Page 1

Upper thermal limits on the oceanic.

distribution of Pacific salmon

(Oncorhynchus spp.) in the spring

D m W m Welch, A m E m Chigirinsky, and YE lshida

Abstract: Pacific salmon are normally thought to be distributed throughout the Subarctic Pacific,

an area where they form the dominant fish fauna. We use a series of generalized additive models

to show that salmon exhibit a sharp step-function response to temperature in the oceanic eastern

north Pacific in spring. The critical temperature defining the southern boundary varied by species:

10.4"C for pink and chum salmon, 9.4"C for coho salmon, and 8.9"C for sockeye salmon. These

thermal limits occur well to the north of the southern boundary of the Transition Zone, at widely

separated geographic positions within the Subarctic Domain, and at temperatures much lower than

the lethal upper limit for each species. The sharp decline in abundance with temperature, and the

remarkably low temperatures at which the response occurs, suggests that thermal barriers form an

effective limit to the offshore distribution of salmon in spring, and can limit the distribution of

Pacific salmon to a relatively small area of the Subarctic Pacific. The strength of this response is

presumably the direct result of strong evolutionary selection. Future temperature changes in the

North Pacific could therefore have a direct impact on the production dynamics of Pacific salmon.

RCsumC : On pense generalement que les saumons pacifiques sont repartis dans 19ensemble du

Pacifique subarctique, zone oh ils constituent les espbces dominantes de l'ichtyofaune. Nous nous

servons d'une skrie de modbles additifs gCnCralisCs pour montrer que les saumons prksentent une

forte reponse il 1'Cchelon de temperature, au printemps, dans la zone ockanique du Pacifique nord-

est. La temperature critique dkfinissant la limite sud varie selon les espbces : 10,4"C pour le

saumon rose et le Eta, 9,4"C pour le coho et $,9"C pour le saumon rouge. Ces barrikes thermiques

se situent bien au nord de la limite sud de la zone de transition, en des points gkographiques

nettement sCpar6s au sein du domaine subarctique, et il des temperatures beaucoup plus basses que

la limite lktale supkrieure de chaque espbce. La baisse marquee de l'abondance en fonction de la

temperature, et les temperatures remarquablement basses auxquelles la reaction se produit, semblent

indiquer que les barri6res thermiques forment une limite effective i i la repartition hauturi6re des

saumons au printemps, et peuvent limiter la distribution des saumons pacifiques il une zone

relativement petite du Pacifique subarctique. La force de cette reaction est probablement un

resultat direct d'une forte selection au fil de l'tvolution. D'Cventuels changements thermiques

dans le Pacifique nord pourraient donc avoir un impact direct sur la dynamique de la production

des saumons pacifiques.

[aiaduit par la Kt5dactionI

Entraduction

environment of the open Pacific Ocean, a behavioural

choice that is under evolutionary control. During this time

most somatic growth is completed (Ricker 1962, 1976),

and a significant fraction of total cohort mortality also

occurs (Parker 1962; Ricker 1942, 1976). Yet, despite the

length of this period in the life cycle, relatively little is

known about the biological dynamics underlying the pelagic

period of the life history.

Despite some 40 years of research, the reasons why Pacific

salmon undertake their vast ocean migrations are still only

poorly understood. The reasons are presumably closely

related to their evolutionary biology and production dynm-

ics. Some two-thirds or more of the life history of Pacific

salmon (Oncsrhynchus) is normally spent in the pelagic

I

I

1 ' Deceased.

Received August 25, 1993. Accepted September 23, 1994.

% 12063

D.W. Welch. Department of Fisheries and Oceans, Biological Sciences Branch, Pacific Biological Station, Nanaimo,

BC V9R 5K6, Canada.

A.I. ~hi~irinsk~.~acific Research Institute of Fisheries and Oceanography, 4 Shevchenko Alley, Vladivostok 690600, Russia.

Y. Ishida. National Research Institute of Far Seas Fisheries, 5-7-1 Chido, Shimizu-Shi, Shizuoka-Ken 424, Japan.

Can. 9. Fish. Aquat. Sei. 52: 489-503 (1995). Printed in Canada / BmprirnC au Canada

Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/05/13

For personal use only.

Page 2

Can. J. Fish. Aquat. Sci. Vsl. 52, 1995

Salmon are widely distributed on the high seas. One

relatively tractable aspect of the study sf the high seas

biology of salmon involves the relationship between the

distribution of salmon and physical and biological factors.

