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Modelling the trappability of tsetse, Glossina fuscipes fuscipes, in relation to distance from their natural habitats
Ecological Modelling 143 (2001) 183– 189 www.elsevier.com/locate/ecolmodel
Modelling the trappability of tsetse, Glossina fuscipes fuscipes, in relation to distance from their natural habitats Adedapo Odulaja *, Mohamed M. Mohamed-Ahmed International Centre of Insect Physiology and Ecology (ICIPE), P.O. Box 30772, Nairobi, Kenya Received 16 February 2000; received in revised form 27 February 2001; accepted 21 March 2001
Abstract The log–logistic probability distribution function was employed to model trappability of Glossina fuscipes fuscipes, with respect to distance from the edge of two types of habitat. The parameters of the model were obtained using the nonlinear maximum likelihood approach. Asymptotic standard errors of the maximum likelihood estimates were computed for the parameters, and the 2 goodness-of-fit test used to assess the predicted trap catches. Simulation technique was used to estimate the radius of attraction of the unbaited biconical trap for the fly, taking the efficiency of the trap into consideration. The log–logistic model fitted well to a series of observed field data. The model enabled the estimation of optimum trapping distances from the different habitat types for G. f. fuscipes. There is an indication that flies were attracted to, and got trapped optimally with, unbaited biconical traps, at distances that are characteristic of both sex of the fly and the type of habitat. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Tsetse; Trap; Habitat; Log–logistic distribution; Radius of attraction
1. Introduction Tsetse flies constitute a nuisance to both humans and livestock, transmitting the human sleeping sickness and animal trypanosomiasis. Riverine tsetse flies live mostly in dense thickets and forests bordering rivers or lakes (Buxton, 1955). In areas near human settlements, these habitats are often small and fragmented, and are bordered by extensive cultivated land or pastures (MohamedAhmed and Mihok, 1999). The flies spend most of their lives resting in the habitats, with only brief * Corresponding author. Fax: + 254-2-860110/803360. E-mail address: [email protected] (A. Odulaja).
forays into the open areas bordering the habitats to search for blood meals. They are known to concentrate at the edge of the habitats (Challier and Gouteux, 1980), probably waiting to locate an approaching host outside the habitat using both or one of visual and olfactory cues. Low metabolic reserves in tsetse preclude extensive flight activity (Bursell and Taylor, 1980), and hence, to avoid exhaustion, flies must expend energy judiciously (Mohamed-Ahmed and Mihok, 1999). Glossina fuscipes fuscipes, a riverine tsetse, is an important vector of human sleeping sickness in the Lake Victoria region (Hide et al., 1996). It is found in large numbers in linear forest patches
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A. Odulaja, M.M. Mohamed-Ahmed / Ecological Modelling 143 (2001) 183–189
and isolated thickets, bordered by extensive cultivated land or pastures, along the shores of Lake Victoria, Kenya (Mohamed-Ahmed and Odulaja, 1997). Many basic ecological studies have been carried out in these habitats with the aim of developing effective trapping technologies (Oloo, 1983; Mwangelwa et al., 1990, 1995; MohamedAhmed and Odulaja, 1997). Riverine tsetse are very difficult to control because of their habitat and behaviour (Laveissie`re et al., 1990). Because of its numerous qualities, trapping is probably the only method that can be used nowadays, as long as it is used wisely (Laveissie`re et al., 1990). Attempts have been made to use traps for the control and survey of this species of tsetse (Lancien et al., 1990; Katunguka-Rwakishaya and Kabagambe, 1996). Tsetse traps have traditionally targeted flies stalking their hosts, and many trap designers therefore, sought to exploit a presumed visual attraction of tsetse to their hosts’ shape (Odulaja and Madubunyi, 1997). Others (Challier and Laveissie`re, 1973) however, targeted the flies’ attraction to specific colors, in their trap designs. By baiting some of these traps with host-odors or their synthetic derivatives, catch sizes were dramatically increased (Hargrove and Vale, 1980; Brightwell et al., 1991; Mihok et al., 1995). An understanding of trappability in relation to habitat is necessary for optimum trap placement for both monitoring and suppression of fly populations. Optimal placement of sampling tools is also essential for studying ecology and behaviour. Many studies have indicated that trapping efficiency is affected by the positioning of the trapping device in relation to tsetse’s habitats. These insights have come from conventional analyses of numbers or percentages of tsetse caught at different distances from their habitat. Typically, 2 or ANOVA tests are used to ascertain significant differences between catches at various distances, and simple regressions used to study trends (Dransfield, 1984; Mohamed-Ahmed and Wynholds, 1997). Such analyses are only indicative; they lack the ability to predict optimum positioning. To address these issues, this study proposes and tests a statistical model to describe a set of data on optimum trap position or radius of at-
traction of the trap, in relation to two habitat types, for G. f. fuscipes along the shores of Lake Victoria, Kenya.
