Detection of activity cycles from capture-recapture data

Transcription

1 See discussions, sas, and auhor profiles for his publicaion a: hps:// Deecion of aciviy cycles from capure-recapure daa Aricle in cological nomology February 1986 Impac Facor: 1.7 DOI: /j b28.x CITATIONS 17 RADS 27 2 auhors: David Rogers Universiy of Oxford 2 PUBLICATIONS 9,996 CITATIONS S PROFIL Sarah Randolph Universiy of Oxford 2 PUBLICATIONS 9,289 CITATIONS S PROFIL All in-ex references underlined in blue are linked o publicaions on ResearchGae, leing you access and read hem immediaely. Available from: Sarah Randolph Rerieved on: 11 May 216

2 cological nomology (1986) 11,95-19 Deecion of aciviy cycles of sese from capure-recapure daa DAID J. ROGRS and SARAH. RANDOLPH Deparmen of Zoology, Universiy of Oxford ABSTRACT. 1. Aciviy cycles of female sese (Glossina palpafis palpalis Robineau-Desvoidy) in he field are conrased wih hose of males, using mark-release-recapure daa from coninuous biconical rap samples over a period of 8 days in wo villages in Ivory Coas. 2. ariabiliy in recapure raes was examined using he echniques of auocorrelaion and specral analysis. In order o do his a wodimensional diffusion model incorporaing boh moraliy and emigraion was firs fied o correced recapure rae daa o produce a rend line, deviaions from which were subjeced o he analysis.. The auocorrelaions for he daa for males sugges considerable variabiliy in aciviy, presumably associaed wih feeding, around a mean period of abou 4 days in one village and seven in he oher. 4. Daa for females show a srong regular periodiciy of abou 9-1 days, reflecing he pregnancy cycle, and shorer, more variable periodiciies probably corresponding o feeding. Key words. Tsese, feeding, pregnancy cycles, capure-recapure, specral analysis. Inroducion Many blood-sucking insecs spend mos of heir ime a res and become acive only for paricular purposes, such as feeding or reproducion. sablishing he lengh of he aciviy cycle of such species is crucial for he correc inerpreaion of mark-release-recapure and oher daa colleced by mehods ha sample only acive individuals (Conway e al., 1974); cycle lengh is also epidemiologically iinporan when aciviy is associaed wih feeding (Aron & May, 1982). Correspondence: Dr D. J. Rogers, Deparmen of Zoology, Souh Parks Road, Oxford OX1 PS. In he case of he sese, Glossina, Jackson (19) recorded inervals of 4-5 days (or muliples hereof) beween caching marked male G.morsiuns Weswood and G.swynneroni Ausen in he same hunger sage (a crude measure of nuriional condiion based on he appearance of he abdomen, wheher replee or shrunken), alhough boh he (Jackson, 197) and anderplank (1947) laer showed ha males of hese wo species, when prevened from feeding by cuing off heir probosces, could survive in he wild for up o 1-12 days. By marking and releasing flies jus afer hey had fed on men or a calf, and recording he ime o he nex feed, Glasgow (1961) showed a fairly wide scaer of feeding 95

