Life Table and Predation of Lemnia biplagiata

ABSTRACT The life history and predation rate of Lemnia biplagiata ( Swartz ) fed on Aphis gossypii Glover was studied at 25 # C in the research lab. The natural informations were analyzed based on the age-stage,

two-sex life tabular array to take the variable developmental rate among persons and both sexes into

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consideration. The intrinsic rate of addition ( R ) is 0.1570 vitamin D # 1, the Tnite rate of addition ( # ) is 1.170

d # 1, the net reproduction rate ( R0 ) is 291.1 offspring per person, the average coevals clip ( T )

is 36.2 vitamin D, and the gross reproduction rate ( GRR ) is 604.8 offspring. L. biplagiata consumed 430 # 42

aphids ( average # SD ) during the larval phase. The average ingestion rate for an grownup during the Trst

25 vitamin D ( aged 14D38 vitamin D from birth ) is 1,548 # 118 aphids. The average ingestion for an older grownup ( aged

60D119 vitamin D from birth ) is 1,319 # 1,259 aphids. When the endurance rate is taken into history, the net

ingestion rate is 3,022 aphids per person during the entire life span. The transmutation rate from

prey population to predator progeny is 10.4. The relationship among GRR, R0, and the preadult

endurance rate ( La ) is proven as R0 # la # GRR # GRR. However, when using the female age-speciTc

life tabular array to a two-sex population, due to the difTculty in finding the preadult mortality of the

females, the deliberate age-speciTc endurance rate and fruitfulness are perchance wrong and accordingly

the relationship among GRR, R0, and Las besides may be wrong.

KEY WORDS Life tabular array, predation, Lemnia biplagiata, Aphis gossypii

Lemnia biplagiata ( Swartz ) ( Coleoptera: Coccinellidae )

is a common predatory ladybug in Taiwan and

mainland China ( Yao and Tao 1972 ) . Its quarry includes

cotton aphid, Aphis gossypii ( Glover ) ; green Prunus persica

aphid, Myzus persicae ( Sulzer ) ; and other Homoptera

( Tao 1990 ) . L. biplagiata has been studied as a biological

control agent in India ( Saharia 1980 ) and China

( Deng et al. 1987 ) . In the former USSR, it was imported

from Vietnam for usage in nurseries to command

A. gossypii on Cucumis sativus and M. persicae on Piper nigrums

( Tverdyukov et al. 1993 ) . The population ecology of

L. biplagiata, nevertheless, remains mostly unknown.

Life table surveies are cardinal to population

ecology. A life tabular array gives the most comprehensive

description of the survivorship, development, and reproduction

of a population. The theory and methods

of the life tabular array are discussed in most ecology text editions

( Monetary value 1997, Ricklefs and Miller 1999 ) . The

aggregation of life tabular array informations for related species at different

trophic degrees in a nutrient concatenation is a basic and

of import undertaking for preservation ( Bevill and Louda

1999 ) and pest direction ( Naranjo 2001 ) . Knowledge

of the life tabular array of both marauder and quarry is

necessary for the mass raising and practical application

of a natural enemy to biological control systems

( Chi and Getz 1988, Chi and Yang 2003 ) . However,

most of the traditional female age-speciTc life tabular arraies

( Lewis 1942, Leslie 1945, Birch 1948 ) ignore the male

population and the phase distinction. They can non

take into history the variable predation rate among

phases and the predation rate of the male. To take the

variable developmental rates among persons and

both sexes into consideration, Chi and Liu ( 1985 ) and

Chi ( 1988 ) developed an age-stage life tabular array theory.

Because fluctuation in developmental rate among persons

and between sexes in a natural population is a

normal happening ( e.g. , Fig. 2 of Chi 1988, Fig. 3 of

Liu et Al. 1997, and Fig. 2 of Liu and Stansly 1998 ) , an

age-stage structured theoretical account aids take the fluctuation in

the predation rate and the survival rate of persons

of the same age but different phase into consideration.