2. Material, methods and results
2.1. Data description Data for this study were obtained by Mohamed-Ahmed and Wynholds (1997) from two locations, Mbita Point (mainland) and Rusinga Island, near Lake Victoria, western Kenya. G. f. fuscipes is found in large numbers in forest patches and isolated thickets, bordered by extensive cultivated land or pastures, along the shores of the Lake (Mohamed-Ahmed and Odulaja, 1997). Two large forest patches, one on the mainland and the other on the island, each able to accommodate five trap sites separated by at least 200 m, were selected. Five isolated thickets, constituting five trap sites, were also selected at each of the two locations. Four experimental areas were thus obtained: mainland forest, mainland thickets, island forest and island thickets, with each area having five trap sites. At each site, five trap positions were selected at specific distances from the edge of the habitat. The five positions were: (a) 1 m inside the habitat; (b) at the edge; (c), (d), and (e) 1, 5 and 10 m from the edge. An unbaited biconical trap (Challier et al., 1977) was used for catching flies at each site. For each area, the five traps were swapped for 5 days between the five positions and five sites, in a 5× 5 Latin square design (five sites, five positions and 5 days). The experiment was repeated once in each experimental area. Traps were emptied daily and the number of flies counted. Conventional analysis of variance of the data set was presented in Mohamed-Ahmed and Wynholds (1997).
2.2. Trappability model Riverine tsetse is believed to hunt largely by vision (Laveissie`re et al., 1990), and since traps considered in this study are unbaited, only visual cues are involved in the trapping. Environmental effect on trapping is assumed to constitute only
A. Odulaja, M.M. Mohamed-Ahmed / Ecological Modelling 143 (2001) 183–189
the habitat types, whereas the effect of other factors on trap sighting and entry is negligible or constant with respect to distance from the habitat. We also assume that G. f. fuscipes populations are ‘one-point’ source when considering host-seeking behaviour of the flies, since the flies usually concentrate at the edge of their habitats (Challier and Gouteux, 1980). The flies are known to use forests as breeding and resting haunt and open area as feeding grounds (Challier and Gouteux, 1980). Plots of the catches against distance from habitat (Fig. 1) are skewed to the right. To describe the distribution of the catches in relation to the habitat, we denote the distance-dependent catch of flies by zd(z). Our model is based on a mathematical representation of the observed cumulative proportions of flies caught at various distances, starting from inside the habitat and proceeding outside. We sought to represent the cumulative proportions by a cumulative distribution function (cdf), F(z), defined for − B zB , to reflect the fact that we are dealing with phenomena inside and outside the habitat, with z =0 as the
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edge of the habitat. The function F(z) should be such that F(x) may be non-zero for all x, to allow for possible catches at any distance. Catches are expected to decrease as one moves away from the edge of the habitat (Challier and Gouteux, 1980). The corresponding probability density function, pdf, should be two-tailed to exhibit a maximum, the direction and degree of skewness being trapand insect-dependent. The log– logistic distribution readily satisfies the required properties. We choose to employ this distribution because of its capability to handle both right- and left-censoring, since the likelihood can be expressed as a special form of binomial likelihood (Bennett and Whitehead, 1981; Aitkin et al., 1989). This is particularly applicable to the situation under study, in that not all distances inside and outside the habitat were considered in the trapping experiment. The log–logistic pdf is given by: f(z)=
n, 1 z− v exp | |
1+ exp
n z− v |
2
(1)
and the cdf by:
Fig. 1. Proportion of G. f. fuscipes caught at different distances from the edge of two habitat types, along the shores of Lake Victoria, Kenya.
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Table 1 Parameter estimates ( 9 asymptotic S.E.) and goodness-of-fit test for the log–logistic model fitted to the data setsa Habitat
Sex
v (m)
| (m)
Goodness-of-fit 2
P\ 2
Female Male
0.75 9 0.12 (0.38–1.12) 0.43 90.10 (0.11–0.76)
0.70 90.13 (0.29–1.11) 0.74 9 0.11 (0.38–1.10)
6.89 3.72
0.857 0.555
Female Male
0.26 90.10 (−0.05–0.57) 0.199 0.11 (−0.15–0.53)
0.62 90.10 (0.31–0.93) 0.64 90.11 (0.30–0.99)
4.13 4.57
0.611 0.665
Forest
Thicket
a
,
n
Figures in parentheses are the asymptotic 95% confidence interval for the parameters.
F(z) =exp
z−v |
1 +exp
z −v |
,
− B z B ,
(2)
where v and | are constants representing the parameters of the distribution. The mean and variance of the distribution are, respectively: Mean =v,
(3)
and Variance=| 2y 2/3.
(4)
We hypothesize that there is a distance inside or outside the habitat, indicated by v, at which the insects tend to be most trappable. Given that the total number of flies caught is N, the number caught between two distances z1 and z2, where z1 B z2, is given by:
&
z2
z1
zd(z)=N
&
z2
f(z) = N[F(z2) − F(z1)].
(5)
z1
To fit the log–logistic function to actual data, the space from inside to outside the habitat is first divided into strips whose boundaries are labelled z − m, z − m − 1, …, z0, z1, …, zn − 1, zn, the total number of strips being n + m. The number of flies caught is then recorded for each interval [zj − 1, zj ], for j= − (m +1), −m, …, 0, 1, 2, …, n. If the distance intervals are relatively small, there may be considerable fluctuation in the data between neighbouring intervals. In this case, several intervals may be combined to obtain observations over larger intervals, which depict the general trend of decrease in catches as one moves away from the habitat. The cumulative distribution function, F(zi ), is then replaced by the observed cumulative
proportions at zi. Estimates of the distribution parameters are then obtained by maximizing the likelihood function, L, given by: n
L=
%
pˆj loge(pj ),
(6)
j = − (m + 1)
where pˆj is the observed relative frequency or proportion of insects in the jth interval, namely [zj − 1, zj ] and pj, is the theoretical probability of getting an observation in this interval, given by: pj = F(zj )− F(zj − 1).