3 96 David J. Rogers and Sarah. Randolph inervals of 1-15 days for male G.swynneroni wih an average of.54.5 days depending on he season. Rogers (1977) found a 4-day periodiciy in he recapure rae of individually marked male G.fiscipes fuscipes Newsead a a saionary human caching pary, and his probably refleced he feeding cycle duraion. Female sese in he laboraory show quie differen sponaneous aciviy paerns from he males (Brady & Gibson, 198; Brady, 1975). wih a grea reducion in aciviy during he 2 days preceding larviposiion. which occurs every 9 or 1 days. Less is known abou heir aciviy in he field, because mehods such as hunger saging canno be applied o hem (he larva in uero affecs he exernal appearance of he abdomen), and because hey are less adequaely sampled by many of he classical sese sampling mehods. Glasgow s (1961) marking experimen, however, suggess ha he field aciviy of female G.swynneroni is also geared o he feeding cycle, wih a -5 day feeding inerval, which, in any one season, is much less variable han he corresponding inerval for he males. The relaively recen invenion of he biconical rap (Challier & Laveissihe, 197), which caches a higher percenage of female flies han does any previous mehod, allows us o focus aenion on his raher negleced sex. This paper describes he analysis of he resuls of coninuous, 8-day mark-release-recapure experimens on village-based populaions of G.palpalis palpalis ( Robineau-Desvoidy) in he pre-fores zone of Ivory Coas. The analysis suppors he esablished feeding cycle inerpreaion of male fly aciviy, bu shows quie clearly ha female aciviy is much more srongly deermined by he 9-1-day iner-larval period. rap sampling during which flies were examined for marks and hen eiher released again (Congo Aboisso 11) or killed (DegbCzCrC). Abou half-way hrough he experimen a furher 5-day mark-release-recapure session was carried ou a each sie o discover wheher he removal rapping a DegbCzCrC had had any noiceable effec on populaion size. In dealing wih capure-recapure daa for sese. Jackson (1948) allowed for he variaion in daily caches by calculaing a correced recapure rae (y,) defined by where R, is he number of flies originally marked on day (when he oal cach was C,) ha are recapured on day n in a oal cach of C, flies. Thus he recapure rae would be y, assuming 1 flies were marked and released on he day of marking and 1 flies capured on he subsequen sampling day (Cn= C,,=lOO). When flies are sampled daily a correced recapure rae can be calculaed for each day, up o he maximum n (abou 8 days in he presen case). The 5-day mark-releaserecapure experimens a each sie can be reaed as five separae experimens, in which case he maximum likelihood esimae for he average correced recapure rae on day n is no he (perhaps obvious) arihmeic average of is value for he five replicaes (as assumed by Rogers. 1977) bu is insead approximaely given by (p,) where k c R,, r=l pn= k x 14 Maerials and Mehods Deails of he field experimens, which were designed o es our undersanding of he local dynamics of G.palpalis, have already been given elsewhere (Rogers e al., 1984; Randolph ef al ). Briefly 5-day mark-releaserecapure experimens were carried ou in wo small villages, Congo Aboisso II and Degbezere, boh near Bouafle, Ivory Coas. There hen followed 76 days of coninuous biconical where here are k replicaes (five in he presen case) (J. W. Hargrove and. M. Landaw, pers. comm.). Thus Cni is he number of flies caugh on day n of he ih replicae of he experimen. Average recapure raes were calculaed according o his formula and used in all he subsequen calculaions. (Since flies a DegbezCrC were sampled wihou replacemen, he Cn values a his sie were reduced as recapures were made.)

