original text of the thesis:
Population dynamics of the Gyrinid beetle Gyrinus marinus Gyll (Coleoptera)
With special reference to its dispersal activities (1987)

CHAPTER VII. DISPERSAL BY SWIMMING

SUMMARY
The amount of exchange by swimming between local populations of the water beetle Gyrinus marinus Gyll. is estimated by capture-recapture methods. The mean emigration chance per week decreases not significantly from about 0.36 in spring to 0.20 in late summer and autumn. Males emigrate more frequently than females. The emigration from pools with several passages to other pools is greater than that from pools with a single outlet. The pools in the centre of the study area therefore show a greater exchange with other ones than the border pools. The exchange between two pools also depends on the number of pools between and on the number of possible routes. Large populations have lower emigration rates and receive a greater proportion of the immigrants than small populations, i.e. there is a tendency to stay and to go to places with relatively high numbers of beetles.
Exchange by swimming occurs at night and is more intensive at nights with high temperatures, and possibly during rain.
A mean survival chance during exchange of 0.70 is estimated (chance to immigrate elsewhere).
During the year and between populations both emigration and immigration vary considerably. In general the number of beetles emigrating from a population is higher than the number of beetles that immigrate. However, in eight out of 24 cases immigration was greater than emigration. On the average, three weeks after release of marked beetles 50 per cent of a local population appears to consist of immigrants.

1. INTRODUCTION

1.1. Whirligig beetles (Gyrinus marinus Gyll.) can disperse by flight and by swimming. Flight activity only occurs during special weather conditions, and is shown by only a small proportion of the beetles (see Chapter VI Dispersal by flight). Flight seems seems to be a reaction to conditions favourable to flying. Swimming, on the contrary, is the normal way of moving, to find food, shelter, or other whirligig beetles. During the daytime, movement is generally limited to an area of a few meters around groups of beetles along the bank, but at sunset the beetles become very active, swarming around for at least several hours. At sunrise the beetles are found again within groups or they have sheltered in the bank vegetation or under water. Apart from the possible functions of swarming (Heinrich and Vogt 1980), a number of the swarming beetles may leave the pool (by accident ?) and keep swimming until they meet another group of whirligig beetles. The company of other whirligig beetles is probably an important stimulus for an individual to stay at a given place (Grooters and Groothuis 1979b, Zijlstra 1979). 1t can thus be expected that a beetle that has swum away from its pool will be found in a group in another pool, unless it has died. 1t also implies that the time between leaving one pool and immigrating into another will probably be short, i.e. less than 24 hours.
1.2. During daytime whirligig beetles are concentrated for the greater part in groups along the banks of pools. We have never observed a group of beetles more than two meters from the bank. Fig III-3 shows that certain parts of the banks were always occupied in the course of several years, whereas other places were occupied for restricted periods only; along considerable parts of the banks groups of beetles were never observed. Apparently, certain areas along the banks are not attractive for the beetles and can be considered a kind of "desserts" that they have to cross to reach another inhabitable place.