(7)
Plots of the observed proportion of flies caught at different distances from the two habitat types are shown in Fig. 1. Table 1 shows the results of the model fitted to the cumulative proportions for each habitat type and both sexes of the fly. The goodness-of-fit tests (H0:pˆj = pj for all distance interval j; H1:pˆj " pj ; for some distance interval j ) gave non-significant 2-values (df=4) for all the data sets (Table 1). The results showed that mean optimum distance, v, from the forest habitat for trapping G. f. fuscipes was significantly greater than zero (edge of forest) for both sexes, using the asymptotic 95% confidence interval for the parameter. Males were caught optimally at about 43 cm from the forest edge, whereas females were caught optimally at about 75 cm. The optimum distances from the forest edge were not significantly different between sexes (the asymptotic 95% confidence intervals overlap). For the thickets, the optimum distances were neither significantly different from zero for both sexes, nor significantly different between sexes. These results suggest that traps should be set at the exact edge
A. Odulaja, M.M. Mohamed-Ahmed / Ecological Modelling 143 (2001) 183–189
of thickets to catch G. f. fuscipes efficiently, but should be set slightly away from the edge of forests at a distance between 40 cm and 1 m.
3. Radius of attraction of the biconical trap: a simulation A critical parameter of trap efficiency is the radius of attraction as this largely determines the density of traps required for population suppression. For this study, this radius, r, is defined as the distance away from the habitat, at which the probability of catching a fly is zero or nearly so. That is, it is the distance z at which F(z) approaches unity. This implies that, given the parameters of the model, v and |, r may be obtained from: F(r) =1−m,
m:0.
(8)
That is, r =F − 1(1− m).
(9)
To estimate r, a simulation is carried out with the parameters (v, |) of the model varied by stepwise iteration within the asymptotic 95% confidence interval obtained when the model is fitted to a data set. The minimum distance, r (representing the radius of attraction), at which F(z) is greater than, or equal to, 1−m, for different combinations of the model’s parameter values, may then be obtained.
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Table 2 shows the results of the simulation setting m= 0.00001, that is, F(z)= 0.99999. The table shows the mean, standard deviation, minimum, first quartile, median, third quartile, and maximum values of r. The mean radii of attraction were shorter for the thicket habitat than for the forest habitat. 4. Discussion When a tsetse fly encounters a trap while looking for a bloodmeal or a mate, we can only guess at what it perceives. Strange objects such as traps contrast with the environment and are effective in eliciting investigation and landing only when they are of the right shape and colour (Green, 1994). This is particularly critical for riverine tsetse like G. f. fuscipes which are believed to hunt largely by sight (Laveissie`re et al., 1990; Moloo, 1993). Models have been used to study the distribution of insects in relations to several activities. Movement and dispersal of insects are traditionally modelled using diffusion equations (Williams et al., 1992; Blackwell, 1997; Schneider, 1999). This present study however models attraction and trappability of insects, as distinct from dispersal. In an approach similar to the method used in this paper, Ogana (1996) employed the Weibull distribution function to describe the vertical distribution of insects. In a different context, Odulaja and Madubunyi (1997) employed both the exponential and beta distribution functions to model the sampling bias of odor-baited tsetse traps.
Table 2 Descriptive statistics obtained from simulations for the radius of attraction (in m) of the biconical trap for G. f. fuscipes Statistic
n (no. of iterations) Mean Standard deviation Minimum 1st quartile Median 3rd quartile Maximum
Forest habitat
Thicket habitat
Female
Male
Female
Male
6225 8.9 2.8 3.8 6.5 8.9 11.3 13.9
4818 9.0 2.4 4.5 6.9 9.0 11.1 13.5
3969 7.4 2.1 3.6 5.6 7.4 9.3 11.3
4830 7.7 2.3 3.4 5.7 7.7 9.7 12.0
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The radius of attraction obtained in this study assumes that the trap is 100% efficient in catching any fly reacting to its presence in the environment. Provisional estimates of the efficiency of the trap for both sexes of G. f. fuscipes in the study area, however put the efficiencies much less than 100% (Odulaja and Mohamed-Ahmed, 1997). Therefore, the values obtained for the range of attraction should be regarded as underestimates, because some flies may be attracted at longer distances without being caught. If efficiency, e, is constant over all distances, the actual probability that a fly is caught when it is attracted to, or sees, the trap at a distance as far away as these estimates of the radius of attraction, is approximately e. Therefore, the estimated radii should be divided by e for a more realistic estimate of the radius of attraction of the trap. With a provisional estimate of an overall efficiency of about 0.51 for G. f. fuscipes in this area, the actual mean radius of attraction of the biconical trap should be about 18 m (i.e. 9.0/0.51) outside the forest habitat, and 15 m (i.e. 7.6/0.51) outside the thicket. The trap was however found to be more efficient for males ( 0.8) than for females ( 0.45). Therefore, the radius of attraction may be shorter for