4 Tsese aciviy cycles 97 Three mehods are available o examine variabiliy in recapure raes ha may be aribuable o repeaed aciviy cycles by he marked flies. Firs, recapure raes may be ploed agains ime and examined visually (e.g. Rogers, 1977). Secondly, a sinusoidal componen may be inroduced ino some descripive (generally exponenial decay) model for he overall fall in recapure raes hrough ime, and he necessiy for his componen judged by he subsequen reducion in he residual sum of squares (Hargrove & Landaw, pers. comm.). The hird mehod, which is relaed o he second, examines how he observed variaion in recapure rae could be regarded as he sum of sinusoidal componens a many differen frequencies, some of which migh be more imporan han ohers. The echnique of specral analysis (Chafield, 198), developed o look for periodiciies in noisy daa such as meeorological records, achieves his objecive, and is he one adoped o analyse he presen resuls. The average recapure raes from he wo sudy sies fell during he course of he experimen, as flies died or emigraed from he sample area. Specral analysis requires he daa o show no rend in he average value, and so he echnique had o be applied o deviaions of daily correced recapure rae from an overall rend line fied o he daa. Preliminary ess showed ha he resuls of he analysis were very sensiive o he ype of rend line fied. Simple, exponenial decay models ended o give overall posiive deviaions a one end of he daa se and negaive deviaions a he oher, a resul ha produces a srong arefacual componen afer specral analysis a a frequency of lin cycles per day (where N is he duraion of he experimen in days) and herefore a period of N days. Two differen rend lines were invesigaed. The firs was a simple (m+l)-poin moving average of he correced recapure rae daa: for each recapure day n he moving average was aken over he poins nfml2, excep a each end of he series where, for example, on he firs day (n=1) he average was aken of he correced recapure raes from day 1 o day l+m/2, on he second day (n=2) from day 1 o day 2+m/2 and so on. alues of m were chosen by rial and error so as o remove any sinusoidal componen in he rend line, which for male 7 flies proved o be 1 and for female flies was 16. The oher rend line chosen was a somewha less arbirary wo-dimensional diffusion model incorporaing a consan moraliy rae. Assuming Brownian diffusion from a cenral release poin (i.e. approximaing he village releases of sese) he proporion (P,) of released, marked flies sill wihin a radius r a ime afer release (and herefore available o a sysem of raps wihin he village) is given by P, = 1 - exp (- r2/4 w) () where w is he diffusion coefficien (Souhwood, 1978). Inroducing moraliy a he daily rae of m, he proporion of flies surviving wihin he radius r is given by P,,, where P,,= exp (-m) x { 1 - exp (-2/4w)} (4) Par of he second exponen can be subsumed ino a single parameer, k, and he equaion muliplied by c, o predic changes in he correced recapure rae hrough ime ( Csr) via he hree-parameer model C,,= c x exp (-m){ 1 - exp (- k/)} (5) This model was fied o he correced recapure rae daa using a non-linear leas squares mehod based on Marquard s algorihm (Conway e al., 197), o generae a smooh rend line ha adequaely described he overall fall in recapure rae. Specral analysis of he deviaions from boh sors of rend line was carried ou according o Chafield (198). Firs, auocorrelaions a increasing lags were calculaed and ploed. These are simply correlaions of he deviaions from he rend line on days n and (n+k), where k is he lag in days. Auocorrelaions of a series of random daa have an expeced value of, wih a 95% confidence inerval of I 2 / m ) where N is he oal number of poins. Auocorrelaions of daa showing sinusoidal paerns hemselves show regular changes, wih negaive values when he lag, k, is half of he period of he cycle in he daa and posiive values when he lag equals he cycle period. A his laer poin he auocorrelaion is beween daa poins separaed by precisely one complee cycle. The more regular and pronounced he cycle in he original daa, he

5 98 David J. Rogers and Sarah. Randolph higher he peak values (boh negaive and posiive) of he auocorrelaion coefficiens. Ploing auocorrelaions agains he lag, k, always gave a useful indicaion of he likely periodiciies in he sese daa. Following auocorrelaions, periodograms were calculaed and smoohed (Chafield, 198). Periodograms essenially aribue he oal variance of he raw daa (i.e. he deviaions from he rend line) o componens a differen frequencies. The oal possible range of frequencies is from lin cycles per day for an experimen run for N days, o one cycle every 2 days (he Nyquis frequency ). Higher frequency componens canno be disinguished if only daily readings are aken. If a plo is drawn of he variance explained by periodic componens in he range of frequencies o f, for increasing values of f up o he Nyquis frequency (a which poin all he variance is accouned for) hen he increase in he explained variance for a small increase in f is he ordinae of he periodogram a ha paricular value of f. Because of his relaionship beween ordinae heigh and explained variance. periodograms (someimes called specrograms) are ploed a regularly increasing frequencies. The alernaive, which iniially may seem more aracive, is o plo he ordinaes agains he period (i.e. l!f) bu his raher disors he picure by over-emphasizing he area under he curve a longer periods. and herefore he conribuion o oal variance made by hese periodiciies. Periodograms end o show quie severe flucuaions. and need o be smoohed o give a more consisen esimae called he (power) specral densiy funcion (Chafield, 198). Trial and error showed ha hree-poin smoohing of he periodogram for he sese daa removed he variable spikes wihou smoohing he periodogram oo severely. Auocorrelaion and specral analvsis are relaed echnique5 ha can be. and ofen are. applied o he same se of daa. Similar conclusions from each are no herefore independen, bu raher complemenary evidence for periodiciy in he original daa. Specral analysis was applied o he combined resuls of hc male flies a each sie (i.e. he wo marking sessions a he sar and half-way hrough he recapure period) bu only o he longer series of recapure daa for he females. This is because he period covered mus be a leas 6 imes he lengh of he longes periodiciy presen in he daa (Chafield, 198) and his was found o be quie differen for he wo sexes. Confidence inervals of specral densiy funcions always seem o be large, even in long ses of daa used o illusrae he echnique (Chafield, 198, example on page 165 e seq.). In he presen case he 95% confidence inervals for he specral densiy funcions span a range of abou one half o 2 or imes he ploed values. Neverheless, he auocorrelaions and specral analyses appeared o be giving consisen resuls beween differen daa ses and, o check how frequenly his would occur in daa wihou any periodiciy, he se of sese recapure rae daa ha showed he mos pronounced periodiciy was sampled randomly o produce arificial ses of recapure daa. One hundred such sequences were analysed according o he mehods applied o he real daa in order o discover how frequenly auocorrelaions of random daa show he clear cycliciy of he sese resuls, and o demonsrae wheher specral densiy funcions of such daa show obvious peaks a paricular frequencies hrough purely chance effecs. Resuls Male flies Correced recapure raes for male flies end o fall away o zero by abou day 4, and auocorrelaions and periodograms seem quie sensiive o he ype of rend line fied. Fig. 1 shows he auocorrelaions and smoohed periodograms for all male flies (i.e. from boh marking sessions) a Degbezere when eiher en-poin smoohing (Fig. la) or he Brownian model (Fig. lb) is firs applied o he daa o produce a rend line. The auocorrelaions from he en-poin smoohing show a more pronounced. regular variaion wih he value of he lag. k (Fig. la, middle); he lowes value is reached a a lag of days and he highes value a a lag of 6 days. This indicaes a periodiciy in he daa of abou 6 days duraion. and his is suppored by he single, fairly broad peak from 6 o 8 days in he periodogram (Fig. la, lower). There is lile difference beween he resuls for he males a Congo

