The future for theory in animal-plant interactions

The talk……

• Conclusion: the future for theory is bright

• Illustrations from– Foraging behaviour– Population ecology

– nothing is so useful as a good theory

Some research goals• Connect population dynamics to foraging

behaviour (via diet selection and intake)• Examine consumer responses to resource

abundance and spatial distribution• Predict impact of herbivores on vegetation

Functional responseAbstract

Ivlev

Reality

) max+1(

max= 1 WDhV

WDVB

Spalinger-Hobbs

0

0.2

0.4

0.6

0.8

1

0 2000 4000 6000

Bite optimisation & diet selectionDaily intakePatch useRange use

1. Foraging behaviour:

max

= 3 :3 Process

max

1= 2 :2 Process

max

1= 1 :1 Process

RShT

DVhT

WDVhT

+

+

+

Spalinger-Hobbs Functional Response

Time taken per bite:

)max+(

max= 3 :3 Process

) max+1(

max= 2 :2 Process

) max+1(

max= 1 :1 Process

hRS

RB

DhV

DVB

WDhV

WDVBHence, bite rate:

0.0

0.2

0.4

0.6

0.8

1.0

02

46

810

200400

600

Bite rate, B (s-1)

Densit

y, D (m

-2 )

Bite mass, S (mg)

Spalinger-Hobbs surface

Bite rate (s-1)

Density (bites m-2)

Spalinger-Hobbs functional response

Bite mass (mg)

How biomass gets depleted

bites get more scarce………

bites get smaller……..

Edible plant biomass (g/m2)0 20 40 60

Inta

ke ra

te (M

J M

E/d)

0

20

40

60

80

100

I

II

III

IV

Mass = 500 kgD = 0.6

Removal of successive itemsreduces bite density; Sconstant (=200 mg)

Sward depletionreduces bite mass S;density constant (=100)

0.0

0.2

0.4

0.6

0.8

Bite mass (mg)0 100 200 300 400 500 600 700

Inta

ke ra

te (m

g/s)

0

20

40

60

80

100

Bite

rate

(s-1

)

0.0

0.2

0.4

0.6

0.8

P Qh

Ac L

Q

F

R

Am

Cr

Ca

Co

Browsing by roe deer

or any model herbivore….

Dai

ly in

take

(MJ

ME)

0

5

10

15

20

Twig diameter (mm)0 2 4 6 8 10

Ener

gy in

take

(m

ult.

of m

aint

.)

0.00

0.25

0.50

0.75

White-tailed deer

Caribou

Moose

1. Bite optimisation

1:1

Number of prey types in diet1 2 3 4 5 6 7 8 9 10

Inta

ke ra

te

0

20

40

60

80

1001 2 3 4 5 6 7 8 9 10

0

20

40

60

80

100a

b

2. Optimal diet

Herbivore

Conventionalforager

3. Patch use

Browsers are probably governed by Process 3

S, bite mass (mg)0 100 200

D, b

ite d

ensi

ty (m

-2)

0

10

20

Process 1

Process 3

Process 2

Time (s)0 20 40 60 80 100

Cum

ulat

ive

gain

(mg)

0

500

1000

1500

2000

2500

3000a b

Linear gain function is predicted for S-H functional response

Conventional forager

Herbivore

II

III

Patch residence time (s)0 50 100 150 200

Cum

ulat

ive

gain

(g)

0

2

4

6

8

10

12

14 PrunusCrataegusQuercus hybridCornusCarpinusFagusA. campestrisQuercusA. monspessulanusRubusLucerne

Roe deer gain functions are virtually linear

Getting from short-term intake rate todaily intake

• Involves crude use of ‘constraints’– grazing time < 10 h– digestive capacity– capacity to use nutrients

• represented as inflexible maxima• seems to work OK………but we need a

better theory

Movement patterns andprediction of localised impacts

• Phenomenological: Matching rules (IDF) +/-suitability factors

• Probabilistic: combines factors such as forage,environmental social etc (HOOFS)

• Mechanistic: Pacman (Derry)

Summary - Foraging behaviourand Intake

• Achievements:– Bite optimisation (inc digestive constraints)– Short-term intake rate

• Progress needed:– Diet selection at botanical scale– Daily intake– Patch use– Modelling movement patterns and space use is

still rudimentary

The ‘New Rangeland ecology’:'Frequent droughts cause mortality of herbivoreswithout having much influence on vegetation,leading to a decoupling of plants and herbivores'

(Galvin & Ellis 1996).

- a new theory of rangeland dynamics

2. population ecology

Accordingly:

'… degradation in non-equilibrial environmentsis limited, as livestock populations rarely reachlevels likely to cause irreversible damage' (Scoones 1994).

Variability• Time - rainfall• Space: heterogeneity in resources

Theory: Livestock populations exploit spatial variation inresource abundance and are dependent on 'key resource'areas during the dry season.

0

500

1000

1500

0 20 40 60 80 1000

250

500

Years

Animals

Vegetation

Constant climate → equilibrium

0

500

1000

1500

0 20 40 60 80 1000

250

500

Variable climate → disequilibriumVegetation

Animals

Rain

Years

What is nonequilibrium?

• Nonequilibrium = anything not at equilibrium(including disequilibrium)

• A metaphor for the complexities of humanexistence under environmental variability

Time

N

Perception of nonequilibrium is a scale-dependent

What is the effect of resource heterogeneityon animal population dynamics?

•relative roles of wet/dry season resources•strength of plant-animal coupling to

different resource types

Method

• Simple animal-plant model to capture themain features:– starvation-induced mortality– state-dependent reproduction– carry-over of body reserves between seasons

• Distinguish wet season range from dryseason range (WSR, DSR)

Wet season range Dry season range

Key resources

100 1000 10000 100000

Log e

(ani

mal

num

bers

)

4

6

8

10

DSR area (ha)

WSRarea =100,000

1000 10000 100000

4

6

8

10

Log e

(ani

mal

num

bers

)

WSR area (ha)

DSRarea =1000

0

1

2

3

4

5

1 10

100 1000

10000 100000

1

10 100

1000 10000

100000

logeN

WSR area (ha)DSR area (ha)

Definition: Key resources are those

related to the keyfactor• Key factor determining livestock population

size is survival over the dry season• Key resources (KR) are those eaten then• Reduction in KR reduces livestock numbers,

and vice versa• Animal population is in long-term equilibrium

with KR

What is nonequilibrium?

• Nonequilibrium is the absence of couplingbetween the animal population’s dynamics andthe subset of resources not associated with keyfactors

• Hence, distinguish KR from nonequilibriumresources (NR)

Key resources

Nonequilibrium resources

Supplementary feed

Diet quality

Abundance

QualityMinimum

(after Hobbs & Swift, 1985)

NR KR

Resource heterogeneity:

Prime resource Secondary resource

DigestibilityLive 0.7 0.7Dead 0.4 0.2

Area (ha) 1000 100000logeN (sd)

1000 5.2 (0.57) 6.6 (0.26)100000 9.5 (0.59) 9.9 (0.57)

Long-term mean animal abundance giventwo resource types (model of Illius & O’Connor 2000)

Conclusions• Herbivores are in long-term equilibrium with KR, and

only weakly coupled to other (=nonequilibrium)resources

• The mix of KR and NR resources is common to allheterogeneous grazing systems, regardless of aridity,climatic variability or management system

• Herbivore impact on NR depends on the relativeabundance of KR, because these limit animal numbers

Theory supporting empiricism