Stano Pekár“Populační ekologie živočichů“
dN
= Nr
dt
a major sub-field of ecology which deals with
description and the dynamics of populations
within species, and the interactions of
populations with environmental factors
expanding field (Price & Hunter 1995):
- populations 52 %, communities 9 %, ecosystems
10 %
main focus on
- Demography = description of populations that
gave rise to Life-history theory
- Population dynamics = describe the change in
the numbers of individuals in a population
populations of member species may show a range of dynamic patterns
in time and space
central question: “WHAT DOES REGULATE POPULATIONS?“
Change in abundance
of Lynx and Lepus in
Canada
density independent factors, food supply, intraspecific competition,
interspecific competition, predators, parasites, diseases
1. Conservation biology
World Conservation Union (IUCN) uses several criterions (population
size, generation length, population decline, fragmentation, fluctuation) to
assess species status
by means of Population viability analysis (PVA) estimates the
extinction probability of a taxon based on known life history, habitat
requirements, threats and any specified management options
Saiga tatarica
critical: 50% probability of extinction within 5 years
endangered: 20% probability of extinction within
20 years
vulnerable: 10% probability of extinction within
100 years
2. Biological control
to assess ability of a natural enemy to control
a pest
in 1880 Icerya purchasi was causing
infestations so severe in California citrus groves
that growers were burning their trees
in winter 1888-1889 Rodolia cardinalis and Cryptochaetum were
introduced into California from Australia, growers took the initiative and
applied the natural enemies themselves
by fall 1889 the pest was completely controlled
Rodolia cardinalis has been exported to many other parts of the world
the interest of growers and the public in this project was due to its
spectacular success: the pest itself was showy and its damage was obvious
and critical; the destruction of the pest and the recovery of the trees was
evident within months
Rodolia cardinalis (Coccinellidae) eating
Icerya purchasi (Hemiptera)
3. Epidemiology
to predict the diffusion of a disease and to plan a vaccination
phocine distemper virus was identified in 1988 and caused death of
18 000 common seals in Europe
during 4 months the disease travelled from Denmark to the UK
the population of common seals in the UK declined by about half
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12 14 16 18 20
week
no.ofdeadseals
observed
predicted Observed and predicted
epidemic curves for virus in
common seals in the UK
Grenfell et al. (1992)
4. Harvesting
to predict maximum sustainable harvest in fisheries and forestry but
also used to regulate whale or elephant hunting
when population is growing most rapidly (K/2) then part of population
can be harvested without causing extinction
Beddington (1979)
Relationship between capture
and fishing effort
Panulirus cygnus
Population + environment
= population system
population conditions
resources enemies
molecules → organels → cells → tissues → organs → organ
systems → organisms → populations → communities →
ecosystem → landscape → biosphere
a group of organisms of the same species that occupies a
particular area at the same time and is characterised by an
average characteristic (e.g., mortality)
characteristics:
Individual → Population
Stage structure
Age structure
Size structure
Sex ratio
Spatial distribution
Developmental stage
Age
Size
Sex
Territorial behaviour
Event – an identifiable change in a population
Process – a series of identical events
• rate of a process – number of events per unit time
Natality (birth rate)
Mortality (mortality rate)
Growth (growth rate)
Population increase (rate of increase)
Consumption (consumption rate)
Birth [inds]
Death [inds]
Increment [gram]
Increment [number]
Acquisition of food [gram]
ProcessEvent
inherent characteristics of the
evironment (pH, salinity,
temperature, moisture, wind
speed, etc.)
not modified by populations
not consumed by population
⇒ no feedback mechanisms
⇒ do not regulate population
size
limit population size
optimal
suboptimal
unfavourable
reproduction
growth
survival
performance
conditions
any entity whose quantity is reduced (food, space, water,
minerals, oxygen, sun radiation, etc.)
modified (reduced) by populations
defended by individuals (interference competition)
regulate population size
non-renewable resources - space
Renewable resources
- regeneration centre outside the population system ⇒ no effect of
the consumer (e.g., oxygen, water)
- regeneration centre inside of the population system ⇒ influenced
by the consumer (e.g., prey)
competitors, predators, parasites, pathogens
negative effect on the population
top-down regulation of the population
Absolute
- number of individuals per unit area
- number of individuals per unit of habitat (leaf, plant, host)
- sieving, sweeping, extraction, etc.
