Studies on sampling larval populations of the Anopheles gambiae complex

Bull. Org. mond. Sante 1971, 45, 169-180 Bull. Wld Hlth Org. Studies on Sampling Larval Populations of the Anopheles gambiae Complex M. W. SERVICE' Better sampling techniques are urgently required for estimating the population size and larval mortalities of the Anopheles gambiae complex. Some preliminary investigations into these problems were therefore made in Nigeria and Kenya. Knowledge of the type of distribution shown by larvae is important since it should enable more accurate sampling to be undertaken; consequently the biological distribution of larvae of the An. gambiae complex was investigated. Because there is often a need in control programmes to compare larval mortalities between populations in different types of habitat, attempts were made to construct time-specific survivorship curves and life tables so that instar mortalities could be calculated. Finally, results from estimating the size of larval populations in different habitats by a selective removal method and by a mark-release-recapture method were compared; the latter are considered more reliable. Larvae of the three freshwater species of the Ano- pheles gambiae complex occur in a great variety of habitats but the most important are small, shallow, sunlit and usually temporary pools. Because of the small size and transient nature of many of these col- lections of water few animal species can successfully colonize them. Consequently, it has been considered that the mortality of An. gambiae larvae in these habitats due to aquatic predators is relatively low. Marshes, rice fields, larger borrow-pits, and wells are examples of larger and more permanent habitats. These can support a variety of both invertebrate and vertebrate predators. Estimates of larval populations of An. gambiae are often required in control programmes to com- pare population sizes in areas where residual insecti- cides have been applied to houses and in those where they have not, or in areas that have been given diffe- rent insecticidal treatments. Furthermore, popula- tion measurements are often needed to demonstrate the factors regulating populations of An. gambiae under different environmental conditions. The small size of many of the most important habitats makes them impossible to sample by many of the normal limnological methods such as drag nets, dredges, sampling cylinders, and cages. Probably the most 1 Principal Scientific Officer, The Nature Conservancy, Monks Wood Experimental Station, Huntingdon, England. common method of recording the density of An. gambiae larvae is to obtain the mean number of larvae caught per dip made with a small bowl or ladle. A variant of this method is to record the num- ber of larvae caught in a small net after sweeping a known length of water surface. Several workers (Cambournac, 1939; Bates, 1941; Goodwin & Eyles, 1942; Hess & Hall, 1943; Russell, West & Manwell, 1946) have counted the total number of Anopheles larvae enclosed within quadrats. However, as pointed out by Christie (1954), the small size of the preferred larval habitats of An. gambiae makes this method difficult to apply to this complex. There have been various attempts to relate the number of larvae collected by these and other sam- pling methods to the total population in the breeding site. Christie (1954) used a direct method to count the population of An. gambiae by evacuating all the water from small habitats and collecting the larvae on a series of sieves. Although, with the exception of first-instar larvae, 95% of the larval population can be collected, the technique can be used only in small collections of water such as small borrow-pits and water-holes. This method cannot be used in shallow seepages or in habitats consisting of more than about 180 litres of water. It therefore has restricted appli- cation. Absolute population estimates have been made of some culicine larvae breeding in ground col- lections of water by mark-release-recapture methods 2715 169 - M. W. SERVICE (Service, 1968; Welch, 1960) and by the Zippin (1956) removal method (Wada, 1962a, 1962b). However, there have been few attempts to estimate populations of An. gambiae by any of these methods. During short visits to Kaduna, Nigeria, and Kisu- mu, Kenya, preliminary studies were