6 + al! 1 + a : 5 U al + g o Tsese aciviy cycles 99 k ,. U Days afer marking and releasing Days afer marking and releasing \ \- u Q Period, days Period, days v I I I I I I I I L u W In a U W +._ v1 W 1..5 I I I I Frequency ('14 cycles /day 1 Frequency ('/4 cycles /day) FIG. 1. Correced recapure raes and fied rend lines (upper), auocorrelaions of deviaions from he rend lines (wih f95% confidence inervals) (middle) and smoohed periodograms (= specral densiy funcion) produced by specral analysis of he deviaions (lower) for male G.palpalis a DegbzCr. (a) Ten-poin running average rend line; (b) Brownian movemen + moraliy model rend line. The auocorrelaions in (a) sugges a 6-day aciviy cycle for male flies in his village (he periods corresponding o he frequency scale of he lower figures are indicaed above he smoohed periodograms). Aboisso I1 analysed afer applying he alernaive rend lines, and one example (using he Brownian model rend line) is shown in Fig. 2; he auocorrelaions are barely significan and he periodogram indicaes a peak a days, bu his occurs wihin a much broader range of periods of beween abou 2.5 and 7 days. Combining he resuls from he wo villages before analysis no surprisingly pro- duces auocorrelaions ha are never significan, and a smoohed periodogram wih a broad peak over abou he same range. In each of hese examples, and in one of he laer periodograms, here is also an increase in he esimaed specrum a he Nyquis frequency (corresponding o a period of 2 days). Since his commonly occurs in specral analysis (Chafield, pers. comm.), wih no obvious

7 1 David J. Rogers and Sarah. Randolph + a z 1? + LI 5 - a + 2 $ Days afer marking and releasing 1 c C.- a c r.5 a u C c Period, days I I I I I I I Frequency ( 144 cycles /day ) FIG. 2. As for Fig. l(b), for males flies a Congo Aboisso 11. A shorer aciviy cycle, of abou 4 days, is suggesed by boh he auocorrelaions and he specral densiy funcion. underlying reason, i may be an arefac, in which case i can be ignored. (Abou one in hree of he 1 random specrograms o be described laer show increases owards he Nyquis frequency.) Alernaively i may resul from aciviy by he flies varying wih a period of 2 days or less; such behaviour can only be invesigaed by sampling a inervals of much less han a day, which was no possible during he presen experimens. Female flies Perhaps because female flies coninue o be recapured over a longer period, here are less pronounced differences beween he analyses

