Death in the Sea Understanding Mortality Rainer Froese

Death in the Sea Understanding Mortality Rainer Froese IFM-GEOMAR (SS 2008)

What is Natural Mortality? Proportion of fishes dying from natural causes, such as: • Predation • Disease • Accidents • Old age

The M Equation Instantaneous rate of mortality M: Dt / Nt = M Where t is the age in years Dt is the number of deaths at age t Nt is the population size at age t

The M Equation Probability of survival (lt): lt = e –M t Where M is the instantaneous rate of natural mortality t is the age in years lt ranges from 1. 0 at birth to 0. 0 x at maximum age

The M Equation Number of survivors N to age t : Nt = N 0 e –M (t) Where N 0 is the number of specimens at start age t=0 Nt is the number of specimens at age t

M = 0. 2

Constant Value of M for Adults (in species with indeterminate growth: fishes, reptiles, invertebrates, . . ) • M is typically higher for larvae, juveniles, and very old specimens, but reasonably constant during adult life • This 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 life – Extrinsic mortality decreases with size and experience

M is Death Rate in Unfished Population In an unfished, stable population – The number of spawners dying per year must equal the number of ‘new’ spawners per year – Every spawner, when it dies, is replaced by one new spawner, the life-time reproductive rate is 1/1 = 1 – If the average duration of reproductive life dr is several years, the annual reproductive rate is α = 1 / dr

The P/B ratio is M (Allen 1971) In an unfished, stable population – Biomass B gained by production P must equal biomass lost due to mortality – M is the instantaneous loss in numbers relative to the initial number: Nlost / N = M – If we assume a mean weight per individual, then we have biomass: Blost / B = M – If Blost = P then P / B = M

Pauly’s 1980 Equation log M = -0. 0066 – 0. 279 log L∞ + 0. 6543 log K + 0. 4634 log T Where L∞ and K are parameters of the von Bertalanffy growth function and T is the mean annual surface temperature in °C Reference: Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. Int. Explor. Mer. 39(2): 175 -192.

Jensen’s 1996 Equation M = 1. 5 K Where K is a parameter of the von Bertalanffy growth function Reference: Jensen, A. L. 1996. Beverton and Holt life history invariants result from optimal trade-off of reproduction and survival. Canadian Journal of Fisheries and Aquatic Sciences: 53: 820 -822

M = 1. 5 K Plot of observed natural mortality M versus estimates from growth coefficient K with M = 1. 5 K, for 272 populations of 181 species of fishes. The 1: 1 line where observations equal estimates is shown. Robust regression analysis of log observed M versus log(1. 5 K) with intercept removed explained 82% of the variance with a slope not significantly different from unity (slope = 0. 977, 95% CL = 0. 923 – 1. 03, n = 272, r 2 = 0. 8230). Data from Fish. Base 11/2006 [File: M_Data. xls]

Froese’s (in prep. ) Equation L∞ = C -0. 45 M This is the L∞ – M trade-off, where L∞ is the asymptotic length of the von Bertalanffy growth function and C is an indicator of body plan, environmental tolerance and behavior, i. e. , traits that are relatively constant in a given species. If C is known e. g. from other populations of a species, M corresponding to a certain L∞ can be obtained from M = (L∞ / C)-2. 2

Hoenig’s 1984 Equation ln M = 1. 44 – 0. 984 * ln tmax Where tmax is the longevity or maximum age reported for a population Reference: Hoenig, J. M. , 1984. Empirical use of longevity data to estimate mortality rates. Fish. Bull. (US) 81(4).

Froese’s (in prep. ) Equation M = 4. 5 / tmax = 4. 5 / M

Charnov’s 1993 Equation E=1/M Where E is the average life expectancy of adults Reference: Charnov, E. L. 1993. Life history invariants: some explorations of symmetry in evolutionary ecology. Oxford University Press, Oxford, 167 p.

Froese’s (in prep. ) Equation dr = 1 / M Where dr is the mean duration of the reproductive phase If mortality is doubled then reproduction is shortened by half

Life History Summary

Fishing Kills Fish Z=M+F Where Z = total mortality rate F = mortality caused my fishing

Size at First Capture Matters

Size at First Capture Matters Impact on Size-Structure (F=M)

What You Need to Know Nt = N 0 e –M (t) B t = Nt * W t Z=M+F

Thank You