• colonization;
  • edge permeability;
  • extinction;
  • movements;
  • random walk;
  • stochastic models


  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

1. I present a stochastic simulation model that describes individual movements of Metrioptera bicolor Philippi in a heterogeneous landscape, consisting of patches of suitable habitat surrounded by a matrix of unprofitable habitats. Although the model is parameterized with information about daily movement behaviour, it can generate spatially explicit predictions about inter-patch dispersal rates for much longer periods, e.g. one generation.

2. Long-term dispersal experiments were conducted to evaluate model predictions. Patch-specific emigration rates and the total distance moved by individuals could be predicted with satisfactory precision. Because of the stochastic nature of the model, it failed to predict which recipient patches emigrating individuals actually chose in a particular situation.

3. Spatially explicit simulations of the movement model were made for the whole natural distribution area of M. bicolor. The results suggest that emigration rates are negatively correlated with patch size. Local populations occurring on small patches may be more prone to extinction than those on large patches, by losing more emigrants than are compensated for by immigration.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Inter-patch dispersal, i.e. the movements of individuals between discrete patches of preferred habitat, is essential for colonization of vacant habitat patches and is therefore a critical feature of all kinds of metapopulation models (e.g. Hanski 1985, 1994; Hastings 1991; Nachman 1991; Hanski & Gyllenberg 1993; Hanski & Thomas 1994). The actual values of emigration and immigration rates are expected to have great impact on the dynamics of local populations. Immigration can reduce the risk of extinction of local populations by a rescue effect (Brown & Kodric-Brown 1977; Sjögren Gulve 1994; Hanski, Kuussaari & Lei 1995). When the number of individuals emigrating from a local population exceeds the number of individuals immigrating from nearby patches, an increased extinction risk is expected (Fahrig & Merriam 1985).

Because inter-patch dispersal affects extinction and colonization probabilities within metapopulations, it regulates the fraction of available habitat patches that are occupied by the organism and, thus, the regional extinction risk (Hanski 1991). Furthermore, the degree of inter-patch exchange of individuals is a fundamental factor delimiting local populations within the metapopulation concept (Kareiva 1990). A local population can be interpreted as the demographic unit where most population processes, i.e. reproduction, competition and predation, take place and where most interaction among conspecifics occurs (den Boer 1981). This group of individuals typically occupy the same habitat patch that are separated from similar patches by surrounding hostile, or, at least, not preferred habitats. In a metapopulation, inter-patch dispersal is assumed to be substantially reduced compared with the amount of movements individuals perform within their native patch.

In models of metapopulation dynamics, emigration rates are usually assumed to be independent of both patch size and population density (e.g. Hanski & Thomas 1994). However, empirical evidence from some insect studies indicate negative relationships between patch size and emigration rates (Bach 1984; Kareiva 1985; Turchin 1986; Hil, Thomas & Lewis 1996; Kuussaari, Nieminen & Hanski 1996). This phenomenon can be explained by a lower edge-to-size ratio for larger patches than for smaller patches. The number of dispersers reaching the edge of a habitat patch, and thus becoming potential emigrants, is expected to be positively correlated with the edge-to-size ratio (Stamps, Buechner & Krishnan 1987). For the same reason, emigration rates are expected to be higher from narrow and elongated habitat patches compared with circular or square patches. Of course, immigration may also be influenced by the geometry of the target patch, i.e. shape and size (Game 1980; Turchin 1986; Hill, Thomas & Lewis 1996).

Only a fraction of the individuals emigrating from local populations are expected to reach another patch of suitable habitat and successfully reproduce there. The number of dispersers reaching new habitats is usually assumed to decline exponentially with distance from the source patch (MacArthur & Wilson 1967; Gilpin 1987; Hansson 1991). Indeed, several empirical studies have reported negative regression coefficients between colonization probability on empty patches and the straight line distance to neighbouring local populations (e.g. Toft & Schoener 1983; Sjögren 1988; Harrison 1989; Kindvall & Ahlén 1992). However, the number of individuals necessary for successful colonization is usually unknown (Ebenhard 1991). Therefore, it is difficult to relate inter-patch dispersal rate to regressions of colonization probability and isolation.

Representative information on inter-patch dispersal is usually hard to get (Turchin, Odendaal & Rausher 1991; Stenseth & Lidicker 1992). Standard mark and recapture procedures require very intensive field work, and are expected to under-estimate inter-patch dispersal distances since long distance dispersers are less likely to be detected than individuals dispersing only short distances (Solbreck 1980). Another problem with estimates of dispersal or colonization distances made from capture–recapture studies or turnover data, is that the observed distances may often reflect the frequency distribution of inter-patch distances set by the landscape configuration, rather than by the dispersal capacities of the animal (Porter & Dooley 1993). Metapopulation models that are based on this type of information are expected to generate less reliable predictions about other systems than were used for parameter estimation.

