Res. Popul. Ecol. (1974) 15, 213--222.

A N E S T I M A T I O N OF P O P U L A T I O N D E N S I T Y OF DACUS

C U C U R B I T A E W I T H M A R K - R E C A P T U R E M E T H O D S

Yosiaki IT6*, Minoru MURAI% Tadashi TERUYA*

Ryoichi HAMADA ~** and Atsushi SUGIMOTO ~*~

* Okinawa Prefectural Agricultural Experiment Station, Naha 903, Japan ** Okinawa Branch, Tropical Agricultural Research Centre, Ishigaki 907, Japan

INTRODUCTION

Estimation of the number of individuals is a prerequisite for the successful

control of insect pests with the sterile male technique, where we have to determine

the number of sterile males to be released. This task is, however, especially difficult

for the fruit flies which live not only in cultivated areas but also in bushland and

forests. As a part of an eradication programme of the melon fly, Dacus (Sturmeta) cucurbitae, from Kume Island, some 80 km west of Okinawa Island, we attempted

to estimate the density of males with the mark-recapture methods. As almost all

the mark-recapture models used to estimate the population density depend on the

recaptured animals being returned to the original population, they are unsuitable

for our purpose because we killed flies (including marked ones) with traps baited

with cue-lure and haled. In addition, we released laboratory reared flies in place of

those captured in the field. All the methods are thus subject to biases. We were,

however, able to use JOLLY's stochastic model (JOLLY, 1965) for the cases when we

released flies on more than two occassions and a conventional method presented by

IT6 (1973) which is suitable for a single release-recapture census. Possible biases

still remaining in IT6's method was taken into account.

MATERIALS AND METHODS

Marking and Recapture

Dacus cucurbitae used in these experiments were initially collected in Ishigaki

Is. and then reared on squashes at a constant temperature of 27~ at the Okinawa

Branch, Tropical Agriculture Research Centre. Male flies were collected with an

insect-sucker from the emergence cage and anaesthesized with carbon dioxide for

about 30 seconds. Anaesthesized flies were then transferred to an open petri dish

chilled by ice and marked with lacquer on the dorsal part of thorax. This double-

anaesthesia (IwAHASHI, 1972) provided a sufficient period of immobility without any

harmful effects. Marked flies were kept in polyethylene bags for a short time

during transportation and then allowed to fly out from the opened bags at several

places in each survey station. The data in Table 1 summarises the releases of

marked flies.

214

Table 1. Summary of mark-release schedule.

Colour Number Date of Age of released Locality Station Area* of mark released release flies in days

Red 446 Oct 25/26 1-2 A 4 ha

White 426 Oct 30/31 2-3 Kume Is. - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Yellow 357 Oct 25/26 1-2 B 1 ha

Blue 228 Oct 30/31 2-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Red 1108 Jun 14/15 4 C 4 ha

Blue 1103 Jun 20 5 Ishigaki I s . - .........................................................................................................................................................

White 893 Jun 14/15 5 D 2 ha

Blue(A)** 1052 Jun 20 5

* Area of square of 18 outer traps. ** Marked with blue on abdomen.

P l a s t i c t r a p s w i t h c o t t o n ro l l s e a c h c o n t a i n i n g 4. 75 g c u e - l u r e a n d 0. 2 5 g n a l e d

w e r e u s e d fo r r e c a p t u r i n g t h e flies. A s a ru le , t h e t r a p s w e r e e x a m i n e d e v e r y 5 t h

day .

E x p e r i m e n t on K u m e Is.

Two survey stations were established in Gushikawa, Kume Is. late m October,

1972. Both of these were located in an area which consisted of small forest, bush,

sugar cane and vegetable fields, but the ecological conditions of Station A (Fig. 1,

0 50m I I

2'

i I i ~ J J . , Z : o . .

20 ~..79 78 r .y/,~/~

Fig. 1. Station A ( le f t : Kume Island) and Station D ( r i gh t : Ishigaki Island).