2. METHODS

2.1. The study area is situated in the northern part of the Netherlands, near Groningen. It is an area of pools and ditches. The poo1s of the Br-complex (Fig III-3 and Fig VII-1) are connected by water, the others are not.
2.2. Exchange between different poo1s can be traced by releasing and recapturing marked beetles. The beetles are marked by means of pin pricks (individual marks) and by paint dots (group marks). The individual-mark method gives information about displacements of individuals and about the composition of local populations of both autochtonous beetles and of immigrated one5 from different sources. However, information about the daily dispersal activities is lost, because in most cases beetles can not be sampled more frequently than once every 10 days. Moreover, the capturing and releasing of beetles will disturb the normal dispersal behaviour. A detailed description of the marking technique is given in Chapter VI Dispersal by flight .
2.3. The method of marking with paint spots enables a daily recording of the distribution of the differently coloured beetles throughout the study area. The beetles do not have to be disturbed: they can be observed and counted with the help of binoculars while swimming around or in groups. Painting was applied in 1978 only, after some years of experimenting to develop a safe, harmless technique. We used non-toxic paint, and before application the central surface of the elytra was sanded gently with fine waterproof sandpaper in order to remove the wax-layer and to make a rough surface. After some experience we were able to mark the beetles without harming them. The marks kept well for a long time (we even recaptured some marked beetles the next spring). Before release, the painted beetles were kept in an iso1ated ditch for 24 hours, to be sure that only vital individua1s were released.
Flight activity is made practically impossible by the painting, because in most beetles the elytra are fixed by the paint dots.
2.4. After the beetles were released. the numbers of each color and that of unmarked beetles were recorded daily at every suitable place in the entire area. After about six weeks the various1y coloured beetles were too dispersed over the whole area to permit further registration of displacements. Moreover, their numbers had decreased to such a low level by mortality as well as by some 1oss of marks, that a new series of paint-marked beetles had to be released. Before a new series of marked beetles was released as many beetles as possible were captured and checked to avoid confusion with beetles of a previous series, as well as to look for beetles with remains of lost paint-marks. It was possible to release such series in four periods: period I (spring): 29.4-6.6 (week 18-23), period II (summer): 19.6-27.7 (week 25-30), period III (late summer): 1.8-15.9 (week 31-37), period IV (autumn): 15.9-30.10 (week 37-44).
2.5. The paint-marked beetles were released in the northern part of the study area, the "Br-complex" (see Fig. III-3 and Fig VIII-1), where the pools are connected by brooks or other passages. The greatest distance between two pools is about 1.5 km. Since only the colours red, blue, green, yellow, orange and white give marks distinguishable from a distance, marked beetles were released at only part of the pools. In period III the colour combinations yellow-blue and orange-red were added.
2.6. Because some places where beetles congregate were situated close to each other at both sides of a passage between two pools (for example at Wz and Sc. cf Fig VIII-1), the exchange between such groups can hardly be considered exchange between different local populations. We therefore divided the Br-complex into eight sectors (Fig VIII-1). Only exchange between different sectors is regarded as exchange between local populations. The pools can also be classified in groups, the BH-group (Kr, Bb, Bn), the WK-group (Wn, Wz, Sc, Ts) and the BM-group (Br, Bs, Me, Kw, see Fig VIII-1).
A local population will be defined as a cluster of groups of individuals (sometimes only a single one) that is clearly separated from other such clusters.
2.7. Within the Br-complex there are pools with only one passage to other pools (Kr, Bb, Me, Wn, cf Fig VIII-1), and others with two or more passages (Bn, Wz, Sc, Br, Kw). Because the pools with a single outlet are mostly situa.ted at the outer edges of the complex these pools will be indicated throughout this article as "border" pools, as opposed to the "centre" pools.
2.8. The period that beetles are present at a site is determined by the balance between emigration (+ mortality) and immigration (+ natality). But dispersal activities may be influenced by local conditions, so that certain sites are more attractive than others (Grooters and Groothuis 1979b). To compare the emigration and immigration at places with different degrees of "occupation" (attractiveness) marked beetles were released at places where beetles were generally found as well as at places where they have been observed only during relatively short periods.
2.9 In the following the survival chance Q refers to the proportion of the population still present after some period. whereas the decrease rate (DR) is the proportion lost from a population or site by death or by emigration. i.e. Q = 1 - DR.

3. RESULTS

3.1. Emigration rates of prick-marked males and females in 1974-1977
3.1.1. The capture-recapture data concerning the prick-marked beetles do not allow a detailed analysis of swimming, but when the numbers of females and males released in 1974 - 1977 in the different pools of the Br-complex are compared with the numbers of females and males recaptured as immigrants elsewhere in the complex, males were more frequently recaptured as immigrants than females ( Table VII-I. Wilcoxon test: n=18. R=25.5. P<O.O2). Males apparently show a higher swim-dispersal activity than females, as was also found for flight-dispersal activity ( Chapter VI Dispersal by flight).

