# Life Table and Predation of Lemnia biplagiata

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

two-sex life table to take the variable developmental rate among individuals and both sexes into

consideration. The intrinsic rate of increase (r) is 0.1570 d#1, the Tnite rate of increase (#) is 1.170

d#1, the net reproduction rate (R0) is 291.1 offspring per individual, the mean generation time (T)

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

aphids (mean # SD) during the larval stage. The mean consumption rate for an adult during the Trst

25 d (aged 14D38 d from birth) is 1,548#118 aphids. The mean consumption for an older adult (aged

60D119 d from birth) is 1,319 # 1,259 aphids. When the survival rate is taken into account, the net

consumption rate is 3,022 aphids per individual during the total life span. The transformation rate from

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

survival rate (la) is proven as R0 # la # GRR # GRR. However, when applying the female age-speciTc

life table to a two-sex population, due to the difTculty in determining the preadult mortality of the

females, the calculated age-speciTc survival rate and fecundity are possibly incorrect and consequently

the relationship among GRR, R0, and la also may be incorrect.

KEY WORDS Life table, predation, Lemnia biplagiata, Aphis gossypii

Lemnia biplagiata (Swartz) (Coleoptera: Coccinellidae)

is a common predatory ladybird in Taiwan and

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

cotton aphid, Aphis gossypii (Glover); green peach

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 use in greenhouses to control

A. gossypii on cucumber and M. persicae on peppers

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

L. biplagiata, however, remains largely unknown.

Life table studies are fundamental to population

ecology. A life table gives the most comprehensive

description of the survivorship, development, and reproduction

of a population. The theory and methods

of the life table are discussed in most ecology textbooks

(Price 1997, Ricklefs and Miller 1999). The

collection of life table data for related species at different

trophic levels in a food chain is a basic and

important task for conservation (Bevill and Louda

1999) and pest management (Naranjo 2001). Knowledge

of the life table of both predator and prey is

necessary for the mass rearing 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 tables

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

population and the stage differentiation. They cannot

take into account the variable predation rate among

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

variable developmental rates among individuals and

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

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

Because variation in developmental rate among individuals

and between sexes in a natural population is a

normal occurrence (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 model helps take the variation in

the predation rate and the survival rate of individuals

of the same age but different stage into consideration.

By using the age-stage, two-sex life table, Chi and Yang

(2003) described the life table and stage-speciTc predation

rate of the predator Propylaea japonica Thunberg

(Coleoptera: Coccinellidae) fed on M. persicae.

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

theory to analyze the life history data and predation

rate of L. biplagiata fed on A. gossypii to incorporate

1 Department of Applied Zoology, Taiwan Agricultural Research

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

2 Corresponding author: Laboratory 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 individuals

and the male population. Furthermore, we mathematically

prove 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 orchard of Taiwan Agricultural

Research Institute (Taichung, Taiwan) in 1996 and

has subsequently been reared on A. gossypii on Cucumis

melo L. in the laboratory for 39 generations. For

the life table study, L. biplagiata were kept in a growth

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

of 12:12 [L:D] h) for one generation. One hundred

eggs laid by 20 pairs of adults within a 1-d period were

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

mesh nylon net covering for ventilation). The box was

kept in a growth chamber under the same conditions.

Hatched larvae were moved daily to individual rearing

boxes, and 140D200 A. gossypii of mixed stages kept on

a leaf of C. melo were supplied as food. When adults

emerged, the females and males were paired, and

#400 aphids of mixed stages on a leaf of C. melo were

supplied. In the rearing box, two pieces of plastic tubes

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

plastic pipette tubes) were offered for oviposition;

small petri dishes (3 cm in diameter) with moistened

cotton were used for water supply. The fecundity and

survival were recorded daily until the death of each

individual.

