Stano Pekár“Populační ekologie živočichů“
dN
= Nr
dt
mortality of prey increases with the prey density due to predation
Total response of a predator
- increasing consumption rate of individual predators → functional
response
- increasing density of predators → numerical response
Holling (1959) found that predation rate increased with increasing prey
population density
- defined three types of functional responses
Type I
number of captured prey is proportional to density
- prey mortality is constant
less common
found in passive predators (web-building spiders)
the handling time exerts its effect suddenly
Daphnia feeding on Saccharomyces - above 105 cells
Daphnia is unable to swallow all food
Rigler (1961)
Type II
predators cause maximum mortality at low prey density
as prey density increases, search becomes trivial and handling takes up
increasing portion of the time
saturation of predation at high densities
- prey mortality declines with density
Thompson (1975)
Ischnura eating Daphnia
Type III
when attack rate increases or handling time decreases with increasing
density
predators respond to kairomones
predators develop search image
polyphagous predators switch to the most abundant prey
- prey mortality increases then declines
Notonecta switched from Cleon to Asellus
based on its abundance
Lawton et al. (1974)
T .. total time
TS .. searching time - searching for prey
TH .. handling time - handling prey (chasing, killing, eating, digesting)
H .. prey density
Ha .. number of captured prey
a .. capture efficiency, “area of discovery”, or “search rate”
Type I
consumption rate of a predator is unlimited
TH = 0
Sa aHTH =
HS TTT +=
Type II
consumption rate of a predator is limited because even if no time is
needed for search, predator still needs to spend time on prey handling
TH > 0
predator captures Ha prey during T
Th .. time spent on handling 1 prey
at low density predator spends most
of the time searching, at high
density on prey handling
haH THT =
aH
H
TaHTH a
SSa =→=
aH
H
THTTT a
haSH +=+=
h
a
aHT
aHT
H
+
=
1
n
h
n
a
HaT
aTH
H
+
=
1
Type III
consumption increases at low densities and decreases at higher
densities
n .. rate of increased consumption at higher densities
if n = 1 → Type II
a .. rate of increase at low densities
H
Ha
T/Th
a
0
n
Increase of predator population may result from:
increased rate of reproduction
- the more prey is consumed the more energy can predator allocate to
reproduction
- delayed response
parasitoids - one host is sufficient
predators, herbivores, parasites
- certain quantity of prey tissue is required
for basic maintenance = lower threshold
Growth rate in Linyphia
Turnbull (1962)
conversion of prey into predators
c .. conversion efficiency
d .. mortality of predators
Ivlev (1955) model
V .. amount of prey
c .. conversion efficiency
a .. mortality of predators H
rp
0
aecr dV
−−= −
)1(
dPcaHPr −=
attraction of predators to prey aggregations
- immediate response
- aggregated distribution makes search of predators more profitable
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
Total refuge
For fixed proportion of prey - certain proportion
of Ephestia caterpillars buried deep enough in flour
are not attacked by Venturia with short ovipositors
For fixed number of prey
- adult Balanus occur in the upper zone
where Thais can not get during short high
tide thus consumes only juveniles
- a fixed number of Balanus is protected
from predation irrespective of Thais density
both refuges stabilise the interaction
Connell (1970)
Carabids are kept in dishes (10 cm2) individually, with a different number
of seeds (H). The seeds are kept at constant density. After 6 hours (T)
consumed seeds were counted.
1. What type of functional response carabids have?
2. Estimate search efficiency (a) [cm2/h] and handling time (Th) [h].
h
a
aHT
aHT
H
+
=
1 T
T
HTaH
h
a
+=
111
TTh α=
β
1
=a
xy βα +=
H Ha
1 2.5
5 6.1
10 7.9
20 10.5
40 12.3
50 11.8
H<-c(1,5,10,20,40,50)
Ha<-c(2.5,6.1,7.9,10.5,12.3,11.8)
plot(H,Ha)
y<-1/Ha
x<-1/(H*6)
plot(x,y)
m1<-lm(y~x)
abline(m1)
coef(m1)
1/1.91424538
0.08445655*6
Grasshoppers were reared individually from egg to adulthood and the
amount of food consumed (V) was determined. The fecundity was
observed for each. From these data the intrinsic rate of increase ® was
estimated.
1. Find relationship between r and V.
2. Estimate parameters of Ivlev model and the minimal amount of
prey needed for reproduction.
množství r
0.5 –1.0
1 –0.6
2 –0.1
5 0.3
10 0.5
20 0.7
40 1
v<-c(0.5,1,2,5,10,20,50)
r<-c(-1,-0.6,-0.1,0.3,0.5,0.7,1)
plot(v,r)
m1<-nls(r~c*(1-exp(-d*v))-a,start=list(a=1,c=2,d=1))
summary(m1)
x<-seq(0,50,1)
lines(x,predict(m1,list(v=x)))
library(rootSolve)
null<-uniroot(function(x) 1.9*(1-exp(-0.3*x))-
1.2,lower=0,upper=10);null