By utilizing the age-stage, two-sex life tabular array, Chi and Yang

( 2003 ) described the life tabular array and stage-speciTc predation

rate of the marauder Propylaea japonica Thunberg

( Coleoptera: Coccinellidae ) fed on M. persicae.

In this article, we use the age-stage, two-sex life tabular array

theory to analyse the life history informations and predation

rate of L. biplagiata Federal on A. gossypii to integrate

1 Department of Applied Zoology, Taiwan Agricultural Research

Institute, Wufeng 413, Taichung. Taiwan, Republic of China.

2 Corresponding writer: Lab of Theoretical Ecology, Department

of Entomology, National Chung Hsing University, Taichung

402, Taiwan, Republic of China ( e-mail: hsinchi @ dragon.nchu.

edu.tw ) .

0013-8746/05/0475D0482 $ 04.00/0 # 2005 Entomological Society of America

the variable developmental rates among persons

and the male population. Furthermore, we mathematically

turn out the relationship among gross reproduction

rate, net reproduction rate, and preadult survivorship.

Materials and Methods

Life Table Study. L. biplagiata was originally collected

in the guava grove of Taiwan Agricultural

Research Institute ( Taichung, Taiwan ) in 1996 and

has later been reared on A. gossypii on Cucumis

melo L. in the research lab for 39 coevalss. For

the life tabular array survey, L. biplagiata were kept in a growing

chamber ( 25 # 1 # C, 70 # 10 % RH and a photoperiod

of 12:12 [ L: D ] H ) for one coevals. One hundred

eggs laid by 20 braces of grownups within a 1-d period were

collected in a plastic box ( 7 by 5 by 3 cm3, with a Tne

mesh nylon cyberspace covering for airing ) . The box was

kept in a growing chamber under the same conditions.

Hatched larvae were moved daily to single raising

boxes, and 140D200 A. gossypii of assorted phases kept on

a foliage of C. melo were supplied as nutrient. When grownups

emerged, the females and males were paired, and

# 400 aphids of assorted phases on a foliage of C. melo were

supplied. In the raising box, two pieces of plastic tubings

( # 1.2 centimeter in diameter, 3 centimeter in length, made from

plastic pipette tubings ) were offered for oviposition ;

little petri dishes ( 3 centimeter in diameter ) with moistened

cotton were used for H2O supply. The fruitfulness and

endurance were recorded daily until the decease of each

single.

Depredation Rate Study. To provide L. biplagiata with

A. gossypii of the same age, 30 grownups of A. gossypii were

set on single foliages of C. melo. After 1 vitamin D, grownup

aphids were removed. The newborn aphids were kept

on the foliages for 3 d. Using this technique, 3-d old

aphids were obtained for the predation survey. Before

a foliage was used in the predation survey, the figure of

aphids was recorded. For the survey of the predation

rate by larvae, 30 larvae of L. biplagiata hatched on the

same twenty-four hours, aged 3-d from birth, were moved into single

rise uping boxes, and were given a foliage of C. melo

with 140D200 aphids daily. After 24 H, the lasting

aphids were counted, the predation rates recorded,

and the larvae of L. biplagiata were transferred to new

rise uping boxes with another 140D200 aphids. This continued

until all larvae pupated. When grownups emerged,

the sex of each person was recorded. Because each

larva was kept in an single raising instance during the

larval phases, the day-to-day predation rate could be recorded

for each person. For the survey of the predation

rate by immature grownups, 15 braces of freshly emerged

grownups ( aged 14 vitamin D from birth ) were collected, paired,

and set into single raising boxes. A foliage of C. melo

with 300D400 aphids was supplied daily. The lasting

L. biplagiata were transferred to new rise uping boxes,

and the endurance and predation rates were recorded

daily for the following 25 d. For the predation rate by older

grownups, we collected 15 braces of 46-d-old grownups, aged

60 vitamin D from birth, and paired them in rise uping boxes with

3-d-old aphids. The endurance and predation rates were

recorded until the decease of all persons. Because the

grownups were kept as braces, we ignored the difference

between sexes, and one-half of the day-to-day predation rate

of a brace was assigned to both male and female as long

as both sexes remained alive. If one sex of a brace died,

the day-to-day predation rate was assigned to the lasting

single.