made on the biological distribution of larvae of An. gambiae, the mortalities of the various aquatic stages, and methods for estimating population size. The present paper describes the techniques used, the difficulties en- countered, and the further application of the methods. LARVAL DISTRIBUTIONS Methods In Kisumu, larvae of An. gambiae belonging to both species A and B (Service, 1970a) were collected at intervals from the edge of a large marsh and from 8 different pools and borrow-pits of different sizes. The numbers of larvae collected per dip with a 100-ml ladle 9.5 cm in diameter were recorded separately. The results of sampling 5 large pools near Kaduna in 1963 and 2 large borrow-pits in Kano, Nigeria, in 1961 by this method are also considered here. Results In all experiments except No. 13 the variances (S2) are greater than the means (Q) (see Table 1), thus indicating a contagious type of larval distri- bution as distinct from a Poisson. In most insect populations so far studied where there is aggregation, the distribution can be adequately expressed by the negative binomial model (Anscombe, 1949; Bliss & Owen, 1958; Evans, 1953; Harcourt, 1965; Ibarra, Wallwork & Rodriguez, 1965), but there have been few attempts to fit the distribution of mosquito larvae to any known type of distribution, and no such attempts with larvae of An. gambiae are known to the author. To see whether the results of the larval sampling given in Table 1 fitted a negative binomial distribution, the exponent k was calcu- lated by the method of maximum likelihood from the following equation: Nl( k) k+x) where Ax = the sum of all frequencies of samples containing more than x larvae. After obtaining values of k, the agreement between the negative binomial as a model and the actual distribution of the larvae in the field was tested by comparing the actual frequencies of the dips con- taining different numbers of larvae with the expected frequencies predicted by the negative binomial distri- bution. The expected values are calculated as fol- lows: F(k+x) x x k k x!Jri(k) x+k/ (k+x) where px = the probability of a sample containing x larvae. The values of x! and r(k) are found from tables of factorials and log-gamma functions. A x2 test is performed on these expected values and those recorded in the field, taking X2 as having 3 fewer degrees of freedom than the number of comparisons. If there is no statistical difference, the model of the negative binomial fits; alternatively, the theory is rejected. Since, in some of the Kisumu experiments, calcu- lation of the negative binomial exponent k by the maximum likelihood method gave inappropriate negative values, the ki index of Bliss & Fisher (1953) was calculated. The low values of k and ki (Table 1) indicate a highly aggregated larval distribution, but the goodness-to-fit test, using k or ki values, shows that the negative binomial adequately describes the observed distributions in experiment 2 only (X2 = 5.48, 0.2 > P > 0.01). An unusual characteristic of all these experiments is the greater number of dips con- taining 2 larvae than those containing 1 larva, and this, together with the high number of dips without larvae, gives a bimodal frequency distribution. Be- cause the negative binomial did not appear a satis- factory model, the results from all the experiments were put through a computer and their frequencies tested to fit the following distributions: normal, Pois- son, double Poisson, Neyman type A, truncated Poisson, truncated Neyman type A, logarithmic, and truncated negative binomial. The observed distri- bution of larvae in experiments 1, 6, 7, and 8 fitted none of these distributions. Experiment 3 (X2 = 4.60; 0.5 > P > 0.4), experiment 4 (X2 = 1.50; 0.7> P> 0.5), and experiment 5 (X2 = 4.93; 0.1 > P> 0.05) fitted truncated Poisson distributions, while experiment 9 satisfied a fit to both the Neyman type A (X2 = 3.76; 0.5> P> 0.4) and the truncated negative binomial (X2 = 4.37; 0.3 > P> 0.2) distributions. There is no general well-defined pattern of distribution fitting all these samples from Kisumu. All that can be said is that the larvae are highly aggregated. In experiment 13 (Kaduna) the variance is smaller than the mean and this obviously deletes as inappro- priate both contagious and truncated distributions. As the variance