regime (1947-76) (Mantua & Hare 2002). The warm regimes were characterized by
increased winter storm activity and atmospheric circulation in the North Pacific Ocean, higher
precipitation in coastal regions, increased offshore upwelling of nutrient rich waters, and
above-normal coastal sea-surface temperatures. The cool regime was characterized by the
opposite conditions (Trenberth & Hurrell 1994).
The climate and oceanic variations have been linked to concurrent variations in
Pacific salmon production, which was higher in Alaska during the warm regimes and lower
during the cool regime (Eggers et al. 2003) in that climate during the first year at sea is
important in determining survival. Alaska salmon stocks fluctuate in phase with decadal scale
fluctuations in North Pacific sea surface temperatures at a 1 year lag for Alaska pink salmon
and 2 and 3 year lag for Alaska sockeye salmon indicating that climate during the first year at
sea is important in determining survival (Mantua et al. 1997). Conversely, salmon production
in Washington and Oregon responded favorably to cool regimes in part due to increased coastal
upwelling (Scarnecchia 1981). Warm regime conditions that suppressed coastal upwelling
along the continental US did not favor the survival more southerly salmon stock inhabiting the
region (Hare & Francis 1994, Hare & Mantua 2000).
Several studies also support the idea that climatic and oceanic conditions can affect
salmon carrying capacity (Myers et al. 2001, Kaeriyama 2007), manifested as densitydependent survival and growth responses to food resource limitations (Salo 1988, Fukuwaka &
Suzuki 2000). The density-dependent responses to increased population abundance were
associated with the 1976-77 shift to a warm regime (Ishida et al. 1993, Helle & Hoffman 1995,
Bigler et al. 1996), was followed by shifts to larger body size salmon from Oregon north to
Western Alaska in the mid-1990s (Helle et al 2007).
From the mid-1970s to the mid-1990s, the increases in overall salmon production
coincided with the decreased growth, decreased size at maturity, and increased age at maturity
of many North American salmon populations (Ishida et al. 1993, Helle & Hoffman 1995,
Bigler et al. 1996). In situ density-dependent growth was observed by inverse relationships
between local densities of salmon and individual’s body weight, feeding rates, and the volume
of prey in stomachs (Fukuwaka & Suzuki 2000, Kaeriyama et al. 2000, Ishida et al. 2002). In
natural conditions, density-dependent growth may be manifested through competition for food
within and among salmon species. Behavioral responses to competition that can reduce growth
include reduced feeding rate, switching from high- to low-quality prey, and changing predator
and prey distributions (Tadokoro et al. 1996, Azumaya & Ishida 2000, Davis et al. 2000,
Fukuwaka & Suzuki 2000). Climatic and oceanic variations can also potentially influence
density-dependent competition by altering salmon distribution (Rogers 1980), changing the
latitudinal boundary of the summer feeding zones (Aydin et al. 2000), and increasing overlap
in the diets of O. nerka and pink O. gorbuscha salmon with chum O. keta and coho O. kisutch
salmon (Kaeriyama et al. 2004).
The potential for intra- and inter-specific competition among Pacific salmon stems
from their high degree of overlap in distribution and feeding in the marine environment.
Juvenile salmon distribute in coastal continental shelf waters during the summer growing
season (Myers et al. 1996). Diet overlap among the five anadromous salmon species is highest
among sockeye and pink salmon (Auburn & Ignell 2000). As juveniles, pink and sockeye
salmon fed primarily on euphausiids in nearshore habitats, fish on the shelf, and euphausiids on
the slope. Immature sockeye from central and southern Alaska distribute and feed with other
salmon from North America and Asia in the Central North Pacific Ocean (Kaeriyama et al.
2004). In offshore waters, the major prey items of sockeye salmon included euphausiids,
copepods, hyperiid amphipods, and large squid; and large squid for pink salmon (Davis 2003).
Maturing sockeye salmon from southern Alaska distributed more eastward and fed primarily
with immature and maturing salmon in offshore waters, and with juvenile salmon in coastal
waters as they return to their natal stream to spawn (Kaeriyama et al. 2004).
To investigate if climatic and oceanic variations and regimes, salmon population
sizes, and body size at the start of the growing season influence the marine growth of salmon at
varied life history stages, we examined scale growth of adult sockeye salmon O. nerka from
the Karluk River, Kodiak Island, Alaska over a 74-year period in relation to marine abundance
of sockeye salmon in central and southeast Alaska based on harvest statistics (1925-1998).
Understanding the density-dependent interactions among sockeye salmon during the marine
juvenile, immature, and maturing life history stages and among ocean regimes will provide
insight into the influence of climate change on the carrying capacity of salmon in the North
Pacific Ocean.
MATERIALS AND METHODS
Although actual fish length information was not available from salmon collected at sea,
scales had been collected over the period 1925 to 1998 (with 7 years of missing data: 1945,
1947, 1958, 1965, 1966, 1969, and 1979) from the age 2.2 sockeye that returned to Karluk
Lake on Kodiak Island, Alaska. Age was designated using the decimal method by Koo (1962)
where the number to the left of the decimal is the number of winters spent in fresh water after
emergence from the gravel and the number to the right of the decimal is the number of winters
spent in saltwater. For example, age 0.3 represented a four year old fish. Marine grow was
estimated from measurements on the scale.
Scale samples and preparation -- For each year, from 30 to 50 scales per year were
selected at equal time intervals though out the collection from the early run (May 1-July 21)
spawning migration. From historical records, scales had been taken from the sockeye at a few
rows above the lateral line and below the posterior insertion of the dorsal fin using a scrape
method (1925-51) and forceps (1952-98) and assumed low variability in the body location
sampled for scales among years (Scarnecchia 1979; Clutter and Whitesel 1956). One scale per
fish had been placed onto gummed cards with the reticulated side facing away from the card
and impressed onto an acetate card using a hydraulic press at 100°C and 224 psi for 3 minutes
(Arnold 1951).