A better understanding of the factors that restrict the pelagic

distribution of Pacific salmon could provide insight into

the interac tion of Pacific salmon with their environment,

particularly with regard to how current predictions of cli-

mate change could influence the salmon resources of the

North Pacific. Because the behaviour of salmon on the

high seas is the result of evolutionary selection, oceano-

graphic factors strongly influencing the distribution of

Pacific salmon should also influence their production

dynamics, because the same selective forces that lead to

dominance of genotypes with high fitness also lead to

maximization of population growth rates (Caswell 1989).

Most published work on the high seas biology of salmon

dates from the late 1950s and early 196Bs, a period when

the extensive ocean migrations of Pacific salmon were

first documented. These studies established the widespread

occurrence of salmon in the surface layer of the open north

Pacific ocean, paticularly the Subarctic Domain. The Sub-

arctic Domain (Ware and McFarlane 1989) is bounded to

the south by the Transition Domain, whose southern bound-

ary is defined in turn by the presence of a vertical 34%0

isohaline structure (Bodimead et al. 19631, with cooler

less saline water lying to the north. The southern limit to

the distribution of Pacific salmon has been variously iden-

tified with the vertical 34%0 isohaline structure (Favorite

et al. 1976; Quinn 1990; Nagasawa et al. 1994) or the sub-

arctic front between the subarctic and transition domains

(Ignell and Murphy 1993).

The fish fauna of the Subarctic Domain is dominated

by Pacific salmon, despite their need to return to freshwater

to reproduce (Ware and McFarlane 1989). Pacific salmon

are therefore the dominant fauna of a cool lens of relatively

fresh ocean water that forms the mixed layer above the

more saline (>34%0) deep waters of the North Pacific.

However, even within the Subarctic Domain salmon are

differentially distributed, by species (French et al. 1976;

Neave et al, 1976; Major et al. 1978; Takagi et al. 1981;

Birman 1985), temperature (Favorite 1969~; Favorite et al.

1976; B h a n 1985; Blackborn 1987; Quinn 1990; Erokhin

199 I), and possibly salinity (Favorite 1969b).

A descriptive understanding of the distribution and gen-

eral migratory routes of salmon on the high seas is now

generally agreed upon. Manzer et al. (1964) reported that

there was an apparent difference in temperature preferences

between species, with different thermal ranges evident,

and preferences seeming to increase over the spring and

summer. Manzer et al. suggested that temperature prefer-

ences dropped again in September although ambient tem-

peratures remained high. Birman (1985), Erokhin (19911,

and lshida (1962) suggested that the offshore migration

of pink salmon (8.

gorbuscha) was a seasonal migration

"following the movement of waters with temperatures of

4-1 1°C."

However, mechanistic questions concerning why salmon

are distributed as they are, and the direct experimental

measurement at sea of the factors influencing the distrib-

ution, have rarely been addressed. General statements about

the oceanic distribution of Pacific salmon are useful, but

they give little insight as to whether and why specific

environmental variables are important to salmon, or how

significant they really are.

Whatever the proximate response to physical or bio-

logical factors, the mechanisms underlying my distributional

patterns are likely to have been strongly shaped by evo-

lutionary selection. Establishing why Pacific salmon exhibit

specific distributional patterns may help to predict their

population response to climatic change, as well as under-

standing the evolutionary factors that cause Pacific salmon

to undertake their remarkable oceanic migrations.

We re-examine the relationship between the physical

distribution of salmon and a range of oceanographic factors

as a first step towards developing a better understanding of

the effects of climate change on Pacific salmon and the

potential impact of the increasing abundance of Pacific

salmon on their own production (Peapcy 192). In particular9

we examine the question of whether or not salmon are

tmly distributed throughout the subarctic Pacific. We show

that there is evidence of a sharp barrier limiting the dis-

tribution of salmon in the North Pacific Ocean in the

spring. However, although the results of high seas surveys

clearly show evidence of a s h q barrier, satisfactory maly-

sis of the data depends on three factors: (d) establishing

a satisfactory means of statistically discriminating between

a number of possible factors that can simultaneously influ-

ence distribution in complicated nonlinear ways; (ii) devel-

oping a reasonable model of the uncertainty or enor inherent

in the individual fishing observations made at sea; and

(iii) providing a parsimonious biological model of the

results. We discuss each of these issues in turn.