215

left) were considered to be bet ter than those of Station B. T w e n t y five traps (5

rows and 5 lines) were hung at intervals of about 50m in Station A and 25m in

Station B. The area of the square formed by the 18 outer t raps was thus 4ha for

A and 1 ha for B . A pre l iminary survey made in 1970, '71 and '72 showed that the

densi ty of flies reached a peak in Kume Is. in June and November.

Experiment in lshigaki Is.

Two survey stat ions (Stations C and D) were established on Ishigaki Is. in mid-

June when the fly densi ty was known to be moderate and considered to be about

the same as that of Kume Is. in November. T w e n t y five (5• t raps were placed

at intervals of 50m in Stat ion C which was located in an area that consisted of

small grass fields, forest, bush, vegetable and pineapple fields. In Stat ion D, which

was set in a nursery of o rnamenta l trees sur rounded by forests, on the other hand,

the distance between rows was reduced to 25m (Fig. 1 r ight) . The area of this

s tat ion was thus 2 ha. Addit ional t raps were also hung outside the stations.

Table 2. Number of marked and unmarked individuals caught with 25 cue-lure traps in two stations in Kume Island from October to December, 1972.

Station A Station B Date . . . . . . . . . . . . .

Unmarked Red White Yellow** Unmarked Yellow Blue

Oct 25/26 446 357 30/31 185 0 426 0 7 0 228

Nov 6 183 18 10 2 28 4 1 11 92 4 9 0 11 0 2 16 1 7 0 " 4 4 0 - - - - - -

21 47* i 0 0 15 0 0

27 74 1 0 0 3 0 0

Dec 1 60 0 0 0 3 0 0 5 24 0 0 0 3 0 0

* Beside these males a female was caught on these days. ** Immigration from Stations B about 1 km apart. Italic figures show the number marked and released.

RESULTS

Exper iment in Kume Is.

Table 2 shows the results of the exper iment in Kume Is. As Dacus cucurbitae

males are a t t rac ted by cue- lu re several days after emergence, none of the adul ts

marked and released on October 25/26 were trapped by the 5th day af ter release.

On the other hand, some males marked and released on October 30/31 had b e e n

recaptured when the t raps were first examined on the 6th day after release and

almost the same number of flies were recaptured on the 12th day. The recapture

data for white marked males were, therefore, considered to be unsui table for t h e

216

Table 3. Estimation of population density of Dacus cucurbitae males in Station A, Kume Island.

Date i n~ m~ 3'/o' y'i log y~

Oct 25 0 446 (3. 449) 0. 5377 Oct 30 0.5 185 446 Nov 6 1.7 201 18 446 2. 008 0. 3028 Nov 11 2. 9 97 4 428 0. 9635 --0. 0162 Nov 16 3. 9 174 4 424 0. 5453 --0. 2634 Nov 21 4. 9 48 1 420 0. 5066 --0. 2953 Nov 27 6. 0 75 1 419 0. 3182 --0. 4973

Note 1 : log y'i=-O. 1783i+0. 5377 (r2=0. 95) Note 2 : Nz(o)= (104/3. 449) -446=2453. Note 3: Constant survival rate=10-~

analysis. The es t imat ion of the populat ion densi ty using IT6's (1973) method was

a t t empted only for the red-marked males released on October 25/26 (Table 3).

IT6's me thod is based on JACKSON's (1939) 'positive method. ' At first, the

number of recaptures on i th day m, is converted to an index of recapture y, as

follows :

104m~ Y~ = Mom" (1)

Here Mo is the n u m b e r of individuals released on the 0th day and n, the number of

individuals caught on the ith day. The y, is an index of the n u m b e r of recaptures

based on an assumpt ion that 100 marked individuals are released on the initial day

and 100 random samples are caught on the i th day. When we plot y~ against t ime

i, we can obtain a survivorship curve of marked individuals. If the morta l i ty rate

of marked individuals is cons tant throughout the exper imenta l period, a l inear

relat ionship can be expected, that is,

log y , = l o g yo+i log S. (2)

Here S is the survival rate (in decimal) dur ing a uni t t ime and yo is a theoretical

value of recapture, when we assume that 100 marked individuals released ins tanta-

neously in termingle into the populat ion and that we take 100 individuals immedia te ly

after the release.

