Community Ecology

BCB331

Mark J Gibbons, Room 4.102, BCB Department, UWC

Tel: 021 959 2475. Email: mgibbons@uwc.ac.za

Image acknowledgements – http://www.google.com

NICHE Definition

In one dimension

Survival

Growth

Reproduction

Environmental Gradient e.g. Temperature

Per

form

ance

or

Ab

un

dan

ce

Temperature range

over which a variety

of plants can achieve

net PHS at low light

intensity

y (Pisek et al., 1973, In: temperature and Light, Prect et al. (Eds), pp102-194 Springer)

FUNDAMENTAL NICHE

Species B

Environmental Condition or Resource

Definition

Species A

Environmental Condition or Resource

REALISED NICHE Definition

Species B

Species A

Environmental Condition or Resource

Inter-specific Interactions – competition, predation, mutualisms

Competition normally (BUT NOT ALWAYS) occurs between congeneric species

WHY?

Tribolium confusum

T. castaneum

Flour Beetles

Types of Competition

Exploitation - Individuals interact with each other

indirectly through resource exploitation

Bombus appositusBombus flavifrons

Interference - Individuals interact with each other directly

Observations on the outcomes of competitive interactions

Exclusion from particular habitats

Coexistence

Practical – Niche overlap in four co-existing Rhus species

Rhus crenata

Rhus glauca

Rhus laevigata

Rhus lucida

Symmetry and Asymmetric Competition

Balanus died of exposure

Overgrowth of Chthamalus by Balanus

Balanus > Chthamalus

angustifolia > latifolia

Typha angustifolia

Typha latifolia

Dep

th

TogetherGrace and Wetzel (1998) Aquatic Botany 61: 137-146 Alone

Under what circumstances do interactions lead to co-existence or competitive

exclusion?

Competitive Exclusion or Coexistence

Lotka-Volterra Models of inter-specific competition

Cast your mind back to BDC222

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1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

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S-Shaped Growth Curves

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Population Size

Net

Rec

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N - Shaped

K

Nt+1 = Nt. R / {1 + [Nt.(R-1)/K]}

Appropriate for populations displaying discrete breeding

For populations displaying continuous breeding

d N

d t= r.N. (1 – N)

K

Nt+1 - Nt

t1 – t0 = 1

K - N

K

Intrinsic rate of natural increase

Nt+1 = Nt + r.Nt

K - NK

Nt+1 = Nt + r.Nt

K - NK

K - NK

Incorporates intra-specific competition

Replace with something that also incorporates inter-specific competition

Suppose that 4 individuals of species 2 have the same

competitive effect on species 1, as one individual of

species 1

The total competitive effect on species 1 (inter- and

intraspecific) will be (N1 + N2.1/4) individuals of species 1.

The constant (1/4 – in this case) is referred to as the

competition coefficient and is given the symbol α, and it

measures the per capita competitive effect of one species

on another. In this case, α1,2 = per capita effect of species 2

on species 1 = 0.25

Multiplying N2 by α12, converts N2 into the number of N1

equivalents.

α12, > 1 means that an individual of species 2 has more of a

competitive effect on an individual of species 1, than does

species 1 itself: i.e. interspecific competition is stronger

than intraspecific competition

α12, < 1 means that an individual of species 2 has less of a

competitive effect on an individual of species 1, than does

species 1 itself: i.e. intraspecific competition is stronger

than interspecific competition

SO….

N1 = Population size of species 1N2 = Population size of species 2K1 = Carrying capacity of species 1r1 = population growth rate of species 1α1,2 = per capita effect of species 2 on species 1

N1,t+1 = N1,t + r1.N1,t

K1 – N1,t – α12N2,t

K1

Nt+1 = Nt + r.Nt

K - NK

Species 1

N1 = Population size of species 1N2 = Population size of species 2K2 = Carrying capacity of species 2r2 = population growth rate of species 2Α2,1 = per capita effect of species 1 on species 2

N2,t+1 = N2,t + r2.N2,t

K2 – N2,t – α21N1,t

K2

Species 2Likewise

N2,t+1 = N2,t + r2.N2,t

K2 – N2,t – α21N1,t

K2

N1,t+1 = N1,t + r1.N1,t

K1 – N1,t – α12N2,t

K1

These then are the basic Lotka-Voltera equations

Open a spreadsheet in MSExcel

How do different values of r, K, N0 and αxy influence the

outcomes of species interactions?

Set a parameter matrix up as follows: labels in ROW 1, values in ROW 2

Trial No r1 r2 K1 K2 N1,0 N2,0 α1,2 α2,1 Outcome1 1 1 1200 1200 100 100 0.5 0.5

At this stage, make both species equal to each other in all respects

Next – project the two populations into the future for 50 time units (using the previous equations), making reference to the values in the above parameter matrix

Time (t) N1 N20 100 1001 188 1882 331 3313 525 5254 706 7065 789 7896 800 8007 800 8008 800 8009 800 80010 800 80011 800 80012 800 800

Leave blank for the moment

Plot the two populations on a line graph

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N1 N2

It should look something like this: both populations co-exist

This is an unrealistic example. WHY?

In the “Outcome” column of the parameter matrix, enter CoE

– species coexistence

To look at how different values of r, K, N0 and αxy

influence the outcomes of species interactions, you must

change the values in the parameter matrix, and note the

response of the two populations on the graph.