Life Table Analysis. The natural life history informations of all

persons of this survey were pooled and analyzed

harmonizing to the age-stage, two-sex life tabular array ( Chi and

Liu 1985 ) and the method described by Chi ( 1988 ) .

The agencies and standard mistakes of the population parametric quantities

were estimated utilizing the Jackknife method

( Sokal and Rohlf 1981 ) . To ease natural informations analysis,

life table analysis, and the Jackknife method, a userfriendly

computing machine plan, TWOSEX-MSChart ( Chi

2004 ) , was designed in Visual Basic for the Windows

operating system. It is available at hypertext transfer protocol: //140.120.197.

173/Ecology/download/TWOSEX-MSChart.zip ( National

Chung Hsing University, Taiwan ) and hypertext transfer protocol: //

nhsbig.inhs.uiuc.edu/wes/chi.html ( Illinois Natural

History Survey, Urbana, IL ) . The age-stage speciTc

endurance rate ( sxj ) ( where ten is the age and J is the phase ) ,

age-stage speciTc fruitfulness ( fxj ) , age-speciTc endurance

rate ( sixty ) , age-speciTc fruitfulness ( maxwell ) , and population

parametric quantities ( R, intrinsic rate of addition ; # , Tnite rate

of addition ; R0, net reproduction rate ; and T, the mean

coevals clip ) are calculated consequently. The

meangeneration clip is deTned as the clip length that

a population needs to increase to R0-fold of its size

( i.e. , erT R0 or # T R0 ) at the stable age-stage

distribution.Themeangeneration clip is calculated as

T InR0/r.

Consequences and Discussion

Of 100 eggs used at the beginning of the life tabular array

survey, 62 eggs hatched successfully. There are four

instars. The agencies of developmental periods for each

developmental phase, length of services for grownup male and

female, and female fruitfulness of L. biplagiata are given

in Table 1. The entire developmental period for preadult

phases was 14.1 vitamin D, whereas grownups lived every bit long as

105.7 d. A maximum day-to-day fruitfulness of 74 eggs was

observed. For the entire life span, a maximum fruitfulness

of 1,711 eggs has been recorded for a individual female.

The average female fruitfulness of L. biplagiata is 939.1

eggs.

Table 1. Developmental clip, grownup length of service, and fruitfulness of

L. biplagiata at 25 Ninety

Parameter Stage n Mean SEM

Developmental clip ( vitamin D ) Egg 62 3.18 0.08

First instar 60 1.97 0.02

Second instar 55 1.15 0.05

Third instar 55 1.73 0.06

Fourth instar 54 2.09 0.07

Pupa 54 4.02 0.02

Entire preadult 54 14.13 0.13

Adult length of service ( vitamin D ) Adult male 23 105.6 6.50

Adult female 31 105.7 3.54

Fecundity ( F ) ( offspring ) Adult female 31 939.1 67.4

476 ANNALS OF THE ENTOMOLOGICAL SOCIETY OF AMERICA Vol. 98, no. 4

The sxj gives the chance that a neonate will

survive to age ten and phase J ( Fig. 1 ) . There are important

convergences during the developmental period. Under

controlled conditions, both male and female can

survive long periods, and there is no lessening in endurance

rates for either male and female for # 60 500 postemergence.

If the natural informations were analyzed utilizing a traditional

female age-speciTc life tabular array ( Lewis 1942, Leslie 1945,

Birch 1948 ) , it would be impossible to see the

alterations of the phase construction, because traditional life

tabular arraies ignore male persons and the variable developmental

rate among persons ( i.e. , the phase distinction ) .

Manyresearchers have ignored the variable

developmental rate among persons and have

used the rounded agencies of each phase to split the life

span into nonoverlapping phases ( e.g. , Fig. 8.5 of Pianka

1994, 153 ; Table 4D4, 4D5, 6D14, and 6D12 of

Carey 1993 ) . These processs necessarily result in

mistakes in life table parametric quantities. Chi ( 1988 ) gave a

comprehensive treatment on the jobs and mistakes

due to disregarding phase imbrication.