The densi ty No can now be calculated by

No= lO'/yo. (3)

JACKSON's method is based on the assupt ion that recaptured individuals are re turned

to the original population. As we remove the recaptured individuals, the survivor-

ship curve (Eq. 2) of marked individuals is affected by the t rapping morta l i ty as

well as the na tura l mortal i ty. IT6 (1973) suggested that it was bet ter to use a

modified number of individuals released M'o(o in place of Mo when i > 2. Tha t is,

t - 1 M ' o ( o = M o - YT, ms. (4)

j=!

and

217

lO~m, Y'~= M'o~)n," (5)

N'o= l O4 /y'o. (6)

As the m a r k e d flies re leased in our case were ar t i f ic ia l ly r ea red insects, Mo mus t

be sub t r ac t ed f rom N'o to obta in the dens i ty of wild males. Th is dens i ty is he rea f t e r

r ep resen ted by Nz(0). T h a t is,

Nlco) = N ' o - M0. (7)

I t was shown by IT6 (1973) tha t this p rocedure is s t i l l insufficient to r emove

the bias due to t r a p p i n g m o r t a l i t y but he p resen ted a g raph showing the nega t ive

bias tha t was inheren t in this me thod?

Tab le 3 shows the p rocedure of the ca lcula t ion us ing da ta for r e d - m a r k e d

individuals . T h e corre la t ion coefficient be tween the t ime and y'~ was so high tha t

the a s sumpt ion of cons tan t mor t a l i t y could be accepted. As nl, the number of

cap tu re s on the 5th day, is not in fact the number cap tu red on tha t day bu t a

cumula t ive n u m b e r of flies t r apped f rom the 1st to the 5th day, this represents ,

ra ther , the number to be cap tu red on a day wi th in a per iod f rom the 1st to 5th

day. Thus the t ime unit 0, 0.5, 1.5, 2 .5 and so on in place of 0, 1, 2, 3 . . . . were

used for the calcula t ion of the regress ion coefficients. Fo r S ta t ion A, a fu r the r

modified t ime scale was used because the in te rva ls of the cap tu re s were not a lways

5 days.

Using 3. 449 as the value of y'o (Table 3, Column 6),

Ni(0) = (104/3. 449) - 4 4 6 = 2453.

If we conven ien t ly cons ider the a rea of S ta t ion A to be 4 ha, the popula t ion dens i ty

of males is 613/ha. Suppos ing tha t this e s t ima te is the t rue one and tha t it d id not

change r e m a r k a b l y f rom the end of October to ear ly in November , 2 the ra te of

cap ture on the October 30 and N o v e m b e r 6 were 185/2453=0. 075 and (213-30) /2453

=0.075, respect ive ly . IT6's g raph (IT6, 1973; Fig. 3) shows tha t if the ra te of

cap tu re is less than 10%, p rov id ing a s t e ady densi ty , the degree of unde res t ima t ion

due to the bias inherent in his me thod m a y be less than 10%. 8 T h u s the number of

male flies in S ta t ion A was e s t ima ted to be ca. 700/ha. If we use the s imple

LINCOLN index (LINCOLN, 1930) wi th the number of r ecap tu re s on Nov. 6,

N~.(o) = Mou _ 446 • 183 m 18 =4534.

Here u means the number of u n m a r k e d flies cap tu red on Nov. 6. Th i s value is, of

course, an ove re s t ima ted value because it neglects the effects of mor t a l i t y and

dilution. The ra t io of Nx(o~ to N~,(o) is 0. 54. In turn, if we use the total of u 's on

Although there was a mistake in the explanation of IT6'S equations (IT6, 1973 ; p. 165), there is no need to change his conclusion (see Appendex).

2 Decrease in ni in the end of November is considered to be mainly due to the inhibition of movement by a cool temperature.