Predation Rate Study. To supply L. biplagiata with

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

set on individual leaves of C. melo. After 1 d, adult

aphids were removed. The newborn aphids were kept

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

aphids were obtained for the predation study. Before

a leaf was used in the predation study, the number of

aphids was recorded. For the study of the predation

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

same day, aged 3-d from birth, were moved into individual

rearing boxes, and were given a leaf of C. melo

with 140D200 aphids daily. After 24 h, the surviving

aphids were counted, the predation rates recorded,

and the larvae of L. biplagiata were transferred to new

rearing boxes with another 140D200 aphids. This continued

until all larvae pupated. When adults emerged,

the sex of each individual was recorded. Because each

larva was kept in an individual rearing case during the

larval stages, the daily predation rate could be recorded

for each individual. For the study of the predation

rate by young adults, 15 pairs of newly emerged

adults (aged 14 d from birth) were collected, paired,

and put into individual rearing boxes. A leaf of C. melo

with 300D400 aphids was supplied daily. The surviving

L. biplagiata were transferred to new rearing boxes,

and the survival and predation rates were recorded

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

adults, we collected 15 pairs of 46-d-old adults, aged

60 d from birth, and paired them in rearing boxes with

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

recorded until the death of all individuals. Because the

adults were kept as pairs, we ignored the difference

between sexes, and one-half of the daily predation rate

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

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

the daily predation rate was assigned to the surviving

individual.

Life Table Analysis. The raw life history data of all

individuals of this study were pooled and analyzed

according to the age-stage, two-sex life table (Chi and

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

The means and standard errors of the population parameters

were estimated using the Jackknife method

(Sokal and Rohlf 1981). To facilitate raw data analysis,

life table analysis, and the Jackknife method, a userfriendly

computer program, TWOSEX-MSChart (Chi

2004), was designed in Visual Basic for the Windows

operating system. It is available at http://140.120.197.

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

Chung Hsing University, Taiwan) and http://

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

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

survival rate (sxj) (where x is the age and j is the stage),

age-stage speciTc fecundity (fxj), age-speciTc survival

rate (lx), age-speciTc fecundity (mx), and population

parameters (r, intrinsic rate of increase; #, Tnite rate

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

generation time) are calculated accordingly. The

meangeneration time is deTned as the time 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 time is calculated as

T InR0/r.

Results and Discussion

Of 100 eggs used at the beginning of the life table

study, 62 eggs hatched successfully. There are four

instars. The means of developmental periods for each

developmental stage, longevities for adult male and

female, and female fecundity of L. biplagiata are given

in Table 1. The total developmental period for preadult

stages was 14.1 d, whereas adults lived as long as

105.7 d. A maximal daily fecundity of 74 eggs was

observed. For the total life span, a maximal fecundity

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

The mean female fecundity of L. biplagiata is 939.1

eggs.

Table 1. Developmental time, adult longevity, and fecundity of

L. biplagiata at 25 XC

Parameter Stage n Mean SEM

Developmental time (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

Total preadult 54 14.13 0.13

Adult longevity (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 probability that a newborn will

survive to age x and stage j (Fig. 1). There are significant

overlaps during the developmental period. Under

controlled conditions, both male and female can

survive long periods, and there is no decrease in survival

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

If the raw data were analyzed using a traditional

female age-speciTc life table (Lewis 1942, Leslie 1945,

Birch 1948), it would be impossible to view the

changes of the stage structure, because traditional life

tables ignore male individuals and the variable developmental

rate among individuals (i.e., the stage differentiation).

Manyresearchers have ignored the variable

developmental rate among individuals and have

used the rounded means of each stage to divide the life

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

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

Carey 1993). These procedures inevitably result in

errors in life table parameters. Chi (1988) gave a

comprehensive discussion on the problems and errors

due to ignoring stage overlapping.

The number of offspring produced by individual L.

biplagiata of age x and stage j per day is shown with

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

only a single curve fx7 (i.e., female is the seventh life

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

Fig. 2. Age-speciTc survival rate (lx), age-stage speciTc fecundity (fx7) of the female stage (the seventh life stage),

age-speciTc fecundity (mx), and the age-speciTc maternity (lxmx) of L. biplagiata at 25#C.

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

stage). The lx, mx, and age-speciTc maternity (lxmx)

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

periodic reproductive peaks approximately every 20 d,

and these may be due to periodicity of the reproductive

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

reproduction in the Australian sheep blowsy,

Lucilia cuprina (Wiedemann) (Diptera: Calliphoridae).