Studying inter-patch dispersal is particularly difficult when emigration rates are so low that only one or two specimens are expected to leave a population of moderate size in each generation. This may often be the case on the spatial scale of metapopulations. Therefore, the construction of stochastic simulation models, that are based on information of individual movement behaviour, may be a fruitful approach to overcome the difficulties of assessing inter-patch dispersal in metapopulation studies.

In this study, I develop a spatially explicit simulation model that can predict inter-patch dispersal rates in the metapopulation of the bush cricket, Metrioptera bicolor Philippi. Various field experiments were made to estimate model parameters and to evaluate simulation results.

Modelling animal movement

  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Two fundamental questions every individual has to answer every second in their life is ‘should I stay or should I go?’ and ‘where should I go?’. Numerous spatially and temporally varying factors are expected to influence this decision-making, e.g. the density and distribution of food resources, mates, competitors and predators (e.g. Bach 1980; Risch 1981; Kindvall et al. 1998). The option is also dependent on the individual's own skills, condition and knowledge of the surroundings.

It would be very tedious to construct a mechanistic dispersal model that includes all factors that are expected to influence individual dispersal behaviour. Besides, many of the parameters are cumbersome to estimate and map. However, it is possible that the outcome of the individual decision-making is expressed in frequency distributions of observed movement distances and turning angles measured on a certain time scale. The ideal time interval is one that is short enough to allow measures of movement distances to correspond with actual straight line movements performed by individuals, and long enough to exclude temporal correlations of movement distances and turning angles. Perhaps it is impossible to find this ideal time scale for many organisms, especially those with complicated movement behaviour (Kareiva & Shigesada 1983). The most informative way of quantifying animal movements can be made when individuals typically make straight line movements between successive stops (Turchin et al. 1991). Then it is possible to estimate the temporal variation of moves instead of using a fixed time interval.

Generally, individuals are expected to stay in favourable habitats and move out as effectively as possible from hostile or unprofitable habitats (Bach 1980; Risch 1981; Coyne et al. 1982; Turchin 1991). Frequency distributions of movement distances measured in different habitats are expected to vary in relation to habitat quality (Aikman & Hewitt 1972). It is also possible that individuals increase their directionality of movement when walking through unpreferred habitats (Zalucki & Kitching 1982). Thus, we can expect that movement speed of a species varies between habitats of different quality.

Individuals that reach the border of a preferred habitat may refuse to move into surrounding habitats. When modelling animal dispersal on the scale of metapopulations it may often be necessary to incorporate a parameter describing the ‘edge permeability’ between different kinds of habitats (Wiens, Crawford & Gosz 1985; Stamps et al. 1987). The edge permeability is probably determined by several environmental and population dynamic factors, e.g. current population density. Thus, the observed edge permeability can be expected to vary spatially within a landscape. Empirical evidence also suggests temporal variation of the edge permeability (Kindvall 1995a).

Time-step specific spatial co-ordinates, xt and yt, of an individual's movement path starting from any location (x0, y0) can be modelled by the following equations:

  • image

By assuming turning angles, vt, and movement distances, dt, to be uncorrelated it is possible to make stochastic simulations of animal replacement by iterating equation 1, using random values of dt and vt sampled at random from specified distributions.

I constructed a computer program, written in Turbo Pascal, to run spatially explicit simulations of a stochastic model, based on equation 1, describing individual movements in a heterogeneous landscape. Two classes of habitats were considered, i.e. preferred habitats and habitats avoided by the species. The program was designed to use different distributions of movement distances relevant for the two kinds of habitat. At each time-step the current habitat at the simulated position was checked on a digitized map. If a simulated individual moved out from a preferred habitat patch, the program allows the individual to emigrate with a specified probability, Pout, describing the edge permeability. If the individual did not move out in the surrounding habitat it remained at its current position until the next time-step.

Material and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

The species

Metrioptera bicolor Philippi, is a medium-sized (12–19 mm) bush cricket (Orthoptera: Tettiogoniidae) living in dry grassland habitats (Holst 1986). Most individuals have reduced wings and cannot fly. Long-winged flying forms rarely exist (Kindvall 1993). The relative dispersal potential of long-winged specimens is not known. In general, M. bicolor seems to be a very resident species that usually moves very little and is unwilling to leave its native habitat patches (Kindvall & Ahlén 1992; Kindvall 1993).

Metrioptera bicolor overwinters in the egg stage. The eggs hatch in early May. There are five larval instars and adults usually appear from the beginning of July (Harz 1969). The mating and oviposition season lasts from July until late September. Adult females experience higher mortality risks than adult males (Kindvall & Ahlén 1992; Kindvall 1993). Therefore, the sex-ratio becomes skewed towards males late in the season.

