prey dependent responses modelling aquatic rates in natural ecosystems biol471 © 2001 school of...

Prey dependent responses

Modelling Aquatic Rates In Natural Ecosystems BIOL471

© 2001 School of Biological Sciences, University of Liverpool

School of

Biological Sciences

School of

Biological Sciences

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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

Prey-dependent responses

Inge

stio

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Prey 0

Gro

wth

rat

ePrey

0

+

-


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

Ing

esti

on

Prey 0Diatoms (ml-1)


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

Ing

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on

Prey 0

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


Ing

esti

on

Prey 0

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

Let us assume that there are two activities involved in consuming a prey:

1. Searching for the prey2. 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)


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*ThWhere:

Hc prey consumed (H)

Th is the handling time of one prey (TH-1)


This can be expressed as

Hc = a * H * TsearchWherea is the searching rate (L2T-1)H is the prey density (HL-2)and


Tsearch =Hc

aH

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

We can now substitute into

Ttotal = Tsearch + Thandle

Thandle = HcTh


Tsearch =Hc

aH

Ttotal = + HcTh

Hc

aH

We can now rearrange this equation to solve for Hc


T = + HcTh

Hc

aH

T = Hc + HcThaHaH

T = +HcThaH

aH

Hc

aH

T = Hc(1+ThaH)

aH

Hc =1+ThaH

aHT

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)

=1+ThaH

aHHc

T

=1+ThaH

aHC

We can now rearrange this equation to solve for Ha


C=1+ThaH

aH

C =(1+ThaH)

aH1a

1a

C =( +ThH)

H1a

C=( +ThH)

H1a

1Th

1Th

C = ( + H)

H1Th

1aThaTh

If = Cmax1Th

1aThaTh

If = k

C =k+ H

CmaxH

C

H

C =k+ H

CmaxH


Cmax

k

Cmax12

Cmax is the maximum grazing rate

k is the half-saturation constant

The experimental approachWe 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 =k+ H

CmaxH

C

H

+a Th

http://www.aad.gov.au/asset/mme/movies/CiliateFeed.mov


a is the searching rate (L3T-1) Th is the handling time (TH-1)

Bea

ds (

H)

Time (t)

H = Ct


C=Ht

C (H

T-1)

[H ] (HL-3)


C =k+ H

CmaxH

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

Sm

artie

s m

in-1

Smarties density (H L-2)


C =k+ H

CmaxH

The experimental approacha 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

*

prey dependent responses modelling aquatic rates in natural ecosystems biol471 © 2001 school of...

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