3 The density of Dacus cucurbitae is, of course, not constant but the change in the density usually takes pIace graduaIIy so that we made calculations assuming the steady density.

218

Oct. 30 and N o v . 6 for the whi te-marked individuals, the LINCOLN index yields

426 x (183_+93) =6188. Nr'(D . . . . (10+9)

The modified value is 6188• 54=3342 or 835/ha and this does not conflict so much

with the est imate based on data for red-marked individuals.

The following procedure was convenient ly applied to the deta obtained in Staion

B, which were insufficient for any model. The mean number of individuals n caught

on Oct. 30, Nov. 6 and 11 was 15. 3. This value was divided by 0.075 (mean rate

of capture calculated for data of Stat ion A) yielding 204 as an es t imate of the

number of male flies in Stat ion B. As the area of Station B is l h a , the densi ty of

males in this s tat ion is roughly est imated to be less than one-thirds of that in

Stat ion A.

Exper imen t in Ishigaki Is.

Table 4 shows the results of the exper iment on Ishigaki Island. The populat ion

parameters that were est imated are tabulated in Table 5. The correlat ion coefficients

between i and y' were again high in all cases. As shown in Table 5, two NI(,)

values (density est imates based on data for individuals released on June 20) were

smaller than those released on June 14/15. This difference may be due to two

factors, that is, (1) as the rate of capture in Ishigaki is es t imated to be high, the

fly densi ty must decrease dur ing a 5 day period, especially in Stat ion D, where the

rate of capture exceeded 20%, and (2) as the flies released on June 20 were 4 days

old, they might be a t t racted to t raps in the morn ing of the next or the second day

before any subs tant ia l na tura l morta l i ty or emigra t ion had occurred, ~

As we released marked flies on Ishigaki twice, JOLLY's (1965) stochastic model

Table 4. Number of marked and unmarked individuals caught with 25 cue-lure traps in two stations in Ishigaki Island from June to July, 1973.

Station C Station D Date

Unmarked Red Blue Blue (A) Unmarked White Blue (A)

Jun 14/15 1108 893 20 202 63 1103 195 155 1052 25 197 28 115 1" 152 54 215 30 77 1 15 98 4 47

July 5 84 2 10 121 2 16 10 127 3 89 2 2 15 99 104 2 25 208 1

* Immigration from Station D about 5 km apart. Italic figures show the number marked and released.

1 HAMADA (unpublished) observed that, in summer, the most of flies come cue-lure traps at the time of sun-rise.

219

could be app l ied and the resul t s of these calculat ion a re also p resen ted in Tab le 5.

Here,

NJo) =/~1 - / ~ l ,

where N1 and /~1 a re JOLLY es t ima tes of the total number of flies and the number

of m a r k e d flies l iving on day 1. We calcula ted V(/V1) and V( /~ I ) bu t did not

a t t e m p t to calculate V(Njo)), because of the difficult s ta t i s t ica l problems. However ,

it is note w o r t h y tha t the s t anda rd devia t ions of .~1 are small , tha t is, 12924-229 and

8 6 2 i 7 4 for S ta t ion C and Sta t ion D, respect ive ly . The es t ima tes a re again smal le r

than Nz(o) bu t near the value of Nzo) for the case of S ta t ion C. Thus cons ider ing

the unde res t ima t ion due to l imi ta t ion of our expe r imen ta l technique, the dens i ty of

male flies in a sui table hab i ta t on Ish igaki I s land in June is e s t ima ted to be ca.

250-500/ha and this is somewha t lower than on Kume Is. in November .

Survival rate The es t ima t ion of surv iva l ra tes is necessary to de t e rmine how many t imes we

mus t release s ter i le flies per month. In IT6'S method, the s ruv iva l ra te of marked

flies ~ per 5 days is a s sumed to be constant . The surv iva l ra tes were 0.663 for

the r e d - m a r k e d flies on K u m e Is. and 0.396 to 0.443 for four ba tches of flies on

Ish igaki I s land (Table 5). JOLLY's es t ima te for i=O was 0. 277 and 0.428 for S ta t ion

C and Sta t ion D, respect ive ly . (It mus t be noted tha t ~o=~/I~/Mo in our case ins tead

of M,+~/(~/I,-m,+s,) in the or iginal equat ion) . F r o m these results , it can be

a s sumed tha t the number of flies which emerge dur ing one month is th ree t imes as

many as the number of flies l iving on a cer ta in day.