males ( 11 m for forest, and 10 m for thicket), than for females ( 20 m for forest, and 16 m for thicket). No studies have been carried out to estimate the radius of attraction of the biconical trap for G. f. fuscipes. However, Dransfield (1984) suggested 15 m as the upper limit for visual detection of an unbaited biconical trap by G. pallidipes Austen. The author also obtained a 10– 15 m detection range of biconical traps set at the edge of the forest, by G. bre6ipalpis Newstead. Turner and Invest (1973) suggested that a fly should be able to resolve a biconical trap at a distance of 10 m. Estimates of the radius of attraction of the biconical trap for G. f. fuscipes, obtained using our model, are within the limits of the various suggestions. The differences in the effect of the two habitats on trap positioning and radius of attraction, may be due to light intensity and temperature around habitat. The riverine tsetse is known to reacts differently, especially in the forest area (Laveissie`re et al., 1990). G .f. fuscipes activity has
been found to be correlated with both light intensity and temperature (Mohamed-Ahmed and Odulaja, 1997). Also, tsetse may become less active at any level of illumination, due to photonegative behaviour at high temperature (Glasgow, 1970; Mohamed-Ahmed and Odulaja, 1997). Forests cast wider and denser shadows in daylight, perhaps prompting flies to venture further outside the habitat. This probably explains the slightly longer optimum positioning, and radius of attraction, obtained for the forest habitat. Our results however strengthen the observation of Laveissie`re et al. (1990), that trapping is a hyperselective form of treatment, and decoys should therefore be installed in a very precise manner in specific places in the ecosystem, to be effective. Installation should also be done differently in different biotopes. Differences between the sexes with respect to optimum trap positioning, and possibly radius of attraction, may be due to differences in their activity patterns. The diurnal distribution of male G. f. fuscipes catches has been found to peak earlier in the day than for females (MohamedAhmed and Odulaja, 1997). Specific temperature thresholds may therefore exist for the different sexes, which is likely to be less for males, suggesting that males are less tolerant to strong light intensity and high temperature, than females. This probably explains why optimum trapping distance, and radius of attraction, were shorter for males. Apart from the data used in this study, there is no other published data for any tsetse species on the effect of distance from vegetation on trap efficiency (Mohamed-Ahmed and Wynholds, 1997). However, the model proposed in this study should be applicable to any experiment studying the optimum positioning of traps in relation distance from any habitat type, for ‘one-point’ source insect populations.
Acknowledgements Thanks to Drs Johann Baumga¨ rtner and Steve Mihok for their critique of this manuscript and useful suggestions.
A. Odulaja, M.M. Mohamed-Ahmed / Ecological Modelling 143 (2001) 183–189
References Aitkin, M., Anderson, D., Francis, B., Hinde, J., 1989. Statistical Modelling in GLIM. Oxford University Press, New York, p. 374. Bennett, S., Whitehead, J., 1981. Fitting logistic and log –logistic regression models to censored data using GLIM. GLIM Newslett. 4, 12 – 19. Blackwell, P.G., 1997. Random diffusion models for animal movement. Ecol. Mod. 100, 87 –102. Brightwell, R., Dransfield, R.D., Kyorku, C., 1991. Development of a low-cost tsetse trap and odour baits for Glossina pallidipes and G. longipennis in Kenya. Med. Vet. Entomol. 5, 153 – 164. Bursell, E., Taylor, P., 1980. An energy budget for Glossina (Diptera: Glossinidae). Bull. Entomol. Res. 70, 187 –196. Buxton, P.A., 1955. The natural history of tsetse flies. In: An Account of the Biology of the Genus Glossina (Diptera). H.K. Lewis & Co., London. Challier, A., Eyraud, M., Lafaye, A., Laveissie`re, C., 1977. Ame´ lioration du rendement du pie`ge biconique pour glossines (Diptera, Glossinidae) par l’emploi d’un coˆ ne infe´ rieur bleu. Cah. Orstom Se´ r. Entomol. Me´ d. Parasitol. 15, 283 – 286. Challier, A., Gouteux, J.P., 1980. Ecology and epidemiological importance of Glossina palpalis in the Ivory coast forest zone. Insect Sci. Appl. 1, 77 –83. Challier, A., Laveissie`re, C., 1973. Un nouveau piege pour la capture des glossines (Glossina, Diptera). Description et essais sur le terrain, Cahiers ORSTOM. Series Entomologie Medicale et Parasitologie 11, 251 –262. Dransfield, R.D., 1984. The range of attraction of the biconical trap for Glossina pallidipes and G. bre6ipalpis. Insect Sci. Appl. 5, 363 – 368. Glasgow, J.P., 1970. The Glossina community. In: Mulligan, H.W. (Ed.), The African Trypanosomiases. Allen and Unwin, London, pp. 348–381. Green, C.H., 1994. Bait methods for tsetse fly control. Adv. Parasitol. 34, 229 – 291. Hargrove, J.W., Vale, G.A., 1980. Catches of Glossina morsitans morsitans Westwood and G. pallidipes Austen (Diptera: Glossinidae) in odour baited traps in riverine and deciduous woodlands in the Zambesi Valley of Zimbabwe. Bull. Entomol. Res. 70, 571 –578. Hide, G., Tait, A., Maudlin, I., Welburn, S.C., 1996. The origins, dynamics and generation of Trypanosoma brucei rhodesiense epidemics in East Africa. Parasitol. Today 12, 50– 55. Katunguka-Rwakishaya, E., Kabagambe, E.K., 1996. Tsetse survey in Mukono District, south-east Uganda: population structure, distribution and blood meal status. Trop. Anim. Health Prod. 28, 151 –167.