3.2. Emigration rates of paint-marked beetles in 1978
3.2.1. After beetles were released in a given pool only some of them could be recorded during the next few days in that pool or elsewhere in the Br-complex. Some may have been overlooked, but a number of the missing beetles presumably died soon after release and should thus be considered as not released. The number of marked beetles effectively released in a pool can be estimated by extrapolating back to day O from the decreasing course of the number of beetles of the concerned colour released in that pool, cf Fig V11-2. The points in the figure give the minimum numbers of beetles still present, i.e. the actual regression curve has to run through or above these points. The decrease rate (DR) determined by survival chance and rate of emigration from the pools concerned can be estimated as

DR =	n          E    (Qd) d=1 —————— n

if Q_d=(P_d/P₀)^265/d.52, P₀ = number of beetles effectively released, P_d = number of beetles present d days after release, according to the regression curve (cf. Fig V11-2) and n = the number of days on which an reliable estimate of the number of beetles is made; e.g. for pool Wn the points in Fig V11-2 (see Table V11-2). Since an only very small variation in survival chance was found between different isolated pools (Chapter V Survival) the differences between the rates ot decrease in inter-connected pools can be regarded as a relative measure for the differences in emigration rate from these pools.
The emigration rates can be estimated roughly for males as E_m = Q_m - Q, and for females as E_f = Q_f - Q, when Q is the survival chance in interconnected pools (Q = 1 - DR), and Q_m and Q_f are the mean survival chances ot males and females in isolated pools in 1974- 1977 (Table V11-2, Table V11-3).
3.2.2. Starting from these rough estimates of emigration rates and from the survival chances as derived in Chapter V Survival of adults more accurate estimates of emigration rates can be made with the help of an iterative computer-model. Introducing a given survival chance (Q) and emigration rate (E) and a given survival chance during dispersal (Q_e=I/E), the model calculates the number of beetles expected to be still present in the population (P_e), the number of beetles that have died (V), the number of beetles that have emigrated (E_e), and the number of the (E_e)-beetles that have immigrated elsewhere (I_e). By comparing the expected numbers with those actually observed the estimates can be corrected such that the best fit all field data. The method is explained in detail in Appendix C. The dispersal-ratio, which is the ratio between the number of immigrated beetles in a population and the number of emigrants from the same population can also be estimated. The results are given in Table VII-4.
3.2.3. In most cases, especially in periods III and IV, the values of the emigration rate in Table VII-4 are somewhat higher than those estimated in Table VII-3. Emigration rates decrease from the first (mean E = 0.36) to the fourth (mean E = 0.20) period, but not significantly (Kruskall-Wallis H-test: z=0.615, P>0.20), also not when the pools are divided in border pools and centre pools.
The border pools show lower emigration rates than the centre pools, i.e. the emigration from a pool is higher when the possibilities to leave the pool are greater (Mann-Whitney U-test: z=2.14. P<0.05). Some sites (Sc, Kr, Kw and Bn) were in 1978 only temporarily occupied by groups of beetles. The emigration rate from these sites seems to be greater than from places occupied more permanently, but this difference is not significant (U-test: n₁ = 5, n₂ = 19, U = 24.5, P>0.10).
3.2.4. The variation in emigration rates can be considered both per population between periods (variation-in-time) and per period between populations (variation-in-place). The variation coefficient of the emigration rates of populations with marked beetles released in all four periods varies between 0.49 and 1.00 (mean var.coef: 0.64), but part of this variation in time is due to the decrease in emigration rates from period I to IV. When the values of the emigration rates in period t are corrected for this decreasing trend by E_c=E_t*(mean E₁)/(mean E_t) the mean variation-in-time coefficient becomes 0.50.
Between populations in the same period variation-in-place coefficients are found between 0.47 in the first period to 0.85 in the third period. Mean variation-in-place for all periods = 0.59; i.e. no important differences occur between the variation in time and in place.