Scale impressions were viewed and scanned using an Indus microfiche reader Model
4601-11 with a 24  objective lens. Images of scales were copied from the reader screen with
the Screenscan Microfiche PC Model high-resolution scanner hardware and saved as TIFF files
using the ScreenScan Application software, version 1.00.0.8. Images were then imported into
the Optimate image analysis software for measuring.
Scale measurements -- In using scale measurements to estimate marine growth of
salmon, we assumed that a) growth along a specified radius of the scale was proportional to the
growth in fish length (Dahl 1909), and b) the distance between adjacent annuli on a scale
depicted one year of somatic growth (Fukuwaka & Kaeriyama 1997).
Scales were read for age and measured by the lead author. Scale measurements were
taken along a reference line drawn from the focus to the edge of the scale along the longest
anterior radial axis in millimeters (Narver 1968). Measurements were adjusted to the original
scale size by dividing by 24. One scale was measured per fish and 30 to 50 scales were
measured per year (N=69 years) for a total of 3,116 scales.
Growth during each year of marine residence was estimated from the measured
distances between adjacent annuli on the scale image (Fig. 1). Total freshwater growth (FW),
an indicator for body length at the start of the first marine year as juveniles, was estimated as
the distance from the center of the focus to the center of the space between the last freshwater
circulus and the first marine circulus. Growth in the first marine year (M1), an indicator of total
growth during the juvenile stage, was estimated as the distance from the space between the last
freshwater circulus and first marine circulus to the leading edge of the first marine annulus.
Second-year marine growth (M2), an indicator for immature growth, was estimated as the
distance from the leading edge of the first marine annulus and the leading edge of the second
marine annulus. Third-year marine growth (M3), an indicator for maturing growth, was
estimated as the distance from the leading edge of the second marine annulus to the outer edge
of the scale. Scales with reabsorbed edges and evidence for being regenerated were not
measured. Mean values for M1, M2, and M3 growth were calculated for each brood. Mean
growth for the seven years of missing scale data were estimated as points along a local ordinary
least squared smoothing line fit to the data to satisfy the statistical analysis requirement of a
complete time series. Because, body size at the start of the growing season may influence
growth, we also created means for the scale radius at the start of the first marine year (FWt), at
the start of the second marine year (L1t=FWt-1+M1t-1), and at the start of the third marine year
(L2t=FWt-2+M1t-2+M2 t-1). Mean values of specified scale growth measurements were
calculated by brood year and compared among broods to assess inter-annual variation in
growth by age group and stock.
Salmon abundance estimates
Information on salmon biomass was unavailable, as was information on the abundance,
biomass, or catch per unit effort of juvenile, immature, and maturing salmon in the ocean.
Therefore, the index of sockeye salmon abundance (SSA Index) by cohort was based on
estimates of commercial harvest (number of fish per year) in central and southeast Alaska
management regions (Eggers et al. 2003). The central Alaska region included areas from Cape
Suckling to Unimak Pass; the southeast Alaska region included areas from British Columbia to
Cape Suckling. In using commercial harvest to estimate salmon abundance, we assumed a
constant marine mortality rate, a low contribution of harvest from sport and subsistence
fisheries compared to the commercial fisheries, and a constant exploitation rate among years.
Marine growth versus salmon abundance -- It was hypothesized that intra-specific
density-dependent growth would be manifested as negative relationships between the estimated
marine growth based on scale measurements (M1-M3) and the SSA Index lagged to the growth
year of cohort. For the juvenile stage, the first-year marine scale growth (M1) in year t was
related to the number of maturing sockeye salmon caught in the fishery in year t+2 (SSAM1),
the abundance index for the juvenile sockeye in year t. For the immature stage, the second-year
marine scale growth (M2) in year t was related to the number of maturing sockeye captured in
the fishery in year t+1 (SSAM2), the abundance index for immature sockeye salmon in year t.
For the mature stage, the third-year marine scale growth (M3) in year t was related to the
number of maturing sockeye captured in the fishery in year t (SSAM3), the abundance index
for maturing sockeye salmon in year t. Text and summary measures are given in Table 1.
Two-way scatter plots between scale growth (dependent variable) and sockeye salmon
abundance indices (independent variable) were created for M1 against SSAM1, M2 against
SSAM2, and M3 against SSAM3 (Fig. 3). Plots were examined for negative growth-abundance
relationships and changes in relationships associated with the three North Pacific Ocean
climatic and oceanic regimes (ie. early warm (1925-46), cool (1947-76), and the late warm
(1977-98) periods). Regime (called SHIFT) was included as a categorical variable in the
models to test whether a change occurred in the growth-abundance relationship associated with
the regime shift. To verify the presence of the regime shift we substitute YEAR in for SHIFT
and allowed the model to automatically detect changes in the relationships between growth and
predictor variables.
Statistical analyses -- To describe density-dependent growth of Karluk sockeye salmon
during each marine life history stage we used ordinary least squares (OLS) and multivariate
adaptive regression spline (MARS) methods. Individual models for the juveniles (M1),
immatures (M2), and maturing (M3) growth were described as a function of the 1) 1976-77
ocean regime shift (SHIFT), 2) autocorrelation lags at one and two years in the scale growth
variable, 3) size at the start of the growing season of the cohort (FW, L1, L2), and 4) the index
of sockeye salmon abundance (Table 1). Density-dependence was inferred from negative
relationship between scale growth and population abundance.
The OLS and MARS model results were compared to measure any possible gains
obtained by relaxing some of the restrictive assumptions of OLS. The ordinary least squares
model of the form y  fˆ ( x1 , x2 ,
, xk ) , where y was the dependent variable and xi , i  1,
,k
were the independent variables, assumed that all effects are linear and that all variables are in the
model for every period. The estimated coefficient for the ith input variable xi in a model
y  ˆ0  ˆ1 x1 
 ˆk xk  e measured the unit change of that input variable in explaining a
change in the dependent variable y and whether the input variable was positively related or
negatively related to the dependent variable. The statistical significance of the estimated
coefficient was measured using the t-value ˆk / S.E.(ˆk ) . Some important restrictions of OLS
include (a) that the effect, if found, was always present, (b) the effect was always the same size
for a one unit change in the independent variable, and (c) unless the independent variable was
transformed it was not related to other independent variables. The MARS technique allowed
testing and relaxing of these restrictions. The MARS model y  f ( x) allows the possibility that
the effect of x on y can be impacted by an unknown threshold  * which alters the relationship.
