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Demography of the female shortfin mako shark, Isurus oxyrinchus, using stage-based matrix models, Leslie matrices, and life history tables. H. F. Mollet and G. M. Cailliet Moss Landing Marine Laboratories, Moss Landing CA 95039-9647, USA Corresponding author email: mollet@pacbell.net; Fax: 1-831-644-7597 WE ’ RE BACK!

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ACKNOWLEDGEMENTS GREG HOOD - POPTOOLS AUTHOR HAL CASWELL – NEW BOOK ON MATRIX POPULATION ANALYSIS KARYL BREWSTER-GEISZ, JASON COPE, ENRIC CORTES AND SELINA HEPPELL – ADVICE ON MATRIX POPULATION ANALYSIS LEANNE LAUGHLIN & JOHN UGORETZ – WEST COAST TAG-RECAPTURE DATA JULIAN PEPPERELL AND PETER SAUL – SOUTHERN HEMISPHERE CATCH DATA LISA NATANSON - BAND COUNTS FOR TWO RECENT, RECORD- SIZED CAPTURES DAVE EBERT, MALCOLM FRANCIS, DAVE HOLTS, & STEVE CAMPANA – HELPFUL ADVICE LYNN MCMASTERS, MLML – GRAPHICS ASSISTANCE MONTEREY BAY AQUARIUM – COMPUTER SUPPORT

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b) a)

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L (t) = 3.21 - (3.21 - 0.76) e (-0.072 t) L (t) = 3.73 - (3.73 - 0.70) e (-0.203 t) Age at Maturity of Female Shortfin Mako (when 10 and 90% are mature) Total Length (m) Age Estimate (yrs)

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Growth Rate (m yr-1) Observed and Calculated (from VBGF) Growth Rates for the Shortfin Mako

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Why Would a Shark Deposit Two Pairs of Bands Per Year? Life Stages Migration Vertical Horizontal Temperature Food Stock differences?

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DEMOGRAPHIC ANALYSIS Is based upon an evaluation of existing and addition of new life history information on the shortfin mako shark Isurus oxyrinchus: SIZE FREQUENCIES TAG-RECAPTURE GROWTH RATES REPRODUCTION MORTALITY ESTIMATES AND CATCH CURVES AND USING STAGE-BASED MATRIX MODELS AGE-BASED LESLIE MATRICES and LIFE HISTORY TABLES

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1234 F n = Fertility value for stage n. P n = probability of surviving/persisting in same stage. G n = probability of surviving/growing to next stage. Stage-based (Lefkovitch) Matrix

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Age-based (Leslie) Matrix

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R o,, r, T, DT, 1, Ā in age- and stage-class models Net Reproductive rate (expected number of offspring by which a newborn individual will be replaced by the end of its life) Ro = l(x) m(x) dx; Ro = l x m x ;Ro = F 1 + P 1 F 2 + P 1 P 2 F 3 + P 1 P 2 P 3 F 4 + ….= F i P i = finite rate of increase (e.g. increase of numbers in pop. in 1 year) r (time -1 ) = ln =( instantaneous) rate of increase Generation Time (yr): T = ln Ro/r & Doubling Time (yr): DT = ln 2/r 1 =Mean age of parents of the offspring produced by a cohort Ā (Abar) = Mean age of the parents of the offspring produced by a population at the stable age distribution. ( 1 = Ã for a stationary population in which =1.

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Estimates of natural mortality (M) for Isurus oxyrinchus using indirect methods from life history parameters (following Simpfendorfer 1999). The Hoenig (1983) log-log equations were back-transformed to facilitate comparison. We used k = 0.203 yr -1 and corresponding longevity of 17.07 yr (from 5 ln2/k, following Cailliet et al., 1992). In our demographic calculations, we used longevity of 19 yr (5 litters) and 13 yr (3 litters) and corresponding natural mortalities of 0.1960 yr -1 (S = 82.2%) and 0.2928 yr -1 (S = 74.6%) respectively.

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ASSUMPTIONS FEMALE SHORTFIN MAKO SHARKS: LIVE 13-19 YEARS BEAR 3-5 LITTERS HAVE A NATURAL MORTALITY (M) BETWEEN 0.196 and 0.293 YEAR -1 MATURE AT AGE 6-7 YEARS HAVE 12.5 (MEAN) PUPS PER LITTER HAVE A 3-YEAR REPRODUCTIVE CYCLE (GESTATION AND RESTING PERIOD OF 18 MONTHS EACH)

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Projection Matrix and Two-stage Life Cycle Model

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Projection Matrix and Three-stage Life Cycle Model

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Projection Matrix and Four-stage Life Cycle Model

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Summary of parameters for shortfin mako shark demography using stage-based models, a Leslie matrix, and a life history table. In the final column, we added fishing mortality (F CRITIICAL; Brewster and Miller, 2000) until lambda ( ) became 1.0, using M = 0.1960 yr –1 (S = 82.2%).

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MATRIX MODEL ELASTICITY ANALYSIS IF FISHING IS ALLOWED AN F CRITICAL OF ONLY 0.07-0.13 yr -1 COULD BE ADDED TO NATURAL MORTALITY (TOTAL MORTALITY Z = 0.37-33 yr -1 ) TO ACHIEVE A STATIONARY POPULATION IN WHICH =1 AND r = e = 0

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Demographic parameters using an annual effective fecundity, 5 litters, and based on three von Bertalanffy growth functions, the first using two band-pairs per yr (Pratt and Casey, 1983) and the second two using one band-pair per yr (Cailliet et al., 1983). The LHT to age 28 has been modified to produce a more reasonable life history scenario.

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Age Estimate from Mass via TL ( yrs) Ln (Frequency Catch Curve for Female Shortfin Makos off South-Eastern Australia 1961-90 (Pepperell 1992; n ~ 2210 / 2; female frequencies were estimated from sex ratios given by Casey and Kohler 1992)

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Z WAS ESIMATED AT 0.30 yr -1 FROM AN ADJUSTED CATCH CURVE FOR FEMALES OFF SOUTHEASTERN AUSTRALIA THUS, THE SHORTFIN MAKO SHARK COULD BE VULNERABLE BOTH TO DIRECTED FISHING AND BY- CATCH FROM OTHER FISHERIES DESPITE ITS RELATIVELY FAST GROWTH

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Two-stage-based Matrix Model and Life Cycle Graphs

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Three-stage-based Matrix Model and Life Cycle Graphs

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Four-stage-based Matrix Model and Life Cycle Graphs

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Eigenvectors & Eigenvalues Ax = x x, y = Eigenvector = Eigenvalue When matrix multiplication equals scalar multiplication yA = y Rate of Population Growth ( ): Dominant Eigenvalue Stable age distribution (w): Right Eigenvector Reproductive values (v): Left Eigenvector

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Four-stage model for shortfin mako sharks using a 3-yr reproductive cycle (Final Answer)

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