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Lancien, J., Muguwa, J., Lannes, C., Bouvier, J.B., 1990. Tsetse and human trypanosomiasis challenge in south eastern Uganda. Insect Sci. Appl. 11, 411 – 416. Laveissie`re, C., E´ ouzan, J.P., Gre´ baut, P., LeMasson, J.J., 1990. The control of riverine tsetse. Insect Sci. Appl. 11, 427 – 442. Mihok, S., Kang’ethe, E.K., Kamau, G.K., 1995. Trials of traps and attractants for Stomoxys spp. (Diptera: Muscidae). J. Med. Entomol. 32, 283 – 289. Mohamed-Ahmed, M.M., Mihok, S., 1999. Responses of Glossina fuscipes fuscipes (Diptera: Glossinidae) and other Diptera to carbon dioxide in linear and dense forests. Bull. Entomol. Res. 89, 177 – 184. Mohamed-Ahmed, M.M., Odulaja, A., 1997. Diel activity patterns and host preferences of Glossina fuscipes fuscipes (Diptera: Glossinidae) along the shores of Lake Victoria, Kenya. Bull. Entomol. Res. 87, 179 – 186. Mohamed-Ahmed, M.M., Wynholds, Y., 1997. Effects of vegetation and weather on trap catches of Glossina fuscipes fuscipes near Lake Victoria, Kenya. Entomol. Exp. Appl. 85, 231 – 236. Moloo, S.K., 1993. The distribution of Glossina species in Africa and their natural hosts. Insect Sci. Appl. 14, 511 – 527. Mwangelwa, M.I., Dransfield, R.D., Otieno, L.H., 1990. Distribution and diel activity pattern of Glossina fuscipes fuscipes Newstead on Rusinga Island and mainland in Mbita, Kenya. Insect Sci. Appl. 11, 315 – 322. Mwangelwa, M.I., Dransfield, R.D., Otieno, L.H., Mbata, K.J., 1995. The response of Glossina fuscipes fuscipes Newstead to odour attractants and traps. J. Afr. Zool. 109, 23 – 30. Odulaja, A., Madubunyi, L.C., 1997. A sampling bias model for odour-baited traps in relation to tsetse hunger cycle and population suppression. Ecol. Mod. 104, 165 – 173. Odulaja, A., Mohamed-Ahmed, M.M., 1997. Estimation of the efficiency of the biconical trap for Glossina fuscipes fuscipes along the lake Victoria shore, Kenya. Entomol. Exp. Appl. 82, 19 – 24. Ogana, W., 1996. Modelling the vertical distribution of insects. Ecol. Mod. 89, 225 – 230. Oloo, F.P., 1983. Ecology of Glossina fuscipes fuscipes Newstead (Diptera: Glossinidae) along the shores of Lake victoria, MSc. thesis, University of Nairobi, Kenya. Schneider, J.C., 1999. Dispersal of a highly vagile insect in a heterogeneous environment. Ecology 80, 2740 – 2749. Turner, D.A., Invest, J.F., 1973. Laboratory analysis of vision in tsetse flies (Diptera: Glossinidae). Bull. Entomol. Res. 64, 343 – 357. Williams, B., Dransfield, R., Brightwell, R., 1992. The control of tsetse flies in relation to fly movement and trapping efficiency. J. App. Ecol. 29, 163 – 179.
Modelling the trappability of tsetse, Glossina fuscipes fuscipes, in relation to distance from their natural habitats Adedapo Odulaja *, Mohamed M. Mohamed-Ahmed International Centre of Insect Physiology and Ecology (ICIPE), P.O. Box 30772, Nairobi, Kenya Received 16 February 2000; received in revised form 27 February 2001; accepted 21 March 2001
Abstract The log–logistic probability distribution function was employed to model trappability of Glossina fuscipes fuscipes, with respect to distance from the edge of two types of habitat. The parameters of the model were obtained using the nonlinear maximum likelihood approach. Asymptotic standard errors of the maximum likelihood estimates were computed for the parameters, and the 2 goodness-of-fit test used to assess the predicted trap catches. Simulation technique was used to estimate the radius of attraction of the unbaited biconical trap for the fly, taking the efficiency of the trap into consideration. The log–logistic model fitted well to a series of observed field data. The model enabled the estimation of optimum trapping distances from the different habitat types for G. f. fuscipes. There is an indication that flies were attracted to, and got trapped optimally with, unbaited biconical traps, at distances that are characteristic of both sex of the fly and the type of habitat. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Tsetse; Trap; Habitat; Log–logistic distribution; Radius of attraction
1. Introduction Tsetse flies constitute a nuisance to both humans and livestock, transmitting the human sleeping sickness and animal trypanosomiasis. Riverine tsetse flies live mostly in dense thickets and forests bordering rivers or lakes (Buxton, 1955). In areas near human settlements, these habitats are often small and fragmented, and are bordered by extensive cultivated land or pastures (MohamedAhmed and Mihok, 1999). The flies spend most of their lives resting in the habitats, with only brief * Corresponding author. Fax: + 254-2-860110/803360. E-mail address: [email protected] (A. Odulaja).