Friedman (1991) is a thorough basic MARS reference. Lewis and Stevens (1991) were early
users of this approach. Stokes (1997) and Stokes and Lattyak (2006) provide additional
information and examples. For example
y    1 x  e
for x  100
    2 x  e for x  100
(1)
In terms of the MARS notation, (1) can be written as
y   ' c1 ( x   * )   c2 ( *  x )   e ,
(2)
where  *  100 in the population but is estimated by MARS for the sample. The term ( )+ is the
right (+) truncated spline function which takes on the value 0 if the expression inside ( ) + less
than or equal to zero and its actual value if the expression inside ( )+ is > 0. Here c1  1 and
c2  2 . Once the transformed vectors ( ( x   * )  , and ( *  x)  ) in equation (2) are determined,
OLS is used to solve for the coefficients (  ', c1 , c2 ).
To determine at what threshold (r ) of the predictor variable (i.e. sockeye salmon
abundance) that corresponds with a change in the relationship of growth (M1, M2, M3) to the
predictor variable (i.e. sockeye salmon abundances, 1976-77 regime shift, size at the start of the
growing season) and/or interacting predictor variables we used the MARS interaction model
y  f ( x, z ) . The model is expressed as
y    c1 ( x   1* )   c2 ( 1*  x )   c3 ( x   1* )  ( z   2* )   e
and can be interpreted as nested three models depending on the values of x and z as follows:
(3)
y    c1 x  c1 1*  e
for x   1* and z   2*
   c2 x  c2 1*  e
for x   1*
(4)
   c1 x  c   c3 ( xz   z   x    )  e for x   and z   .
*
1 1
*
1
*
2
* *
1 2
*
1
*
2
Model results reported as ( xi   i* )  and ( i*  xi ) are displayed as max((x - c),0.0) and max((cx),0.0)
respectively where c   * . For example, a model y  c( x  3.0)  indicates that if
x  3.0, y  0 . For cases x  3.0, y  cx  3c .
To show the exact years in which the dependent variables added to the prediction of the
growth variables y , (M1, M2, M3) we presented line plots of the transformed vectors. For each
plot, the effect of the predictor variables on the M1, M2, M3 growth in millimeters can be
interpreted as the coefficient of the model multiplied by the value in the y-axis. The direction of
the relationship between the predictor and dependent variable is interpreted as the product of
signs of the coefficient and the value. Finally, the overall MARS model results for the
relationship between marine growth and sockeye salmon abundance were plotted to examine the
overall density-dependent relationship. Three-dimensional plots were used to represent the
growth-abundance term with one interaction variable and other variables held constant.
RESULTS
Line and scatterplots
Marine growth as indicated by scale measurements varied inversely with the sockeye
salmon abundance index (Figures 2-3). Two clusters were observed among the three regimes
indicating a change in the growth-abundance relationship occurred at about the 1976-77 ocean-
climate regime shift, but not the 1946-47 regime shift (Figure 3). M1 declined for the combined
1925-46 (white dots) and 1947-76 (black dots) period as sockeye salmon abundance increased
from 2 million to 10 million, and was high as sockeye salmon abundances increased for the
1977-98 period (triangles) (top Figure 3). M2 was not related to SSAM2 prior to 1977, but M2
increased as SSAM2 increased for the 1977-98 period (middle Figure 3). M3 showed a similar
pattern as M1 (bottom Figure 3).
Due to the change in the growth abundance relationship around the 1976-77 regime and
the detection of a shift around 1976 in the MARS regime test, the 1976-77 regime shift was
included as a covariate in the models where SHIFT=0 from years 1925 to 1976 and SHIFT=1 for
years from 1977 to 1998. For SHIFT coded as YEAR, the MARS analysis detected a break in the
regime for M1 in 1980, for M2 in 1950, 1956, 1968, 1980 and for M3 in 1974. Based on this
evidence, the 1976 regime shift assumption used in this analysis appeared warranted.
Juvenile Growth Model
Juvenile marine growth (M1) was described as a function of the 1976-77 regime shift and M1 at
lag year 2 (SSR=0.157) in the OLS model, but not M1 at lag year 1 or body size at the start of
the first marine growing season (FW) (Table 2). When a MARS model was estimated (Table 3),
using the same variables, the sum of squares was reduced to 0.114 (Table 4) and FW and M1{1}
entered into the model at certain threshold ranges and interactions (Table 3). Unlike OLS, where
all vectors are constant and active in the equation over the time, for the MARS M1 model the
number of active vectors, from 1 to 6, and variables varied over time in the equation (Figure 4).
Plots of each vector and its associated model (Figure 5) form the basis of the following MARS
model findings. The activity and magnitude of the effects of the predictors on growth varied over
time as indicated by plots of the vectors of the MARS model (Figure 6-8).
In the MARS model, M1 growth was negatively affected (t=-6.19) when M1 growth two
years prior M1{2} was decreasing and below the threshold of 1.078 mm (Fig 5A). The effect
was stronger during the early warm regime and during odd-numbered years and may represent
inter-specific density-dependent interactions with a species having a two-year abundance cycle,
such as pink salmon. A positive effect (t=2.19) on M1 due to either decrease in growth two years
prior and or decrease in sockeye salmon abundances at thresholds less than 6.0 million was
strong in 1955, 1958, 1967, 1969, 1971 and 1973 (Fig. 5B). In Figure 5C, a negative effect (t=3.20) on M1 occurred when M1{2} was decreasing below 1.078 and smolt size was relative
large (FW=0.659) (Fig. 5C). In Fig. 5D, a positive effect on M1 (t=3.64) occurred when growth
of the past two cohorts was decreasing from average to below average. This 13 year effect
occurred during the early warm regime in 1928, 1930, 1932-35, 1938, 1940-44 and 1954 (Fig.