3.2.5. As could be expected, not every emigrant arrived in another population; some were lost on the way, because they die from predation or some other cause. On the average the chance Q_d, to survive during swim-dispersal (i.e. the chance that an emigrated individual will arrive in another population in the area) is found to be 0.72 (st.dev. 0.21, var.coef. = 0.30): that is, about a quarter of the emigrants is lost. The Q_d-values of border pools and of centre pools are not significantly different (U-test: z=0.347. P>0.20), nor are those of permanently occupied pools and of pools that were occupied temporarily (Table VII-4, U-test: n₁=5, n₂=19, U=45, P>0.20). The survival chance during dispersal in the third period appear to be higher than in the other periods (Table VII-4), even if we assume that the values in the third period are somewhat overestimated (U-test: n₁=7, n₂=17, U=27.5, P<=0.05).
3.2.6. The emigrants from each population can be arranged according to the distance at which they were reobserved. From these data the mean survival chance per 100 m. can be estimated. Starting from the actual distribution of the emigrated beetles according to distance, the expected distribution is estimated for an introduced survival chance per 100 m. The total number of thus estimated immigrants elsewhere is compared with the number of emigrants as found in Table VII-4. By iteration several survival chances per 100 m are tried out until the thus estimated total number of redistributed beetles equals the number of emigrated beetles from Table VII-4. A mean survival chance of 0.92 per 100 m is thus estimated (st.dev. = 0.07. var.coef. = 0.07). Since different survival values per 100 m for emigrants from different populations were found (cf Table VII-5) the survival chance per unit of distance seems not to be constant. The survival chances of emigrants from population Wn (mainly immigrating into Wz) and from Br (mainly immigrating into Me) are rather stable (var.coef. = 0.03 and 0.02 respectively), but those of emigrants from populations Wz and Me that immigrated into a number of other populations varied much more (var.coef. = 0.10 and 0.12 respectively). Apparently, the risks at the routes between different populations differ, and also change between periods.
3.2.7. Generally, in theoretical analyses of the dispersal phenomenon the dispersal-ratio (Db) plays - sometimes implicitly - an important role. In most theories it is assumed that a population will lose more individuals byemigration than it wins by immigration. In our experiments on the average a population indeed lost more beetles by emigration than it received as immigrants (mean Db = 0.84, st.dev. = 0.88, var.coef = 1.05), but we also found that in eight out of 24 cases a population got more immigrants than it lost emigrants (cf Db>l. Table VII-4). No significant differences were found between different kinds of pools, nor between different periods (U-tests and H-tests P>0.20). Different patterns were, however, found between certain pools.
3.2.8. Whether exchange between pools is substantial in relation to the survival chances in the populations (Chapter V Survival of adults) can be examined by comparing the exchange-rates of the populations with the survival chances. The exchange-rate is the net emigration or immigration rate, estimated as E_x = E.(l-Db). The same conclusions can be drawn here as in regard to the Db-values. Between different pools and between different periods at the same pool considerable differences in the flow of beetles occur, e.g. Wn in periods I and II, or Br in periods III and IV (Table VII-6). The differences between the border pools and the centre-pools are more evident here than they were in Table VII-5 with respect to the Db-values, but far from significantly different (U-test: z=0.75, P>0.20). On the average 3 per cent each week is lost from border-pools (var.coef. = 2.10), and 11 per cent from centre-pools. By way of comparison, the estimates of the survival chances in isolated populations (Chapter V Survival of adults) give a mean loss by mortality increasing during period I to IV from 11 to 24 per cent per week (Table VII-6). On the average the losses by dispersal activity and by mortality do not differ significantly, although in cases that E_x<O dispersal gave a net gain of individuals (Wilcoxon pair test: E_x-values against the mortality rates as expected values: n=17, T=75, P>O.20). In Chapter VIII Discussion and Simulations , dealing with simulation of the field data, it will appear that there is an important relation between dispersal activity, survival from dispersal and survival in the population.