8 Tsese aciviy cycles 11 of female recapure rae daa wih he alernaive rend lines fied. In general, however, he analyses wih an (m+ 1)-poin running average rend line give slighly more significan auocorrelaions. The correced recapure raes, Brownian model rend line, auocorrelaions and smoohed periodogram for he female flies a DegbCzCrC are shown in Fig. (and he raw daa in he Appendix). There was one anoma- a, + z Q u a, L - a, I - I - I ?O 8 Days afer marking and releasing c.- a,._ Lc u- a, C._ - I U - Y- 2 ) Q In - a, o._ In W Period, days I I I I I\ Bandwidh I\ 87 U Lag, days Frequency ('/?8 cycles/day) FIG.. Correced recapure raes and fied Brownian model rend line for female G.pafpafis a DegbCzCr (above), auocorrelaion of he deviaions from he rend line (middle) and smoohed periodogram for he daa (below). The auocorrelaion reveals a pronounced 9-1-day aciviy cycle, and he periodogram suggess anoher componen, wih a period of from 4 o 5 days. The original daa for his analysis are given in he Appendix.

9 12 David J. Rogers and Sarah. Randolph lous, high value righ a he end of he series, arising from he recapure of a single marked female in a small oal cach, and his poin has been omied by runcaing he recapure series a he 78h day. The auocorrelaions show a clear cycling, wih significan negaive values a lags of. 6 and 16 days, and significan posiive values a lags of 9 and 1 days. This resul, which indicaes an aciviy cycle of abou 9 or 1 days duraion, is confirmed by a peak in he smoohed periodogram a he same period (Fig. ). In addiion, he periodogram has anoher peak a a period of abou 4-5 days. This peak is probably no a simple W 2 8 L a f - W ) L Days afer marking and releasing c.- W._ 'c 1c al u C e c - W L a.5 "Oli --5 'i -1 O L Period, days I v <- + L a v) U, + + v) W I I I I I Frequency (1/8 cycles /day FIG. 4. As for Fig., for female G.palpalis a Congo Aboisso 11. The cycle wih a 9-1-day period is again demonsrafed, and he smoohed periodogram suggess wo shorer cycles wih periods of jus under and 4 5 days.

10 Tsese aciviy cycles 1 harmonic of he firs peak, because (in he un-smoohed periodogram) i does no occur a an inegral muliple frequency of i. Thus he values of he unsmoohed periodogram are.6,.44,.582 and.45 for frequencies of 6-9/78 cycles per day, and.,.214,.16,.76,.247 and.77 for frequencies of cycles per day; he small peak a a frequency of 15/78 cycles per day may well represen an harmonic of ha a 7-8/78 cycles ? 8 Days afer marking and releasing C.- al U c.- u Period, days - d <- L u al (1 ul U al c + ul w I 1 I I w - Bandwidh Frequency (l/?8 cycles/ day) FIG. 5. Analysis of a combinaion of he female recapure daa from DegbzerC and Congo Aboisso I1 (upper) shows srong auocorrelaions (middle), and a smoohed periodogram (lower) indicaing a 9-1-day aciviy cycle.

11 14 David J. Rogers and Sarah. Randolph -~ I. /\ /yo 4.. *, 2 -- I Lag,!-- \ /* '/ ' '-' '*' -.-\/ days -5 - grams on he righ per day. bu i is los in he smoohed periodogram in he sronger peak a 17-18i78 cycles per day. This second peak in he smoohed periodogram herefore indicaes aciviy on a shorer ime-scale ('?he feeding cycle) han he larger peak which. no presen in he daa for male flies. prohahly reprzsens aciviy on he ime-scale of he iner-larval period. The auocorrelaions for he daa from femalch a Congo Ahoisso I1 show a similar bu Icsb marked paern o ha shown in Fig.. wih significan negaive values a lags of 5 and 7 days and significan posiive values a lags of 8 and 2 days (Fig. ). The smoohed periodogram again has a large peak a a period of 9 days and smaller peaks a periods of 4-5 and jus under days. When all he female recapure daa are combined before analysis (Fig. 5) he auocorrelaions are significan and posiive a lags of 9, 1, 18 and 19 days, and significan and negaive a lags of -7 days and 1, 15 and 16 days. Now he periodogram is dominaed by a peak a a period of abou 1 days, wih a smaller peak a 4-5 days (Fig. 5). The deviaions in his combined series were randomly sampled as described in he Maerials and Mehods secion o generae 78-day