5D). A weaker negative effect (t=-3.39) on M1 during the early warm regime occurred when
previous years growth was M 1{1}  1.015 (Fig. 5E). During the cool regime, a negative effect on
M1 growth when smolts were small and deceasing and sockeye salmon abundances decreased
from below 4.9 in 1953, 1956, 1962, 1971 and 1972 (Fig. 5F).
Immature Growth Model
In the OLS model, immature M2 growth was a significant positive function of the 197677 regime shift and sockeye salmon abundance with the sum of squares = .188 (Table 2). When a
MARS model was estimated, the sum of squares fell to .144 and the additional variables, length
at the start of the growing season (L1) and growth of the previous two cohorts (M2{1} and
M2{2}), entered into the model (Table 3).
In the MARS model, M2 was a significant function of the 1976-77 regime shift, size at
the start of the growing season, M2 growth of the two previous cohorts, and sockeye salmon
abundance. A significant positive effect (t=2.54) on M2 occurred at lower and decreasing
sockeye salmon abundances SSMA2  6.0 and as SSAM 2  in 29 year and mostly during the
1947-76 cool regime. At the time of the 1976-77 regime shift, there was a 5.7% and significant
(t=2.15) increase in M2 of .0435 mm (Fig. 6B). A positive and the strongest significant (t=4.28)
effect on M2 at higher and increasing sockeye salmon abundances ( SSAM 2  4.6 and
SSAM 2  ) occurred in 54 years during warm regimes and was twice as strong in 1977-98 warm
regime than the 1925-46 warm regime (Figure 6C). Higher and increasing M2 growth of the
previous years cohort (Figure 6D) corresponded with a significant negative effect (t=- 3.10) on
M2, and a stronger negative effect in odd-numbered years during the late warm regime.
Interaction between decreasing M2 growth of the previous cohorts M 2{1}  .820 as M 2{1} 
and a decrease below a small body (1.663 mm) at the start of the immature growing season
corresponded with a significant negative (t=-3.04) on M2 that was active in 1942, 1954, 1963,
and 1972.
Maturing Growth Model
Maturing growth was a significant positive function of the 1976-77 regime shift, M3
growth of the previous cohort, and a negative function of sockeye salmon abundance, but was
not a significant function of body size at the start of the marine growing season L 2{1} or M3
growth in two years prior M 3{2} (Table 2) in the OLS model (SSR=0.0869). However, when
including all variables in the MARS model the residual sum of squares fell to 0.07548 (Table 3
and 4). More importantly, the insignificant variable M 3{2} in the OLS model became significant
(t=3.57) when it became part of an interaction with M 3{1} .
In the MARS model, maturing growth was a significant function of sockeye salmon
abundance and growth of the cohort two years prior M3{2}, but not the 1976-77 warm regime or
size at the start of the marine growing season (L2) (Table 3). When growth of the previous years
cohort was higher than average and increasing there was a positive and significant (t=6.16) effect
on M3 that occurred in 30 years from the mid-1950s to the mid-1980s (Figure 7A). As found
with M2, in 35 years primarily during the cool regime a positive and significant effect (t=4.4) on
M3 by up to 16% in 1975 occurred when sockeye salmon abundances decreased from below 6.8
million (Fig. 7B). M3 was negatively affected (t=-4.50) when M3 growth of the two prior
cohorts was increasing in 16 years from 1964 to 1985 and strongest in 1964-63, 1970, 1975, and
1985 (Fig. 7C). For the similar period as the previous interaction term, there was a less
significant positive effect on M3 (t=4.17) (Fig. 7D). In 19 years (1944, in even numbered years
from 1950 to 1962, and in 1969, 1974, 1980, 1990, and 1996), M3 was negatively affected (t=4.10) when the cohort two years prior had higher and increasing M3 growth (Figure 7E). Finally,
a lesser positive effect (t=3.57) on M3 during similar years as the previous model period
occurred when the previous years growth was increasing from low to high growth and
decreasing from high to low growth two years prior
Overall MARS results
In the overall MARS models, negative relationships between marine growth and
sockeye salmon abundance occurred at lower population abundances and cool regime
conditions. For juvenile growth, M1 was decreasing from high to low growth as sockeye
salmon abundance increased from 0 to 4.6 million (Fig. 8). A below average body size at the
start of the juvenile growing season and lower abundances less than 4.9 million, resulted in a
negative effect on growth (Figure 8). In Figure 9, M2 had a negative response to SSAM2 from
0 to 6.0 million, whereas when growth in the prior year was high there was a decrease in the
response magnitude of the negative response to SSAM2. M2 growth increased at sockeye
salmon abundances greater than 6.0 million associated with warm regimes. Figure 10, maturing
growth decreases from high to average growth at lower abundances, and remains constant at
higher abundances associated with cool regimes.
DISCUSSION
Life history stage and density-dependence
For Karluk sockeye, all marine life stages experienced density-dependent growth as
inferred from inverse relationships between marine growth and sockeye salmon abundance.
The magnitude of the density-dependence increase throughout the life stages, as the sockeye
salmon abundance increased from 2 million to 6 million scale growth was reduced by 1% in
juveniles, 5-7% in immatures, and 20% in maturing fish (Fig. 8-10). Reduced detection of
density-dependence in the early life history may be due to the measuring past growth histories
of the cohort taken from the scales of a portion of the surviving adults. As maturing sockeye
migrate through multiple marine habitat en route from oceanic water to their natal stream they
may experience a wider range of competitors, habitats, and prey fields than juvenile and
immature salmon.
Climate oceanic regimes and density-dependence
Density-dependence was stronger during the cool regime than during the warm regimes
as indicated by the negative correlations between marine growth and salmon abundance during
the cool regime and the positive or lack of correlations during the warm regimes. The warm
ocean conditions, being more favorable for growth and survival, may have offset the densitydependent effects of higher sockeye salmon abundance. Alternatively, the lower abundances of
sockeye salmon during the cool regime reduced the relative numbers to a competitor species that
increases intra-specific competition for resources. Cool regime conditions may reduce primary
and secondary production that in turn reduce prey quality and quantity that increases competition
for food. We question whether a scenario of higher abundances during a cool regime or
excessively warm regime would further result in a strong density dependent effect on the marine
growth of Alaska sockeye salmon.
