Stano Pekár“Populační ekologie živočichů“
 dN
= Nr
dt
 consume small amount of many different plant
species
 consume a lot during life to obtain sufficient
amount of N
 grazers, granivores, frugivores, herbivores
 plants are not killed only reduced in biomass
 bottom-up control – herbivore abundance
is regulated by quantity and quality of plants
top-down control – herbivore abundance is
regulated by enemies
specialised herbivores (aphids) are alike
parasites
hfHT
fHV
K
V
r
t
V








1
1
d
d
V .. plant biomass
H.. herbivore density
r.. intrinsic rate of regrowth
K.. carrying capacity
f .. efficiency of removal
Th.. handling time
Herbivory-regrowth model
 Turchin (2003)
 assumptions
- continuous herbivory (grazing)
- herbivore is polyphagous
- plant biomass is homogenous
- functional response Type II
- herbivore density may be constant
- only small quantity of biomass is removed
 hyperbolic biomass growth because only
small part of aboveground tissues is consumed
time
V
0
Leishmania
 microparasites: viruses, bacteria, protozoans
- reproduce rapidly in host
- level of infection depends not on the number
of agents but on the host response
 macroparasites - helminths
- reproduce in a vector
- level of infection depends on the number
incidence .. number of new infections
per unit time
prevalence .. proportion of population
infected [%]
swine flu virus
cercaria
nematode
E. coli (EHEC)
 predicts rates of disease spread
 predicts occurrence of epidemics
 predicts expected level of infection
number of human deaths caused by diseases exceeds that of all wars
affects also animals
- rinderpest introduced by Zebu cattle to South Africa in 1890
- 90% buffalo population was wiped out
biological control
- Cydia pomonella granulosis virus
Type I
Type II
Type III
periodic eruptions
regular pattern
irregular pattern
time
N
epidemics occur in cycles
follows 4 stages:
- establishment - pathogen increases
after invasion
- persistence - pathogen persists
within host population
- spread - spreads to other
non-infected regions, reaches peak
- epidemics terminates
 rabies in Europe spread from Poland
1939
- hosts: foxes, badgers, roe-deer
 spread rate of 30-60 km/year
Spread of rabies (Bacon 1985)
virus
used to simulate spread of a disease
pathogen is much smaller than host
 models:
- Kermack & McKendrick (1927)
- later developed by Anderson & May (1980, 1981)
 3 components:
- S .. susceptible
- I .. infected
- R .. resistant/recovered and immune - can not transmit disease
- latent stage - infected but not infectious
- vectors (V) and pathogens (P)
- malaria is transmitted by mosquitoes, hosts become infected only when
they have contact with the vector
- the number of vectors carrying the pathogens is important
- such system is further composed of uninfected and infected vectors
  .. transmission rate - number of new infections per unit time
SI.. density-dependent transmission function (proportional to the
number of contacts)
- mass action
- analogous to search efficiency in predator-prey model
1/ .. average time for encountering infected individual
 .. recovery rate of infected hosts
(either die or become immune)
 = 1/duration of disease
Assumptions:
- S0 >> I0
- ignores population change (increase of S)
- incubation period is negligible
SI
t
S

d
d
ISI
t
I
 
d
d
SI model
outbreak (epidemics) will occur if
- i.e. transmission threshold, when density of S is high
making the population size small will halt the spread:
- e.g. by vaccination (not necessary to use for all)
culling or isolation of I will stop disease spread


0S


0S
Outbreaks
Assumptions:
- host population is dynamic
- newborns are susceptible
- b .. host birth rate
=1/host life-span, given exponential growth and constant population size
- m .. host mortality due to other causes
Susceptible
S
Infected
I
Resistant
R
death death death
m mm
 
birth
b
bb
recoverytransmission
mSSIRISb
t
S
 )(
d
d
mIISI
t
I
 
d
d
mRI
t
R
 
d
d
SIR model
RISN 
N .. total population of hosts
per area:
 R0 .. basic reproductive rate of the disease
- number of secondary cases that primary infection produces
- if R0 > 1 .. disease will persist, if R0 < 1 .. disease will disappear
- is dependent on N – R0 is larger in large populations
- after immunization the equilibrium of infection will decrease
mb
N
R




0
fast biocontrol effect is achieved only with viruses with high 
regulation is possible if pest r << mortality due to disease
low host population is achieved with pathogens with lower 
0
200
400
600
800
1000
1200
1400
1600
1800
1949
1951
1953
1955
1957
1959
1961
1963
1965
mothdensity
0
10
20
30
40
50
60
%infected
moth infected
Population dynamic of a moth and the associated
granulosis virus
Biological control