3.3. Exchange between pools of the Br-complex
3.3.1. The distribution of the emigrants from a certain site over the other sites will now be considered, together with the distribution of the origins of the immigrants at a certain site.
3.3.2. If the emigration rate were determined by random processes, each pool (subpopulation) should proportionally contribute to the number of marked beetles released to the total number of dispersing beetles in the complex. In Table VII-7 the expected random distribution is compared with the observed distributions of paint-marked emigrants. The contribution of emigrants from each population to the total number of dispersing beetles indeed shows some relationship to the number of beetles released per population (corr.test: n=24, r=0.51, z=2.59, P<0.01). On the average fewer emigrants depart from the border pools (Wn -Kr) than expected (D<0), whereas from the centre pools (Br -Bn) usually more emigrants depart than expected (U-test on E_fn-values, n₁ = n₂ = 12, U=38.5, P<=0.05). Temporarily occupied pools (Kw, Sc, Bn) did not give significantly more emigrants than the permanently occupied ones (U-test on E_fn-value: n₁ = 5, n₂ = 19, U=24, P>0.05), but there is a weak tendency in that direction. We would have expected that if the temporarily occupied sites were less favourable, emigration would be higher there than from permanently occupied sites. The flow of emigrants is not very consistent per population (cf D-values of pools with series in three or four periods, Table VII-7). For the relationship between emigration and population size see 3.4.3.
3.3.3. The expected distribution of immigrants over the pools would only be random if it is assumed that there is no relation with the relative position of the pools in the complex (accessibility, distan- ce to other pools). In Table VII-8 the observed distribution of immigrants is compared with such an expected one. In the pools of the BH-group (cf Fig VII-1) fewer immigrants are found than in the other pools. The Bn pool is only temporarily occupied by beetles, and it may be less attractive for passing beetles to stay there when no other beetles are available. The Bb and the Kr pools are probably less accessible than the others: the opening to Bb is in summer filled with water-lilies and the route to Kr is relatively long, irregular and with a number of alternative routes. As could be expected, fewer immigrants arrived in in the border pools than in the centre pools (U-test on I_fn-values: n₁=8, n₂=12, U=20, z=2.162, P<0.05); this is also the case for temporarily and permanently occupied pools respectively (U-test: n₁=16, n₂=20, U=103, P<=O.05).
3.3.4 Obviously the exchange between two pools depends on the distances between them. The proportional distribution of the emigrants from one sector over the other sectors in 1978 is shown in Table V11-9.
The distances from one sector, from which the beetles emigrated, to the other sectors are expressed as rank numbers that are related to the numbers of pools between. There is an overall inverse relationship between distance and amount of exchange between two sectors (Spearman-test: R_s = -0.777, df = 8, P<0.001). But there are also exceptions, e.g. in period III the flow of individuals from Bb to Br and that from Br and Me to Kr (see Table V11-9); obviously other aspects than distance are important too.
3.3.5. On the average there is a relatively high influx of immigrants into pool Br and a relatively small one into the pools Kr, Bb and Bn (Table V11-9). Remarkable is that most emigrants from Wn stay behind in Wz/Sc, whereas beetles from other pools that arrive in Wz/Sc usually continue dispersal activities.
The distribution of emigrants from one sector can be different in different periods. One cause of this may be the growth of waterplants, such as water-lilies, so that local situations may change such that the routes and choices of direction of the beetles will be affected.
3.3.6. At places where beetles have to choose between two or three possible routes. the choice seems to be influenced by the direction in which they were already moving, proportionally beetles from pool Bb swim less to Kr than beetles from Kr go to Bb, whereas beetles from Bn mainly move to Kr. In Table V11-10 the choice of direction of beetles passing through Wz/Sc is compared with that of the beetles released in Wz/Sc. In 6 of the 12 comparisons the choices of the passing beetles do not differ distinctly trom those of Wz/Sc; in one case the passing beetles on the average went in the opposite direction; and in the other five cases their movements were intermediate between those of the Wz/Sc-beetles and the opposite direction. These differences are significant according to the Fisher-test (n=24, A=12, B=0, C=6, P=0.05)