mean ratio (0.9914) approaches 1 this should indicate a Poisson distribution, but the good- 170 SAMPLING POPULATIONS OF ANOPHELES GAMBIAE XCD LU- cD Co > 0 > _ (3 N N 0 0 0 0 0 0 CD et O Co) N Io co 005 - OLID -ID-0 N v-OOO00 OO0 0 0 co) COu X N- CV) W- N N- ID Nl CoLU 0 0' LU N4 LI) N 0C') co N co CO CIO) N1 0 0 0 0 0ON1 CY) N1 LU N4 V~) v ON o C 0 N v-- 0 00 000 Co Co) CV LID ID X, 0 LO'-I co t 40 9LU ciC5~~0 N4 co ~t N, ID cv) 0'- -0 00 0 co N4 Co Clf)X,.. N1 ID) N 0 N4 ID Coq NlLU N - 0 0' Co .0 Co T- N- CD 0 00 0 0 000 N Clf LIDX 4 Cl, 0 V) CDLU N4 6CY) 0 o C C Co0 ID) lR ON IDU N O-'-0 0 0 0 0 NxC Coe N Cl) - 0 co N' CD~LU N N1 - CY) 0 XC rN N4N' 0 0 0 0 00 0 m IL eD CD0 IDW _ O0 0 0 0 CD Nr, LU ' - -J N C ~ x CD x ID LU x q x l X N W X V. cD 0N CY) D 0 0O 0 0 0 00 N ID IO co6i C-, co6 LRCD co C ID 0 N _ O Co CID N~ __N (CD N N0 IDCo 00 O N N 0 0 0 ON004 0 0 IoN 1-4 CD C3) N'4- - N et Cl O I) C3) 0o O Cl) C C C)CO CD 0 - co 'C ID N Co CD N CD CD t 0 0 0 Co N 0 o N N 1 Cv) N coD 0 IO 0N1 1-4 ~-: 0 _- N * I C N Co Co _- N D) co -a 0 C. 0- N PC1 0 : _C .W o E m> --k 171 1- C 0 0._(D 0 0 0 0C -o 0 0 C 0. 0 6 z 2 . S Cm 'a cn . E 50 Z 4C- c 0.E (Dx ._ 0 c) 0 q) ._ -0 Co E 0 - Q z C) I.- CDawco 6c yW CDmco ui aco Ne a)co _ -, CD E a) -o 0 6 z 3 _ M. W. SERVICE ness-to-fit test refutes this (X2 = 14.39, 0.2> P> 0.01). This may be because of the low zero class and large numbers of dips with only 1 larva. Experiment 10 has a large number of dips in the zero class and only a few with 1 larva, and like experiment 13 cannot be adequately fitted to any of the tested distributions. The frequency distributions of the larvae in the three other Kaduna experiments and the two Kano ex- periments fit the negative binomial or, in the case of experiment 15, the truncated negative binomial after censoring the zero class. The inability to fit some of the sampling data from both Kenya and Nigeria to known distributions may be due either to sampling errors or to the larvae con- forming to a distribution not tested for. In the last context it is interesting to note that the samples from Kisumu that gave most difficulty in fitting any of the tested models were characterized by a bimodal distribution. There is, however, no doubt that larvae of An. gambiae have a contagious distribution. INSTAR MORTALITIES AND SURVIVORSHIP CURVES Bates (1941) realized that if the duration of the larval instars of the An. maculipennis group were taken into consideration there was a relationship between the numbers collected in the different in- stars and their survivorship. By dividing the numbers of each of the four instars caught by their instar du- ration he attempted to compare the survivorships of the instars in different larval habitats. In the present investigations this idea has been greatly expanded and improved, so that life tables can be constructed for the immature stages of An. gambiae. The pro- cedures and calculations are outlined below. During November and December 1969, 200 dips were made with the standard-sized ladle on a number of consecutive days from a large marsh and from 4 borrow-pits near Kisumu. The total numbers of each larval instar and of pupae obtained from the 200 dips are given in Table 2. It was considered that during the limited period of time over which the collections were made from each habitat the popu- lation of An. gambiae was approximately stable; that is, it had reached an approximate state of equilibrium where the numbers of eclosions just balanced out deaths in all stages. This seems a reasonable assump- tion for such short periods during this time of the year, and the raw data from the collections in no way contradict it. If the population is more or less stable its age distribution can be assumed to give Table 2. Number of immature stages of An. gambiae caught each day in 200 dips from larval habitats near Kisumu No. of larval instars Habitat gColect- (I-IV) and pupae (P) caught days I __ I I l lP 1 21 53 21 8 4 2 38 48 19 7 0 3 25 37 11 9 1 4 25 38 29 10 3 marsh 5 47 75 27 14 0 6 49 89 33 18 5 7 15 17 3 6 0 8 48 75 21 13 5 9 31 39 20 4 3 10 27 59 20 13 4 total from marsh 326 530 204 102 25 1 28 36 19 11 2 2 25 49 24 13 3 borrow-pit 1 3 38 58 28 14 4 4 31 54 26 13 2 5 27 34 17 12 1 ....... 