The only Scandinavian occurrence of M. bicolor is restricted to a minor area (<100 km2) in the southernmost province of Sweden (55°40′ N 13°35′ E). About 500 ha of suitable grassland habitat are available within this area, divided in 116 separate patches that are surrounded by mainly pine forest. The habitat patches that are occupied by M. bicolor change from year to year as a consequence of local extinctions and colonizations of vacant habitat patches (Kindvall & Ahlén 1992). Thus, it is appropriate to use the term metapopulation when describing the regional population dynamics of M. bicolor (Hanski & Gilpin 1991).

Field work

A number of field experiments with M. bicolor were designed to estimate model parameters and to evaluate the predictions from model simulations. In most experiments, it was necessary to mark the animals with individual codes. In most cases, this was done by gluing small pieces of reflective material (4 mm2) on the back of the pronotum. Individual numbers were typed with a type writer directly on the reflecting material. This technique makes it possible to resight the bush crickets during darkness using a head-lamp. Very high resighting probabilities are generally experienced with this method (Heller & von Helversen 1990; Kindvall 1993). In some experiments, I marked the individuals with a pen or by gluing small plastic marks commonly used on bees with individual numbers. All individuals of M. bicolor involved in this study were captured in the field just prior to the experiments.

Information on male and female daily movements in preferred habitat, i.e. dry grassland (Kindvall & Ahlén 1992), is taken from a data set reported in another paper (Kindvall 1993). These data (n = 440) were obtained during the mating seasons in 1990–93 (July–September) from repeated resights of individually marked specimens.

To get a data set of daily movements relevant for the most common matrix habitat in the Swedish distribution area of M. bicolor, individually marked males were released in a minor pine forest (>3 ha) in Eriksberg, situated in the outskirts of Uppsala (59°50′ N 17°37′ E). This experiment started in 18 July 1994 and lasted for 3 days. All marked males (n = 46) were released around midnight at a single point. The shortest distance from the release point to the border of the forest was 50 m.

Three types of experiments were designed to estimate the probability of leaving a patch of preferred habitat once an individual has come to the edge. Marked males or females were released at points situated at sharp borders between the preferred grassland habitat and a barrier type of habitat. One experiment was made on an edge to a north-facing forest and another experiment was made on an edge to a south-facing forest. The third experiment was made on narrow corridors of suitable grassland (<1 m) surrounded by cropfields on one side and roads (4–10 m wide) on the other. Altogether, 21 replicates were made of the last experiment. Different sites located in the vicinity of Sankt Olof (55°38′ N 14°10′ E), 30 km east of the Swedish distribution area of M. bicolor, were chosen for each replicate. These experimental replicates lasted 24 h.

Four study areas, located outside the natural distribution area of M. bicolor, were used in 1993 for long-term dispersal experiments (Fig. 1). Unmarked male nymphs (n = 70) were released in mid-June and were recaptured as adults in mid-July. The males stridulate during sunny weather and it is therefore possible to find them with high probability. Their positions were noted and all recaptured individuals were marked with specific codes. During the summer, two more attempts were made to resight and mark individuals in these experiments. A circular area with an approximate radius of 2 km was surveyed around each release point.


Figure 1. Maps of the four study sites used for long-term experiments in 1993: (a) Ilstorp (55°37′ N 13°40′ E), (b) Löderups strandbad (55°19′ N 14°07′ E), (c) Sandhammaren (55°23′ N 14°10′ E) and (d) Järahusen (55°24′ N 14°11′ E). The cross indicates the release point. Grassland patches suitable for Metrioptera bicolor (white) are numbered. Grey areas are unsuitable matrix habitats consisting of forest (dark grey) and arable fields (light grey). Roads are indicated with broad black lines. The black area in (b) is the Baltic sea.

One of the study sites used for long-term dispersal experiments consisted of a pine forest (4 ha) surrounded by grassland suitable for M. bicolor (Fig. 1a.). At this site, I released the nymphs at a point situated approximately in the centre of the forest. The distance from the release point to the forest edge varied between 100 and 180 m. In the other experiments, all nymphs were released at single points within suitable habitat (Fig. 1b–d).


To evaluate the predictive power of the stochastic movement model (equation 1), I made spatially explicit simulations of two kinds. The first set of simulations was performed to predict net displacement of M. bicolor in long-term dispersal experiments made in four areas with different spatial configuration of habitat patches (Fig. 1). The other set of simulations was made to predict emigration and inter-patch dispersal rates among the 116 patches of suitable habitat available within the natural Swedish distribution area of M. bicolor.