3.4. The relationship between exchange between subpopulations and population size and composition
3.4.1. The composition and size of the population at each pool will change as a result of exchange. Table VII-11 shows for each subpopulation in which paint-marked beetles were released, the proportion of immigrants af ter about three weeks of dispersal activities (after correction for the number of marked beetles released). From the table it appears that after some weeks immigrants are a substantial part of most subpopulations. In centre-pools immigrants dominate more than in the border pools (U-test: n₁=9, n₂=12, U=20.5, P<0.025). Sometimes the high proportion of immigrants will only be due to the small size of the subpopulation concerned (e.g. Wz/Sc and Bn in period III), but in general no relationship was found between population size and the proportion of immigrants in the subpopulation (cf Table VII-12). See also par. 3.4.3.
3.4.2. In Fig VII-3 the number of beetles observed per week in each pool-group and in the whole Br-complex is given (unmarked and marked together). The total numbers decrease in spring and increase in summer and autumn. But the course in numbers is not similar in the three pool-groups. In BH the numbers follow those of the total complex, but in the WK and BH the numbers decrease af ter week 31 (period III) in contrast with the increasing numbers in pool-group BH. These differences between pool-group BH and the others may be explained by
a) a possibly higher number of emerged tenerals (as a consequence of the higher number of adults during egg production in spring en summer) anb by
b) an exchange between the pool-groups favouring BH. The Db-values per pool-group can be calculated from the I- and E-values in Table VII-4, see Table VII-12. In all four periods Db-values for all pool-groups are below 1 (emigration>immigration), except for BH in the third period with DB=I.98, i.e. in that period BH got twice as much immigrants than it lost beetles byemigration. In accordance with this we can derive from Table VII-7 and Table VII-8 that in the third period BH lost less emigrants than expected and got more immigrants than expected (Table VII-12). WK got also proportionally more immigrants in the last period, which may explain its strong increase in numbers in week 40 and 41.
3.4.3. As an example of how changes in the distribution occur on a more detailed scale Fig VII-4 shows the course in numbers at five sites in the BH-pool-group. In spring the beetles are concentrated at the east side of the pool-group (Kw, Hz and BIH). Rather quickly all beetles disappear at Kw. and Mz and Bz become the more important sites with groups of beetles. During summer also a concentration of beetles is observed in the blind ditch Bs.
3.4.4. If we consider the total number of beetles observed per subpopulation as a measure for the population size, and compare that number per period with the emigration rate estimated in Table VII-4, then it appears that emigration from large subpopulations is less than from small ones, whereas the former got relatively more immigrants than the smaller subpopulations (Table VII-12: E_fn increases from left to right. whereas I_fn decreases).

3.5. Dispersal activities and weather
3.5.1. Since the paint-marked beetles were recorded daily we can examine whether there are particular days with more or with less dispersal activity. A Kolmogorov-Smirnov test and a chi² goodness-of-fit test show that the numbers of beetles daily exchanged (X in Table VII-13) deviate significantly from the expectations according to a normal distribution of exchange-events (K-S test: n = 32, D = 0.340, P < 0.001; chi²-test: df = 1. X² = 12.56, P < 0.001). High or low dispersal activities may be connected with particular weather conditions. In Table VII-13 some data concerning weather are added, and the numbers of beetles exchanged under different weather conditions are compared with the U-test. We only found a significant relation between exchange and minimum temperature. As exchange by swimming occurs mainly at night the lack of a correlation with maximum temperature or radiation (i.e. sunshine} is understandable. More exchange at higher minimum temperatures could be expected. On the one hand more exchange can also be expected during rain and wind, because the beetles may be disturbed by rain and waves, and the chance that they lose their way may increase. On the other hand, swim activity might be diminished during rain and wind, so that fewer beetles will run the risk of disappearing from a subpopulation. Possibly, both phenomena occur, because no significantly different exchange was found between dry days and days with rain.

