0851996884.pdf

Working example

A short-distance flight test was conducted

for Encarsia formosa(J.C. van Lenteren and

co-workers, unpublished data). The flight

ability was compared between parasitoids

emerging from old or new pupae, and the

data obtained were as in Table 20.2.

So the tvalue is:

which is greater than 1.96. Thus, the flight

ability of E. formosa significantly differs

between parasitoids emerging from old and

new pupae.

Studying the Relationship Between a

Regular Quantitative Trait and a

Percentage

Sometimes, both a quantitative trait and a

percentage are estimated simultaneously

with data from one sample. In this situation,

since the quantitative trait is measured on all

individuals separately but these individuals

are used all together to estimate the percent-

age, a real correlation cannot be estimated

between the two traits. What can be done

instead is to compare the two average values

of the quantitative trait computed after split-

ting the sample according to the binomial

trait expressed as a percentage. For example,

suppose that both the sex of adults and their

longevity are quantified. The comparison

can be done by comparing the males’ and

females’ average longevity. In order to do

this, the whole sample must first be split

according to the two categories from which

the binomial trait is studied. Then the two

subsamples obtained are described for the

quantitative trait measured with standard

descriptive parameters (i.e. n, x–, σx) and a

graph can be produced showing the distribu-

tion summaries of the two subsamples.

Finally, the tvalue is computed:

where n 1 , x– 1 , σ 12 are the descriptive parame-

ters of the first subsample, and n 2 , x– 2 , σ 22 are

those of the second subsample. If the

obtained value is greater than 1.96, there is a

significant difference between the average

values of the quantitative trait between the

two subsamples, at a probability level of 5%.

This test is valid only if the sizes of the two

subsamples (n 1 and n 2 ) are both greater than

or equal to 30.

Working example: is there a difference in

adult longevity between males and females in

Trichogramma?

Both the sex ratio and adult longevity were

quantified for T. brassicae. Thirty females and

30 males were measured. For all of them, the

number of days that adults remained alive

was quantified. The data obtained were:

t

xx

nn

=

−

+

12

12

1

22

2

σσ

t =

××−×()

×××

=

145 30 23 53 39

83 62 69 76

3 192

2

.

312 E. Wajnberg

Sex ratio

Females

Adult mortality

Dead

Alive

b

d

Males

a

cc + d

a+ b

a+ c b+ d a+ b + c + d

Fig. 20.5.Contingency table for relationship

between sex ratio and adult mortality.

Table 20.2.Results of short-distance flight test.

Flight No flight Total

Old pupae 30 39 69

New pupae 53 23 76

Total 83 62 145

Longevity of females in days:

1615 9 271915201912 7 1716162426

17 16 15 10 2 10 14 15 9 19 18 21 23 17 11