Many researchers ignore the differences in preadult

development among individuals and organize fecundity

data based on adult 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? 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 example, Liu and

Stansly (1998) observed a signiTcant variation in the

developmental rate among individuals of Bemisia argentifolii

Bellows & Perring (Homoptera: Aleyrodidae)

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

developmental rate and organized the survivorship

and fecundity based on adult age (Fig. 3 in their

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

developmental time for female Eretmocerus eremicus

Rose & Zolnerowich (Hymenoptera: Aphelinidae)

attacking B. argentifolii on cotton ranged from 16

to 27 d (Table 3 of Headrick et al. 1999). Their calculations

of the daily oviposition, however, were

based only on adult age. Because the Trst reproduction

days of individual females actually vary according to

the range of the adult emergence, ignoring the differences

in preimaginal development results in errors

in the fecundity curve, and, eventually, in errors in the

population parameters. Thus, if the age-speciTc survival

rate is constructed based on the means of nonoverlapping

stages and the age-speciTc fecundity is

constructed based on the adult stage, the curves will

be different from the lx and mx that are based on the

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

history raw data are organized according to the model

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

problem as using adult age, because CaswellOs model

classiTes individuals by age within stages. Chi (1988)

discussed explicitly the differences between the traditional

female life table and the age-stage, two-sex life

table.

When data of all 100 individuals of L. biplagiata in

this study are used to calculate the population parameters,

the r is 0.1565 d#1, # is 1.1694 d#1, R0 is 291.1

offspring,meangeneration time (T) is 36.3 d, and gross

reproduction rate (GRR) is 604.8 offspring. We also

estimated the means and standard errors of the population

parameters by using the Jackknife method

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

is 0.1570 # 0.0069 d#1 (mean # SEM), # is

1.1700 # 0.0080 d#1, R0 is 291.1 # 48.3 offspring, T is

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

are minor differences between the results estimated

by using the Jackknife method and that calculated by

pooling data of all individuals. Discussion concerning

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 parameters 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: Miridae)

at 27.5#C of 0.0981 d#1, 49.94, and 46.62, respectively.

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

Because the results of Perdikis and Lykouressis (2002)

showed that T # ln R0/r, their data may be in error.

Similar errors are found in Morales-Ramos and Cate

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

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

R0 and mean female fecundity, F, is given as

follows:

R0 # F # Nf/N [1]

whereNis the total number of individuals used for life

table study and Nf is the number of female adults. In

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

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

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

studied the life table of Catolaccus hunteri (Hymenoptera:

Pteromalidae). In their report, GRR was

291.60 and R0 was 216.84 when reared on cowpea

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, respectively (Table

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

on the relationship between GRR and R0, we give the

following proof. In the female age-speciTc life table,

the gross reproduction rate is deTned as follows:

GRR # #

x 0

## #

mx [2]

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

rate is deTned as follows:

R0 # #

x 0

## #

lxmx [3]

Before the adult emergence, all mx values are zero.

Thus, if the adult emerged on age a, then

## #

x 0

a#1

lxmx # 0 [4]

R0 # #

x a

## #

lxmx [5]

and

GRR # #

x a

## #

mx [6]

Because lx is a monotone decreasing sequence of age,

it gives

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

1 # la # la

1 # la

2 # . . . # l# [7]

Therefore, it follows that

R0 # #

x a

## #

lxmx # #

x a

## #

mx # GRR [8]

The extreme case of R0 GRR exists if and only if lx

1 when mx # 0. Because lx decreases with age and

Tnally diminishes to zero, it is safe to expect that

R0 # GRR [9]

and

## #

x a

## #

lamx #

x a

## #

lxmx # R0 [10]

Thus, 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 table and the female agespeciTc

life table:

R0 # la # GRR # GRR [12]

However, when applying the female age-speciTc life

table to a two-sex population, due to the difTculty in

determining the preadult mortality of the females, the

calculated age-speciTc survival rate and fecundity are

possibly incorrect and consequently the relationship

among GRR, R0, and la also may be incorrect. In the

report of Seal et al. (2002), the age-speciTc survival

rate at adult emergence is signiTcantly #0.5 at 25#C,

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

then the following relationship should exist:

R0 # la # GRR # 0.5 # 291.60 # 145.8

Thus, if the GRR is 291.60 as reported in Seal et al.