Equipment, methods, and data sousses

USSR-Canadian Surveys

A joint USSR-Canadian research cruise aboard the USSR

research vessel TINRO examined the southern limits to the

offshore distribution of Pacific salmon during late spring,

1990. The results reported here are based on data from

two cruises, the first occurring from 29 March to 2 B April,

and involving 28 trawl stations taken along a line between

55ON 145"W and 47"N 13 1OW (Morris et al. 1992). The

second cruise, involving 42 trawl stations, occurred between

27 April and 14 May within a rectangle bounded by the

co-ordinates 52"N 129"W and 39"N 156"W (Fig, 1).

Individual north-south transects near the observed south-

ern limit to the salmon distribution were spaced 3" longitude

apart and usually involved three stations sampled during

daylight hours with a rope trawl. Movement to the next

transect was completed overnight. The original cruise plan

was intended to extend south of the northern boundary of

the Japanese squid driftnet fishing zone in June, at 40'N.

However, because of the rapid decline in salmon abundance

evident during the first southern transect at BSOOW lati-

tude, the southern extent of each planned noah-south tran-

sect was reduced in order to increase the east-west coverage.

All sampling used a rope trawl, with mouth dimensions

40 m (height) X 60 m (width), and length of 108 rn. The

wet was towed at 5 knots, generally for two contiguous

30-min periods at depths of 28 and 40 m (depth to top.o%

Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/05/13

For personal use only.

Page 3

Welch et al.

Fig. 1. Cruise track of the RbV Tinro in 1990. a, location sf trawl fishing operations between 29 March and 21 April;

R, locations between 27 April and 14 May. Gillnet (a) and longline (A) samples taken spportunisbieally by the WE. RWicker

in 1987-1998 are also shown.

f

head rope), for a total sampling time of 1 h. However, in

cases where echo sounding indicated that fish were located

at a particular depth, trawling was restricted to these strata.

This protocol followed standard USSR survey practice.

Results presented later are in units of numbers caught per

trawl hour.

Vertical profiles to 300 m were made using a Neil Brown

CTD probe to record temperature, salinity, O,, and chloro-

phyll levels. At all stations the mixed layer depth exceeded

1W.l m, and the vertical 34760 isohaline denoting the limit of

the Transition Domain lay well beyond the southern-most

extent of the survey area (see below).

We used sea surface temperature and salinity as the

physical variables to relate to the salmon distribution at

each station. Pacific salmon are largely confined to the

upper 50 m im the open meam (Mazer 1964) and dl sampling

occurred in regions where the mixed layer depth exceeded

100 m, thus justifying the use of single measurements of

sea temperature and salinity. Oxygen and chlorophyll mea-

surements showed significant variability with depth and

between stations, but a preliminary analysis showed no

clear relationship with salmon density, so we did not pur-

sue the analysis sf these variables further.

Canadian surveys

During 1987, 1988, and 1998 the Canadian research vessel

RW/ WE. Ricker collected salmon in southern regions of the

NE Pacific using gillnets and surface longlines. Details of

these cruises are described elsewhere (EeBrasseur et al.

1987, 1988; McKinnell et a1. 1990). Additional data on

the distribution of salmon in the NE Pacific conducted

between 1961 and 1967 by Canadian and American vessels

using surface longline gear is also compiled in Turner and

Aro (1968). None of these studies were designed to specif-

ically examine the physical factors limiting the distribution

of salmonids on the high seas. However, we use these data

Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/05/13

For personal use only.

Page 4

Can. J. Fish. Aquat. Sci. VQI. 52, 1995

to examine the replicability of the results from the W

Tinro cruise.

Statistical methods

Error model

The sampling distribution for Pacific salmon caught on

the high seas is heavy-tailed because of the patchy nature

of the distribution of salmon at sea, 'This patchiness directly

effects the ability to reliably measure salmon abundance.

Hgnell and Murphy (1993) found that patchiness (higher

variance in estimates of salmon abundance) increased to

the south. They concluded that "patchiness directly affects

the error structure of any statistical model of salmon abun-

dance near the subarctic frontal zone", and that statistical

methods for analyzing the change in salmon abundance

must be able to handle this variability-particularly

increase in relative variability that occurs as salmon abun-

dance decreased.