1 21 32 18 11 0 2 26 39 20 1 3 2 borrow-pit 2 3 15 34 14 14 1 4 39 52 27 9 .0 5 21 38 16 10 2 1 23 38 14 9 1 2 27 44 15 10 2 borrow-pit 3 3 21 38 19 13 0 4 23 37 10 9 1 5 28 49 12 7 0 ................. .............. . ........ 1 29 43 16 11 1 2 28 48 18 12 2 borrow-pit 4 3 33 52 21 12 0 4 29 61 20 10 1 5 25 38 18 9 3 6 21 35 17 10 0 total from borrow-pits 558 909 389 232 28 172 SAMPLING POPULATIONS OF ANOPHELES GAMBIAE z ~~IV - P ° 1 2 3 4 5 6 7 8 9 10 11 12 Age in days Fig. 1. Age distribution and survivorship curve of the immature stages of An. gambiae collected from 4 borrow-pits in Kenya; vertical bars show the confidence limits for the mean total frequencies (I-IV = larval instars; P = pupae). the same shape as the survivorship curve. To obtain a graph of the age distribution of the aquatic stages the total numbers of pupae and different larval in- stars collected over the entire collecting period are divided by the appropriate instar durations. (From field experiments in Kisumu instar durations of An. gambiae were 1.5 days for first-, 3 days for second-, 2 days for third-, and 4 days for fourth-instar larvae and 2 days for the pupae.) These values are plotted against age in days of the larvae and pupae. Smooth lines are fitted to the points on the graphs to give the age distribution curves, and if the steady-state assumptions hold, this profile will simulate the time- specific survivorship curve. The construction of pre- liminary age distributions for collections from the 4 different borrow-pits showed very similar profiles; results have therefore been combined to give an over- all figure for the age distribution of An. gambiae in borrow-pits (Fig. 1). The age distribution curve of larvae from the marsh shows a slightly different shape and is given separately (Fig. 2). From the survivorships curves the numbers of lar- vae surviving to each age in days are read off to give the values in the Nx columns of Table 3. Life- tables have been constructed (Tables 4 and 5), and the Ix column is headed by an arbitrary but con- venient number (1 000). An overall mortality of 95.2% and 96.2% occurs among the immature stages in the marsh and pools, respectively (Tables 4 and 5). Because of the limited data that were collected from the field in the present experiments the construction of time-specific life tables is highly ambitious. A simplification would be to assume that in any given instar the mortality is constant, and to estimate av- erage daily mortalities of the different instars. The appropriate steps for this are set out in Tables 6 and 7. The numbers of larvae entering the instars are ob- tained from the survivorship curves. It is clear that in the marsh most mortality will occur in the third and fourth instars, whereas in the pools pupal mor- tality will also be relatively high. The different sources of error that can exist in this method of estimating instar mortality are dis- cussed later, but sampling errors can conveniently be dealt with here. Since there are sampling replicates from both the marsh (10) and pools (21), the sample variance for each instar frequency can be calculated and 95% confidence limits provided for the mean number of larvae in all samples. The vertical lines drawn through the points of the survivorship curves (Fig. 1 and 2) are based on these estimates. Clearly discrepancies due to sampling can be a serious source 173 M. W. SERVICE A E200- 2 \\ z z 100 II III ~~~~~~~IVI S 1 2 3 4 5 6 7 3 9 10 11 12 Age in days Fig. 2. Age distribution and survivorship curve of the immature stages of An. gambiae collected from a marsh in Kenya; vertical bars show the confidence limits for the mean total frequencies (I-IV = larval instars; P = pupae) of error in calculating mortality rates, but more care- ful sampling will provide samples more represen- tative of the populations, and therefore reduce biases and systematic errors but not the sampling error, which depends on the variability between individuals and sample size. There was, for example, consi- derably less sampling error in the collections from the pools than in those from the marsh. POPULATION ESTIMATES Methods The three larval mutants first described from la- boratory specimens (Mason, 1967) were common in populations of An. gambiae in both Kaduna (Service, 1970b) and Kisumu. The proportion of mutants in the populations varied in collections from different larval