Table 5. Population parameters estimated by Ir6's and JOLLY'S methods in Station C and Station D, Ishigaki Is.

Parameters Station C (4 ha) Station D (2 ha)

Red Blue White Blue (A)

,N'I (0) 2092 478 Nx (1) 623 0r 0. 408 0. 436 0. 443 NJcl) 983 480 ~J(o) 0. 277 0. 428

negative 0. 396

The survival rate �9 is expressed as that per 5 days.

ESTIMATION OF NUMBER OF MALES ON KUME ISLAND

Regula r census of re la t ive dens i ty of D. cucurbitae has been made with 50 cue-

lure t r aps d i s t r ibu ted over K u m e Is. F r o m the resu l t s of the census it can be said

tha t the dens i ty of D. cucurbitae is h igh in cu l t iva ted land ( including smal l bush and

forests) and vi l lages (TERUYA et al. unpubl ished) . Only a few flies were caught

by t raps h u n g in sub t rop ica l b road leaved forests which cover the mounta inous pa r t s

of this is land and in bamboo bush. Rela t ive ly smal l number of flies were caught

220

by t r aps located in pine fores ts and coasta l b road leaved fores ts on upheaved coral

leaf. Fig. 2 is a s implif ied vege ta t ion map of K u m e Is. in re la t ion to the dens i ty of

D. cucurbitae. F r o m this, we e s t ima ted the a p p r o x i m a t e a reas of major vege ta t ion

types as fol lows :

Total area 7, 100 ha

I Cul t iva ted land, 'vi l lage inc luding

smal l fores ts and bush 4, 200 ha

II Pine fores ts and coasta l b road

leaved fores ts 1, 610 ha

I I I Sub t rop ica l b road leaved fores ts

and bamoo bush 1, 290 ha

A ~

2

3

~ l 4 N [ZI] 5

\

>

Fig. 2. Simplified vegetation map of Kume Island. 1 : Pine forest, 2 : Broad leaved forest on upheaved coral reef, 3 : Subtropical broad leaved forest, 4 : Bamboo bush, 5 : Village and cultivated land including bush and smalt secondary forest. Symbols A and B mean Stations A and B.

I t is t en ta t ive ly e s t ima ted f rom the t r ap census da ta that , of the a rea of

cu l t iva ted land and vil lages, about a half ( including vi l lages where the fly is most

abundan t ) m a y be as sui table a hab i t a t for D. cucurbitae as Sta t ion A while ano ther

half m a y be not so su i tab le and comparab le wi th Sta t ion B. If we assume tha t the

mean dens i ty of male flies in the most sui table cu l t iva ted land and vi l lages is 800

per ha (based on the resu l t s of m a r k - r e c a p t u r e expe r imen t s ) and tha t in unsui tab le

cu l t iva ted land is 200 per ha, the to ta l number of males in cu l t iva ted land and

221

vi l lages is e s t ima ted to be 1, 680, 000+420, 000=2, 100, 000. T h e r e is not enough da ta

to de t e rmine the re la t ive densi t ies in vege ta t ion types II and III, bu t if we t en ta t ive ly

use f igures of 1/5 and 1/10 of the most sui table habi ta t , respect ive ly , the to ta l

numbe r s a re ca lcula ted as 257,600 for II and 103, 200 for III. T h u s the to ta l number

of males on K u m e Is land in the most a b u n d a n t season a moun t s to ca. 2,500,000.

