Biodiversity of Fishes Sex under Water Rainer Froese GEOMAR 06.02.14.
Biodiversity of Fishes: Life-History Allometries and Invariants Rainer Froese 10.12.2015.
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Transcript of Biodiversity of Fishes: Life-History Allometries and Invariants Rainer Froese 10.12.2015.
Biodiversity of Fishes:Life-History Allometries and
Invariants
Rainer Froese10.12.2015
What is Life History?
• The stages of life an organism passes through from birth to death
• The study of the timing of life cycle events such as maturity, max growth and death
• Keywords: life span, longevity, mortality, survival, reproduction, fecundity, eggs, larvae, juveniles, adults, …
Life History Allometries
Typically a power function describing how one trait changes in relation to another.
Example: How body weight scales with length
W = a Lb
where a is a proportionality factor and
b ~ 3 is the typical scaling of weight with length
Body Weight Allometries
• Y = a W 0.75
– where Y is a whole body rate such as oxygen consumption, ingestion, heat production, blood flow and W is body weight
• Y = a W 1 – where Y is another weight or volume such as weight at maturity,
gonad weight, heart volume [exception: brain weight scales 1/3]
• Y = a W 0.25
– where Y is age such as age at maturity, life span, longevity
• Y = a W -0.25 – where Y is a rate per year such as natural mortality, annual
reproductive rate, growth rate (individual and population)
Note: these are empirical rates typically observed in plots across many species
Traits that change with body weight
The von Bertalanffy Growth Function
• dW/dt = H W 2/3 – k W 1 – where H W 2/3 stands for anabolism assumed proportional to resorbing
surfaces scaling as 2/3 = 0.666 with weight
– and k W 1 stands for catabolism scaling proportional to weight
• Integrating, rearranging and simplifying gives
• Wt = W∞ (1 – e-K(t – to))3
– where K = 3 k.
Note: the within-population scaling of 2/3 = 0.67, which is close to the expected 0.75
Life History Invariants:Maximum growth (weight of add-on tissue)
is obtained at
0.296 Winf
if b~3 this corresponds to
0.667 Linf the growth curve in length has no inflexion,
growth rate in length is max at origin
Average Adult Life Expectancy
x
x
y
xl
dl
E
y
MEm
1
where Ex is the average life expectancy after reaching age x and l are the probabilities of reaching x and subsequent ages y. If the mortality rateis constant then
Mortality and Growth
• In species that grow throughout their lives, maximum size is determined by life span
• Life span is determined by mortality
Therefore
• Maximum size and growth is determined by mortality
• K ~ 2/3 M
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
max. growth rate
Winf
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Probabilityof survival
max. growth rate
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Probabilityof survival
max. growth rate
Expected weight
M/K = 3/2
M/K > 3/2Peak left and smaller
M/K < 3/2Peak right and smaller
M observed vs M = 1.5 K
0.01
0.10
1.00
10.00
100.00
0.01 0.1 1 10 100
M from 1.44 K
M o
bse
rved
M from 1.5 K
1:1
Life History Invariants:Length at Maximum Reproductive Biomass
L
KM
LLopt 3
2
3
3
00
1.1)
31ln(
1t
Kt
M
K
Ktopt
Note: Since cohort biomass and fecundity peak at topt, this is also the most common age of parents, which is the definition of generation time.
Western Baltic Cod Life History
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25
Age (years)
Wei
gh
t (k
g)
asymptotic weight
Gadus morhua , Linf = 120 cm,Winf = 16.2 kg, K = 0.14, M = 0.2
maturityaverage adult life span
max growth
max reproductivebiomass of cohort
max age
Reproductive Strategies
Froese & Pauly 2013, Fish Stocks, Encyclopedia of Biodiversity, Academic Press
Length at Maturity for Different Reproductive Strategies
Froese & Pauly 2013, Fish Stocks, Encyclopedia of Biodiversity, Academic Press
Variability in Maturity
1
10
100
1000
10000
1 10 100 1000 10000
L∞ (cm)
Lm
(cm
)
L∞
0.67 L∞
0.35 L∞
Longevity as Size Invariant
• Taylor (1958) suggests maximum age is reached at 95% Linf -> tmax = 3/K
• A good fit is obtained at 96% Linf
Longevity vs Age at 96% Linf
0.1
1
10
100
1000
0.1 1 10 100 1000
t max = 3.22/K (years)
Ob
serv
ed lo
ng
evit
y (y
ears
)
1:1
Approximate Relation of Key Parameters
rmax ≈ 2 M ≈ 3 K ≈ 9 / tmax
where rmax is the maximum intrinsic rate of population increase
M is the rate of natural mortality
K is the somatic growth rate
tmax is maximum age
Summary
• Growth, average adult lifespan, maximum reproductive biomass, and longevity have co-evolved so that maximum reproductive output is reached as fast as possible and maximum lifespan is reached near maximum size
• Maturity may start before Lopt if successful reproduction is uncertain
Exercise
• Find species with growth and maturity data and high versus low fecundity
• Compare Lm/Linf with 0.67 and discuss differences