Welch and Ishida (1993) showed that the error structure

for high seas salmon catches was closely described by a

negative binomial distribution with parameters p, the true

mean abundance or density, and k, the number of degrees

of freedom on which the sample is based. This distribution

has long tails and at Bow densities or limited sampling

effort is highly asymmetric, probably because of the hetero-

geneous distribution of salmon into small schools of varying

sizes. At large sampling efforts the distribution approaches

the Poisson.

Welch and Ishida (1993) found that the spatial coherence

of Pacific salmon on the high seas disappeared at separa-

tions of ca. 15m. Samples taken at greater spatial separations

are therefore statistically independent, and contribute addi-

tional degrees of freedom (do on which observations of

salmon abundance or density can be based. This estimate

provides a basis for estimating the uncertainty in the trawl

survey estimates.

Each one hour tow using the Russian rope trawl results

in a single observed catch that is collected over a transect

5 nautical miles (9.26 km) long. The trawl gear therefore

provides a single catch equivalent to a set of k = 9260/15 =

614 statistically independent samples taken under similar

conditions, which provides a sampling distribution very

close to the Poisson. For sampling efforts involving large

degrees of freedom the negative binomial distribution is

very close to the Poisson, but the slightly heavier tails.

As a result, the sampling distribution has higher relative

variance at the low densities that occur near the limits to the

salmon distribution, and therefore captures a number of

the important qualitative elements of the sampling data

discussed by Ignell and Murphy (1993). We use this esti-

mate of k = 617 df in the statistical analysis described later.

the

GAM analysis

Given an acceptable error model, the question remains of

assessing how multiple factors contribute to determining the

distribution of Pacific salmon. This issue is particularly

important because observations collected at sea cannot be

collected according to a preplanned experimental design

and are invariably intercomelated. In addition, some or all

of these influences may be nonlinear, and it is important

that the nature of this relationship not be distorted by a

poor initial choice of a functional model to relate to the

observations.

We therefore conducted a preliminary analysis of the

relationship between the distribution of Pacific salmon

and physical factors using a series of generalized additive

models (GAM) (Hastie and Tibshirani 1990; Hastie 1992;

Swamman et al. 1992, StatSci 1993). We define the dis-

tribution of salmon in terns of their abundance, expressed

as the number of individuals caught at the ith station per

trawl-hour, I%,. In general, a GAM model is defined as

where $,(Ti) and js(Si) represent arbitrary smooth univari-

ate functions of temperature and salinity, a represents the

mean response (i.e., average abundance), and E, represents

the error distribution for the ith observation. In GAMs,

locally weighted fitting is used to calculate a nonparametric

estimate of the functional relationship between salmon

abundance and potentially significant explanatory vari-

ables. The advantage of this approach is that it does not

require the prior specification of a series of satisfactory

mathematical relationships and instead allows the data to

more clearly indicate the important variables and their

functional responses.

As negative binomial distributions are not available in

current GAM software, we used the Poisson distribution

a s our error model instead; this assumption is slightly con-

servative, and results in underestimating the true width of

confidence limits on potentially important factors (i.e.,

overestimating the true number of significant factors;

McCullagh and Nelder 1989). However, we use the gen-

eralized additive model framework chiefly as a means of

identifying candidate factors influencing the salmon dis-

tribution and for determining the nature of their influence.

The parametric analysis discussed next uses the negative

binomial distribution to more accurately calculate the

uncertainty in the parameter estimates.

For ease of interpretation, we expressed our abundance

observations as log,,(ni + I), and used b-splines to form

our nonparametric smoothing functions to describe the

local influence of salinity and temperature on salmon abun-

dance (Hastie and Tibshirani 1990; Mastie 1992). This

model was fit to the log,,(n, + 8 ) observations using the

statistical modelling language S-Plus (StatSci 1993).

An edge model for the salmon distribution

The GAM analysis presented later indicates that salmon

density is related to ambient temperature but not to other

measured factors. This relationship appears as a threshold,

with no discernable influence below a specific value and a

strong negative influence above. To better define the influ-

ence of temperature on the southern limit to the distribution

of salmon, and to provide a biological interpretation of

our observations, we now describe a parametric mathe-

matical model. We concentrate on defining the southern

bomdaq, where the effect of temperature is most pronounced.

Regression analysis when Poisson or negative binomially

distributed errors occur has been discussed by Lawless

(1984). We limit our presentation to the derivation of the

likelihood equations necessary for our parameter estimation.

Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/05/13

For personal use only.