Th i s is, of course, an a p p r o x i m a t e e s t ima te and p robab ly an ove re s t ima ted value

since we assume densi t ies in different hab i ta t s tha t a re p robab ly h igher than t rue

values. A n ove res t ima ted value is, however , a sui table bas is for the de t e rmina t ion

of the n u m b e r of s te r i le males to be re leased because i t is essent ia l to ensure

overf looding of s ter i le males for the successful cont ro l of th is pest. Ac tua l ly ,

7, 500, 00 flies should be re leased when we consider the m o r t a l i t y ra te d iscussed in

the p rev ious section.

SUMMARY

The dens i ty and su rv iva l ra te of Dacus dorsMis males were e s t ima ted using

re l ease - recap tu re data. Modified JACKSON's method and JOLLY's s tochas t ic model

gave an a p p r o x i m a t e e s t ima te of popula t ion dens i ty of 200-700/ha and 300-600/ha in

cu l t iva ted a reas of K u m e and Ish igaki Islands, respect ive ly , in months when the fly

was most abundant . The surv iva l ra te per 5 days ranged f rom 0.3 to 0.6. T h e

number of male flies inhabi t ing K u m e Is land (from which we are p lann ing to

e rad ica te D. cucurbitae with s te r i le male technique) was e s t ima ted to be 2,500,000

in abundan t seasons.

ACKNOWLEDGEMENT : The authors wish to thank Dr.B.S. FLETCHER, C.S.I .R.O. Division of

Entomology, Sydney, Australia for reading the manuscript and to Mr.K. MIYARA and Mr.K.

NAKASATO for giving facilities. Mr.H. KAKtNOHANA, Yaeyama Branch of Okinawa Prefectural

Agricultural Experiment Station, and many persons in Kume Island helped us during the course

of field study.

LITERATURE CITED

IT6, Yosiaki (1973) A method to estimate a minimum population density with a single recapture

census. Res. Popul. Ecol. 14: 159-168.

IWAHASHI, Osamu (1972) Movement of the oriental fruit fly adults among islets of the Ogasawara

Islands. Environmental Entomology 1: 176-179.

JACKSON, C.H.N. (1939) The analy sis of an animal population. I Anim. Ecol. 8: 234-246.

JolLY, G.M. (1965) Explicit estimates from capturerecapture data with both death and immigra-

tion-stochastic model. Biometrika 52: 225-245.

LINCOLn, F.C. (1930) Calculating waterfowl abundance on the basis of banding returns. U.S.D.A.

Circular No. 118.

222

A~PENDEX

There was a careless mistake in the explanations of equations (Eq. 10-Eq. 15) in IT6 (1973).

The sentence (from line 24 to line 30, p. 165) "When the natural mortal i ty is acting, as the

survival rate becomes less than unity, (a) the value in brackets of the denominator of Eq. (14)

becomes larger than (Mo-m~- . . . -M~) in Eq. (15), and (b) the value in brackets of the

numera tor becomes less than unity. Thus in the case we use Eq. (15) in place of Eq. (14), we

calculate y~+~ with a denominator smaller than the true value and with a numerator larger than

the true value. The values of yi+~ thus calculated is always overestimated" should be read "When

the natural mortal i ty is acting, as the survival rate becomes less than unity, the value in brackets

of the denominator of Eq. (14) becomes smaller than (Mo--m~--...--too in Eq. (15) and the

difference between the both increases wi th t ime (i). The values of the numerator of Eq. (14) are

always less than those of Eq. (15) but the effect of neglect of terms in brackets of the numera tor

of Eq. (14) is not large as compared with the effect of denominator , because only 1//100 of the

value of �9 affects here. In addition, y~'s calculated by Eq. (14) and Eq. (15) are the same

because there is no m~-terms in the denominator . Thus Yo calculated by Eq. (15) in place of

Eq. (14) may be always overestimated." Despite this mistake, the conclusions are the same.

~ 5 ~ 0 3 ~ l ~ J ~ ~ 2 0 0 ~ 7 0 0 / h a ~d:O"300~600/ha "~5 9, ~ t ~ ' ~ 5 H~?'~ 9 0 . 3 ~ 0 . 6 W ~