12 Tsese aciviy cycles 15 random recapure rae daa ha were subjeced o he same analyses as he original daa. This was done 1 imes, and auocorrelaions and smoohed periodograms calculaed. Of a oal of 2 auocorrelaions (i.e. a lags of up o 2 days for each series), eighy (4%) were significan a he 5% level, suggesing ha he significance limis on Figs. 1-5 are, if anyhing, slighly conservaive. Two ou of he 1 series of random daa on analysis had four significan auocorrelaions, and one had hree (Fig. 6), bu none showed he obvious and regular paern of Figs. and 4. The corresponding smoohed periodograms of hese hree random rials are also shown in Fig. 6. Two of he periodograms have a peak a quie shor periods (2.5- days) and he hird also has a peak a a much longer period (15-2 days). In ha hese periodograms show a peak a some frequency, hey are raher more similar o he smoohed periodograms of he original daa han are he respecive auocorrelaions. Ou of 1 random rials one or wo are likely o presen paerns ha in some way resemble hose in he original resuls, and so i becomes necessary o adop some crierion ha can be applied o reduce he risk of seeing periodiciies ha in fac do no exis. In he case of sese recapure daa i is unlikely ha longer-erm records could be colleced, since moraliy and emigraion of he flies reduces he number of marked individuals available afer 8 days or so o insignifican levels. A possible crierion suggesed iself when he numbers of significan auocorrelaions amongs he 1 random series was found TABL 1. The frequency disribuion of he number of significan auocorrelaions (ou of a oal of 2, i.e. lags of 1-2) obained by he analysis of 1 ses of random recapure daa (see ex). The disribuion is no significanly differen from a Poisson disribuion wih he same mean. No. of significan Frequency Frequency auocorrelaons observed prediced (ou of 2) Toal =1.69, d.f., no significan. 8 o follow approximaely a Poisson disribuion wih a mean of.8 per series (Table 1). There is no reason o believe ha he Poisson disribuion would coninue o apply if many more han 1 random series were analysed; neverheless he chance of obaining he very high number of significan correlaions seen in he sese daa (i.e. welve ou of weny in Fig. 5) seems very remoe indeed. The periodiciy of he female recapure rae daa is herefore a real phenomenon. Discussion In a previous paper we showed ha he iner-larval period of female G.pa1palis in our sudy area was of he order of 9 days (Rogers e al., 1984). This resul was based on he recapure of flies ha were noed a he ime of marking o be sof o he ouch (i.e. relaively newly emerged); on recapure such flies were disseced o esablish heir ovarian age (Challier, 1965) which was hen compared wih heir calendar age. The presen resuls from much more exensive recapure daa show ha he aciviy of female sese sampled wih biconical raps is more obviously geared o he inerlarval period han o he shorer duraion feeding cycles ha are he dominan componen of male aciviy. Whils some of he presen resuls for he males are raher disappoining (i.e. auocorrelaions ha are rarely significan, and broad periodogram peaks), hey may genuinely reflec a greaer variabiliy of male behaviour (i.e. feeding cycle inerval). This was mos convincingly demonsraed in G.swynneroni by Glasgow (1961) who showed ha whereas male flies marked afer one feed reurned for heir nex meal beween 1 and 15 days laer, females almos always reurned wihin 8 days. Glasgow agreed wih he suggesion of Mellanby (197) ha i is imporan o a female sese o ge her meals a exacly he righ ime. This is presumably a reference o he demands made by he growing larva wihin he female. Tha he righ ime did no necessarily imply a equal inervals during he larval cycle was also shown in Glasgow s experimen, since in he monh wih he greaes number of recapures (June) abou equal numbers of females were caugh afer -, 4- and 5-day