The figure of offspring produced by single L.

biplagiata of age ten and phase J per twenty-four hours is shown with

fxj in Fig. 2. Because lone females reproduce, there is

merely a individual curve fx7 ( i.e. , female is the 7th life

Fig. 1. Age-stage speciTc endurance rate of L. biplagiata at 25 # C.

Fig. 2. Age-speciTc endurance rate ( sixty ) , age-stage speciTc fruitfulness ( fx7 ) of the female phase ( the 7th life phase ) ,

age-speciTc fruitfulness ( maxwell ) , and the age-speciTc pregnancy ( lxmx ) of L. biplagiata at 25 # C.

July 2005 YU ET AL. : LIFE TABLE OF L. biplagiata 477

phase ) . The sixty, maxwell, and age-speciTc pregnancy ( lxmx )

besides are plotted in Fig. 2. It shows that there are

periodic generative extremums about every 20 vitamin D,

and these may be due to cyclicity of the reproductive

physiology. Abou Zied et Al. ( 2003 ) found a periodic

reproduction in the Australian sheep blowsy,

Lucilia cuprina ( Wiedemann ) ( Diptera: Calliphoridae ) .

Many research workers ignore the differences in preadult

development among persons and form fruitfulness

informations based on grownup age ( Fig. 3 of Liu and Stansly

1998, Fig. 1 of Calvitti and Remotti 1998, Fig. 2 of Tsai

1998, Fig. 3 of Riudavets and Castan? vitamin E? 1998, Fig. 1 of

Hansen et Al. 1999, Fig. 4 of Joyce et Al. 1999, Table 3

of Havelka and Zemek 1999, Fig. 1 of Abdel-Salam and

Abdel-Baky 2001, Fig. 2 of Chabi-Olaye et Al. 2001, Fig.

2 of Tsai and Wang 2001, Fig. 4 of Greenberg et Al.

2003, and Stenseng et Al. 2003 ) . For illustration, Liu and

Stansly ( 1998 ) observed a signiTcant fluctuation in the

developmental rate among persons of Bemisia argentifolii

Bellows & A ; Perring ( Homoptera: Aleyrodidae )

( Fig. 2 in their article ) but ignored the variable

developmental rate and organized the survivorship

and fruitfulness based on grownup age ( Fig. 3 in their

article ) . Headrick et Al. ( 1999 ) reported the preimaginal

developmental clip for female Eretmocerus eremicus

Rose & A ; Zolnerowich ( Hymenoptera: Aphelinidae )

assailing B. argentifolii on cotton ranged from 16

to 27 vitamin D ( Table 3 of Headrick et Al. 1999 ) . Their computations

of the day-to-day oviposition, nevertheless, were

based merely on grownup age. Because the Trst reproduction

yearss of single females really vary harmonizing to

the scope of the grownup outgrowth, disregarding the differences

in preimaginal development consequences in mistakes

in the fruitfulness curve, and, finally, in mistakes in the

population parametric quantities. Therefore, if the age-speciTc endurance

rate is constructed based on the agencies of nonoverlapping

phases and the age-speciTc fruitfulness is

constructed based on the grownup phase, the curves will

be different from the sixty and maxwell that are based on the

age counted from the birth of the person. If the life

history natural informations are organized harmonizing to the theoretical account

of Caswell ( 1989, p. 83 ) , it will ensue in the same

job as utilizing grownup age, because CaswellOs theoretical account

classiTes persons by age within phases. Chi ( 1988 )

discussed explicitly the differences between the traditional

female life tabular array and the age-stage, two-sex life

tabular array.