habitats. No extensive survey on their inci- dence was made, but from 5 localities near Kisumu the range and mean incidence of mutants and normal larvae in 1 645 examined were redstripe 1-12% (7 %), black diamond 3-18% (12%), collarless 37-78% (51 %), normal larvae 19-38 % (30%.). G. Davidson (Service, 1970b) has pointed out that some fourth-in- star larvae that appear to be collarless may have minute collars, but in the following experiments they are counted as collarless. Since these mutants are easily recognized in the field, they can be used in applying the selective re- moval method of Kelker (1940) to estimate popu- lations of fourth-instar larvae. In this method use is made of the change in the ratio of two distinctive components of the population that occurs after a number of one of the components has been re- moved. In the experiments in Kisumu the two components of the population were taken to be normal (n) and mutant (m) larvae. About 300-500 larvae were col- 174 SAMPLING POPULATIONS OF ANOPHELES GAMBIAE 175 Table 3. Numbers of larvae (Nx) of An. gambiae surviving to age x Age x Marsh Borow-pits(days) (Nx) 1-4 (cNxe) 0 229 387 1 214 365 2 196 335 3 177 303 4 151 265 5 121 220 6 80 169 7 47 117 8 29 73 9 21 44 10 17 27 11 13 17 12 11 11 Table 4. Life table for An. gambiae in the marsh * x /x dx px qx 0 1 000 66 0.93400 0.06600 1 934 78 0.91649 0.08351 2 856 83 0.90304 0.09696 3 773 114 0.85252 0.14748 4 659 131 0.80121 0.19879 5 528 179 0.66098 0.33902 6 349 144 0.58739 0.41261 7 205 78 0.61951 0.38049 8 127 35 0.72441 0.27559 9 92 1 8 0.80435 0.19565 10 74 1 7 0.77027 0.22973 1 1 57 9 0.84211 0.15789 12 48 x = age in days; Ix = no. of larvae surviving to age x; dx = mortality between ages x and x + 1: px = probability that a larva of age x would survive to age x + 1; qx = probability that a larva of age x would die before reaching age x + 1. Table 5. Life table for An. gambiae in the borrow-pits * x [ x dx J px - qx 0 1 000 57 0.94300 0.05700 1 943 77 0.91835 0.08165 2 866 83 0.90416 0.09584 3 783 98 0.87484 0.12516 4 685 117 0.82920 0.17081 5 568 131 0.76937 0.23063 6 437 135 0.69108 0.30892 7 302 1 '3 0.62583 0.37417 8 189 75 0.60317 0.39683 9 114 44 0.61404 0.38596 10 70 27 0.61429 0.38571 11 43 15 0.65116 0.34884 12 28 For symbols, see Table 4. lected from each of 5 pools and the numbers of these two components recorded; the mutant, but not the normal, larvae were then returned to the pools. A further collection was made and the numbers of nor- mal and mutant larvae again recorded. The size of the change in the ratio of normal to mutant larvae in the two collections depends on the size of the population (P) being sampled, which is calculated as follows: Dml x Dn2 P = Kn Dn1- Di2 where Kn = the number of normal larvae that are removed after the first collection (in the present ex- periments these represented all normal larvae), DnL and Dn2 = the proportions of normal larvae as a decimal of the total numbers of larvae caught in the two collections, and Dmi, and DM2 = the propor- tions of mutant larvae in the two collections.' The population estimates of fourth-instar larvae in the 1 n1 and n, are the numbers of normal larvae, and ml and m, the numbers of mutant larvae, in the first and second collections, respectively. M. W. SERVICE Table 6. Instar mortalities of An. gambiae from the marsh Instars Age in days No. entering Deaths Relative proportion Proportion dying instars instars in instars dying in instars daily in instars5 DiS ! i tt-. Stij- Di d *- I 0 229 24 0.10480 0.07115 11 1.5 205 68 0.33171 0.12571 lIl 4.5 137 76 0.55475 0.33273 IV 6.5 61 46 0.75410 0.29581 pupa 10.5 15 5 0.33333 0.18350 adult 12.5 10 a d = instar duration in days. Table 7. Instar mortalities of An. gambiae from the borrow-pits Age in days No. entering Deaths Relative proportion Proportion dyingInstars at beginning instars in instars dying in instars daily in instarsainstars l ti-, | ~~~stji- Di DSi- | Sti ) I Il0 387 36 0.093023 0.06373 11 1.5 351 106 0.30199 0.588251 III 4.5 245 102 0.41633 0.23600 IV 6.5 143 121 0.84615 0.37372 pupa 10.5 22 12 0.54545 0.32577 adult 12.5 10 a d = instar duration in days. 5 pools calculated by this method are shown in Table 8. After these collections were made, all normal lar- vae removed from each pool in the first collection, together with some of