13 16 David J. Rogers and Sarah. Randolph inervals. In all monhs he overall female recapure inerval disribuions were much more fla-opped han hose of he males. Glasgow suggess ha he shorer feeding inervals are shown by he younger females (which have no ye maured heir fligh muscles), alhough i is no clear how his argumen can explain he difference beween he wo sexes, boh of which maure fligh muscles afer emergence from heir puparia. An alernaive explanaion is ha females have differen feeding inervals depending on heir curren sage of pregnancy. There is some evidence from boh laboraory and field ha his migh be he case. Female G.morsiuns given daily access o food in he laboraory end o feed only on cerain days of heir pregnancy cycles (Randolph & Rogers. 1981), wih unequal inervals beween hem. whils he blood meal residues in field flies sugges ha hey oo feed in a similar way (Rogers & Randolph, 1978). I is emping o sugges ha he smaller peaks in he periodograms for female C.palpalis represen feeding cycle inervals, alhough he resuls from he wo villages are no idenical in his respec. Females oh villages showed one peak a a period of from 4 o 5 days. bc a Congo Aboisso II hey sh:)wed an addiional peak a a period of jus under days, suggesing a shorer average aciviy cycle. The resuls for he male flies also indicae a shorer cycle in Congo Aboisso I1 (i.e. 4)). 6 8 days in Degbezerk. Figs. and 1 respecively). Acceping ha his aciviy is relaed o feeding in boh sexes. he resuls aken ogeher sugges ha he Degbezere flies are beer fed han are he Congo Aboisso 11 flies. since, wihin limis, he rae of discovering hoss on which feeding occurs decreases wih increasing meabolic reserves in he flies (Rogers. 1984). i.e. beer-fed flies on a:.erage feed less ofen and so. when heir recapure daa are analysed. reveal aciviy wih longer average periods. A census of he domesic animal populaions in he wo villages found ha a he ime of our sudy Degbezere possessed beween and 4 imes as many pigs as Congo Aboisso I1 (Rogers e al., 1984). and hese animals are known o be an imporan source of food for he flies. Such a difference beween he wo sies may explain he differences in he periodograms of he recapure daa. If his is he case, i appears ha female sese a Degbezere may feed only wice during each pregnancy cycle whereas hose a Congo Aboisso I1 may feed wo or hree imes (i.e. every 4-5 days or every days), perhaps depending on heir curren nuriional saus. Regardless of he variabiliy of feeding inerval in females during each pregnancy cycle, he periodograms and field daa (Rogers e al., 1984) indicae ha he pregnancy cycle imposes a consan periodiciy which, as i were, re-ses aciviy associaed wih feeding a one or more key poins (e.g.?larviposiion) - a suggesion for which here is some laboraory evidence (Brady & Gibson, 198). Finally i is perhaps imporan o sress he large confidence inervals of he periodograms. Whils auocorrelaions of he sese recapure daa are so frequenly significan ha hey are unlikely in he exreme o be deermined by a purely random process, he paerns of he smoohed periodograms from he sese and from random daa may be qualiaively much more similar. Alhough fiing a rend line o he recapure daa removed one of he obsacles o applying specral analysis, here remained he endency for he deviaions from he rend line o diminish wih ime. as flies were los hrough moraliy and emigraion. If specral analysis indicaes a cyclic effec despie such damping, hen he cyclic effec is almos cerainly real (Chafield, pers. comm.). alhough periodiciies in smoohed periodograms ha are no suppored by significan auocorrelaions should always be inerpreed wih cauion. Acknowledgmens The work in Africa was made possible by Dr F. A. S. Kuzoe. Direcor, OMS Tryprespro, Dr A. Sekeeli and Dr K. Kangha; our field assisans were Jules Yao, Fofana Korofo and Kouame Cyrille; and we were also helped by he oher members of he enomological eam a Bouafle led by Siaka Coulibaly. In ngland Professor D. H. Molyneux and Dr F. H. C. Marrio provided valuable advice, Dr C. Chafield kindly commened on he manuscrip and Mike Amphle drew he ex figures.

