Stano Pekár“Populační ekologie živočichů“
dN
= Nr
dt
Net reproductive rate (R0)
average total number of offspring produced by a female in her
lifetime
Average generation time (T)
average age of females when they give birth
not valid for populations with generation overlap
Expectation of life
age specific expectation of life – average age that is expected
for particular age class
o .. oldest age
∑=
=
n
x
xxmlR
0
0
0
0
R
mxl
T
n
x
xx∑=
=
2
1++
= xx
x
ll
L∑=
o
x
xx LT
x
x
x
l
T
e = where
Growth ratesGrowth rates
Discrete time/generations
- estimate of λ (finite growth rate) from the life table:
where is vector at stable age distribution
λ is dominant positive eigenvalue of A
- or
Continuous time
- r can be estimated from λ
- by approximation
or by Euler-Lotka method
tt NNA
~~
λ=
T
R
r
)ln( 0
≈
T
R0
≈λ
)ln(λ=r
tN
~
0)det( =− IA λ
∑ −
=
ω
x
rx
xx eml1
- relative abundance of different life history age/stage/size categories
population approaches stable age distribution:
N0 : N1 : N2 : N3 :...:Ns is stable
- once population reached SCD it grows exponentially
w1 .. right eigenvector (vector of the dominant
eigenvalue)
- provides stable age distribution
- scale w1 by sum of individuals
Stable Class distribution (SCD)
∑=
= S
i iw
SCD
1 1
1w
111 wAw λ=
Reproductive value (vx)
measures relative reproductive potential and identifies age class
that contributes most to the population growth
such class is under highest selection force
when population increases then early offspring contribute more
to vx than older ones
is a function of fertility and survival
v1 .. left eigenvector (vector of the dominant
eigenvalue of transposed A)
- v1 is proportional to the reproductive values
and scaled to the first category
vx
age
1
0
111 vAv λ=′
11
1
v
v
v x
x = 1≠x
Sensitivity (s)
identifies which process (p, F, G) has largest effect on the
population increase (λ1)
- examines change in λ1 given small change in processes (aij)
- sensitivity is larger for survival of early, and for fertility of older
classes
- not used for postreproductive census with class 0
Elasticity (e)
weighted measure of sensitivity
- measures relative contribution to the population increase
- impossible transitions = 0
wv,
ijij
ij
wv
s
′
=
ij
ij
ij s
a
e
1λ
=
← sum of pairwise products
to adopt means for population promotion or control
Conservation/control procedure
1. Construction of a life table
2. Estimation of the intrinsic rates
3. Sensitivity analysis - helps to decide where
conservation/control efforts should be focused
4. Development and application of management plan
5. Prediction of future