When informations of all 100 persons of L. biplagiata in

this survey are used to cipher the population parametric quantities,

the R is 0.1565 vitamin D # 1, # is 1.1694 vitamin D # 1, R0 is 291.1

progeny, meangeneration clip ( T ) is 36.3 vitamin D, and gross

reproduction rate ( GRR ) is 604.8 offspring. We besides

estimated the agencies and standard mistakes of the population

parametric quantities by utilizing the Jackknife method

( Sokal and Rohlf 1981 ) . The estimated R of L. biplagiata

is 0.1570 # 0.0069 500 # 1 ( average # SEM ) , # is

1.1700 # 0.0080 500 # 1, R0 is 291.1 # 48.3 progeny, T is

36.2 # 1.0 vitamin D, and GRR is 604.8 # 85.3 offspring. There

are minor differences between the consequences estimated

by utilizing the Jackknife method and that calculated by

pooling informations of all persons. Discussion refering

the general application of the Jackknife method can be

found in standard statistics books such as Sokal and

Rohlf ( 1981 ) . Discussion on speciTc applications of

the Jackknife method on population parametric quantities can

be found in Meyer et Al. ( 1986 ) . Perdikis and Lykouressis

( 2002 ) reported R, R0, and T of the predatory

bug Macrolophus pygmaeus Rambur ( Hemiptera: Capsidae )

at 27.5 # C of 0.0981 500 # 1, 49.94, and 46.62, severally.

Harmonizing to life table theory, T ln R0/r.

Because the consequences of Perdikis and Lykouressis ( 2002 )

showed that T # ln R0/r, their informations may be in mistake.

Similar mistakes are found in Morales-Ramos and Cate

( 1992 ) and Urbaneja et Al. ( 2001 ) . As proven by Chi

( 1988 ) for the two-sex life tabular array, the relationship between

R0 and average female fruitfulness, F, is given as

follows:

R0 # F # Nf/N [ 1 ]

whereNis the entire figure of persons used for life

tabular array survey and Nf is the figure of female grownups. In

this survey, the value of N, Nf, F, and R0 for L. biplagiata

is 100, 31, 939.1, and 291.1, severally. Their relationship

is consistent with equation 1. Seal et Al. ( 2002 )

studied the life tabular array of Catolaccus hunteri ( Hymenoptera:

Pteromalidae ) . In their study, GRR was

291.60 and R0 was 216.84 when reared on black-eyed pea

weevil, Callosobruchus maculatus ( F. ) , at 25 # C ( Table

3 of Seal et Al. 2002 ) . In Lee and Ahn ( 2000 ) , GRR and

R0 for Amblyseius womersleyi ( Schicha ) ( Acari: Phytoseiidae )

at 24 # C are 20.42 and 12.48, severally ( Table

8 of Lee and Ahn 2000 ) . For a clear apprehension

on the relationship between GRR and R0, we give the

following cogent evidence. In the female age-speciTc life tabular array,

the gross reproduction rate is deTned as follows:

GRR # #

x 0

#

maxwell [ 2 ]

where # is the last age of the cohort. The net reproduction

rate is deTned as follows:

R0 # #

x 0

#

lxmx [ 3 ]

Before the grownup outgrowth, all maxwell values are zero.

Therefore, if the grownup emerged on age a, so

#

x 0

a # 1

lxmx # 0 [ 4 ]

R0 # #

x a

#

lxmx [ 5 ]

and

GRR # #

x a

#

maxwell [ 6 ]

Because sixty is a drone diminishing sequence of age,

it gives

478 ANNALS OF THE ENTOMOLOGICAL SOCIETY OF AMERICA Vol. 98, no. 4

1 # la # La

1 # La

2 # . . . # fifty # [ 7 ]

Therefore, it follows that

R0 # #

x a

#

lxmx # #

x a

#

mx # GRR [ 8 ]

The utmost instance of R0 GRR exists if and merely if sixties

1 when maxwell # 0. Because sixty lessenings with age and

Tnally diminishes to zero, it is safe to anticipate that

R0 # GRR [ 9 ]

and

#

x a

#

lamx #

x a

#

lxmx # R0 [ 10 ]

Therefore, if la # 1 ( i.e. , there is preadult mortality ) , it gives

R0 # #

x a

#

lxmx # #

x a

#

lamx # La #

x a

#

mx # #

x a

#

mx # GRR

[ 11 ]