When simulating the long-term experiments, I parameterized the model in two ways. First, I considered movements in a homogeneous landscape with no edge effects (Pout = 1) and a distribution of daily movement distances equivalent to the one observed for M. bicolor within preferred habitat (Fig. 2a). In the second model, I assumed that daily movement distances vary with habitat quality and that individuals experience a reduced edge permeability (Pout = 0·11, Table 1) when moving out from preferred habitat. Log-normal distributions of daily movement distances equivalent to the ones observed within preferred habitats and avoided habitats, i.e. forest, were used for random number generation (Fig. 2). In all simulations, turning angles were generated at random from a uniform distribution.


Figure 2. The relative frequency distribution of observed daily movement distances of males (n = 151) and females (n = 289) of Metrioptera bicolor within preferred habitat (a). A log-normal distribution function is plotted for comparison (mean ± SD = 3·2 ± 13·7). The relative frequency distribution of male daily movements (n = 85) observed within forest (b) and the corresponding distribution function expected from a lognormal distribution (mean ± SD = 49·3 ± 31·1).

Table 1.  Experimental estimates of edge permeability, Pout, at edges of forest and roads or crop fields
Edge habitatResidentsEmigrantsTotalPout
  1. Difference between northern and southern forest edges: χ2= 2·44, d.f. = 1, P > 0·10.

  2. Difference between forest edges and other edges: χ2= 9·56, d.f. = 1, P < 0·01.

Northern forest104161200·267
Southern forest582600·067
Roads and crop fields377143910·072

When simulating movements in the natural distribution area of M. bicolor, I used the same parameter values as mentioned above, which are relevant for a heterogeneous landscape. To resemble life-time dispersal, each individual was simulated with 150 time-steps. This time-period corresponds to the whole active season of M. bicolor, i.e. 5 months. I make the unrealistic assumption that dispersal parameters do not change temporally (With 1994; Mason, Nichols & Hewitt 1995). The reason for this simplification is the lack of information about seasonal variation in movement behaviour of M. bicolor.

Separate simulations were made for each patch, starting from a number of points that were uniformly distributed over the whole patch. A uniform distribution does not necessarily describe the natural dispersion pattern. Habitat quality may differ within preferred habitat patches (Kindvall 1995a). This heterogeneity may lead to aggregations of individuals at certain parts of a patch. Of course, the simplified assumption of even distributions is expected to impose biases of model predictions.

Because the simulations were very time-consuming, usually not more than 100 individuals were simulated for each patch with the appropriate value of Pout. For some larger patches it was necessary to simulate up to 400 individuals. Because of the stochastic nature of the present model, many more observations are needed for representative estimates of inter-patch dispersal rates. Therefore, I made a complementary set of simulations where Pout was 1·00 for the focal patch and 0·05 for all the recipient patches. By doing this it was sometimes possible to get about 50 times more observations of inter-patch movements. I used the emigration rate estimated from the simulation where Pout equals 0 05 to recalculate the inter-patch dispersal rates generated from the extra simulations.

To test the hypothesis of patch-independent emigration rates, commonly used as an assumption in models of metapopulation dynamics, I incorporated the estimates of inter-patch dispersal rates obtained from the movement model into a structured metapopulation model. The ramas/gis program package (Akcakaya 1994) was used for this purpose. With this program, local population dynamics can be simulated explicitly according to a discrete logistic equation of population growth. I used the same parameter values of maximum growth rate (Rmax = 7·09, carrying capacity (K = 59 females per hectare), and environmental stochasticity as described in detail elsewhere (Kindvall 1995b). Simulations were made with two different sets of inter-patch dispersal matrixes. One set with the original rates predicted by the movement model and another where all inter-patch dispersal rates were standardized by the mean value of all predicted emigration rates.

I used patch specific estimates of male population size sampled annually in the natural distribution area of M. bicolor between 1989 and 1994 to calculate expected numbers of inter-patch dispersers. Actual counts of males were only made on 45 patches (Kindvall 1996). However, occupancy data exist from all years for all other patches (Kindvall 1996). Therefore, I calculated the expected local population sizes on occupied patches by multiplying the observed mean density, i.e. 35 males per ha (Kindvall & Ahlén 1992) by patch area.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Daily movements

There is no statistically significant difference in daily movement distances between males and females of M. bicolor when moving within preferred habitat (Fig. 2a, t-test on log10-transformed data: t = 0·97, n = 440, P = 0·33 NS). The mean (±SD) daily movement distance was 2·25 ± 4·21 m for males (n = 151) and 2·16 ± 4·05 m for females (n = 289). Most individuals moved very little per day (median = 0·90 m, n = 440). The maximum daily movement distance observed during the study was 40·2 m.