During the warm regimes, immature growth elicited a positive response to increases in
sockeye salmon abundance and the reduced negative response of juvenile and maturing growth
to sockeye salmon abundance (Figures 8-10). Mechanisms for increased growth during warm
regimes include changes in predator abundance, prey-switching by competitors, and improved
climate and ocean conditions. Since the mid-1970s, an increase in the numbers of salmon
predators, such as salmon shark Lamna ditropis, that prey on the smaller sockeye has resulted
in a greater percent of larger sockeye in the population (Ruggerone et al. 2003). Second, the
50% reduction in the abundance of piscivorous birds that fed on schooling fish in the Gulf of
Alaska between 1972 and 1989 (Agler et al. 1999) led to an increase in forage fish abundances
that provided competitors with alternatives to the preferred prey of sockeye. Third, warmer
coastal surface waters in the eastern North Pacific, cooler temperatures and increased offshore
upwelling of nutrient rich-waters offshore in the central North Pacific, lower winter sea level
pressure that enhanced cyclonic atmospheric and ocean circulation, that favored higher survival
of Alaska salmon (Mantua & Hare 2002) also improve the marine growth of immature sockeye
in offshore waters. Increased immature growth at higher population levels and in response to
the 1976-77 warm regime indicates an increased the carrying capacity for salmon in the Central
North Pacific Ocean (Fig. 9B). Similar physical processes affecting the survival of Alaska
salmon may be detectable in the growth of immature sockeye salmon one year prior to
returning to the fisheries.
The cool regime period was more favorable for juvenile and maturing growth and the
warm regimes more favorable for immature growth. Juvenile and maturing growth was
relatively high and decreasing with increased sockeye salmon abundances during the cool
regime, while during the warm regime growth was low and had no relationship to sockeye
abundance, while immature growth was relatively low and decreasing with population
abundance during the cool regime and high and increasing with abundance during the warm
regime (Fig. 8-10). Immature sockeye inhabit waters off the continental shelf with nutrient
upwelling increases in windier conditions associated with an eastward shift in the Aleutian
Low Pressure cell and increased storm activity.
Growth had a positive response to the 1976-77 regime shift but no response to the 194647 regime. The post hoc regime shift detection in out MARS model failed to detect a negative
response to the 1946-47 shift. Similarly, Mantua and Hare (2002) found the positive 1976-77
shift in the total harvest of central and western Alaska sockeye salmon and central and southeast
Alaska pink salmon was six times greater than the negative 1946-47 shift. The higher frequency
of shift detection in M2 than M1 and M3 implicate M2 as an indicator for climate variation in the
ocean.
Body size and density-dependence
Body size at the start of the marine growth season was important in the densitydependent growth at the juvenile stage (Fig. 5F), but not the immature and maturing stage (Fig.
6A, 7B). A density-dependent relationship occurred when smolts were in the lower 25%
(FW=0.6210) size range (min=0.5646, max=0.80085). This scenario occurred during cold
years (1953, 1956, 1962, 1971-72) as indicated by negative sea surface temperature anomalies
in the north or 20N in the Pacific Ocean (Mantua et al. 1997), within the cool regime, and at
sockeye salmon abundances less than 6.0 million (Fig. 5F). Following the cohort into the next
growing season shows that the smaller size translated to smaller size at the start of the
immature growing season and negative effects on immature growth in 1954, 1963, 1972 (Fig.
6E). Negative effects on M2 not related to sockeye salmon abundance occurred in cold years
(1938, 1944, 1946, 1948, and 1955) and warm years (1942, 1994). Colder sea surface
temperatures can direct and indirectly affect the marine growth of salmon by reducing body
size, metabolic rates, food availability that in turn increases competition for food.
Inter-specific density-dependence
Alternate year patterns in the magnitude of the negative effects on juvenile and
immature growth may be explained by inter-specific competition with a species with a 2 year
generation cycle such as the strict age 0.1 pink salmon and variations in physical
oceanography. In the ocean, higher densities of maturing pink salmon in odd-numbered years
than even-numbered years corresponded with slower growth rates of coho in the western North
Pacific Ocean, smaller size of pink salmon in the central North Pacific Ocean, lower growth of
Russian sockeye salmon, and reduced second- and third- year scale growth of adult sockeye
that returned to Bristol Bay in western Alaska (Ogura et al. 1991, Walker 1998, Bugaev et al.
2001, Ruggerone et al. 2003).
For the juvenile stage, the alternate year pattern of negative growth was stronger in the
odd-numbered years 1929-49, 1967-73, and 1989, 1995, and in the even-numbered years 195064 and 1992 (Fig. 5A). The harvest patterns of maturing pink salmon returning to Kodiak
management region near the Karluk River system was higher in odd-numbered years from
1927 to the mid 1940s in even-years from 1954-66, low from 1967-73 (1968-73 cold years),
low in 1989 (cold year), and extremely high 1995. These findings indicate that maturing pink
salmon compete for food with juvenile sockeye rather than the juvenile pink salmon. In 1996,
diets of juvenile sockeye and pink salmon in coastal waters of the Gulf of Alaska overlapped
from 25% to 79%, but authors found no evidence of food limitations (Auburn & Ignell 2000).
Maturing pink salmon feed on similar prey as juvenile pink, but consume larger sized prey
similar to juvenile sockeye, therefore, sockeye salmon from the Karluk stock likely compete
for food with the maturing pink salmon returning to Central Alaska.
