Stano Pekár“Populační ekologie živočichů“
 dN
= Nr
dt
 study of organisms with special attention to stage or age structure
 processes are associated to age, stage or size
- fecundity is dependent on age (e.g., mammals), stage (e.g., insects)
or size (e.g., fish)
Four concepts:
1. Every population has a structure – individuals in each class have
similar rate of reproduction and mortality
2. Every population has a specific intrinsic rate of increase
3. Every population has specific mortality
x .. age/stage/size category
px .. age/stage/size specific survival
4. Every population has a specific reproductive rate
mx .. reproductive rate (expected average number of offspring
per female)
x
x
x
S
S
p 1

main focus on births and deaths
immigration & emigration is
ignored
 no adult survive
 one (not overlapping)
generation per year
 egg pods over-winter
 despite high fecundity they just
replace themselves
Chorthippus
Richards & Waloff (1954)
Annual species
 breed at discrete
periods
 no overlapping
generations
Biennal species
 breed at discrete periods
 adult generation may overlap
adults
adults
0
birth
t0
t1
adults
pre-adults
0
birth
t0
t1
adults t2
p
pre-adults
birth
t0
t1adults
t2
0
pre-adults
p
 breed at discrete periods
 breeding adults consist of
individuals of various ages (1-5 years)
 adults of different generations are
equivalent
 overlapping generations
Perennial species
Parus major
Perins (1965)
 age/stage
classification is based
on developmental time
 size may be more
appropriate than age
(fish, sedentary
animals)
 Hughes (1984) used
combination of
age/stage and size for
the description of coral
growth
Age-size-stage life-table
Agaricia agaricites
 show organisms‘ mortality and reproduction as a function of age
 examination of a population in a
cohort = a group of individuals born
at the same period
 followed from birth to death
 provide reliable information
 designed for short-lived organisms
 only females are included
Cohort (horizontal) life-table
Vulpes vulpes
x Sx Dx lx px qx mx
0 250 50 1.000 0.800 0.200 0.000
1 200 120 0.800 0.400 0.600 0.000
2 80 50 0.320 0.375 0.625 2.000
3 30 15 0.120 0.500 0.500 2.100
4 15 9 0.060 0.400 0.600 2.300
5 6 6 0.024 0.000 1.000 2.400
6 0 0 0.000
Sx .. number of survivors
Dx .. number of dead individuals
lx .. standardised number of
survivors
qx .. age-specific mortality
px .. age-specific survival
0S
S
l x
x 
x
x
x
S
D
q 
1 xxx SSD
x
x
x
l
l
p 1

 examination of a population during
one segment (time interval)
- segment = group of individuals of
different cohorts
- designed for long-lived organisms
 ASSUMPTIONS:
- Birth rate and survival are constant
over time
- population does not grow
- proportions of age classes in a sample corresponds to the real state
 DRAWBACKS: confuses age-specific changes in e.g. mortality with
temporal variation
Static (vertical) life-tables
Cervus elaphus
Lowe (1969)
x Sx Dx lx px qx mx
1 129 15 1.000 0.884 0.116 0.000
2 114 1 0.884 0.991 0.009 0.000
3 113 32 0.876 0.717 0.283 0.310
4 81 3 0.628 0.963 0.037 0.280
5 78 19 0.605 0.756 0.244 0.300
6 59 -6 0.457 1.102 -0.102 0.400
7 65 10 0.504 0.846 0.154 0.480
8 55 30 0.426 0.455 0.545 0.360
9 25 16 0.194 0.360 0.640 0.450
10 9 1 0.070 0.889 0.111 0.290
11 8 1 0.062 0.875 0.125 0.280
12 7 5 0.054 0.286 0.714 0.290
13 2 1 0.016 0.500 0.500 0.280
14 1 -3 0.008 4.000 -3.000 0.280
15 4 2 0.031 0.500 0.500 0.290
16 2 2 0.016 0.000 1.000 0.280
 survival and reproduction depend on stage / size rather than age
 age-distribution is of no interest
 used for invertebrates (insects, invertebrates)
 time spent in a stage / size can differ
Lymantria dispar
Campbell (1981)
x Sx Dx lx px qx mx
Egg 450 68 1.000 0.849 0.151 0
Larva I 382 67 0.849 0.825 0.175 0
Larva II 315 158 0.700 0.498 0.502 0
Larva III 157 118 0.349 0.248 0.752 0
Larva IV 39 7 0.087 0.821 0.179 0
Larva V 32 9 0.071 0.719 0.281 0
Larva VI 23 1 0.051 0.957 0.043 0
Pre-pupa 22 4 0.049 0.818 0.182 0
Pupa 18 2 0.040 0.889 0.111 0
Adult 16 16 0.036 0.000 1.000 185
 display change in survival by plotting log(lx) against age (x)
 sheep mortality increases with age
 survivorship of lapwing (Vanellus) is independent of age
but survival of sheep is age-dependent
Pearls (1928) classified hypothetical age-specific mortality:
 Type I .. mortality is concentrated at the end of life span (humans)
 Type II .. mortality is constant over age (seeds, birds)
 Type III .. mortality is highest in the beginning of life (invertebrates,
fish, reptiles)
ln(Survivorship)
0
Type I
Type II
Type III
1
Time
- Sum of intrinsic
and extrinsic
mortality
 fecundity - potential number of offspring
 fertility - real number of offspring
 semelparous .. reproducing once a life
 iteroparous .. reproducing several times during life
 birth pulse .. discrete reproduction
(seasonal reproduction)
 birth flow .. continuous
reproduction Numberofoffsprings
0
Time
reproductivepre-reproductive post-reproductive
0
0.1
0.2
0.3
0.4
0.5
0.6
0 20 40 60 80 100 120 140
Time [Days]
Fecundity
Triaeris stenapsis
Geospiza scandensnumber.ofbirths/individual
0
0.4
age 16
Cervus elaphus
Odocoileus
numberofbirths/individual
0 6age
0.8
 k-value - killing power - another measure of mortality
 k-values are additive unlike q
Key-factor analysis - a method to identify the most important
factors that regulates population dynamics
 k-values are estimated for a number of years
 important factors are identified by regressing kx on log(N)
)ln(pk 
x
kK 
 over-wintering adults emerge in June  eggs are laid in
clusters on the lower side of leafs  larvae pass through 4 instars
 form pupal cells in the soil  summer adults emerge in August
 begin to hibernate in September
 mortality factors overlap
Leptinotarsa decemlineata
Harcourt (1971)
 highest k-value indicates the role of a factor in each generation
 profile of a factor parallel with the K profile reveals the key
factor
 emigration is the key-factor
Summary over 10 years