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The daily natural mortality of marine pelagic organisms ranging in size from bacteria to whales scales with weight to the power -0.301. This exponent is significantly lower than those for fish, -0.397, and for pelagic crustaceans, -0.537. The difference may reflect the action of secondary ecological factors within taxa. Spatial patchiness is one secondary factor that explains a significant amount of the variation in natural mortahty of pelagic fish eggs and earlystage larvae. The relationship remains significant if the weight exponent used to standardize mortality for size is changed from an ecosystem value of -0.25 to a 'fish' value of -0.397. To explain this observation, it is proposed that fish eggs and early-stage larvae are more vulnerable to predators when the embryos are aggregated in patches than when they are dispersed because these young fish lack the close-range antipredator behaviour that accompanies schooling in older fish. The effect on survival of the presence or absence of this component of schooling behaviour is not included in an earlier model of the relationship between predation and schooling. Introduction. In a recent paper McGurk (1986b) proposed that natural mortality, M, of pelagic fish eggs and early-stage larvae was controlled primarily by their body size, W, and secondarily by their spatial patchness, p, as measured by Lloyd's (1967) index. It was suggested that fish eggs and early-stage larvae are more vulnerable to predators than would be expected on the basis of their body size because they have not developed the motor skills and behaviour necessary to evade predators. Thus, patches of fish eggs and earlystage larvae produced by mass spawning and hatching may offer exceptional feeding opportunities to any predator that encounters them. The young fish should continue to suffer from heavy predation until the patches are dispersed by turbulent diffusion and until the larvae develop effective anti-predator behaviour. Gulland (1987) criticizes the mortality-patchiness hypothesis on 2 grounds. First, he argues that the original observation from whlch the hypothesis was developed, the deviation between the observed M of fish eggs and early-stage larvae and the M predicted from Peterson & Wroblewski's (1984) allometric model of M for fish, was not due to the secondary action of O Inter-Research/Printed in F. R. Germany spatial patchiness, but was due instead to a poor fit of the model to the data. GuUand claims that the weight exponent of M for fish is about -0.5, rather than the value of -0.25 used by Peterson & Wroblewski and McGurk. Second, Gulland cites Brock & Riffenburgh's (1960) theoretical model in support of the argument that patchiness reduces predation rather than increases it because a predator may encounter fewer prey if thdse are patchily distributed than if the prey are randomly distributed. I dispute Gulland's first point on the grounds that the correlation between W-independent M and patchiness for fish eggs and early-stage larvae remains valid even when a weight exponent with an absolute value greater than 0.25 is used to remove the effect of size. Furthermore, M of fish eggs and early-stage larvae is even more highly correlated with patchiness when size is not factored out. I dispute Gulland's second point because Brock & Riffenburgh's model is an oversimplified description of the relation between patchiness a'nd mortality in fish of all life history stages. The mohel does nbt take into account the effect on survival of close-range predator evasion behaviour by schooling juvenile i n d adult fishes, and it does not take into account the effect on survival of the absence of this behaviour in fish eggs and early-stage larvae. The evasion behaviour associated with schooling may be as important a survival tactic as aggregation itself. Moreover, the model is entirely theoretical and has ,never.been tested with field data. : Sources of data. Peterson & Wroblewski (1984) assigned a value of -0.25 to the weight exponent of M &ing biomass spectrum theory and data on the I bioenergetics of fish. They did not calculate their exponent from the M-W data itself. In order to compare empirical weight exponents for the pelagic ecosystem, fishes, and crustaceans with Peterson & Wroblewski's estimate, linear regressions of 1nM on In W were calculated using the data in McGurk's (1986b) Table 1 and Appendix. The invertebrates Illex illecebrosus and 202 Mar. Ecol. Prog. Ser. 39: 201-206, 1987 Pleurobrachia bachei were excluded in order to produce an all-crustacean sub-group. Values of M for pelagic bacteria of the Belgian coastal zone reported by S e ~ a i s et al. (1985) were included in order to expand the Mf scale to cover a larger range of the pelagic community. A single estimate of the