Conclusively, the following relationship exists for both

the age-stage, two-sex life tabular array and the female agespeciTc

life tabular array:

R0 # la # GRR # GRR [ 12 ]

However, when using the female age-speciTc life

tabular array to a two-sex population, due to the difTculty in

finding the preadult mortality of the females, the

calculated age-speciTc endurance rate and fruitfulness are

perchance incorrect and accordingly the relationship

among GRR, R0, and Las besides may be wrong. In the

study of Seal et Al. ( 2002 ) , the age-speciTc endurance

rate at grownup outgrowth is signiTcantly # 0.5 at 25 # C,

i.e. , la # 0.5 ( Fig. 1 of Seal et Al. 2002 ) . IfGRR 291.60,

so the following relationship should be:

R0 # la # GRR # 0.5 # 291.60 # 145.8

Therefore, if the GRR is 291.60 as reported in Seal et Al.

( 2002 ) , so R0 must be # 145.8. Their consequences, R0

216.84 and GRR 291.60, are perceptibly inconsistent

with the above-named cogent evidence ( equation 12 ) . In the

study of Lee and Ahn ( 2000 ) , the mortality of the

entire immature phase of A. womersleyi is 60 % at 24 # C

( Table 1 of Lee and Ahn 2000 ) , i.e. , la 1 # 0.6 0.4.

If the GRR 20.42, so it must give

R0 # la # GRR # 0.4 # 20.42 # 8.168

Obviously, R0 must be # 8.168. Therefore, their consequences,

R0 12.48 and GRR 20.42, are seemingly inconsistent

with the above-named cogent evidence ( equation

12 ) . The above-named two illustrations demonstrate

an extra job that may ensue from the application

of the age-speciTc female life tabular array to stagestructured

populations. Detailed treatments on the

jobs are given in Chi ( 1988 ) and Chi and Yang

( 2003 ) . The GRR for L. biplagiata is 604.8. The R0 is

291.1. The La is 0.54. Our consequences are consistent with the

relationship as proven in equation 12. Lemos et Al.

( 2003 ) , who reported the GRR, R0, and survival rate to

maturity for Euborellia annulipes ( Lucas ) ( Dermaptera:

Anisolabididae ) , besides had consequences consistent

with equation 12. In equation 2, GRR is a simple summing up

all maxwell. At the beginning of reproduction, maxwell is

calculated based on the fruitfulness of all lasting females.

However, at older ages, maxwell is by and large calculated

based on the fruitfulness of a few surviving females,

sometimes even a individual female. Therefore, maxwell of the

older ages contribute signiTcantly less to the population.

Because GRR ignores the different weight of maxwell

of different age, it should be interpreted with cautiousness.

However, equation 12 can be surely used as a

standard for double-checking the statistical consequences in

life table surveies.

The age-speciTc predation rate ( kx ) during the larval

phase of L. biplagiata is shown in Fig. 3. The agespeciTc

predation rate is the average figure of aphids

consumed by L. biplagiata of age ten. By taking the

endurance rate into consideration, Chi and Yang ( 2003 )

deTned the age-speciTc net predation rate ( qx ) as the

leaden figure of quarry consumed by marauder of

age ten and it is calculated as follows:

qx # lxkx

The qx besides is plotted in Fig. 3. The consequence shows that

the larval predation rate increased signiTcantly from

age 3 to 8 d. Then, because some larvae entered the

pupal phase, the predation rate decreased on age 9 vitamin D.

During the full larval phases, an person of L.

biplagiata consumed 430 # 42 ( average # SD ) aphids.

