1. Modelling Aquatic Rates In Natural Ecosystems BIOL471
Prey dependent responses
School of
Biological Sciences
© 2001 School of Biological Sciences, University of Liverpool

2. Add examples

3. Prey-dependent responses
Solomon (1949) separated consumer response to prey density into 2 types:
Functional the consumption rate of individual consumers with respect to resource density
Numerical the per capita reproductive rate with resource density
Holling (1959) identified 3 types of functional responses
Ingestion
Prey
Growth rate
Prey + -

4. Prey-dependent responses
Type I (linear) response
The attack rate of the individual consumer increases linearly with prey density but then reaches a constant value when the consumer is satiated
Ingestion
Diatoms (ml-1)
Prey

5. Prey-dependent responses
Type II (cyrtoid) functional response
The attack rate increases at a decreasing rate with prey density until it becomes constant at satiation
Cyrtoid responses are typical of predators that specialise on one or a few prey
Ingestion
Prey

6. Prey-dependent responses
Type III (sigmoid) functional response
The attack rate accelerates at first and then decelerates towards satiation
Sigmoid responses are typical of generalists that switch from one prey species to another and/or increase their feeding when resources are abundant
Ingestion
Prey

7. C = aH 1+ThaH Prey-dependent responses The “Disk” Equation
Holling (1959) derived a mechanistic mathematical model for the Type II response from experiments in which blindfolded people acted as predators by searching a table top with their finger tips for sandpaper disk prey
We can derive the disk equation
C =
1+ThaH aH

8. Ttotal = Tsearch + Thandle
Prey-dependent responses
Let us assume that there are two activities involved in consuming a prey:
Searching for the prey
Handling or processing the prey
Then the total time (Ttotal) to capture prey is:
Ttotal = Tsearch + Thandle
But we want to know the prey consumed (Hc) over time Ttotal
Then we can determine a consumption rate C (HT-1)

9. Thandle = Hc*Th Prey-dependent responses
A predator will consume Hc prey in time T
There is a handling time (Th)
Total time handling (Thandle) will be the product of handling time (Th) and the prey consumed (Hc)
Thandle = Hc*Th
Where:
Hc prey consumed (H)
Th is the handling time of one prey (TH-1)

10. Hc = a * H * Tsearch Hc Tsearch = aH Prey-dependent responses
Also a predator will capture a number of prey (Hc) over a searching time (Tsearch) if it has a constant searching rate (a)
But this will depend on how many prey (H) there are
This can be expressed as
Hc = a * H * Tsearch
Where
a is the searching rate (L2T-1)
H is the prey density (HL-2)
and
Tsearch = Hc aH

11. Ttotal = Tsearch + Thandle
Prey-dependent responses
We can now substitute into
Ttotal = Tsearch + Thandle
Thandle = HcTh
Tsearch = Hc aH
Ttotal =
+ HcTh Hc aH

12. = = Prey-dependent responses
We can now rearrange this equation to solve for Hc
T =
+ HcTh Hc aH
Hc = prey captured (H)
a is the searching rate (L2T-1)
H is the prey density (HL-2)
Th is the handling time (TH-1)
T is total time (T) = 1
C is consumption rate (HT-1)
T = +
HcThaH aH Hc
T =
Hc + HcThaH aH =
1+ThaH aH Hc T
T =
Hc(1+ThaH) aH =
1+ThaH aH C
Hc =
1+ThaH
aHT

13. Prey-dependent responses
We can now rearrange this equation to solve for Ha C=
1+ThaH aH
C =
( H) H 1 Th
aTh
C =
(1+ThaH) aH 1 a
If = Cmax 1 Th
aTh
If = k
C =
( +ThH) H 1 a C=
( +ThH) H 1 a Th
C =
k+ H
CmaxH

14. Prey-dependent responses
Cmax
C =
k+ H
CmaxH C k
Cmax 1 2
Cmax is the maximum grazing rate
k is the half-saturation constant H

15. The experimental approach
We run experiments to determine grazing rates
Then we can use these rates in models
We can also use these experiments to determine constants that tell us about the biology of the organisms
The formula we just examined was based on biological mechanisms
It is called a mechanistic equation
Other models that are not based on mechanisms are called phenomenological equations C H
C =
k+ H
CmaxH

16. a is the searching rate (L3T-1) Th is the handling time (TH-1)
Prey-dependent responses + a Th
a is the searching rate (L3T-1) Th is the handling time (TH-1)

17. Prey-dependent responses
H = Ct
Beads (H) C= H t
Time (t)

18. Prey-dependent responses
H = Ct
Beads (H) C= H t
Time (t)

19. Prey-dependent responses
C =
k+ H
CmaxH
C (HT-1)
[H ] (HL-3)

20. The experimental approach
Determine the rate of eating Smarties
Provide various amounts to students
Experiment (consume Smarties)
Plot data
Determine a mechanistic equation
Examine biological parameters

21. Prey-dependent responses
C =
k+ H
CmaxH
Smarties min-1
Smarties density (H L-2)

22. * The experimental approach a the searching rate (L2T-1)
The time it takes to touch your nose and then the desk the area encounter
Th the handling time (TH-1)
This is the time it takes you to eat a Smarties *