4. DISCUSSION

4.1. Comparison of flight and swim activity
4.1.1. Exchange between populations by swimming can be interpreted as a result of random dispersal of individuals during activities such as looking for food. However, in the case of Gyrinus marinus flight may be real dispersal behaviour. It is likely that the beetles do not leave the population by flight accidentally, but because they are motivated in some way to fly. Flight is highly determined by good weather conditions.
For exchange between pools by swimming no such strong dependence on weather was found, although there is some relation with temperature.
4.1.2. Flight activity is observed in only a small part of the beetles (<5%) and obviously population sizes will not be changed substantially by the number of beetles emigrating or immigrating by flight. However, exchange by swimming may change populations substantially. In general this exchange will occur between populations relatively close to each other. Flight occurs over a large area but with low frequency. probably with high risks. and is possibly especially important for the (re)founding of populations, whereas swimming occurs on a smaller scale with high frequency, probably with lower risks and with direct effects on the distribution of the beetles over the habitats in the area. See also below (par.4.3.)

4.2. Exchange between pools
4.2.1. The emigration from and the immigration into a pool occur not randomly, but also depend on local circumstances. Such as the layout of the habitat: the position of the openings to other pools, the number of alternative routesway. distances between populations, etc. Since we rarely found beetles along marshy or bare banks we may assume that local qualities are also important. From experiments we know that a group of beetles is attractive to a swimming beetle and May cause a beetle to stay in that group (Grooters and Groothuis 1979a/b. Zijlstra 1979). The groups change in size and location. This may account for the variation in exchange rate between one pool and the rest of the pools. For example, the exchange between the pools Bb and Kr and the rest of the complex is more intensive in the third period, when several groups are present in Bn, than in the previous periods when no groups were present in Bn. That beetles emigrate less from and immigrate more to subpopulations of large size than from or into populations of small sizes may also be due to the attraction of groups. In a preceding study it was found that with increasing population size not so much the size of the groups, but the number of groups increased (Fig V11-5). We may assume that with more groups per pool the chance will increase that a beetle will have found a group before leaving the pool; the same holds for an immigrating beetle.
4.2.2. The effects of dispersal activities upon the composition and size of the subpopulation will be different for each pool, and also the influence of the course of events in one pool upon the dynamics in other pools will be different from pool to pool. Although we know some of the factors that play a part, the total process of exchange as a whole is highly stochastic, i.e. many factors are unknown and variable in time and/or place in an unpredictable way.

4.3. The effects of exchange between pools upon population size
4.3.1. Exchange by swimming between pools can be considerable, a subpopulation can consist for an important part of immigrants (cf pool Br), and population size can thus be changed substantially by emigration and immigration. We found that in most cases the loss of individuals from a population byemigration is greater than the gain by immigration. In some populations sizes are decreased substantially byemigration. To this extent exchange by swimming seems to be unfavourable for the maintenance of a population. On the other hand, in one-third of the cases, not restricted to some subpopulation or period, a dispersal-ratio greater than I was found, i.e. more beetles were immigrating than were emigrated. Six of the nine populations studied gave at least once a Db>l, and Db-values greater than 1 occured in periods I to III. This variation in displacement of beetles in time and in space will decrease the chance of local extinction and will cause some sites to be re-occupied by a new local subpopulation. In this way the risk of unfavourable changes in the overall dynamics are spread over a variabIe number of places, which also change in position, so that the chance of extinction of the population as a whole in the complex may decrease ('spreading of risk', e.g. den Boer 1968, 1981)
4.3.2. Theoretically the exchange between subpopulations may result in a greater stability of population numbers (e.g. den Boer 1981). This is also confirmed by simulations (e.g. Reddingius and den Boer 1970). Furthermore Kuno (1981) added a special effect of exchange between subpopulations that fluctuate asynchronously. In such case mean population size even increases due to exchange of individuals followed by reproduction (see also Metz et al 1983).
Obviously the risks of dispersal are crucial to population dynamics and may generate alternative hypotheses to understand dispersal activities: Why should an individual leave its population when the risk of death during dispersal is high? Why should emigration occur if the loss by emigration is greater than the gain by immigration?
4.3.3. To judge the significance of exchange between populations the negative effects (losses by death, disappearance from the complex of subpopulations) have to be weighed against the positive effects (spreading of risk, the 'Kuno'effect, (re)founding of subpopulations). Theoretically, variation in the numerical processes within and between populations are determining the power of the positive effects of dispersal activities (Southwood 1962, den Boer 1981, Kuno 1981). Therefore, such a weighing of negative and positive effects of dispersal activities can hardly occur without simulation experiments.
Such experiments will be discussed in Chapter VIII Simulations and Discussion. At the moment we can only report empirical findings that:

1. there is a considerable emigration by swimming,
2. swim-activities are probably necessary for daily life,
3. exchange between pools possibly occurs by accident,
4. exchange between subpopulations depends on the distance between them, the structure of the route and the number of alternatives,
5. emigration can lead to extinction of local subpopulations as well as to founding of new ones,
6. the dispersal ratio can be greater than 1, and
7. the composition and size of subpopulations can change considerably because of exchange by swimming.

REFERENCES
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APPENDIX
Estimation of the emigration rate by swimming activities

In par 3.2.2. the emigration rates by swimming activity were estimated by an iterative computer-model. This model is made with the help of a spreadsheet program (SuperCalc 3). A spreadsheet-model is a computer-model, that (re)calculates the values of all dependent variables when the value of one of the data or of an independent variable is changed. In this way it is possible via sensitivity analyses to achieve optimal estimates. The model is organized in a grid. Columns are designated by letters, rows are designated by numbers. Each cel of the grid can be indicated by its column-letter and its row-number and to each cel we can award a value, a variable, a function or a formula, by which relations with other cels can be made. In our model we introduced per population the number of effectively released marked beetles, the number of beetles found elsewhere as immigrant, the number of beetles still available in the population after the last day an immigration elsewhere was recorded and the number of weeks that exchange was recorded. Introducing some survival chance (Q) and an emigration rate (E) as independent variables the model calculates as dependent variables the number of beetles that was expected to be still available in the population (P_e, the number of beetles that should have died (V) and the number of beetles that should have been emigrated (E_e), see Table VII-14. Assuming that by the daily counts of the beetles in the field approximately all beetles present at some place should have been noticed, the number of beetles expected to be still present in the population (cel A08, Table VII-14) has to be equal or one or two specimens higher than was actually observed (cel AO9), whereas the number of emigrants (cel A14) should be at least equal to (but usually will be more than) the number of beetles observed elsewhere as immigrants (cel A29). By iteration, adapting the value of the emigration rate, and if necessary also that of the survival rate, those estimates for the emigration (cel AO6) and the survival in the population (cel A07) are found that fit best the expected numbers of the still present (P_f) and of the emigrated beetles (E_e) as compared with the numbers observed in the field (P_f and E_f respectively). The value for the survival chance was only altered when the value for the emigration rate would otherwise deviate considerably from the estimate in Table V11-2. From the expected total number of emigrants (Ee in cel A14) and the expected number of these beetles elsewhere immigrated (I_e in cel A29) the survival chance during swimming-dispersal can be estimated as Q_ee = I_e/E_e (cel A30). Also the dispersal-ratio (Db, cel A34), which is the ratio between the number of immigrated beetles in a population and the number of emigrants from the same population, can be estimated from E_e (cel A14) and the number of beetles immigrated (I, cel A33) from elsewhere in the population. The results are produced in Table VII-4.
Two examples of iteration excercises are given in Fig VII-6.