Copy the values of the parameter matrix down, and adjust

the values of the different cells in different trials. Note the

outcomes in each case…

So……..

Suggestions

To start off with, only change 1 value and keep the others

the same

What happens if you adjust more than one value?

Under what conditions do the two populations co-exist?

What role does r play in determining the competitive

outcome?

Under what conditions do N0 or K play an important role in

influencing the outcome of competition?

Trial No r1 r2 K1 K2 N1,0 N2,0 α1,2 α2,1 Outcome1 1 1 1200 1200 100 100 0.5 0.5 CoE2 1 1 1200 1200 100 50 0.5 0.5 CoE3 1 1 1200 1500 100 100 0.5 0.5 CoE4 1 2 1200 1200 100 100 0.5 0.5 CoE5 1 1 1200 1200 100 100 0.75 0.5 CoE6 2 1 1200 1200 100 100 0.75 0.5 CoE7 1 1 1200 1200 100 100 1.5 0.5 CE - 28 2 1 1200 1200 100 100 1.5 0.5 CE - 29 2 1 1200 1200 1000 100 1.5 0.5 CE - 2

10 2 1 1500 1200 1000 100 1.5 0.5 CE - 211 1 2 1200 1200 100 100 1.5 0.5 CE - 212 1 1 1200 1200 100 100 0.5 1.5 CE - 113 1 1 1200 1200 100 100 1.2 1.2 CoE14 1 1 2000 1200 100 100 1.2 1.2 CE - 115 1 1 1200 1200 100 500 1.2 1.2 CE - 216 1 1 1200 3000 100 100 0.5 0.5 CE - 2

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Species 2

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N1

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Species 2

N1

N2

Species 1

Yes – but perhaps better summarised in a different way

If you construct a figure showing all possible outcomes

of N2 on N1 for species 1, for a given r, k and αxy you will

end up with a figure that looks like this

You should have worked out that varying r made no

difference to the eventual outcomes of the competitive

interactions

BUT – varying the other parameters did

Was there a pattern to the results?

The pink line represents

the line along which

there is neither an

increase nor a decrease

in the abundance of

species 1: Zero Net

Growth Isoline (ZNGI)

Species 1 increases in numbers if it occurs to the left of

the ZNGI, but decreases in numbers if it is to the right of

the ZNGI

Species 2

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N1

N2

Species 2

N1

N2

Species 2 Similarly for species 2

In order to draw a ZNGI for species 1, N1,t+1 = N1,t

N1,t+1 = N1,t + r1.N1,t

K1 – N1,t – α12N2,t

K1

Therefore

0 = r1.N1,t

K1 – N1,t – α12N2,t

K1

becomes

N1,t = N1,t + r1.N1,t

K1 – N1,t – α12N2,t

K1

Species 2

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N1

N2

Species 2

N1

N2

Species 1

K1

K1

α12

0 = r1.N1,t

K1 – N1,t – α12N2,t

K1

This is true IF r1 = 0, or IF N1,t = 0BUT….

Also true if 0 = K1 – N1,t – α12N2,t

Rearranging: K1 – α12N2,tN1,t =

This equation is similar to that for a straight line:

Y = C + m X

IF N1,t = 0

α12

Then N2,t = K1

Then N1,t = K1IF N2,t = 0and

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Species 1 Species 2

K1

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K2

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N1

N2

Species 1 Species 2

K1

K1

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K2

K2

α21

Need to fuse the ZNGI for both species and examine the

outcomes of the joint population

Joint population

Lines are vectors – direction of number flow

Individual populations of different species

There are four different ways that the ZNGI can be arranged

– and the outcome of the competitive interaction will be

different in each case

Here K1

K2

α21

> ANDK1

α12

K2>

Intra-specific effects of

species 1, greater than

inter-specific effects of

species 2

Intra-specific effects of

species 2, less than inter-

specific effects of species

1

What is the OUTCOME?

Species 1 out-competes Species 2

TRY IT OUT

Make sure that

α21 is >1

K1 K2 α12> K2 K1α21

<

INTER-

INTRA-

Here K2

K1

α12

>ANDK2

α21

K1>

Intra-specific effects of

species 2, greater than

inter-specific effects of

species 1

Intra-specific effects of

species 1, less than inter-

specific effects of species

2

What is the OUTCOME?

Species 2 out-competes Species 1

TRY IT OUT

Make sure that

α12 is >1

K1 K2 α12<K2 K1α21

>

Here K1

K2

α21

> AND

Inter-specific effects of

species 1, greater than

intra-specific effects of

species 2

Inter-specific effects of

species 2, greater than

intra-specific effects of

species 1

What is the OUTCOME?

Unstable equilibrium – varies with N0

K2

K1

α12

>

A situation whereby

inter-specific

competition is

stronger in both

species than intra-

specific competition

is seen in allepopathy

TRY IT OUT

Make sure that

α12 AND α21 are >1

K1 K2 α12<K2 K1α21

<

Here AND

Intra-specific effects of

species 1, greater than

inter-specific effects of

species 2

Intra-specific effects of

species 2, greater than

inter-specific effects of

species 1

What is the OUTCOME?

Stable coexistence at equilibrium

K2

α21

K1>K1

α12

K2>

TRY IT OUT

Make sure either that

α12 AND α21 are <1

K1 K2 α12> K2 K1α21

>

THE END

Image acknowledgements – http://www.google.com