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The story of this edition is a testament to an almost legendary ®gure in theoretical ecology and to the in¯uence his work and charisma has had on the ®eld. It is also a story that can only be told by a trip back in time, to the genesis of the First Edition and before.Akira Okubo and I were students together, but never knew it at the time. He was a graduate student at The Johns Hopkins University, where I was an undergraduate in mathematics. We both studied ``modern physics,'' taught by Dino Franco Rasetti, and we decided years later that we must have been in the same class. Akira was then a chemical oceanographer, but ship time and his stomach did not agree. So he turned to theory, and the rest is history. His impact has been phenomenal, and the First Edition of this book was his most in¯uential work. Building on his famous work with dye-di¤usion experiments, he turned his attention to organisms and created a unique melding of ideas from physics and biology.In the early 1970s, Lee Segel and I began to work on problems of planktonic patchiness, following some pathways that were simultaneously being explored by Akira (on di¤usive instabilities). This brought Akira and me together, and he presented me with a copy of his 1975 book, Ecology and Di¨usion, published in Japanese by Tsukji Shokan, Tokyo. I could understand all of the Greek in the book, but none of the Japanese. Still, I recognized enough that was familiar to know that this was an important book, but one whose in¯uence was likely to be a bit limited if it remained only in Japanese. I was at the time Editor of the Biomathematics Series for Springer-Verlag, and I encouraged Akira to produce an updated version of his work for us, in large part so that I could read it. He readily accepted.The next several years produced unexpected bene®ts for me. As Akira developed his chapters and sent them to me for comments and editorial suggestions, he began frequent pilgrimages from the Marine Sciences Research Center at Stony Brook to Cornell, where I was a faculty member. This led to fruitful collaborations between us, while he became a de facto member of our family, and an additional adviser for many of my students.

Abstract. The mussel Mytilus californianus is a competitive dominant on wave-swept rocky intertidal shores. Mussel beds may exist as extensive monocultures; more often they are an everchanging mosaic of many species which inhabit wave-generated patches or gaps. This paper describes observations and experiments designed to measure the critical parameters of a model of patch birth and death, and to use the model to predict the spatial structure of mussel beds. Most measurements were made at Tatoosh Island, Washington, USA, from 1970-1979. Patch size ranged at birth from a single mussel to 38 m 2 ; the distribution of patch sizes approximates the lognormal. Birth rates varied seasonally and regionally. At Tatoosh the rate of patch formation varied during six winters from 0.4-5.4% of the mussels removed per month. The disturbance regime during the summer and at two mainland sites was 5-10 times less. Annual disturbance patterns tended to be synchronous within II sites on one face of Tatoosh over a 10-yr interval, and over larger distances (16 km) along the coastline. The pattern was asynchronous, however, among four Tatoosh localities. Patch birth rate, and mean and maximum size at birth can be used as adequate indices of disturbance.Patch disappearance (death) occurs by three mechanisms. Very small patches disappear almost immediately due to a leaning response of the border mussels (0.2 em/d). Intermediate-sized patches ( <3.0 m 2 ) are eventually obliterated by lateral movement of the peripheral mussels: estimates based on 94 experimental patches yield a mean shrinking rate of 0.05 cm/d from each of two principal dimensions. Depth of the adjacent mussel bed accounts for much of the local variation in closing rate. In very large patches, mussels must recruit as larvae from the plankton. Recovery begins at an average patch age of 26 mo; rate of space occupation, primarily due to individual growth, is 2.0-2.5%/mo. ' Winter birth rates suggest a mean turnover time (rotation period) for mussel beds varying from 8.1-34.7 yr, depending on the location. The minimal value is in close agreement with both observed and calculated minimal recovery times.Projections of total patch area, based on the model, are accurate to within 5% of that observed. Using a method for determining the age of patches, based on a growth curve of the barnacle Balanus cariosus, the model permits predictions of the age-size structure of the patch population. The model predicts with excellent resolution the distribution of patch area in relation to time since last disturbance. The most detailed models which include size structure within age categories are inconclusive due to small sample size. Predictions are good for large patches, the major determinants of environmental patterns, but cannot deal adequately with smaller patches because of stochastic effects.Colonization data are given in relation to patch age, size and intertidal position. We suggest that the reproductive season of certain long-lived, patch-dependent species is moulded by the distu...

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