14 Tsese aciviy cycles 17 S..R. graefully acknowledges a gran from he Leverhulme Trus for her paricipaion in his work. The daa analysis was carried ou on equipmen purchased wih a generous gran from he Overseas Developmen Adminisraion, London (under Research Scheme no. R72). This invesigaion received financial suppor from he UNDPiWorld Bank/WHO Special Programme for Research and Training in Tropical Diseases (projec no. 82). References Aron, J.L. & May, R.M. (1982) The populaion dynamics of malaria. Populaion Dynamics of Infecious Diseases: Theory and Applicaions (ed. by R. M. Anderson), pp Chapman & Hall, London. Brady, J. (1975) Hunger in he sese fly: he nuriional correlaes of behaviour. Journal of Insecf Physiology, 21, Brady, J. & Gibson, G. (198) Aciviy paerns in pregnan sese flies, Glossina morsians. Physiological nomology, 8, Challier, A. (1965) AmClioraidn de la mchode de derminaion de 1 Bge physiologique des glossines. udes faies sur Glossina palpalis gambiensis anderplank, Bullein de la Sociee de Pahologie xoique, 58, Challier, A. & Laveissikrre, C. (197) Un nouveau piege pour la capure des glossines (Glossina: Diperz, Muscidae): descripion e essais sur le errain. Cahiers de I Office de la Recherche Scienifique e Technique Oure-Mer Skrie nomologie Medicale e Parasiologie, 11, Chafield, C. (198) The Analysis of Time Series: An Inroducion. Chapman & Hall, London. Conway, G.R., Glass, N.R. & Wilcox, J.C. (197) Fiing nonlinear models o biological day Marquard s algorihm. cology, 51, Conway, G.R., Trpis, M. 8( McClelland, G.A.H. (1974) Populaion parameers of he mosquio Aedes aegypi (L.) esimaed by mark-releaserecapure in a suburban habia in Tanzania. Journal of Animal cology, 4, Glasgow, J.P. (1961) The feeding habis of Glossina swynneroni Ausen. Journal of Animal cology,, Jackson, C.H.N. (19) The causes and implicaions of hunger in sese flies. Bullein of nomological Research, 24, Jackson, C.H.N. (197) Some new mehods in he sudy of Glossina morsians. Proceedings of he Zoological Sociey of London, 196, Jackson, C.H.N. (1948) The analysis of a sese-fly populaion Annals of ugenics, Cambridge, 14, Mellanby, H. (197) xperimenal work on reproducion in he sese fly, Glossina palpalis. Parasiology, 29, Randolph, S.. & Rogers, D.J. (1981) Physiological correlaes of he availabiliy of Glossina morsians cenralis Machado o differen sampling mehods. cological nomology, 6, Randolph, S.., Rogers, D.J. & Kuzoe, F.A.S. (1984) Local variaion in he populaion dynamics of Glossina palpalis palpalis (Robineau-Desvoidy) (Dipera: Glossinidae). 11. The effec of insecicidal spray programmes. Bullein of nomological Research, 74, Rogers, D.J. (1977) Sudy of a naural populaion of Glossina fuscipes fuscipes Newsead and a model of fly movemen. Journal of Animal cology, 46, Rogers, D.J. (1984) The esimaion of sampling biases for male sese flies. Insec Science and is Applicaion, 5, Rogers, D.J. & Randolph, S.. (1978) Meabolic sraegies of male and female sese (Dipera: Glossinidae) in he field. Bullein of nromological Research, 68, Rogers, D.J., Randolph, S.. & Kuzoe, F.A.S. (1984) Local variaion in he populaion dynamics of Glossina palpalis palpalis (Robineau- Desvoidy) (Dipera: Glossinidae). I. Naural populaion regulaion. Bullein of nomological Research, 74, Souhwood, T.R.. (1978) cological Merhods. Chapman & Hall, London. anderplank, F.L. (1947) Some observaions on he hunger-cycle of he sese-flies Glossina swynneroni and G.pallidipes (Dipera) in he field. Bullein of nomological Research, 8, Acceped 11 May 1985

15 ~ 18 David J. Rogers and Sarah. Randolph Appendix. Raw recapure daa for female G.palpnlis a Degbzrk Marking days, n -. ~~ No. new marks released Recapure day a h loo loo crr

16 ~ ~ ~~ ~ Appendix (coninued) Murking days, n 2 No. new marks released Recapure day ~~ 1 ~ Tsese aciviy cycles crr a=oal number of flies caugh; b=number of recapures from marking day n; crr=correced recapure rae allowing for removal of rapped marks (ex and formula 2). Noe: Since he flies were marked on 5 successive days he numbers in column a of any one marking day are he same as he numbers in column a of he previous marking day displaced by one recapure day.