Plotting net reproduction (reproductive potential of the adults obtained) against the density of stock which produced them, for a number of fish and invertebrate populations, gives a domed curve whose apex lies above the line representing replacement reproduction. At stock densities beyond the apex, reproduction declines either gradually or abruptly. This decline gives a population a tendency to oscillate in numbers; however, the oscillations are damped, not permanent, unless reproduction decreases quite rapidly and there is not too much mixing of generations in the breeding population. Removal of part of the adult stock reduces the amplitude of oscillations that may be in progress and, up to a point, increases reproduction.

A number of regression situations in fish and fishery biology are examined, in which both of the variates are subject to error of measurement, or inherent variability, or both. For most of these situations a functional regression line is more suitable than the ordinary predictive regressions that have usually been employed, so that many estimates now in use are in some degree biased. Examples are (1) estimation of the exponent in the weight:length relationship, where almost all published values are somewhat too small; and (2) estimating the regression of logarithm of metabolic rate on log body weight of fish, where the best average figure proves to be 0.85 rather than 0.80. In the very common situation where the distribution of the variates is non-normal and open-ended, a functional regression is the most appropriate one even for purposes of prediction. Two ways of estimating the functional regression are (1) from arithmetic means of segments of the distribution, when computed symmetrically; and (2) from the geometric mean of one predictive regression and the reciprocal of the other. The GM regression gives a more accurate estimate when it is applicable; it is appropriate in all situations where the variability is mainly inherent in the material (little of it due to errors of measurement), or where the measurement variances are approximately proportional to the total variance of each variate; and it is the best estimate available for short series with moderate or large variability even when neither of these conditions applies. When error in X results solely from the measuring process the predictive regression of Y on X is also the functional regression if observations of X are not taken at random but rather have pre-established values, as is usual in experimental work. The uses of the various regressions are summarized in Table 8.

No abstract

Of the five species of Pacific salmon in British Columbia, chinook salmon (Oncorhynchus tshawytscha) and coho salmon (O. kisutch) are harvested during their growing seasons, while pink salmon (O. gorbuscha), chum salmon (O. keta), and sockeye salmon (O. nerka) are taken only after practically all of their growth is completed. The size of the fish caught, of all species, has decreased, but to different degrees and over different time periods, and for the most part this results from a size decrease in the population. These decreases do not exhibit significant correlations with available ocean temperature or salinity series, except that for sockeye lower temperature is associated with larger size. Chinook salmon have decreased greatly in both size and age since the 1920s, most importantly because nonmaturing individuals are taken by the troll fishery; hence individuals that mature at older ages are harvested more intensively, which decreases the percentage of older ones available both directly and cumulatively because the spawners include an excess of younger fish. Other species have decreased in size principally since 1950, when the change to payment by the pound rather than by the piece made it profitable for the gill-netters to harvest more of the larger fish. Cohos and pinks exhibit the greatest decreases, these being almost entirely a cumulative genetic effect caused by commercial trolls and gill nets removing fish of larger than average size. However, cohos reared in the Strait of Georgia have not decreased in size, possibly because sport trolling has different selection characteristics or because of the increase in the hatchery-reared component of the catch. The mean size of chum and sockeye salmon caught has changed much less than that of the other species. Chums have the additional peculiarity that gill nets tend to take smaller individuals than seines do and that their mean age has increased, at least between 1957 and 1972. That overall mean size has nevertheless decreased somewhat may be related to the fact that younger-maturing individuals grow much faster than older-maturing ones; hence excess removal of the smaller younger fish tends to depress growth rate. Among sockeye the decrease in size has apparently been retarded by an increase in growth rate related to the gradual cooling of the ocean since 1940. However, selection has had two important effects: an increase in the percentage of age-3 "jacks" in some stocks, these being little harvested, and an increase in the difference in size between sockeye having three and four ocean growing seasons, respectively.Key words: Pacific salmon, age changes, size changes, fishery, environment, selection, heritability

A bivariate array of naturally variable observations can take many different forms, depending on the relative lengths of the measurement units used. Each of these has a different central trend or major axis. In a standard presentation the major axis has a slope of ± 1 obtained when 1 standard deviation (s) of each variate, Y and X, occupies the same distance on its coordinate axis. With any other presentation the position of the standard trend is indicated by a line whose slope is the ratio of the standard deviations; it is called the standard (or reduced) major axis, or geometric mean regression line (GMR). The GMR is symmetrical, invariant with change of scale, and "robust." Besides indicating the central trend, it is a suitable line for estimating Y from X, or X from Y, in two common situations where ordinary regressions fail: (i) when the sampling procedure was not random with respect to the entire population (but was random with respect to its standard trend); (ii) when the population sampled departs seriously from a bivariate normal configuration. In the latter case an alternative "Schnute" line is appropriate if components of the population may have different sY/sX ratios.