For the immature stage, growth was more negatively affected in odd-numbered years
than to even-numbered years from 1987 to 1997 (Fig. 6D). The lower growth of Karluk
sockeye corresponded with higher densities of chum and pink salmon in odd-numbered year
than in even-numbered years captured in gillnet survey in the central Pacific Ocean from 1987
to 1997 (Azumaya & Ishida 2000). In years of higher pink salmon abundance in the Bering
Sea, Azumaya & Ishida (2000) observed that chum salmon move from the Bering Sea into the
eastern North Pacific Ocean. In the Pacific Ocean, immature chum salmon responded to higher
pink salmon abundances by switching from feeding on the higher-quality crustacean and squid
diet preferred by sockeye and pink salmon to feeding on lower-quality gelatinous zooplankton
(Davis 2003) hence increasing the relative competition between pink and sockeye salmon for
prey resources. Alternatively, a two-year cycle in the physical oceanography was present with
a more northern latitudinal position of the SubArctic Current. In the 1994-98 study, cooler seasurface temperatures were associated with larger body size of salmon that fed on higher quality
diet of squid in 1996 and 1998, while a more southern boundary current and warmer seasurface temperatures coincided with smaller size salmon that fed on lower-quality zooplankton
in 1997 (Aydin et al. 2000) that could account for the alternate year pattern in immature growth
of sockeye salmon inhabiting the Central North Pacific Ocean.
Conclusion
The relatively long time series and threshold analysis on salmon growth highlights the
temporal changes in the influences of population abundance, climate regimes, climate shifts,
and body size at the start of the growing season on the marine growth and density-dependent
growth of sockeye salmon in the North Pacific Ocean. Although the scales represent the
survivors, we found that density-dependent reductions in the marine growth occurred in all
marine life history stages, at lower population levels, during the cool regime, cold years, and at
smaller body size at the start of the juvenile growing seasons. The finding that growth was
negatively related to sockeye salmon abundance during the cool regime and lower abundance
levels, and positively related to sockeye salmon abundance at higher abundances during the
warm regimes lead us to question whether a shift to a cool regime or an extremely warm
regime at higher abundance levels may drastically reduce the marine growth of salmon.
Acknowledgements. We thank Bill Lattyak from SCA for providing the SCA®
WorkBench software that provides an interface into the B34S® Software used for MARS
estimation (Stokes & Lattyak 2006). Bill in addition made substantial contributions in the initial
model selection and interpretation. For MARS estimation, the B34S Software version 8.11D,
that uses the GPL MarsSpline software library developed by Hastie-Tibshirani (1986, 1990) for
R, was employed. Stokes (1997) is a basic published reference for B34S and in Chapter 14
discusses MARS estimation in some detail. The MarsSpline GPL library, distributed with R, is
distinct from and is an alternative to the proprietary MARS software initially developed by
Friedman (1991). A number of figures were produced using the RATS version 7.0 software
developed by Estima (Doan 2007a, 2007b). Use of trade names does not imply endorsement by
the National Marine Fisheries Service, NOAA.
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M3, third-year marine growth
M2, second-year marine growth
M1, first-year marine growth
FW, total freshwater growth
Fig. 1. Scale from an age 2.2 sockeye salmon from Karluk Lake, Alaska showing the
measurements for total freshwater (FW), first-year marine juvenile (M1), second-year
immature (M2), and third-year marine maturing (M3) growth.
30
1.3
25
M1
1.2
20
SSAM1
15
1.1
10
1.0
0.9
0
1.0
25
Scale distance (mm)
M2
0.9
20
SSAM2
15
0.8
10
0.7
5
0.6
0
0.5
25
Sockeye salmon abundance index
5
M3
20
SSAM3
0.4
15
10
0.3
5
0.2
1920
1940
1960
1980
0
2000
Year
Fig. 2. Trends in the mean annual juvenile (M1), immature (M2), and maturing (M3) marine
scale growth of the age 2.2 sockeye salmon that returned to Karluk Lake, Alaska in relation to
the index for the abundance of juvenile (SSAM1), immature (SSAM2), and maturing (SSAM3)
of sockeye salmon from central and southeast Alaska from 1925 to 1998.
31
A
M1 (mm)
1.2
1.1
1.0
0.9
1.0
B
M2 (mm)
0.9
0.8
0.7
0.6
0.5
M3 (mm)
C
1925-46 warm regime
1947-76 cool regime
1977-98 warm regime
0.4
0.3
0.2
0
5
10
15
20
25
Sockeye salmon abundance index
Fig. 3. Ocean-regime comparison of the relationships between the mean annual marine growth in
the first-year (M1) and the juvenile sockeye abundance index (SSAM1) in plot A, second-year
(M2) and immature sockeye abundance index (SSAM2), and third-year (M3) and the maturing
sockeye abundance index (SSAM3). Growth is measured on the scale of age 2.2 sockeye salmon
that returned to Karluk Lake, Alaska. Abundance is estimated from the numbers of sockeye
salmon harvested in the central and southern Alaska management regions from 1925 to 1998.
32
33
Number of Active Vectors by Year
Vectors Active
Vectors Active
Vectors Active
Models Estimated using MARS
M1 Equation - Juvenile Growth
6
4
2
0
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
M2 Equation - Immature Growth
4
2
0
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
M3 Equation - Maturing Growth
4
2
0
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Fig. 4. Numbers of active vectors in the M1, M2 and M3 models by year. For further detail on each vector's value see Figures 5-7.
34
Significant Vectors for M1 - Juvenile Growth
Coef * vector(s) Displayed
Value
A: -.932 * max(1.078 - M1{2},0.)
0.100
0.000
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
B: .240 * max(1.078 - M1{2},0.) * max( 6.- SSAM1{0},0.)
0.30
0.15
0.00
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
C: -9.15 * max(1.078 - M1{2},0.) * max(FW{0} - .659,0.)
0.0150
0.0075
0.0000
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
Year
Value
D: 21.96 * max(1.015 - M1{1},0.) * max(1.078 - M1{2},0.)
0.008
0.000
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
E: -1.72 * max(1.015 - M1{1},0.)
0.06
0.00
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
F: -1.23 * max(.621 - FW{0},0.) * max(4.9 - SSAM1{0},0.)
0.04
0.00
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Fig. 5. Values of significant vectors in M1 model showing periods of activation. For further detail on the model estimated using
MARS and variable descriptions, see Table 3.