average W of a bacterium was calculated as 1.2 X 10-l3 g by assuming a cell volume of 0.6 ym3 (Fenchel 1986), a density of 1 g cmp3, and a dry weight/wet weight ratio of 1 : 5. W of the school shark Galeorhinus australis was corrected to 1.1 X 104 g from the value of 1 .l X 105 g that was shown in the Appendix and M of Paracalanidae spp. (pelagic crustaceans) was corrected to 5.2 X d-' from 5.2 X 10-' d-l. Both predictive and functional regressions (Ricker 1973, Jensen 1986) were calculated in order to show thqt the weight exponent of M may depend strongly on the type of regression used to calculate it. Functional regressions are the best estimate of the central tendency of a relation when both variables are measured w i n the same amount of error, but predictive regressions are best when the dependent variable has been measured with much more error than the independent vayiable. Functional regressions always have higher slopes than predictive regressions. Therefore, as a conservative assumption, functional regressions were used to examine the effect of using an exponent other than -0.25 to factor out size from M. Results. The slope (k 1 SE) of the functional regression for the entire data set, bacteria to whales, was -0.301 f 0.011 d-' (Table l ) , which was lqwer than the functional slope (+ 1 SE) for the data set excluding the bacteria, -0.343 + 0.011 d-l. The slope of the predictive regression for the entire data set was -0.26 k 0.011 d-l. This result suggests that the estimate of the ecosystem slope depends strongly on the distribution of data along the Wscale, and on the distribution of error between the 2 variables. In this case, the estimates of the ecosystem slope tend to approach the values peculiar to large, easily sampled organisms such as larval, juvenile and adult fish because more than 90 % of the data fell within the loP5 to lo7 g Wrange. This argument depends partly on the validity of Servais et al.'s (1985) estimates of bacterial M. These were verified by comparing them with field estimates of growth rates of aquatic bacteria, since stable bacterial biomass can only be maintained if growth and mortality balance each other. Field estimates of daily growth rate of aquatic bacteria reported by Moriarty (1986) were plotted against W in Fig. 1. The ranges of daily bacterial growth rate bracket Servais et al.'s estimates of M, thereby supporting them. The functional slopes (f l SE) for fish, -0.397 f 0.010 d-l, and for crustaceans. -0.537 + 0.082 d-l, were both significantly (p < 0.05) higher than the slope for the entire data set (bacteria to whales). The predictive slopes ( f l SE) for fish and crustaceans were -0.375 k 0.010 and -0.401 k 0.082 d-l, respectively. The crustacean slopes were significantly higher than the fish slopes. This analysis supports Gulland's assertion that the weight exponent of M for fish is higher than -0.25, but it does not support Gulland's assertion that the exponent is about -0.5. The use of the weight exponent of M for fishes does not invalidate the mortality-patchiness hypothesis, as Gulland claimed. The ratio of the observed M of pelagic fish eggs and early-stage larvae to Mpredicted by the functional allometric equation for fish, MF (Table l), is highly correlated with the geometric mean patchiness, p, of the fish eggs and early-stage larvae. The functional regression of the ratio M/MF on p is and the standard error of the slope is 0.03. The predictive version of Eqn (1) has an r of 0.56 and a p of 0.009. The scatter of data about Eqn (1) may be caused in part by the effects of variables other than dry weight and patchiness. Pauly (1980) reported a significant and Table 1. Linear regressions of 1nM on In W for pooled and separate taxa and ecological groups of marine pelaqc organisms I Taxonlgroup Regression SE of n r' P I I type Slope Slope Intercept I Bacteria, crustaFunctional ceans, fish and Predictive whales Crustaceans, fish Functional and whales Predictive Fish Functional Predictive Crustaceans Functional Predictive I Functional regressions assume r = 1.0 (Jensen 1986) I McGurk: Natural mortality and spahal patchiness 203 Fig. 1. Plot of instantaneous daily natural mortality rates, M, on dry weight. W, for marine pelagic organisms. Data for fish, crustaceans and whales from McGurk (1986b); data for bacteria from Servais et al. (1985). Vertical bars are ranges of growth rates of natural populations of aquatic bacteria from Moriarty (1986). h n e A IS the functional regression of 1nM on In W for all organisms (bacteria to whales): M = 7.13 X I O ~ w ~ . ~ ~ ~ . Line B is the functional regression of 1nM on InW for fish only: M = 8.41 X 10-3 w-~ .~$ ' . Line C is the functional regression for pelagic crustaceans only: M = 1.42 X 10-U W-0.537 + B a c t e r i a

Natural mortality and spatial patchiness: reply to Gulland