The observed frequency distribution of daily movement distances within preferred habitat can be approximated by a lognormal distribution function with a mean ± SD equal to 3·2 ± 13·7 m (Fig. 2, χ2 = 7·39, d.f. = 7, P = 0·39 NS). An exponential distribution function was also fitted to the observed distances, but the fit was extremely poor (χ2 = 96·2, d.f. = 4, P < 0·0001).

The frequency distribution of observed turning angles between successive daily moves within preferred habitat is significantly different from a uniform distribution (χ2 = 27·2, d.f. = 15, P < 0·05). It seems as if individuals of M. bicolor usually turn backward, either to the right or the left. However, when moving forward they seem to move as straight as possible (Fig. 3a). The frequency distribution of observed turning angles is symmetrical around 180°, i.e. the number of observed turns to the left (n = 54) and turns to the right (n = 64) is not statistically different from random (χ2 = 0·85, d.f. = 1, P > 0·20).


Figure 3. The frequency distributions of turning angles between successive daily moves made by Metrioptera bicolor in (a) preferred habitat (n = 118) and in (b) forest (n = 43). Line shows the expected uniform distribution.

Greater daily dispersal distances of M. bicolor males were observed within pine forest than within preferred habitat (t-test on log10-transformed data: t = 21·44, n = 525, P < 0·0001). The frequency distribution of daily movement distances observed in forest can be approximated with a lognormal distribution with the mean ± SD equal to 49·3 ± 31·1 m (Fig. 2b; χ2 = 7·45, d.f. = 3, P = 0·059). The observed frequency distribution of turning angles within pine forest can not be distinguished from what is expected from a uniform distribution (Fig. 3b; χ2 = 5·14, d.f. = 3, P = 0·16).

Among the males released in Eriksberg, 16 (35%) reached the border of the forest during the first day. The first individual was found at the northern forest edge already at 9·30 a.m. Two more individuals came out from the forest during the second day. The rest of the individuals remained within the forest during the whole experiment. Although night-time observations of individual positions were used for estimation of daily movements and turning angles, many males could be resighted also during daytime. Most males stridulated even within the shade of the trees. The overall impression from the observations made during daytime was that the individuals moved in almost straight directions. It was apparent that individuals finding small temporary sun spots within the forest could stop moving for longer periods. Only two individuals were not resighted at least once during the 3 days this experiment lasted.

Edge permeability

The proportion of individuals observed to move into matrix habitats when experimentally released on the edge of preferred grassland patches differed between types of matrix habitat (Table 1). It seems as if individuals are more likely to leave their preferred habitat patch when released in the shade of north-facing forest edges than when released on the southern edges. In all experimental trials the observed edge permeability is substantially lower than 0·5, i.e. Pout = 1·0.

Dispersal experiments

Among the 70 male nymphs of M. bicolor that were released in mid-June in the long-term dispersal experiments, between 31 and 75% males were resighted more than 1 month later (Table 2). During later resighting attempts, only four more individuals were found in all the experiments. Thus, the resight probability was high (Table 2).

Table 2.  Comparison between emigration rates observed in three long-term dispersal experiments with Metrioptera bicolor (Fig. 1) and predictions (mean ± SD, n = 10) made by the movement model with habitat specific parameters. Information about the number of days until the first resight attempt, the number of individuals observed that day, Nobs, the number of emigrants, Nem, the resight probability, Pres, and the fraction of individuals that were lost during the experiment. In all experiments 70 male nymphs were released
Emigration rate
ExperimentDaysNobsNemPresLost (%)ObservedPredicted
  • *

    Emigration is here interpreted as the movement from forest to the surrounding area of suitable grassland habitat.

Ilstorp452626*1631*0992 ± 0·016*
Löderup362200·926600·005 ± 0·014
Sandhammaren393331·00530·0910·146 ± 0·053
Järahusen395330·962100570·059 ± 0·023

All individuals resighted at Ilstorp (n = 26), i.e. the experiment where male nymphs were released within pine forest, were observed within the surrounding grassland habitat. According to the simulations made with the movement model parameterized for a homogeneous landscape consisting of suitable habitat only, almost no specimens should be expected to come out from the forest within the study period, i.e. 45 days. The mean number of simulated individuals that left the forest was 0·2, calculated from 10 replicates of 26 individuals. In contrast, simulations made by the model that take habitat specific dispersal behaviour into consideration, predict that most individuals will reach the surrounding grassland habitat (Table 2).

The emigration rates observed in the three long-term experiments where male nymphs were released on patches of preferred habitat are presented in Table 2. Predictions about patch specific emigration rates, made by the movement model that is parameterized for a heterogeneous landscape, correspond approximately with observed emigration rates.