forays into the open areas bordering the habitats to search for blood meals. They are known to concentrate at the edge of the habitats (Challier and Gouteux, 1980), probably waiting to locate an approaching host outside the habitat using both or one of visual and olfactory cues. Low metabolic reserves in tsetse preclude extensive flight activity (Bursell and Taylor, 1980), and hence, to avoid exhaustion, flies must expend energy judiciously (Mohamed-Ahmed and Mihok, 1999). Glossina fuscipes fuscipes, a riverine tsetse, is an important vector of human sleeping sickness in the Lake Victoria region (Hide et al., 1996). It is found in large numbers in linear forest patches
0304-3800/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 0 0 ( 0 1 ) 0 0 3 2 9 - 5
184
A. Odulaja, M.M. Mohamed-Ahmed / Ecological Modelling 143 (2001) 183–189
and isolated thickets, bordered by extensive cultivated land or pastures, along the shores of Lake Victoria, Kenya (Mohamed-Ahmed and Odulaja, 1997). Many basic ecological studies have been carried out in these habitats with the aim of developing effective trapping technologies (Oloo, 1983; Mwangelwa et al., 1990, 1995; MohamedAhmed and Odulaja, 1997). Riverine tsetse are very difficult to control because of their habitat and behaviour (Laveissie`re et al., 1990). Because of its numerous qualities, trapping is probably the only method that can be used nowadays, as long as it is used wisely (Laveissie`re et al., 1990). Attempts have been made to use traps for the control and survey of this species of tsetse (Lancien et al., 1990; Katunguka-Rwakishaya and Kabagambe, 1996). Tsetse traps have traditionally targeted flies stalking their hosts, and many trap designers therefore, sought to exploit a presumed visual attraction of tsetse to their hosts’ shape (Odulaja and Madubunyi, 1997). Others (Challier and Laveissie`re, 1973) however, targeted the flies’ attraction to specific colors, in their trap designs. By baiting some of these traps with host-odors or their synthetic derivatives, catch sizes were dramatically increased (Hargrove and Vale, 1980; Brightwell et al., 1991; Mihok et al., 1995). An understanding of trappability in relation to habitat is necessary for optimum trap placement for both monitoring and suppression of fly populations. Optimal placement of sampling tools is also essential for studying ecology and behaviour. Many studies have indicated that trapping efficiency is affected by the positioning of the trapping device in relation to tsetse’s habitats. These insights have come from conventional analyses of numbers or percentages of tsetse caught at different distances from their habitat. Typically, 2 or ANOVA tests are used to ascertain significant differences between catches at various distances, and simple regressions used to study trends (Dransfield, 1984; Mohamed-Ahmed and Wynholds, 1997). Such analyses are only indicative; they lack the ability to predict optimum positioning. To address these issues, this study proposes and tests a statistical model to describe a set of data on optimum trap position or radius of at-
traction of the trap, in relation to two habitat types, for G. f. fuscipes along the shores of Lake Victoria, Kenya.
2. Material, methods and results
2.1. Data description Data for this study were obtained by Mohamed-Ahmed and Wynholds (1997) from two locations, Mbita Point (mainland) and Rusinga Island, near Lake Victoria, western Kenya. G. f. fuscipes is found in large numbers in forest patches and isolated thickets, bordered by extensive cultivated land or pastures, along the shores of the Lake (Mohamed-Ahmed and Odulaja, 1997). Two large forest patches, one on the mainland and the other on the island, each able to accommodate five trap sites separated by at least 200 m, were selected. Five isolated thickets, constituting five trap sites, were also selected at each of the two locations. Four experimental areas were thus obtained: mainland forest, mainland thickets, island forest and island thickets, with each area having five trap sites. At each site, five trap positions were selected at specific distances from the edge of the habitat. The five positions were: (a) 1 m inside the habitat; (b) at the edge; (c), (d), and (e) 1, 5 and 10 m from the edge. An unbaited biconical trap (Challier et al., 1977) was used for catching flies at each site. For each area, the five traps were swapped for 5 days between the five positions and five sites, in a 5× 5 Latin square design (five sites, five positions and 5 days). The experiment was repeated once in each experimental area. Traps were emptied daily and the number of flies counted. Conventional analysis of variance of the data set was presented in Mohamed-Ahmed and Wynholds (1997).
2.2. Trappability model Riverine tsetse is believed to hunt largely by vision (Laveissie`re et al., 1990), and since traps considered in this study are unbaited, only visual cues are involved in the trapping. Environmental effect on trapping is assumed to constitute only
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the habitat types, whereas the effect of other factors on trap sighting and entry is negligible or constant with respect to distance from the habitat. We also assume that G. f. fuscipes populations are ‘one-point’ source when considering host-seeking behaviour of the flies, since the flies usually concentrate at the edge of their habitats (Challier and Gouteux, 1980). The flies are known to use forests as breeding and resting haunt and open area as feeding grounds (Challier and Gouteux, 1980). Plots of the catches against distance from habitat (Fig. 1) are skewed to the right. To describe the distribution of the catches in relation to the habitat, we denote the distance-dependent catch of flies by zd(z). Our model is based on a mathematical representation of the observed cumulative proportions of flies caught at various distances, starting from inside the habitat and proceeding outside. We sought to represent the cumulative proportions by a cumulative distribution function (cdf), F(z), defined for − B zB , to reflect the fact that we are dealing with phenomena inside and outside the habitat, with z =0 as the
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edge of the habitat. The function F(z) should be such that F(x) may be non-zero for all x, to allow for possible catches at any distance. Catches are expected to decrease as one moves away from the edge of the habitat (Challier and Gouteux, 1980). The corresponding probability density function, pdf, should be two-tailed to exhibit a maximum, the direction and degree of skewness being trapand insect-dependent. The log– logistic distribution readily satisfies the required properties. We choose to employ this distribution because of its capability to handle both right- and left-censoring, since the likelihood can be expressed as a special form of binomial likelihood (Bennett and Whitehead, 1981; Aitkin et al., 1989). This is particularly applicable to the situation under study, in that not all distances inside and outside the habitat were considered in the trapping experiment. The log–logistic pdf is given by: f(z)=
n, 1 z− v exp | |
1+ exp
n z− v |
2
(1)
and the cdf by:
Fig. 1. Proportion of G. f. fuscipes caught at different distances from the edge of two habitat types, along the shores of Lake Victoria, Kenya.
