Stano Pekár“Populační ekologie živočichů“
dN
= Nr
dt
True predators - consume several animals and gain sustenance for
their own fitness (spiders, lions)
Parasitoids - free adults but larvae developing on or within a host,
consuming it prior to pupation, consume about single host
(Hymenoptera, Diptera)
Parasites - live in close association with a host, gain sustenance
from the host, but often do not cause mortality (Acari, Trematodes)
Herbivores - feed on plants, may totally consume plants (seedeaters)
or partially (aphids, cows)
monophagous (single prey type)
oligophagous (few prey types)
polyphagous/euryphagous (many prey
types)
- not capable of consuming all prey types
predators choose most profitable prey
- select prey items for which the gain is
greatest (energy intake per time spent
handling)
Krebs (1978)
predators tend to specialise to a greater or lesser extent during evolution
- monophagy evolved where prey exerts pressures which demand
morphological adaptations
- polyphagy evolved where prey was unpredictable
true predators - majority are polyphagous
parasites - commonly monophagous due to intimate association with
hosts, their life-cycle is tuned to that of their host
parasitoids - often monophagous but some are polyphagous presumably
because adults are free living
herbivores - rather polyphagous, many insect herbivores
are specialised as a result of adaptation to plant
secondary metabolites (Drosophila pachea consumes
rotten tissues of Senita cactus which contain poisonous
alkaloids)
even polyphagous predators prefer certain prey
- constant preference irrespective of prey density
- switching to more common prey
Thais preferred Mytilus edulis over M.
californianus
Murdoch & Oaten (1975)
Murton et al. (1964)
Seasonal shift in Columba
switching
- on individual level: certain individuals develop „searching image“ that
facilitate the search for prey
- on population level: proportion of specialists is changing their preference
Effect of experience on the foraging success of
Notonecta in the capture of Asellus
Lawton et al. (1974)
predation has positive effect on population of prey because reduce
intraspecific competition - stabilise prey population dynamic
true predators and parasitoids reduce fitness of prey to „0“
- Mustela consumed mainly solitary and injured individuals, so it has
little effect on the Ondatra population growth
caterpillars defoliate partially so
that re-growth can occur, but cause
reduction in fertility
parasites - reduce fitness partially,
effect is correlated with the burden
Negative effect of mite
parasites on Hydrometra
Lanciani (1975)
consume small amount of many different plant species
consume a lot during life
functional response Type II and III
plants are not killed only reduced in biomass
similar to predator-prey models
V .. plant biomass
a .. assimilation rate
F .. efficiency of removal
hFNT
FNV
K
VK
rV
t
V
+
−




 −
=
1d
d
mN
FNT
aFNV
t
N
h
−
+
=
1d
d
Model
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 until time
prevalence .. proportion of population
infected =1/N
swine flu virus
cercaria
nematode
E. coli (EHEC)
predicts rates of disease spread
predicts expected level of infection
number of deaths caused by disease exceeds of all wars
affect 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
iregular 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 in the human
population or in the biological control
models:
- Kermack & McKendrick (1927)
- later developed by Anderson & May (1980, 1981)
3 components:
- S .. susceptible
- I .. infected
- R .. resistant/recovered and immune + dead individuals - can not
transmit disease
- latent population - 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
β .. transmission rate - number of new infections per untit time
βSI.. density-dependent transmission function (proportional to the
number of contacts)
- mass action
- analogous to search efficiency in predator-prey model
1/β .. average time for encountering infected individual
γ.. recovery rate of infected hosts
(either die or become immune)
γ = 1/duration of disease
S0 >> I0
- ignores population change (increase of S)
SI
t
S
β−=
d
d
ISI
t
I
γβ −=
d
d
SI model
outbreak (epidemics) will occur if
- i.e. when density of S is high
making the population size small will halt the spread:
vaccination of S, culling or isolation of I will stop disease spread
β
γ
<S
β
γ
>S
Outbreaks
host population is dynamic
b .. host birth rate
=1/host life-span, given exponential growth and constant population size
- newborns are susceptible
m .. host mortality due to other causes
Susceptible
S
Infected
I
Resistant
R
death death death
m mm
β γ
birth
b
bb
recoverytransmission
mSSIRISb
t
S
−−++= β)(
d
d
mIISI
t
I
−−= γβ
d
d
mRI
t
R
−= γ
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 .. outbreak is plausible
mb
N
R
++
=
γ
β
0
fast biocontrol effect is achieved only with viruses with high β
low host population is achieved with pathogens with lower β
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
Rabies has occurred in two cities. In one city 75% of dogs were
vaccinated, in the other only 5%. In both cities there are 20 dogs/km2.
