Stano Pekár"Populační ekologie živočichů"
dN
= Nr
dt
instead of concentration on profitable patches
perspective predators and prey may play " hide-and-seek"
Huffaker (1958): Typhlodromus fed upon Eotetranychus
that fed upon oranges
- Eotetranychus maintained fluctuating density
- addition of Typhlodromus led to extinction of both
Experimental setup Eotetranychus population dynamic Predator-prey dynamic
making environment patchy
- by placing Vaseline barriers
- facilitating dispersal by adding sticks
each patch was unstable but whole cosmos was stable
- patch with prey only  rapid increase of prey
- patches with predators only  rapid death of predator
- patches with both  predator consumed prey
Sustained oscillations of the predator-prey systemAltered experimental setup
microparasites undergo population growth within host
epidemiology
- predicts rates of disease spread
- predicts expected level of infection
used to simulate spread of a disease (viruses, bacteria) and parasites in
the human population or in the biological control
model suggested by Kermack & McKendrick (1927), later developed
by Anderson & May (1980, 1981)
3-component system: susceptible (S), infected (I) and
recovered/immune (R) individuals
systems may include 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
recovered hosts may have long-life immunity
transmission might be vertical, horizontal or both
Susceptible
S
Infected
I
Recovered
R
death death death
d d+d
 
birth

b
bb
loss of immunity
recoverytransmission
RISN ++= N .. total population of host
RSIdSbN
dt
dS
 +--=
IdSI
dt
dI
)(  ++-=
RdI
dt
dR
)(  +-=
dt
dR
dt
dI
dt
dS
dt
dN
++= IrN
dt
dN
-=
b .. host birth rate
=1/host life-span
d .. host mortality due to other causes
 .. disease-induced mortality
 .. transmission rate
 .. rate of loosing immunity
= 1/disease duration
 .. recovery rate of infected hosts
S.. density-dependent
transmission function
R = dead + resistant individuals
prevalence =1/N
SIR model
where dbr -=
outbreak (epidemics) will occur if i.e. when density is high
- making the population size small will halt the spread
- vaccination of S will stop disease spread if
fast biocontrol effect is achieved
only with viruses with high 
low host population is achieved
with pathogens with lower 


<S


>S
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.
Disease outbreaks
Develop an optimal foraging model for a predator (shrew) that
minimises time for prey capture - it attempts to acquire most food
(worms or beetles) in the shortest time. Find under which conditions his
foraging strategy is optimal if you know that handling time of a worm
is 10 s, handling time of a beetle is 90 s, abundance of worms is 0.005-
0.03 per sec and abundance of beetles is 0.0025-0.06 per sec.
aw .. abundance of worms per second
ab .. abundance of beetles per second
Ts .. searching time
Th .. handling time
p .. probability of being a prey
tw .. handling time of a single worm = 10
ta .. handling time of a single beetle = 90
Shrew moves through a habitat with both worms and beetles. The total
foraging time (T) = searching + handling time
Searching time: the more prey, the shorter time to find it:
The probability that shrew encounters a worm is
Handling time for worms is
and for beetles
The average time to find and capture a prey is
bw
w
w
aa
a
p
+
=
w
bw
w
h t
aa
a
T ×
+
=
bw
s
aa
T
+
=
1
b
bw
b
w
bw
w
bw
t
aa
a
t
aa
a
aa
T ×
+
+×
+
+
+
=
1
b
bw
b
h t
aa
a
T ×
+
=
hs TTT +=
aw<-seq(0.005,0.03,0.001)
ab<-aw
t1<-1/(aw+ab)+10*aw/(aw+ab)+90*ab/(aw+ab)
plot(aw,t1)
ab<-0.5*aw
t2<-1/(aw+ab)+10*aw/(aw+ab)+90*ab/(aw+ab)
lines(aw,t2)
ab<-2*aw
t3<-1/(aw+ab)+10*aw/(aw+ab)+90*ab/(aw+ab)
lines(aw,t3,lty=2)
Three diseases has occurred in a population: measles, cholera and
mononucleosis. You know values of the following parameters:
Use the SIR model with 999 susceptible and 1 infected individual at
the start and determine:
1. Which disease results in epidemics (more than 50% infected)?
2. Will any of the diseases persist in a population?
3. If so what proportion of population will be infected?
4. When the epidemics will reoccur?
Use POPULUS Infectious microparasitic disease model with densitydependent
transmission.
b d alpha beta gamma v
measles 0.01 0.01 0.02 0.01 0.01 0.75
cholera 0.01 0.01 0.03 0.05 0.1 0.8
mononucleosis 0.01 0.01 0.25 0.05 0.01 0.2