Biodiversity of Fishes Death in the Sea Understanding Natural Mortality

1
Biodiversity of FishesDeath in the
SeaUnderstanding Natural Mortality

• Rainer Froese
• GEOMAR
• 03.12.2015

2
What is Natural Mortality?

• Proportion of fishes dying from natural causes,
  such as
• Predation
• Disease / parasites
• Accidents, natural disasters
• Old age

3
The M Equation

• Instantaneous rate of natural mortality M
• Dt / Nt Mt
• Where
• t is the age in years
• Dt is the number of deaths at age t
• Nt is the population size at age t
• M has the unit 1/year or year-1

4
The M Equation

• Probability of survival (lt) to age t
• 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 near zero at
  maximum age

5
The M Equation

• Number of survivors N to age t
• Nt Nstart e M (t-tstart)
• Where
• Nt is the number of individuals at age t
• Nstart is the number of individuals at age tstart

6
Cohort numbers if M 0.2
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 life
• This stems from a balance between intrinsic and
  extrinsic causes of 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

8
The M Equations

• If M is different in years 1, 2, 3 and constant
  thereafter
• lt e (M1M2M3Mconstant(t-3))
• Nt N0 e (M1M2M3Mconstant(t-3))

9
M is Death Rate in a Stable Population

• In a stable, equilibrium 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 a
  is
• a 1 / dr

10
How to Estimate M ???
11
The P/B ratio is M (Allen 1971)

• In a stable, equilibrium population
• Biomass gained by production (P) must equal
  biomass lost (Blost) due to mortality
• M is the instantaneous loss in numbers relative
  to the initial number Nlost / N M
• If we assume an average weight per individual,
  then we have biomass Blost / B M
• If Blost P then P / B M
• Reference Allen, K.R. 1971. Relation between
  production and biomass. Journal of the Fisheries
  Research Board of Canada, 1971, 28(10) 1573-1581

12
Paulys 1980 Equation

• log M -0.0066 0.279 log L8 0.6543 log K
  0.4634 log T
• Where
• L8 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.

13
Jensens 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
  Sciences53820-822

14
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 11 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,
r2 0.8230). Data from FishBase 11/2006 File
M_Data.xls
15
Hoenigs 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).

16
Charnovs 1993 Equation

•  

If the time E at which 50 of a group have died
can be determined, then M 1/E
17
Life History Summary
Note Blue line is not to scale. Froese and
Pauly 2013. Fish Stocks, p. 477-487 In
Encyclopedia of Biodiversity, Academic Press
18
Fishing Kills Fish

• Z M F
• Where Z total mortality rate
• F mortality caused my fishing

19
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 a single, rare survivor of fishing.
The absolute slope Z 0.82 represents total
mortality from natural causes M and from fishing
F. Without fishing, Z M.
20
Conclusions

• Natural mortality M is high in early life and
  near constant in adults
• M determines life expectancy, growth and
  reproduction (and everything else)
• Total mortality is Z M F
• Death rules

21
Exercises

• Select 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 ratio
• Determine adult life expectancy E