It is known that rabies lasts for 5 days (d). The dog lifespan (l) is
10 years. One dog per 10 days (T) becomes infected. Density of
dogs is constant, thus mortality (m) is equal to natality (b).
1. Estimate parameter (b, m, β, γ) values from given data.
2. Use SIR model for each city for next 60 days.
3. Will there be epidemics (more than 50% infected)?
4. How the disease dynamic will be affected by dog isolation?
T
1
=β d
1
=γ
m = b = 0
sir<-function(t,y,param){
S<-y[1]
I<-y[2]
R<-y[3]
with(as.list(param),{
dS.dt<-b*(S+I+R)-B*I*S-m*S
dI.dt<-B*I*S-g*I-m*I
dR.dt<-g*I-m*R
return(list(c(dS.dt,dI.dt,dR.dt)))})}
g<-1/5
b<-0
B<-1/10
m<-b
N<-20;I<-1;R<-1;S<-N-I-R
time<-seq(0,60,0.1)
pa<-c(b=b,B=B,m=m,g=g)
library(deSolve)
out<-data.frame(ode(c(S,I,R),time,sir,pa,hmax=0.01))
matplot(time,out[,-1],type="l",lty=1:3,col=1)
legend("right",c("S","I","R"),lty=1:3)
N<-20;I<-1;R<-15;S<-N-I-R
time<-seq(0,60,0.1)
pa<-c(b=b,B=B,m=m,g=g)
library(deSolve)
out<-data.frame(ode(c(S,I,R),time,sir,pa,hmax=0.01))
matplot(time,out[,-1],type="l",lty=1:3,col=1)
legend("right",c("S","I","R"),lty=1:3)
N<-20;I<-1;R<-1;S<-N-I-R
time<-seq(0,60,0.1)
pa<-c(b=b,B=1/365,m=m,g=g)
library(deSolve)
out<-data.frame(ode(c(S,I,R),time,sir,pa,hmax=0.01))
matplot(time,out[,-1],type="l",lty=1:3,col=1)
legend("right",c("S","I","R"),lty=1:3)
L S
N
-
+
-
+
-
+
Construct an intraguild model composed of two predators (L, S).
Both feed on prey (N), the larger predator (L) also feeds on the
smaller one (S). Use Lotka-Volterra predation model with
functional response of Type I with capture efficiency (a),
conversion rate (b), r = 1.5 and K = 1000.
1. Find parameter estimates producing stable dynamic.
LmLSbaLNba
t
L
LSSNN −+= 11
d
d
SmLSaSNba
t
S
SSNN −−= 22
d
d
SNaLNa
K
N
Nr
t
N
NN 211
d
d
−−





−=
Parameter estimates should meet the following conditions:
- L is by half less effective in prey capture of N than of S (aN1 = 0.02)
- S is twice more effective in prey capture of N than L
- N is by half less nutritious for L than for S (bN1 = 0.03)
- S is twice more nutritious for L than N is
- mortality of L and S is identical (mS = mL = 0.1)
- density of N is twice higher than that of S and that is twice higher
than of L (L0 = 20)
igp<-function(t,y,param){
L<-y[1]
S<-y[2]
N<-y[3]
with(as.list(param),{
dL.dt<-an1*bn1*L*N+as*bs*L*S-ml*L
dS.dt<-an2*bn2*S*N-as*L*S-ms*S
dN.dt<-r*N*(1-N/K)-an1*L*N-an2*S*N
return(list(c(dL.dt,dS.dt,dN.dt)))})}
L<-20;S<-40;N<-80
param<-c(an1=0.02,bn1=0.03,as=0.01,bs=0.06,ml=0.1,
an2=0.04,bn2=0.06,ms=0.1,r=1.5,K=1000)
time<-seq(0,30,0.1)
library(deSolve)
out<-data.frame(ode(c(L,S,N),time,igp,param))
matplot(time,out[,-1],type="l",lty=1:3,col=1)
legend("right",c("L","S","N"),lty=1:3)