The age-speciTc predation rates and age-speciTc cyberspace

predation rate during the Trst 25 vitamin D of the grownup phase

( aged 14 to 38 vitamin D from birth ) are shown in Fig. 4. It

increased signiTcantly with the age for # 15 vitamin D and so

decreased for a few yearss. In comparing with the

fruitfulness curve ( Fig. 2 ) , a similar periodic predation

rate of 20 vitamin D can be observed. The entire mean ingestion

rate during the Trst 25 vitamin D of the grownup phase

is 1,548 # 118 aphids. The age-speciTc predation rates

and age-speciTc net predation rate for older grownups

( aged 60 to 119 vitamin D counted from birth ) are shown in

Fig. 5. For older grownups, the predation rate decreased

with age and no obvious cyclicity of predation rate

is observed. The entire ingestion rate for an older

grownup is 1,319 # 1,259 aphids with a coefTcient of

fluctuation ( CV ) of 95 % . The high CV value is due to the

signiTcant fluctuation in endurance in older grownups. Because

experiments on predation rate are really time-consuming,

we did non roll up informations for the age interval from

39 to 59 d. Alternatively, we calculated the mean of the day-to-day

predation rate for the age intervals from 29 vitamin D to 38 vitamin D

and from 60 vitamin D to 69 vitamin D ( counted from birth ) , and so

we used it as the estimated predation rate for the age

interval from 39 to 59 d. Chi and Yang ( 2003 ) calculated

the net predation rate ( C0 ) as follows:

C0 # #

x 0

#

kxlx

July 2005 YU ET AL. : LIFE TABLE OF L. biplagiata 479

where # is the last age of the population and kx is the

age-speciTc predation rate. In this survey, because the

informations on predation is recorded merely to age 119 vitamin D, we

obtained a net predation rate C0 3,022 for # 119.

Chi and Yang ( 2003 ) showed that the part of

older marauders to the net predation rate is minor.

Because of the low predation rate after age 120 vitamin D, we

ignore the predation rate from age 120 to 152 d. Chi

and Yang ( 2003 ) deTned the transmutation rate from

prey population to predator offspring as follows:

Qp #

C0

R0

.

The Qp for L. biplagiata Federal on A. gossypii is 10.4. This

agencies that L. biplagiata demands 10.4 persons of 3-dold

A. gossypii for the reproduction of one marauder

egg. This Qp gives an demographic appraisal for the

relationship between the reproduction rate and predation

rate of marauder. Sahayaraj and Paulraj ( 2001 )

reported that the predation rate of Rhynocoris marginatus

F. ( Heteroptera: Reduviidae ) on Spodoptera

litura F. ( Lepidoptera: Noctuidae ) larvae increased

with phase. Xia et Al. ( 2003 ) studied the functional

responses of Coccinella septempunctata L. ( Coleoptera:

Coccinellidae ) fed on A. gossypii and found

signiTcant difference in predation rates among marauder

phases. The age-stage variableness of predation of

marauder and that of exposure of quarries have been

observed by many research workers ( Isenhour and Yeargan

1981, Clements and Yeargan 1997, Hu and Frank 1997,

Chi and Yang 2003 ) . All of these facts about stagespeciTc

predation rates could non be taken into ac-

Fig. 3. Age-speciTc predation rate ( kx ) and age-speciTc net predation rate ( qx ) of larva of L. biplagiata at 25 # C ; the age

is counted from birth.

Fig. 4. Age-speciTc predation rate ( kx ) and age-speciTc net predation rate ( qx ) of immature grownup of L. biplagiata at 25 # C ;

the age is counted from birth.

480 ANNALS OF THE ENTOMOLOGICAL SOCIETY OF AMERICA Vol. 98, no. 4

count in simple predation theoretical accounts without age or phase

construction, e.g. , LotkaDVolterra predation theoretical account and its

derived functions. Actually, Hassell ( 1978 ) had pointed out

that the inclusion of the marauder and prey age construction

is an of import measure in understanding predatorD

quarry relationship. Because most carnal species are

age-structured or age-stage-structured, farther accretion

of the cognition of the stage-speciTc predation

rate and stage-structured life tabular array will be necessary

for a proper mold of predatorDprey

kineticss.

Recognitions

We thank Y. H. Yeh for aid with the experiments.

We are thankful to Cecil L. Smith for generous aid in rectifying

our English.Wethank the editor and two anon.

referees for valuable remarks that greatly improved the

manuscript.

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