(2002), then R0 must be #145.8. Their results, R0

216.84 and GRR 291.60, are noticeably inconsistent

with the above-mentioned proof (equation 12). In the

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

total immature stage 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, then it must give

R0 # la # GRR # 0.4 # 20.42 # 8.168

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

R0 12.48 and GRR 20.42, are apparently inconsistent

with the above-mentioned proof (equation

12). The above-mentioned two examples demonstrate

an additional problem that may result from the application

of the age-speciTc female life table to stagestructured

populations. Detailed discussions on the

problems 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 results are consistent with the

relationship as proven in equation 12. Lemos et al.

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

adulthood for Euborellia annulipes (Lucas) (Dermaptera:

Anisolabididae), also had results consistent

with equation 12. In equation 2, GRR is a simple summation

all mx. At the beginning of reproduction, mx is

calculated based on the fecundity of all surviving females.

However, at older ages, mx is generally calculated

based on the fecundity of a few surviving females,

sometimes even a single female. Thus,mx of the

older ages contribute signiTcantly less to the population.

Because GRR ignores the different weight of mx

of different age, it should be interpreted with caution.

Nevertheless, equation 12 can be certainly used as a

criterion for double-checking the statistical results in

life table studies.

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

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

predation rate is the mean number of aphids

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

survival rate into consideration, Chi and Yang (2003)

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

weighted number of prey consumed by predator of

age x and it is calculated as follows:

qx # lxkx

The qx also is plotted in Fig. 3. The result shows that

the larval predation rate increased signiTcantly from

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

pupal stage, the predation rate decreased on age 9 d.

During the entire larval stages, an individual of L.

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

The age-speciTc predation rates and age-speciTc net

predation rate during the Trst 25 d of the adult stage

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

increased signiTcantly with the age for#15 d and then

decreased for a few days. In comparison with the

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

rate of 20 d can be observed. The total average consumption

rate during the Trst 25 d of the adult stage

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

and age-speciTc net predation rate for older adults

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

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

with age and no obvious periodicity of predation rate

is observed. The total consumption rate for an older

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

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

signiTcant variation in survival in older adults. Because

experiments on predation rate are very time-consuming,

we did not collect data for the age interval from

39 to 59 d. Instead, we calculated the mean of the daily

predation rate for the age intervals from 29 d to 38 d

and from 60 d to 69 d (counted from birth), and then

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 study, because the

data on predation is recorded only to age 119 d, we

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

Chi and Yang (2003) showed that the contribution of

older predators to the net predation rate is minor.

Because of the low predation rate after age 120 d, we

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

and Yang (2003) deTned the transformation rate from

prey population to predator offspring as follows:

Qp #

C0

R0

## .

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

means that L. biplagiata needs 10.4 individuals of 3-dold

A. gossypii for the reproduction of one predator

egg. This Qp gives an demographic estimation for the

relationship between the reproduction rate and predation

rate of predator. Sahayaraj and Paulraj (2001)

reported that the predation rate of Rhynocoris marginatus

F. (Heteroptera: Reduviidae) on Spodoptera

litura F. (Lepidoptera: Noctuidae) larvae increased

with stage. 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 predator

stages. The age-stage variability of predation of

predator and that of vulnerability of prey have been

observed by many researchers (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 not 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 young adult 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 models without age or stage

structure, e.g., LotkaDVolterra predation model and its

derivatives. Actually, Hassell (1978) had pointed out

that the inclusion of the predator and prey age structure

is an important step in understanding predatorD

prey relationship. Because most animal species are

age-structured or age-stage-structured, further accumulation

of the knowledge of the stage-speciTc predation

rate and stage-structured life table will be necessary

for a proper modeling of predatorDprey

dynamics.

Acknowledgments

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

We are grateful to Cecil L. Smith for generous help in correcting

our English.Wethank the editor and two anonymous

reviewers for valuable comments that greatly improved the

manuscript.