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Table 1 Parameter estimates ( 9 asymptotic S.E.) and goodness-of-fit test for the log–logistic model fitted to the data setsa Habitat
Sex
v (m)
| (m)
Goodness-of-fit 2
P\ 2
Female Male
0.75 9 0.12 (0.38–1.12) 0.43 90.10 (0.11–0.76)
0.70 90.13 (0.29–1.11) 0.74 9 0.11 (0.38–1.10)
6.89 3.72
0.857 0.555
Female Male
0.26 90.10 (−0.05–0.57) 0.199 0.11 (−0.15–0.53)
0.62 90.10 (0.31–0.93) 0.64 90.11 (0.30–0.99)
4.13 4.57
0.611 0.665
Forest
Thicket
a
,
n
Figures in parentheses are the asymptotic 95% confidence interval for the parameters.
F(z) =exp
z−v |
1 +exp
z −v |
,
− B z B ,
(2)
where v and | are constants representing the parameters of the distribution. The mean and variance of the distribution are, respectively: Mean =v,
(3)
and Variance=| 2y 2/3.
(4)
We hypothesize that there is a distance inside or outside the habitat, indicated by v, at which the insects tend to be most trappable. Given that the total number of flies caught is N, the number caught between two distances z1 and z2, where z1 B z2, is given by:
&
z2
z1
zd(z)=N
&
z2
f(z) = N[F(z2) − F(z1)].
(5)
z1
To fit the log–logistic function to actual data, the space from inside to outside the habitat is first divided into strips whose boundaries are labelled z − m, z − m − 1, …, z0, z1, …, zn − 1, zn, the total number of strips being n + m. The number of flies caught is then recorded for each interval [zj − 1, zj ], for j= − (m +1), −m, …, 0, 1, 2, …, n. If the distance intervals are relatively small, there may be considerable fluctuation in the data between neighbouring intervals. In this case, several intervals may be combined to obtain observations over larger intervals, which depict the general trend of decrease in catches as one moves away from the habitat. The cumulative distribution function, F(zi ), is then replaced by the observed cumulative
proportions at zi. Estimates of the distribution parameters are then obtained by maximizing the likelihood function, L, given by: n
L=
%
pˆj loge(pj ),
(6)
j = − (m + 1)
where pˆj is the observed relative frequency or proportion of insects in the jth interval, namely [zj − 1, zj ] and pj, is the theoretical probability of getting an observation in this interval, given by: pj = F(zj )− F(zj − 1).
(7)
Plots of the observed proportion of flies caught at different distances from the two habitat types are shown in Fig. 1. Table 1 shows the results of the model fitted to the cumulative proportions for each habitat type and both sexes of the fly. The goodness-of-fit tests (H0:pˆj = pj for all distance interval j; H1:pˆj " pj ; for some distance interval j ) gave non-significant 2-values (df=4) for all the data sets (Table 1). The results showed that mean optimum distance, v, from the forest habitat for trapping G. f. fuscipes was significantly greater than zero (edge of forest) for both sexes, using the asymptotic 95% confidence interval for the parameter. Males were caught optimally at about 43 cm from the forest edge, whereas females were caught optimally at about 75 cm. The optimum distances from the forest edge were not significantly different between sexes (the asymptotic 95% confidence intervals overlap). For the thickets, the optimum distances were neither significantly different from zero for both sexes, nor significantly different between sexes. These results suggest that traps should be set at the exact edge
A. Odulaja, M.M. Mohamed-Ahmed / Ecological Modelling 143 (2001) 183–189
of thickets to catch G. f. fuscipes efficiently, but should be set slightly away from the edge of forests at a distance between 40 cm and 1 m.
3. Radius of attraction of the biconical trap: a simulation A critical parameter of trap efficiency is the radius of attraction as this largely determines the density of traps required for population suppression. For this study, this radius, r, is defined as the distance away from the habitat, at which the probability of catching a fly is zero or nearly so. That is, it is the distance z at which F(z) approaches unity. This implies that, given the parameters of the model, v and |, r may be obtained from: F(r) =1−m,
m:0.
(8)
That is, r =F − 1(1− m).
(9)
To estimate r, a simulation is carried out with the parameters (v, |) of the model varied by stepwise iteration within the asymptotic 95% confidence interval obtained when the model is fitted to a data set. The minimum distance, r (representing the radius of attraction), at which F(z) is greater than, or equal to, 1−m, for different combinations of the model’s parameter values, may then be obtained.
