Transcript M - FishBase
Biodiversity of Fishes Death in the Sea Understanding Natural Mortality
Rainer Froese GEOMAR 08.01.2015
What is Natural Mortality?
Proportion of fishes dying from natural causes, such as: • Predation • Disease / parasites • Accidents, natural disasters • Old age
The
M
Equation
Instantaneous rate of natural mortality of
M
:
D t / N t = M t
Where
t
is the age in years
D t N t
is the number of deaths at age
t
is the population size at age
t
The
M
Equation
Probability of survival (
l t
) to age
t
:
l t
=
e
–
M t
Where
t M
is the instantaneous rate of natural mortality is the age in years
l t
ranges from 1.0 at birth to near zero at maximum age
The
M
Equation
Number of survivors
N
to age
t
:
N t
=
N 0 e
–
M t
Where
N 0
is the number of individuals at start age
t=
0
N t
is the number of individuals at age
t
Cohort numbers if
M
= 0.2
1200 Nt = Nts * exp(-M*(t - ts)) 1000 800 600 400 200 0 0 5 10 15
Cohort age (years)
20 25
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 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
The
M
Equations
If
M
is different in years 1, 2, 3 and constant thereafter
l t
=
e
–(
M 1 +M 2 +M 3 +M constant* (t-3)) N t
=
N 0 e
–(
M 1 +M 2 +M 3 +M constant* (t-3))
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
d r
is several years, the annual reproductive rate α is α = 1 /
d r
The
P/B
ratio is
M (Allen 1971)
In a stable,
equilibrium
population – Biomass gained by production (
P
) must equal biomass lost (
B lost
) due to mortality –
M
is the instantaneous loss in numbers relative to the initial number:
N lost
/
N
– If we assume an average weight per =
M
individual, then we have biomass: – If
B lost
=
P
then
P
/
B
=
M B lost
/
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
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
100 10 1 1 : 1 0.1
0.01
0.01
0.1
1
M = 1.5 K
10 100
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, r2 = 0.8230). Data from FishBase 11/2006 [File: M_Data.xls]
Hoenig’s 1984 Equation
ln
M
= 1.44 – 0.984 * ln
t max
Where
t max
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).
Charnov’s 1993 Equation
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
Fishing Kills Fish
Z
=
M
+
F
Where
Z
= total mortality rate
F
= mortality caused my fishing
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
.
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
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