Stano Pekár“Populační ekologie živočichů“
 dN
= Nr
dt
Net reproductive rate (R0)
 average total number of offspring produced by a female in her
lifetime
 equals to finite growth rate
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 rates
 Discrete time/generations
- estimate of  (finite growth rate) from the life table:
where is vector at stable age distribution
 is dominant positive eigenvalue of A
- or
 Continuous time
- r can be estimated from 
- by approximation
or by Euler-Lotka method
- valid only for population with SCD
tt NNA
~~

T
R
r
)ln( 0

T
R0

)ln(r
tN
~
0)det(  IA 
 


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 
Reproductive value (vx)
measures relative reproductive potential and identifies age class
that contributes most to the population growth (Fisher 1930)
such class is under highest selection force
sum of all expected offspring produced in age x and further
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
(class 1 = 1)
vx
age
1
0
111 vAv 
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)
measures absolute change
- 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
1

 sum of pairwise products
to adopt means for population promotion (threatened) or
control (pests) or sustainable yield
in populations with short generation time and higher natality
population decline stabilisation will take some delay
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 - on parameters with high
elasticities
4. Development and application of management plan
5. Prediction of future