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Table 2 shows the results of the simulation setting m= 0.00001, that is, F(z)= 0.99999. The table shows the mean, standard deviation, minimum, first quartile, median, third quartile, and maximum values of r. The mean radii of attraction were shorter for the thicket habitat than for the forest habitat. 4. Discussion When a tsetse fly encounters a trap while looking for a bloodmeal or a mate, we can only guess at what it perceives. Strange objects such as traps contrast with the environment and are effective in eliciting investigation and landing only when they are of the right shape and colour (Green, 1994). This is particularly critical for riverine tsetse like G. f. fuscipes which are believed to hunt largely by sight (Laveissie`re et al., 1990; Moloo, 1993). Models have been used to study the distribution of insects in relations to several activities. Movement and dispersal of insects are traditionally modelled using diffusion equations (Williams et al., 1992; Blackwell, 1997; Schneider, 1999). This present study however models attraction and trappability of insects, as distinct from dispersal. In an approach similar to the method used in this paper, Ogana (1996) employed the Weibull distribution function to describe the vertical distribution of insects. In a different context, Odulaja and Madubunyi (1997) employed both the exponential and beta distribution functions to model the sampling bias of odor-baited tsetse traps.
Table 2 Descriptive statistics obtained from simulations for the radius of attraction (in m) of the biconical trap for G. f. fuscipes Statistic
n (no. of iterations) Mean Standard deviation Minimum 1st quartile Median 3rd quartile Maximum
Forest habitat
Thicket habitat
Female
Male
Female
Male
6225 8.9 2.8 3.8 6.5 8.9 11.3 13.9
4818 9.0 2.4 4.5 6.9 9.0 11.1 13.5
3969 7.4 2.1 3.6 5.6 7.4 9.3 11.3
4830 7.7 2.3 3.4 5.7 7.7 9.7 12.0
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The radius of attraction obtained in this study assumes that the trap is 100% efficient in catching any fly reacting to its presence in the environment. Provisional estimates of the efficiency of the trap for both sexes of G. f. fuscipes in the study area, however put the efficiencies much less than 100% (Odulaja and Mohamed-Ahmed, 1997). Therefore, the values obtained for the range of attraction should be regarded as underestimates, because some flies may be attracted at longer distances without being caught. If efficiency, e, is constant over all distances, the actual probability that a fly is caught when it is attracted to, or sees, the trap at a distance as far away as these estimates of the radius of attraction, is approximately e. Therefore, the estimated radii should be divided by e for a more realistic estimate of the radius of attraction of the trap. With a provisional estimate of an overall efficiency of about 0.51 for G. f. fuscipes in this area, the actual mean radius of attraction of the biconical trap should be about 18 m (i.e. 9.0/0.51) outside the forest habitat, and 15 m (i.e. 7.6/0.51) outside the thicket. The trap was however found to be more efficient for males ( 0.8) than for females ( 0.45). Therefore, the radius of attraction may be shorter for males ( 11 m for forest, and 10 m for thicket), than for females ( 20 m for forest, and 16 m for thicket). No studies have been carried out to estimate the radius of attraction of the biconical trap for G. f. fuscipes. However, Dransfield (1984) suggested 15 m as the upper limit for visual detection of an unbaited biconical trap by G. pallidipes Austen. The author also obtained a 10– 15 m detection range of biconical traps set at the edge of the forest, by G. bre6ipalpis Newstead. Turner and Invest (1973) suggested that a fly should be able to resolve a biconical trap at a distance of 10 m. Estimates of the radius of attraction of the biconical trap for G. f. fuscipes, obtained using our model, are within the limits of the various suggestions. The differences in the effect of the two habitats on trap positioning and radius of attraction, may be due to light intensity and temperature around habitat. The riverine tsetse is known to reacts differently, especially in the forest area (Laveissie`re et al., 1990). G .f. fuscipes activity has
been found to be correlated with both light intensity and temperature (Mohamed-Ahmed and Odulaja, 1997). Also, tsetse may become less active at any level of illumination, due to photonegative behaviour at high temperature (Glasgow, 1970; Mohamed-Ahmed and Odulaja, 1997). Forests cast wider and denser shadows in daylight, perhaps prompting flies to venture further outside the habitat. This probably explains the slightly longer optimum positioning, and radius of attraction, obtained for the forest habitat. Our results however strengthen the observation of Laveissie`re et al. (1990), that trapping is a hyperselective form of treatment, and decoys should therefore be installed in a very precise manner in specific places in the ecosystem, to be effective. Installation should also be done differently in different biotopes. Differences between the sexes with respect to optimum trap positioning, and possibly radius of attraction, may be due to differences in their activity patterns. The diurnal distribution of male G. f. fuscipes catches has been found to peak earlier in the day than for females (MohamedAhmed and Odulaja, 1997). Specific temperature thresholds may therefore exist for the different sexes, which is likely to be less for males, suggesting that males are less tolerant to strong light intensity and high temperature, than females. This probably explains why optimum trapping distance, and radius of attraction, were shorter for males. Apart from the data used in this study, there is no other published data for any tsetse species on the effect of distance from vegetation on trap efficiency (Mohamed-Ahmed and Wynholds, 1997). However, the model proposed in this study should be applicable to any experiment studying the optimum positioning of traps in relation distance from any habitat type, for ‘one-point’ source insect populations.
Acknowledgements Thanks to Drs Johann Baumga¨ rtner and Steve Mihok for their critique of this manuscript and useful suggestions.
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