Page 5

Welch et %I.

A simple functional form relating the observed salmon

abundance at the i-th station to temperature, n(;F,), is

n(Ti) = p ( l - @(T~IT, ud)

where @(T~JT, a,) is the value of the cumulative normal

probability distribution with parameters T and cr, at tem-

perature q, and p is the mean salmon density in the interior

of the geographic distribution.

Equation 2 posits that there is some mean threshold

temperature level T which salmon actively avoid exceeding,

and some normally distributed variance in the response of

individual salmon to this temperature threshold, a , . The

average population response is then obtained by integrat-

ing over the behaviour of all individuals, which results in

the cumulative distribution (Fig. 2). The mean temperature

therefore defines the threshold value at which the location

of the edge of the salmon distribution is fixed, while the

variance will influence the rate at which abundance declines

near the edge of the distribution. For example, if o, = Q,

and all individuals respond exactly alike, then the edge

will be a step function located at T, with abundance drop-

ping to zero instantaneously. In general, 95% of the decline

in abundance will occur over an interval of 920, centered

on this mean, or roughly a two order-of-magnitude decline

in abundance.

The third parameter, p, describes the mean abundance in

interior regions, away from the edge of the salmon distri-

bution, This value is affected by both gear efficiency and

year-to-year fluctuations in abundance. As we are pri-

marily interested in describing the limits to the salmon

distribution, md the GAM analysis indicates that the effect

of temperature is most reasonably modelled as a thresh-

old, we treat the mean abundance in the interior as a nui-

sance parameter, and concentrate on the estimation of the

parameters T and a , .

Equation 2 is a biologically based parametric model of

the salmon distribution. However, it still lacks a firm sta-

tistical basis for estimation. As discussed above, the uncer-

tainty in the salmon catches can be described by the neg-

ative bin~mial distribution. We therefore calculated final

parameter estimates and associated confidence intervals

for the effect of temperature initially identified in the GAM

analysis using maximum likelihood estimation.

Assuming that the negative binomial distribution holds,

the exact likelihood equation is derived as follows. The

probability of observing n, fish at the ith station when the true

abundance is pi and the sampling effort is k, = 617 df is

I21

where the I? function is the analytic continuation of the

factorial function for non-integer real numbers and, for

integer x, r(x + 1) = x!.

The likelihood of observing a set of ni catches at the h =

1, ..., rn stations when the true abundances are pi is

theref~re

Fig. 2. A behavioural model of the edge of the salmon

distribution. Individual salmon actively avoid temperatures

greater than some threshold; individual variation in the

temperature at which this response is expressed results in

a range of temperatures over which abundance changes.

As temperature increases, a greater fraction of the total

population will avoid any given temperature level, leading

to a decrease in population density. The rapidity sf the

decline depends on the degree of individual variation.

Behavioural Response to Temperature

Temperature, Ti

The likelihood is therefore dependent on the observations

n,, the sampling efforts or df k,, and the temperature con-

trolling the true abundance at the ith location, pi(T'). As

noted earlier, the negative binomial distribution reduces

to the Poisson distribution in the limit as the df ki increase

infinitely. Thus even gross overestimation of the degrees of

freedom is equivalent to assuming that the Poisson distri-

bution applies.

Maximum likelihood estimates of the parameters (p, T,

B,) can be obtained by minimizing the negative log-

likelihood of the data with respect to the parameters. Sub-

stituting the functional form for the parametric temperature-

density relationship (2) into the theoretical likelihood (4)

and taking the negative of the logarithm,

Pn

x(ni + k,) ln(n(q) + kj) - n, ln(n(q))

i=B

where we neglect the contribution of an additive constant

and n, and n(Ti) are the observed and predicted salmon

abundances. We used the simplex algorithm (Press et al.

1986) as implemented by Mittertreiner md Schnute (1985),

to estimate the maximum likelihood values of the param-

eters T9 a,. using [5] and their associated uncertainty.

A critical upper or lower level for some physical factor

can be defined as that value at which the decline in density

is most rapid. These values correspond to the mean

responses T within our edge model. We calculate 95% con-

fidence intervals on individual estimates of

finding the limits such that twice the difference in log-

likeliho~ds from the maximum likelihood estimates (allow-

ing all other parameters to vargr freely) is less than or equal

to a X : = 3.81 distribution. This calculation is asymptotically

and Q,. by

Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/05/13

For personal use only.