the larvae from the second collection, were stained red by placing them for 12 hours in a solution containing 0.1 mg of Rhodamine B, a non toxic dye, per litre. After staining and wash- ing in water, all healthy larvae were placed at inter- vals around the perimeters of the pools and the water was stirred to ensure random dispersal of marked lar- vae. After an interval of 2 hours three separate col- lections were made from each pool, and the numbers of marked larvae (r) in the total catches (n) were recorded for each collection. Population estimates are obtained by the simple Lincoln index, p a(n+1) r+1 where a = total number of marked larvae placed in the pools. In all but the last pool the estimates for the three collections are in good agreement (Table 8). By summing all the larvae caught in the three col- lections (n) and the total numbers that were marked (r), a mean population estimate is obtained (Table 8). Its variance is calculated as follows: a2(n+ 1) (n-2) varP= -(r+l)2(r+2) Results Kelker's method ranked the pools in the same or- der of population size as did the mark-release-re- 176 SAMPLING POPULATIONS OF ANOPHELES GAMBIAE Table 8. Population estimates of fourth-instar larvae of An. gambiae in pools |Surface Mark-release-recapture method Mean x iSurfa of___-____ no. of iFx pool WilliamsPools watreao Kelker's Mean larvae water area prmtr meanPoswater° method 1 st 2nd 3rd estimate per dip perimete estimate estimate estimate and (im2) variance (x) (m2) (m) (MW) 1 79 1 027 1 323 1 591 1666 1 541 0.84 66 52 0.62 :±:159 2 64 2 903 2 817 2 852 2 512 2 749 1.32 84 40 1.09 ±218 3 166 6 381 4100 4 230 3 373 4 032 0.23 38 21 0.16 ±526 4 118 11 460 5 809 6 378 5 945 6 000 1.08 127 84 0.84 ±828 5 921 12584 36630 17013 47619 36121 0.95 874 208 0.68 ±12000 capture method, but there is no good agreement be- tween estimates obtained by the two methods. The author has not previously used the method of Kel- ker, but has successfully applied the mark-release-re- capture method to estimate populations of Aedes lar- vae in marshes (Service, 1968), and believes that this method gave the most valid estimates in the present experiments. Probably the commonest method of comparing the numbers of larvae of An. gambiae in different habitats is to count the mean number oflarvae caught per dip with a ladle. However, the mean numbers of larvae obtained from 200 dips from each pool in Kisumu show no relationship to the estimated popu- lations (Table 8). For example, it was estimated that pool 2 had relatively few larvae, but the largest mean number per dip was in fact recorded from this pool. Obviously when two different-sized habitats con- tain the same number of larvae, the numbers per dip will be larger in the smaller habitat; dips record only the density of the larvae. Only when similar-sized pools are sampled can the mean number per dip be used directly to compare population sizes. Attempts have been made to take the size of habitats into account (Belkin, 1954; Husbands, cited by Knight, 1964; Shemanchuk, 1959) by multiplying the mean number per dip by the surface area of the water. However, when the mean numbers of larvae per dip are multiplied by either the surface areas of the pools or the lengths of their perimeters, there is still no agreement between the indices and the estimated populations (Table 8). Expressing the numbers of larvae per dip as William means (Haddow, 1960) still ranks the pools in the same order as do the arith- metic means. Because larvae of An. gambiae show a non-ran- dom type of distribution any differences between the numbers caught from different pools cannot be tes- ted for significance by an analysis of variance or by any other related tests, because these calculations pre- suppose a normal distribution with the variance inde- pendent of the mean. This is a limitation that is too often ignored in analysing non-random data. To overcome this difficulty the original data (i.e., num- ber oflarvae per dip) are transformed to values whose distribution will either normalize the data or stabilize the variances. Methods of obtaining precise trans- formations are given by Taylor (1965) and Forsythe & Gyrisco (1961), but in general, when sampling and other errors are relatively large, little is gained by de- termining precise transformations. Usually data from