In the long-term experiment at Sandhammaren, emigrating males were found at two habitat patches. Two males were found at the nearest patch (Fig. 1c: 1), while one male had moved to one of the most distant patches (Fig. 1c: 6). According to the movement model for heterogeneous landscapes, most emigrating individuals should reach the nearest recipient patch, while the model predicts no immigration to patch number 6.

All emigrants (n = 3) observed in the experiment at Järahusen were resighted at the patch situated nearest to the patch where the initial release was made (Table 3, Fig. 1d: 1). Although this patch was predicted to have the highest immigration among the surrounding patches, the mean predicted inter-patch dispersal rates were lower than the observed.

Table 3.  Observed and predicted inter-patchdispersal in two long-term dispersal experiments, i.e. Sandhammaren and Järahusen. Predicted mean inter-patch dispersal rates (±SD) are based on 10 simulations of the movement model for heterogeneous landscapes. The patch index refers to the potential recipient patches, ranked in descending order according to the distance from the source patch (Figs 1c, 1d)
Patch indexObservedPredictedObservedPredicted
10·0610·048 ± 0·0380·0570·027 ± 0·025
200·015 ± 0·02900·010 ± 0·015
300·038 ± 0·02400·006 ± 0·012
400·010 ± 0·02100·010 ± 0·020
8– – 00
9– – 00
Matrix00·035 ± 0·04200·006 ± 0·012

The frequency distribution of net displacement, i.e. the straight line distance from the release point to the resight location, observed in the four long-term dispersal experiments is compared with model predictions (Fig. 4, Table 4). For all areas, net displacement is well predicted by the movement model that considers habitat heterogeneity and edge effects. The movement model made for a homogeneous landscape apparently cannot predict net displacement on suitable patches that are relatively small, i.e. at Sandhammaren and Järahusen, or when M. bicolor move in matrix habitat (Fig. 4a).


Figure 4. Frequency distributions of observed net displacements made by males of Metrioptera bicolor in four release experiments: (a) Ilstorp, (b) Löderup, (c) Sandhammaren and (d) Järahusen (Fig. 1). Solid line indicates the frequency distribution predicted by a movement model where Pout is 0·11 and daily movements varies with habitat type. Dotted line indicates the frequency distribution predicted by a movement model that assumes no edge effects, Pout = 1·00, and where daily movements correspond to what is observed within preferred habitat.

Table 4.  Differences between observed net displacement in the long termdispersal experiments, and predictions made by the movement model in a heterogeneous landscape (a) and a homogeneous landscape consisting only of preferred habitat (b). Differences are tested with t-test on log10-transformed data
Experimentnmean ± SD nmean ± SD tP
  • *

    Estimates of net displacements made by emigrants are not included.

(a) Ilstorp26130·6 ± 29·570126·2 ± 25·9 0·69 0·49 NS
Löderup22* 28·8 ± 26·7100 25·5 ± 15·8 1·89 0·061 NS
Sandhammaren30* 8·9 ± 4·7100 7·8 ± 4·7 1·02 0·31 NS
Järahusen50* 18·7 ± 10·2100 20·6 ± 9·7 1·30 0·20 NS
(b) Ilstorp26130·6 ± 29·570 38·2 ± 21·110·1<0·0001
Löderup22* 28·8 ± 26·7100 35·4 ± 22·4 3·21<0·01
Sandhammaren30* 8·9 ± 4·7100 37·1 ± 22·710·0<00001
Järahusen50* 18·7 ± 10·2100 37·0 ± 22·6 5·8<0·0001

Dispersal in the natural distribution area

Spatially explicit simulations of the present movement model of M. bicolor indicate that emigration rate varies between 0·0027 and 0·82 among the 116 habitat patches available within the Swedish distribution area. The mean emigration rate ± SD was 0·17 ± 0·19. There was a clear negative relationship between the simulated emigration rate and the area of habitat patches (Spearman rank correlation: rs = – 0·87, P < 0·001).

By incorporating the simulated inter-patch dispersal rates in a structured metapopulation model it is possible to predict patch specific population densities in the M. bicolor system. The local population density, i.e. males per hectare, was estimated annually on 45 habitat patches in the years 1989–94. There is no statistically significant correlation between observed mean population density and the area of habitat patches (rs = 0·25, P = 0·10 NS). Neither was the relationship significant for the same set of patches, between mean population density, predicted by the structured metapopulation model (50 replicates) and patch size (rs = 0·04, P = 0·79). However, if the inter-patch dispersal rates are adjusted so that the emigration rates become equal to the mean value on all patches, a negative relationship appears between the local population densities predicted by the structured metapopulation model and the patch size (rs = –0·35, P < 0·05).