35
Significant Vectors for M2 - Immature Growth
Models Estimated using MARS
Value
A: .0166* max(6.0-SSAM2{0} )
3.0
1.5
0.0
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
1975
1980
1985
1990
1995
1975
1980
1985
1990
1995
1975
1980
1985
1990
1995
1980
1985
1990
1995
Year
B: .04354 * max(SHIFT{0}-0.0))
Value
1.00
0.50
0.00
1930
1935
1940
1945
1950
1955
1960
1965
1970
Year
Value
C: .01005 * max(SSAM2{0} - 4.6))
15.0
7.5
0.0
1930
1935
1940
1945
1950
1955
1960
1965
1970
Year
Value
D: -.6231 * max(M2{1} - .8202)
0.150
0.100
0.050
0.000
1930
1935
1940
1945
1950
1955
1960
1965
1970
Year
E: -7.571*max(.820 - M2{1})*max(1.663-L1{0})
Value
0.012
0.006
0.000
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
Year
Fig. 6. Values of significant vectors in M2 model showing periods of activation. For further detail on the model estimated using
MARS and variable descriptions, see Table 3.
36
Significant Vectors for M3 - Maturing Growth
Models Estimated using MARS
Value
A: 1.482 * max(m3{1} - .346,0.)
0.10
0.00
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
B: .0135 * max(6.8- SSAM3{0},0.)
4
0
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
C: -64.54 * max(M3{1}-.346,0.) * max(M3{2}-.3819,0.)
0.0025
0.0000
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
Year
Value
D: 1.923 * max(M3{2} - .366,0.)
0.07
0.00
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Value
E: -58.77 * max(M3{1}-.327,0.) * max(.366 - M3{2},0.)
0.0035
0.0000
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
Year
Value
F: 29.82 * max(M3{1} - .295,0.) * max(.366 - M3{2},0.)
0.005
0.000
1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996
Year
Fig. 7. Values of significant vectors in M3 model showing periods of activation. For further detail on the model estimated using
MARS and variable descriptions, see Table 3.
37
M1=f(Sockeye, FW) 1977-1998 Scenario & median controls
M
1
1.08
1.06
1.04
1.02
1.00
.98
.96
.94
.92
.80
.75
FW
20
.70
15
.65
.60
10
5
1)
SSAM
(
e
ey
Sock
Fig. 8. First-year marine scale growth (M1) of age 2.2 sockeye salmon that returned to Karluk Lake, Alaska in relation to the index of
abundance for juvenile sockeye salmon from south central and southeast Alaska (SSAM1) at varied levels of SSA abundance. Models
in Table 1.
38
M2 = f(Sockeye & M2{1}) 1925-1976 Scenario & mean controls
M
2
M2 = f(Sockeye & M2{1}) 1977-1998 Scenario & mean controls
.90
.88
.86
.84
.82
.80
.78
.76
.74
.72
.70
.68
.66
M
2
.94
.92
.90
.88
.86
.84
.82
.80
.78
.76
.74
.72
.70
20
.90
M2{1
.70
}
M
(SSA
eye
Sock
M2{1
2)
M
2
20
15
.80
M2{2
}
.70
10
5
e
Sock
ye
10
5
M2
(SSA
)
SSA
ye (
M2)
M2 = f(Sockeye & M2{2}) 1977-1998 Scenario & mean controls
.90
.88
.86
.84
.82
.80
.78
.76
.90
.70
}
e
Sock
M2 = f(Sockeye & M2{2}) 1925-1976 Scenario & mean controls
M
2
15
.80
10
5
20
.90
15
.80
.94
.92
.90
.88
.86
.84
.82
.80
20
.90
15
.80
M2{2
}
.70
10
5
e
Sock
SSA
ye (
M2)
Fig. 9. Second-year marine scale growth (M2) of age 2.2 sockeye salmon that returned to Karluk Lake, Alaska in relation to the index
of abundance for immature sockeye salmon from south central and southeast Alaska (SSAM2) at varied levels of SSAM2.
39
M3=f(Sockeye & M3{1}) & mean controls
M
3
.42
.40
.38
.36
.34
.32
.30
.45
20
.40
15
.35
M3
{1
10
.30
.25
}
5
So
ck
e
ye
(S
SA
M
3)
M3=f(Sockeye & M3{2}) & mean controls
M
3
.50
.48
.46
.44
.42
.40
.38
.36
.34
.32
.30
.45
20
.40
15
.35
M3
{2
10
.30
}
.25
5
So
ck
e
ye
(S
SA
M
3)
Fig. 10. Third-year marine scale growth (M3t) of age 2.2 sockeye salmon that returned to Karluk Lake, Alaska in relation to the index
of abundance for maturing sockeye salmon from central and southeast Alaska (SSAM3) on the at varied levels of SSAM3 and
lag year 1 autocorrelation in M3. Models are given in Table 2.
40
Table 1. Data used in study.
Variable
Description
Mean
SD
Max
Min
FW{0}
M1
SSAM1
L1{0}
M2
SSAM2
L2{0}
M3
SSAM3
SHIFT
Total Smolt Length; aligned with M1{0}
1st Year Marine Juvenile growth
Southern Alaska Sockeye; aligned with M1
FW{1} + M1{1}; aligned with M2{0}
2nd Year Marine Immature Growth
Southern Alaska Sockeye; aligned with M2
FW{2} + M1{2} + M2{1}; aligned with M3{0}
3rd Year Marine Maturing growth
Southern Alaska Sockeye; aligned with M3
0 from 1925-76; 1 from 1977-98
0.6533
1.0600
8.3266
1.7139
0.7771
8.3014
2.4891
0.3346
8.1622
0.2973
0.5370E-01
0.6086E-01
4.7978
0.7568E-01
0.6747E-01
4.7784
0.1079
0.5295E-01
4.66734
0.460188
0.8085
1.1958
22.700
1.9345
0.9458
22.700
2.7505
0.4550
22.700
1.0000
0.5646
0.9165
2.2000
1.5529
0.6279
2.2000
2.2281
0.2450
2.2000
0.0000
For further discussion of data see text.
