Controls and additive series

Group exercise:

Read your stream control example, and decide on:

(1) What is wrong with the design?

(2) How you might fix it.

Scenario 1

A B C A B C

Before After

Scenario 2

A B C

D E F

+ pollutant

- pollutant

What is the probability that the 3 “worst” streams are randomly assigned to the pollutant treatment?

3/6 * 2/5 * 1/4 = 2/40 or 5%

Scenario 3

A B C A B CBefore After

D E F D E F

Before After

+ chemical in alkaline solution

control

Scenario 4

A B C A B CBefore After

D E F D E F

Before After

+ pollutant

control

0

5

10

15

20

25

30

35

40

45

control + pollutant

Det

rita

l los

s (m

g / w

eek)

with insectsno insects

Scenario 5

?

Insect abundance =

m1 * width +

m2 * dioxin +

m3 * width*dioxin +

Y-intercept

(and error)

Summary of control types

Which scenarios lacked:

• Control for initial conditions?

• Unmanipulated, contemporaneous control?

• Control for side effect of manipulation?

• Control for covariates?

• Control for non-target response?

BACI design

• Unmanipulated, contemporaneous control

• Initial conditions

Eg. Scenario 3

Before After

Before After

+ pollutant

control

Before After Control Impact

BACI design

• Unmanipulated, contemporaneous control

• Initial conditions

Before After

+ pollutant

control

Before After Control Impact

Study SiteRoadsHiking trail

WaterContour 100m ((10m)

Major Roads

Study Site

Legend

Camp

Sky

line

SICAMOUS

N

EW

S

Kamloops

Sicamous Sicamous

Kamloops

Example of BACI design:Ernest Leupin’s study

on forest fragments and birds

Forest residue

Roads Openings Selection cut

N

C a m p M t . M a r a

H i k i n g

T r a i l

S k y l i n e

0 1 2 K i l o m e t e r s

Sicamous Creek Research Forest

How can we analyze BACI designs?

Randomized block?

What is n?

What is k?

How many independent experimental units in total?

A treatment x date ANOVA?

Before After

Before After

+ pollutant

control

A B C A B C

D E F D E F

How can we analyze BACI designs?

Randomized block?

A treatment x date ANOVA?

Before After

Before After

+ pollutant

control

A B C G H I

What is n?

What is k?

How many independent experimental units in total?D E F J K L

How can we analyze BACI designs?

Two separate ANOVAs / t-tests?

Before After

Before After

+ pollutant

control

Different? Different?

How can we analyze BACI designs?

Two separate ANOVAs / t-tests?

A B Cbefore after before after before after

Y variable

before after

Impact sites

How can we analyze BACI designs?

• Need to have match the number of datapoints with the number of experimental units

• Need to take advantage of built-in control for stream identity

How can we analyze BACI designs?

One solution:

Use difference between before and after as the data!

Before After

Before After

+ pollutant

control

A B C A B C

D E F D E F

Difference

Difference

A B C

D E F

Example: Additive series design for container mosquito larvae

                                                             

                                                             

                                                             

1985

1996

Aedes albopictus invades N America from SE Asia in 1985, via used tire trade at Houston

Breeds in containers habitats (old tires, treeholes), like native species, Aedes aegypti

Aedes albopictus

Ranges overlap, potential for interspecific competition

Experimental design (“Additive series”)

Juliano, S. 1998. Species introduction and replacement amongst mosquitoes: interspecific resource competition or apparent competition? Ecology 79: 255-268.

Aedes aegypti

Aed

es a

lbop

ictu

s

Substitutive or

replacement series

Experimental design (Additive series)

Juliano, S. 1998. Species introduction and replacement amongst mosquitoes: interspecific resource competition or apparent competition? Ecology 79: 255-268.

Aedes aegypti

Aed

es a

lbop

ictu

s

Addition design

Experimental design

Juliano, S. 1998. Species introduction and replacement amongst mosquitoes: interspecific resource competition or apparent competition? Ecology 79: 255-268.

Aedes aegypti

Aed

es a

lbop

ictu

s Can asses Aedes aegypti performance in these treatments

Hypotheses:

Aedes aegypti

Aed

es

alb

op

ictu

s

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

re

spo

nse

Albo has an effect on Aeg, and effect of 1 Albo = 1Aeg

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

re

spo

nse Albo has no effect

on Aeg, so effect of 1 Albo = 0 Aeg

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

re

spo

nse

Albo has an effect on Aeg, but effect of 1 Albo < 1Aeg

Hypotheses:

Aedes aegypti

Aed

es

alb

op

ictu

s

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

re

spo

nse

Albo has an effect on Aeg, and effect of 1 Albo = 1Aeg

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

re

spo

nse Albo has no effect

on Aeg, so effect of 1 Albo = 0 Aeg

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

re

spo

nse

Albo has an effect on Aeg, but effect of 1 Albo < 1Aeg

Results

aeg 20 20 40 60albo 0 40 20 0

Aed

es

aeg

ypti

su

rviv

ors

hip

ANOVA: treatment x food x tire(=block)

Followed by t-tests (posthoc)