According to model simulations, inter-patch dispersal rates, i.e. the relative number of individuals dispersing from their native habitat patch and reaching another patch, vary between 0·0 and 0·42 in the M. bicolor system. The median of nonzero inter-patch dispersal rates was 0·016 (n = 406). On average, 66% of the emigrating individuals reached new habitat patches, while 34% were lost in the matrix.

By using estimates of inter-patch dispersal, based on model simulations and information on population sizes on every habitat patch, it is possible to calculate the number of individuals expected to immigrate on each patch. Among the habitat patches that were known to be unoccupied by M. bicolor in 1989 (n = 33), 21 patches became colonized in the period of 1990–94. During this period, the total number of individuals of one sex that were expected to reach the patches that were colonized varied between 0 and 52·8 (median = 3·2). The corresponding values for uncolonized patches was between 0 and 4·2 (median = 0). The difference is statistically significant (Mann–Whitney U-test: Z = 3·73, P < 0·001).

Among the patches that were occupied in 1989 (n = 83), six became extinct before 1994. Six additional extinctions occurred on patches that were colonized in 1990. Thus, a total number of 12 local extinctions were observed between 1990 and 1994. The median emigration rate, estimated by the movement model, was 0·27 on patches that became extinct and 0·08 on patches where no extinctions occurred. Hence, local extinctions are associated with higher emigration rates (Mann–Whitney U-test: Z = 3·36, n = 89, P < 0·001).

A patch specific immigration rate can be calculated by dividing the mean number of individuals expected to reach each patch with its carrying capacity, i.e. 59 males per hectare (Kindvall 1995b). There is no apparent difference between the predicted immigration rates on patches with local extinctions (median = 0·027) and patches with extant local populations (median = 0·021) (Mann–Whitney U-test: Z = 0·12, P = 0·90 NS). However, local populations that became extinct seem to lose more individuals by emigrations than are compensated by immigration. The median difference between the patch specific estimates of immigration and emigration rate was –0·03 on patches where local populations survived and –0·12 on patches with local extinctions (Mann–Whitney U-test: Z = 3·82, P < 0·001).


  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

Model evaluation

Despite the simplicity of the stochastic movement model developed here, it is capable of predicting emigration rates of M. bicolor from specific patches of different size and shape with acceptable precision. Note that parameter values of the model were independent of the data that were used to test model predictions. Hence, there seems to be some degree of generality of the model presented.

The present model could predict the frequency distribution of total distances moved by individuals during considerable periods of time in heterogeneous landscapes, consisting of both preferred and avoided habitats. However, the model failed to make exact predictions about which habitat patches emigrating individuals actually chose. Obviously, repeated replicates of the long-term experiments at the same sites are necessary to test whether the observed inter-patch dispersal pattern was caused by deterministic factors rather than by the probabilistic process that is the base of the present model.

This study has clearly demonstrated that individual movement behaviour is affected by landscape composition. A stochastic movement model that ignores individual responses to habitat quality and spatial configuration fails to predict dispersal patterns on the scale of landscapes. Therefore, animal movements within patchy environments are not expected to fit simple diffusion functions (Skellam 1951; Levin 1974; Okubo 1980).

Although the present model makes realistic predictions of observed movement patterns, there is no evidence that individual movement behaviour is particularly stochastic. In fact, one of the basic model assumptions, that turning angles should be temporally uncorrelated, is not consistent with data. The frequency distribution of turning angles observed within preferred habitat suggests that M. bicolor has a apparent homing behaviour or preferences for certain vegetation structures. Earlier studies have also reported homing behaviour of Orthoptera species (e.g. Clark 1962).

Social interactions are expected to influence movements of animals (e.g. Ray, Gilpin & Smith 1991). The male stridulation of bush crickets not only attracts females, even males may respond phonotactically to the conspecific song (e.g. Morris & Fullard 1983; Keuper et al. 1986). Acoustic interactions between males may also force subdominant specimens to move away (e.g. McHugh 1972). Thus, adult individuals of M. bicolor are not expected to chose directions and movement distances by chance very often. Of course, when individuals search for food resources or oviposition sites, random decisions may occur (Cain 1985). A plausible explanation of why a stochastic movement model can predict patterns that are expected to arise mainly from deterministic decisions, is that the various stimuli experienced by individuals are randomly distributed in time and space.

Probably, a more precise prediction about the net displacement observed at Löderups strandbad would be possible if the observed rather than a uniform distribution of turning angles was considered in the simulations (Fig. 4b). The observed distribution of turning angles may be a result of ignorance about the habitat heterogeneity within preferred grassland patches. Values of movement parameters may vary significantly even between different types of preferred vegetation. It would be interesting to make a further development of the present model that deals with a finer resolution of habitat composition. To make prediction about dispersion patterns of M. bicolor within habitat patches it is probably necessary to invoke information about movements in relation to habitat heterogeneity on a more detailed scale. Improved quality of predictions about inter-patch dispersal is also expected from a model based on a finer resolution of the spatial heterogeneity of both preferred and avoided habitats.