41
Table 2. Ordinary least squared regression model coefficients and results used to describe the mean annual marine scale growth of age
2.2 sockeye that returned to Karluk Lake, Alaska as a function of the 1976-77 ocean regime shift, autocorrelation in growth, mean
cumulative cohort scale growth, and sockeye salmon abundance indices from 1925 to 1998.
Variable
M1 Model
SHIFT
M1
M1
FW
SSSAM1
CONSTANT
Lag
Coefficient
Standard
Error
t-value
0
1
2
0
0
0
0.0793
0.1055
0.2860
-0.0265
-0.0050
0.6812
0.0278
0.1187
0.1167
0.1088
0.0022
0.1826
2.852
0.889
2.449
-0.243
-2.218
3.730
72
# Observations
M2 Model
SHIFT
M2
M2
L1
SSAM2
CONSTANT
0
1
2
0
0
0
0.0526
-0.0951
0.0317
0.0485
0.0048
0.6887
0.0254
0.1209
0.1218
0.0876
0.2260
0.1950
2.0753
-0.7867
0.2610
0.5531
2.1400
3.5310
72
M3 Model
SHIFT
M3
M3
L2
SSAM3
CONSTANT
0
1
2
0
0
0
0.0488
0.3989
0.1334
-0.0364
-0.0059
0.2819
0.0181
0.1194
0.1147
0.0499
0.0017
0.1255
2.6985
3.3410
1.1627
-0.7299
-3.5162
2.2469
72
Adjusted-R2 SSR
0.371
0.376
0.611
0.157
0.188
0.008
Note:
Shift is a categorical variable, where 0 is years from 1925 to 1976, and 1 is years from 1977 to 1998. Response variables
include mean scale growth in the first-marine year, M1, second-marine year M2, and third-marine year M3. SASM1, SASM2 and
SASM3 which are Southern Alaska Sockeye aligned with the appropriate series. FW = Total body length in fresh water. L1{0} =
FW{1) +M1{1) where { } refers to the lag. L2{0} = FW{1} + M1{1}.
42
Table 3. Multivariate adaptive regression spline model coefficients and results used to describe the mean annual marine scale growth
of age 2.2 sockeye that returned to Karluk Lake, Alaska as a function of the 1976-77 ocean regime shift, autocorrelation in growth,
mean cumulative cohort scale growth, and sockeye salmon abundance indices from 1925 to 1998.
M1 =
Coefficients
Thresholds
1.1002
- 0.9318 *
+ 0.2403 *
*
- 9.1506 *
*
+21.9580 *
*
- 1.7161 *
- 1.2290 *
*
1.0775
1.0775
6.0000
1.0775
FW{0}
1.0150
1.0775
1.0150
0.6210
4.9000
M2 =
+
+
+
M3 =
0.7301
.01663
.04354
.01005
0.6231
7.5709
*
*
*
*
*
*
max(
max(
max(
max(
max(
max(
max(
max(
max(
max(
max( 6.0000
max(SHIFT{0}
max(SSAM2{0}
max(
M2{1}
max( 0.8202
max( 1.6626
0.2862
+ 1.4818 * max(
+ .01352 * max(
-64.5434 * max(
* max(
+ 1.9227 * max(
-58.7729 * max(
* max(
+29.8197 * max(
* max(
M3{1}
6.8000
M3{1}
M3{2}
M3{2}
M3{1}
0.3658
M3{1}
0.3658
M1{2}, 0.0)
M1{2}, 0.0)
- SSAM1{0}, 0.0)
M1{2}, 0.0)
0.6586, 0.0)
M1{1}, 0.0)
M1{2}, 0.0)
M1{1}, 0.0)
FW{0}, 0.0)
- SSAM1{0}, 0.0)
Standard
Error
t-value
Non-Zero
#
Importance Vector
%
Rank
0.0070
0.1504
0.1093
157.00
-6.19
2.19
72
41
16
100.
56.
22.
100.0
35.5
1
2
3
2.8562
-3.20
16
22.
51.7
4
6.0235
3.64
13
18.
58.8
5
0.5057
0.3901
-3.39
-3.15
17
9
23.
12.
54.8
50.9
6
7
59.5
50.3
100.0
72.5
71.0
1
2
3
4
5
6
#
-
SSAM2{0},
0.0000 ,
4.6000 ,
0.8022 ,
M2{1},
L1{0},
0.0)
0.0)
0.0)
0.0)
0.0)
0.0)
0.0109
0.6530
0.2019
0.2346
0.2007
2.4894
67.20
2.54
2.15
4.28
-3.10
-3.04
72
29
22
54
24
14
100.
40.
30.
75.
33.
19.
-
0.3461 ,
SSAM3{0},
0.34606 ,
0.3819 ,
0.3658 ,
0.3269 ,
M3{2}
,
0.2951 ,
M3{2}
,
0.7198
0.0) 0.2404
0.0) 0.3067
0.0) 14.3292
0.0)
0.0) 0.4603
0.0) 14.3066
0.0)
0.0) 8.3421
0.0)
39.70
6.16
4.40
-4.50
72
30
35
16
100.
41.
48.
22.
100.0
71.5
73.1
1
2
3
4
4.17
-4.10
24
14
33.
19.
67.8
66.6
5
6
3.57
30
41.
58.0
7
43
Table 4. Multivariate adaptive regression spline model results for models in Table 3.
GCV with only the constant
Total sum of squares
Final GVC
Variance of Y Variable
R2 = (1 - (var(res)/var(y)))
Residual Sum of Squares
Residual Variance
Residual Standard Error
Sum Absolute Residuals
Max Absolute Residual
M1 Model
M2 Model
M3 Model
3.838E-03
0.269
2.358E-03
3.785E-03
0.576
0.114
1.606E-03
4.007E-02
2.187
9.564E-02
4.6408E-03
0.325
2.795E-03
4.576E-03
0.556
0.144
2.034E-03
4.510E-02
2.255
0.123
2.773E-03
0.194
1.713E-03
2.734E-03
0.611
7.548-02
1.063E-03
3.261E-02
1.879
7.631-02
44