slightly contagious populations can be adequately transformed to square roots and those from distinct- ly aggregated populations to logarithms. The latter is probably the most widely used transformation. To overcome difficulties of zero counts in logarithmic transformations a constant, normally 1, is added to the count to give log (x+ 1). Therefore, if any differences between the numbers of An. gambiae caught from different habitats are to 177 M. W. SERVICE be tested for significance the original data must be transformed. A logarithmic transformation will pro- bably be suitable, but a rough check on the adequacy of a transformation can be obtained by plotting the variances and means on double logarithmic paper to show their independence. A better method is to calculate correlation coefficients between the trans- formed sets of variances and means. PREDATORS The large mortality of the immature stages that has been shown to occur can be caused by a variety of factors, including adverse climatic conditions, limi- ted food supply, competition, parasites, and patho- gens, but predation is probably the most important limiting factor. In certain habitats, such as large collections of permanent water and wells, the impor- tance of predators is recognized (Christie, 1958, 1959; Gillies & de Meillon, 1968). Despite this there have been no critical assessments of the extent to which various predators regulate the numbers of An. gam- biae. Because of the absence of potential aquatic pre- dators from most temporary pools (water-filled hoof- prints and other small and transient collections of water) colonized by An. gambiae, it has been assumed that there is little loss of larvae by predation. This is not always true. In Kisumu on many occasions the author observed adult ffies settling on both small and large collections of water preying on adults emerging from the pupae and also on larvae. Pre- dation on the larvae appeared to be concentrated on the fourth instar. A small number of the preda- tors was collected. Some were identified as muscids belonging to a common species, Lispe irvingi Curran. Species of this genus are commonly found flying around streams and pools and several have been recorded as predators of both mosquito larvae and adults (Jenkins, 1964). Other predacious diptera were dolichopodids belonging to two species-Pelasto- neurus congoensis Parent, previously known only from the Congo (Kinshasa) and Uganda, and an unidentified species of Thinophilus. Dolichopodids have been recorded as predators of mosquito larvae in North America (Bishop & Hart, 1931; Darrow, 1949; Laing & Welch, 1963), Panama (Howard, Dyar& Knab, 1912), the Pacific region (Travis, 1947; Williams, 1939), and the Congo (Kinshasa) (Collart, 1927), but their predation on An. gambiae has not pre- viously been reported. Lycosid spiders were often abundant near the vegetation at the water's edge and several times they were seen to prey upon emerging adults. Predation on emerging mosquitos by lycosids has been reported by Bishop & Hart (1931). It is evident that predation by non-aquatic in- sects and spiders may be important in regulating lar- val numbers of An. gambiae. The presence of empty pupal skins on the water surface does not necessarily indicate successful adult emergence. DISCUSSION Because of the short time spent in Kisumu only very limited data were obtained from sampling larval populations of An. gambiae; therefore many of the actual results must be regarded as tentative. The main purpose, however, was to evaluate certain methods for sampling larval populations and consi- derable information was obtained from these studies. It is clear that larvae of An. gambiae are not random- ly distributed, but are clumped. In some instances the model of the negative binomial seems to satisfy the observed distribution but many more samples need to be taken before any general pattern or pat- terns of larval distribution can emerge. Knowledge of the type of distribution should enable more accu- rate sampling to be undertaken. For example, if the distribution mimics a negative binomial, the number of dips (N) required to sample reliably a habitat is given by Rojas (1964): 1/x+ 1/k D2 where D is the required level of accuracy expressed as a decimal (normally 0.1). F Since larvae are not randomly