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**Fig. 1.** Convergence of arithmetic means of the
maximum eigenvalues of matrices for all permutations to the
maximum eigenvalue of the mean matrix. Relative error is ^{t}√*m*/λ_{1}(**R**). Modified from *Bull. Jpn. Soc. Fish.
Oceanogr*., **74**, Akamine, Mathematical study of matrix models for
fish population dynamics in random environments, 208–213, © 2010, with permission from the Japanese Society of
Fisheries Oceanography.

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