Relative
- number of individuals
- trapping, fishing, pooting
Capture-recapture method
Assumptions:
- marked individuals are not affected and marks will not be lost
- marked animals become mixed in the population
- all individuals have same probability of capture
- capture time must be short
Closed population
- population do not change over sampling period - no death,
births, immigration, emigration
Petersen-Lincoln estimator:
N - number of individuals in population
a - total number of marked individuals
r - total number of recaptured marked individuals
n - total number of individuals recaptured
r
an
N = 3
2
)(
r
rnna −
=νVariance:
Open population
- changes due to death, births, immigration, emigration
- at least 3 sampling periods
Stochastic Jolly-Seber method
Ni - estimate of population on day
ai - number of marked individuals on day i
ni - total number of individuals captured on day i
ri - sum of recaptured marked individuals on day i
Zi - sum of marked individuals before day i
Ri - sum of all marked individuals on day i
i
i
ii
i r
R
Za
M +=
i
ii
i
r
nM
N = where
Stano Pekár“Populační ekologie živočichů“
dN
= Nr
dt
aim: to simulate (predict) what can happen
models are tested by comparison with observed dynamic
realistic models - complex (many parameters), realistic, used to
simulate real situations
strategic models - simple (few parameters), unrealistic, used for
understanding of model behaviour
a model should be:
1. a satisfactory description of diverse systems
2. an aid to enlighten aspects of population dynamics
3. a system that can be incorporated into more complex models
deterministic models - everything is predictable
stochastic models - including random events
discrete models:
- time is composed of discrete intervals or measured in generations
- used for populations with synchronised reproduction (annual species)
- modelled by difference equations
continuous models:
- time is continual (very short intervals) thus change is instantaneous
- used for populations with asynchronous and continuous overlapping
reproduction
- modelled by differential equations
STABILITY
stable equilibrium is a state (population
density) to which a population will
move after a perturbation
stable equilibrium
unstable equilibrium
focus on rates of population processes
number of cockroaches in a living room increases:
- influx of cockroaches from adjoining rooms → immigration [I]
- cockroaches were born → birth [B]
number of cockroaches declines:
- dispersal of cockroaches → emigration [E]
- cockroaches died → death [D]
population increases if I + B > E + D
rate of increase is a summary of all events (I + B - E - D)
growth models are based on B and D
spatial models are based on I and E
Blatta orientalisEDBINN tt −−++=+1
Assumptions:
immigration and emigration are ignored
all individuals are identical
reproduction is asexual
resources are infinite
for population with discrete generations (annual reproduction)
if births and deaths do not depend on population size
exponential (geometric) growth
Malthus (1834) realised that any species can potentially increase in
numbers according to a geometric series
N0 .. initial density
b .. birth rate (per capita)
d .. death rate (per capita)
Discrete (difference) model
λ1−= tt NN
11 −− −=∆ tt dNbNN
11 )( −− −=− ttt NdbNN
1)1( −−+= tt NdbN
λ=−+ db1where
λ < 1 .. population declines
λ > 1 .. population increases
λ = 1 .. population does not change
time0
Nt
t
t NN λ0=
λλλ 012 NNN ==
population number in generations t is equal to
number of individuals is
multiplied each time - the larger the
population the larger the increase
λ = finite growth-rate, per capita rate
of growth
λ = 1.23 .. 23% increase
R ..average of finite growth rates
t
t
tt
i
iR
1
21
1
1
)...( λλλλ =





= ∏=
Comparison of discrete and continuous generations
populations that are continuously reproducing
when change in population number is permanent
Nt
time
Continuous (differential) model
t
t NN λ0=
)ln()ln()ln( 0 λtNNt +=
)ln()ln()ln( 0 λtNNt =−
)ln(
1
λ=
Ndt
dN
)ln(λN
dt
dN
=
Nr
dt
dN
=)ln(λ=rif
Solution of the differential equation:
- analytical or numerical
at each point it is possible to determine the rate of change by
differentiation (slope of the tangent)
when t is large approximated by the exponential function
r < 0 .. population declines
r > 0 .. population increases
r = 0 .. population does not change
time
N
r - intrinsic rate of natural increase,
instantaneous per capita growth rate
Nr
dt
dN
=
r
Ndt
dN
=
1
∫∫ =
TT
rdtdN
N 00
1
)0()ln()ln( 0 −=− TrNNT
rT
N
NT
=







0
ln
rt
t eNN 0=
rTT
e
N
N
=
0
t
t NN λ0= rt
t eNN 0=
rtt
e=λ
)ln(λ=r
r versus λ
r is symmetric around 0, λ is not
r = 0.5 ... λ = 1.65
r = -0.5 ... λ = 0.61
doubling time: time required for a
population to double
r
t
)2ln(
=
MODULARIZACE VÝUKY EVOLUČNÍ A EKOLOGICKÉ BIOLOGIE
CZ.1.07/2.2.00/15.0204
S. Pekár
podzim 2011
Cvičení z Populační
ekologie
Capture
Day ni ai 1 2 3 ri
1 60 58
2 125 123 15 15
3 154 150 5 38 43
4 189 187 9 20 45
Ri 58 45
Zi+1 14 20
Recapture day
Cockroaches were captured using traps with baits for 4 consecutive
days. Each day the specimens were marked and released.
1. Estimate population density assuming closed population.
2. Estimate population density assuming open population.
3. Estimate average population size for both closed and open
populations.
R2 = 58, R3 = 45Z2 = 14, Z3 = 20 r2 = 15, r3 = 43
Population density of the true bugs Coreus marginatus was
recorded for 10 years. Here are the densities:
160, 172, 188, 154, 176, 185, 168, 194, 170, 169
Does population increase or decrease?
What is the average population growth (R)?
Project population for another 10 years using R and N0 = 90.
Simulate population growth for the next 20 years using observed
finite-growth rates.
Population density of the mite Acarus siro was recorded every 3
days during 28 days. The following densities were found:
165, 145, 139, 125, 105, 101, 88, 81, 73, 69
What is the intrinsic rate of increase (r) and what was the initial
density ?
How long it takes for a population to decrease to half size?
Project population growth for another 5 weeks using estimated r
and N0 = 69.
What would be the estimated rate if you know the initial and
final density?