Presentation on theme: "Demography of the female shortfin mako shark, Isurus oxyrinchus, using stage-based matrix models, Leslie matrices, and life history tables. H. F. Mollet."— Presentation transcript:
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 , USA Corresponding author Fax: WE ’ RE BACK!
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
L (t) = ( ) e ( t) L (t) = ( ) e ( t) Age at Maturity of Female Shortfin Mako (when 10 and 90% are mature) Total Length (m) Age Estimate (yrs)
Growth Rate (m yr-1) Observed and Calculated (from VBGF) Growth Rates for the Shortfin Mako
Why Would a Shark Deposit Two Pairs of Bands Per Year? Life Stages Migration Vertical Horizontal Temperature Food Stock differences?
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
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
Age-based (Leslie) Matrix
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.
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 = yr -1 and corresponding longevity of 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 yr -1 (S = 82.2%) and yr -1 (S = 74.6%) respectively.
ASSUMPTIONS FEMALE SHORTFIN MAKO SHARKS: LIVE YEARS BEAR 3-5 LITTERS HAVE A NATURAL MORTALITY (M) BETWEEN and 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)
Projection Matrix and Two-stage Life Cycle Model
Projection Matrix and Three-stage Life Cycle Model
Projection Matrix and Four-stage Life Cycle Model
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 = yr –1 (S = 82.2%).
MATRIX MODEL ELASTICITY ANALYSIS IF FISHING IS ALLOWED AN F CRITICAL OF ONLY yr -1 COULD BE ADDED TO NATURAL MORTALITY (TOTAL MORTALITY Z = yr -1 ) TO ACHIEVE A STATIONARY POPULATION IN WHICH =1 AND r = e = 0
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.
Age Estimate from Mass via TL ( yrs) Ln (Frequency Catch Curve for Female Shortfin Makos off South-Eastern Australia (Pepperell 1992; n ~ 2210 / 2; female frequencies were estimated from sex ratios given by Casey and Kohler 1992)
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
Two-stage-based Matrix Model and Life Cycle Graphs
Three-stage-based Matrix Model and Life Cycle Graphs
Four-stage-based Matrix Model and Life Cycle Graphs
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
Four-stage model for shortfin mako sharks using a 3-yr reproductive cycle (Final Answer)