distributed, col- lections are needed from different types of habitat and the simplest transformation must be found that will allow any differences between the numbers caught in two or more collections to be tested by an ana- lysis of variance or by other related statistical tests. More attempts to estimate larval populations in habitats of different size and with different popu- lation levels are urgently required. One of the more promising methods appears to be the mark-release- recapture technique, but any one method, including this one, may not work under all conditions. Other methods for estimating population size should be evaluated, and the selective removal method of Kel- ker merits reassessment. It may be possible to find a relationship between reliable population estimates and a simple comparative index, such as larvae per dip (Service, unpublished results), so that only a few 178 SAMPLING POPULATIONS OF ANOPHELES GAMBIAE 179 absolute estimates are taken, the population size at other times being derived from the number per dip. Such a process will be unlikely to give very precise estimates, but they may be well within acceptable limits of accuracy. One of the most useful outcomes of larval sampl- ing was the method for the construction of life tables and the calculation of instar mortalities. The cal- culation of confidence intervals showed that there were considerable sampling errors; consequently the mortalities given here must be regarded as approxi- mations. More reliable samples should be taken and the instar durations must be determined more accu- rately, in hours rather than days. If this is done, the method presented here for the construction of life tables and the estimation of mortality should prove very useful, especially in comparing differences be- tween survivorships of larvae in different habitats. ACKNOWLEDGEMENTS The author thanks the junior and senior staff of the WHO Anopheles Control Research Unit No. 2 for their co-operation during the investigations in Kisumu. The dolichopodids were kindly identified by Mr. C. E. Dyte and the muscids by Mr. A. C. Pont. Thanks are also expressed to Dr G. Murdie for computer analysis of the biological distributions of the larvae and for many helpful comments. The author is especially indebted to Mr K. Lakhani for many beneficial discussions concerning the statistical treatment of some of the results. RESUME' ETUDES SUR L'ECHANTILLONNAGE DES POPULATIONS LARVAIRES DU COMPLEXE ANOPHELES GAMBIAE On a analyse les modalites de la repartition des larves d'Anopheles gambiae dans des gites, au Kenya et au Nigeria, pour voir si elle pouvait etre identifiee a un type connu de distribution: d. normale, d. de Poisson, d. double de Poisson, d. de Neyman type A, d. binomiale n6gative, d. tronqu6e de Poisson, d. tronquee de Neyman type A, d. logarithmique et d. binomiale negative tronquee. I1 est apparu que la distribution des larves n'6tait pas du type al6atoire mais du type ((tres groupe *. Aucun des modes de distribution etudi6s ne pouvait lui etre applique de fagon satisfaisante, sauf peut-etre, dans certains cas, la distribution binomiale negative. L'auteur expose les m6thodes utilisees pour calculer le facteur k de la distribu- tion binomiale negative et v6rifier si ce genre de distribu- tion estcompatible avecles donnees recueillies sur le terrain. On s'est efforce d'etablir des courbes de survie et des tables de vie concemant les stades immatures d'A. gambiae recoltes dans divers gites au Kenya. On decrit les methodes employees pour calculer les mortalit6s journalieres de l'ensemble des larves et des differents stades appartenant a une population relativement stable au moment de l'echantillonnage. La mortalite d'A. gambiae dans les gites est due en partie a l'activite de predateurs qui detruisent les insectes a l'etat larvaire ou lors de l'eclosion imaginale. Pour evaluer le nombre des larves presentes dans un gite, on peut marquer certains specimens a l'aide d'un colorant, les replacer dans le milieu et mesurer leur proportion dans les lots de larves recoltes ulterieurement. On peut aussi 6tudier les changements apportes aux proportions de deux composants (larves normales et larves mutantes) d'une population larvaire apres preleve- ment d'une partie de l'un ou de I'autre. 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