7 Constant Value of M for Adults (in species with indeterminate growth: fishes, reptiles, invertebrates, ..)M is typically higher for larvae, juveniles, and very old individuals, but reasonably constant during adult lifeThis stems from a balance between intrinsic and extrinsic mortality:Intrinsic mortality increases with age due to wear and tear and accumulation of harmful mutations acting late in lifeExtrinsic mortality decreases with size and experience
8 The M EquationsIf M is different in years 1, 2, 3 and constant thereafterlt = e –(M1+M2+M3+Mconstant*(t-3))Nt = N0 e –(M1+M2+M3+Mconstant*(t-3))
9 M is Death Rate in a Stable Population In a stable, equilibrium populationThe number of spawners dying per year must equal the number of ‘new’ spawners per yearEvery spawner, when it dies, is replaced by one new spawner, the life-time reproductive rate is1/1 = 1If the average duration of reproductive life dr is several years, the annual reproductive rate α isα = 1 / dr
10 The P/B ratio is M (Allen 1971) In a stable, equilibrium populationBiomass gained by production (P) must equal biomass lost (Blost) due to mortalityM is the instantaneous loss in numbers relative to the initial number: Nlost / N = MIf we assume an average weight per individual, then we have biomass: Blost / B = MIf Blost = P then P / B = MReference: Allen, K.R Relation between production and biomass. Journal of the Fisheries Research Board of Canada, 1971, 28(10):
11 Pauly’s 1980 Equationlog M = – log L∞ log K log TWhereL∞ and K are parameters of the von Bertalanffy growth function andT is the mean annual surface temperature in °CReference: Pauly, D On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. Int. Explor. Mer. 39(2):
12 Jensen’s 1996 EquationM = 1.5 KWhere K is a parameter of the von Bertalanffy growth functionReference: Jensen, A.L Beverton and Holt life history invariants result from optimal trade-off of reproduction and survival. Canadian Journal of Fisheries and Aquatic Sciences:53:
13 M = 1.5 KPlot of observed natural mortality M versus estimates from growth coefficient K with M = 1.5 K, for 272 populations of181 species of fishes. The 1:1 line where observations equal estimates is shown. Robust regression analysis oflog observed M versus log(1.5 K) with intercept removed explained 82% of the variance with a slope not significantly differentfrom unity (slope = 0.977, 95% CL = – 1.03, n = 272, r2 = ). Data from FishBase 11/2006 [File: M_Data.xls]
14 Hoenig’s 1984 Equation ln M = 1.44 – 0.984 * ln tmax Where tmax is the longevity or maximum age reported for a populationReference: Hoenig, J.M., Empirical use of longevity data to estimate mortality rates. Fish. Bull. (US) 81(4).
16 Life History SummaryNote: Blue line is not to scale. Froese and Pauly Fish Stocks, p In Encyclopedia of Biodiversity, Academic Press
17 Fishing Kills Fish Z = M + F Where Z = total mortality rate F = mortality caused my fishing
18 Total Mortality of Turbot Numbers at age in survey catches of North Sea turbot (Scophthalmus maximus).Points at the left are not fully selected by the gear. The point at the right is asingle, rare survivor of fishing. The absolute slope Z = 0.82 represents total mortalityfrom natural causes M and from fishing F.
19 ConclusionsNatural mortality M is high in early life and near constant in adultsM determines life expectancy, growth and reproduction (and everything else)Total mortality is Z = M + FDeath rules
20 ExercisesSelect a species from FishBase with several estimates of natural mortality (M is under Growth)Discuss M relative to other species (M-K Graph)Determine mean M/K ratioDetermine adult life expectancy E