The bias of model predictions that is expected when assuming a uniform distribution of turning angles may to some extent be compensated by the skewness of the assumed distribution of movement distances. Simulated individuals will move very short distances most of the time. Therefore, they are expected to stay within limited regions for several time-steps and only occasionally move to another part of the patch. Skewed distributions of movement distances are also reported for some other insects, e.g. the grasshopper Myrmeleotettix maculatus Thunberg (Aikman & Hewitt 1972).

Another basic assumption of the current movement model is that individuals move in straight pathways each time-step. If individuals move around frequently within the habitat patch, net displacements observed between successive days may not be realistic approximations of actual movement distances. Bush crickets and grasshoppers are known to be stationary most of the time and only occasionally move from one site to another. For example, the gomphocerine grasshopper Opeia obscura Thomas only moves for 10–20% of the time, and when moving they usually proceed straight ahead (With 1994). These observations correspond with my own studies of M. bicolor for both males and females (unpublished data). Actually, movements are so rarely observed, compared with the time M. bicolor spends on sedentary activities, e.g. sun basking, stridulation and feeding, that shorter intervals than 24 h between successive observations are not expected to reveal significantly more information about movement behaviour within preferred habitats (Turchin et al. 1991).

M. bicolor moves much faster in unpreferred habitats, like pine forest, than is observed within preferred grassland. The observations made during day-time at Eriksberg, suggest that M. bicolor choose a movement direction apparently at random in the morning, when the temperature has become high enough, and then keep the current direction until a more favourable site is reached, e.g. the forest edge or a sunny spot within the forest. The observed directionality between moves performed within the same day suggests that M. bicolor is able to orientate in relation to sun position or the plane of polarized light (Clark 1962).

Habitat quality and edges

Several studies of animal movement, including this one, have demonstrated that individuals move with different speed within different kinds of environments (e.g. Riegert, Fuller & Putnam 1954; Baldwin, Riordan & Smith 1958; Coyne et al. 1982). Although, movement behaviour is expected to be related to habitat quality, I expect no linear relationship (Fig. 5).


Figure 5. Expectations concerning movement speed performed by animals in habitats of different quality. Net displacements may be greatest in habitats that lack resources utilized by the species and lowest in habitats that are either most hostile or of best quality.

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Some habitats may be so hostile that movements become impossible (Baur & Baur 1995). These types of habitats function as physical dispersal barriers (Fig. 5). However, habitats that lack profitable resources may not be impossible to penetrate by a species. Actually, individuals may move through these habitats with such a high velocity (Fig. 5) that mortality risks, caused by starvation or predation, can be neglected compared with the risks normally experienced within habitats of better quality. Interestingly, individuals are expected to reach new patches of suitable habitat situated much further away compared with total movement distances performed by individuals within native habitats.

Within the range of profitable habitats, the movement speed is expected to be negatively correlated with habitat quality (Fig. 5). No drastic edge effects are expected between different profitable habitats, i.e. Pout is close to one. In heterogeneous environments that only consist of more or less profitable habitats, individual dispersion patterns may be successfully predicted by movement models where information on edge permeabilities is ignored (Turchin 1991).

Because unprofitable habitats may inhibit inter-patch dispersal, despite being highly permeable, these habitats may be interpreted as psychological dispersal barriers rather than physical (Stamps et al. 1987). The fraction of individuals that decide to cross psychological barriers is expected to be dependent on the conditions experienced by individuals on the local patch. Therefore, it is not likely that the edge permeability remains constant through time. Temporal changes in the availability of resources and local population density are likely to affect the motivation of individuals to leave a patch (Hansson 1991). Weather fluctuations are also expected to affect edge permeabilities (Kindvall 1995a).

One reason why observed edge permeabilities towards unprofitable habitats may be low for several species, despite no apparent physical constraints, is that individuals may not improve their fitness by moving to other patches. A resident dispersal strategy is expected to be favoured by natural selection when local carrying capacities do not change too much temporally and patches only occasionally become vacant (Comins, Hamilton & May 1980). By contrast, high edge permeabilities are likely to be observed in systems with high levels of environmental stochasticity, where dispersers easily may find empty patches that are free from competitors.

Implications for metapopulation theory

When simulating animal movements in a heterogeneous landscape on the scale of metapopulations it is important that life-time dispersal of individuals can be described properly. Several assumptions made in this study are not confirmed with data. For example, very little is known about the seasonal variation of the model parameters. It is often assumed that juveniles, because of their smaller body size, move shorter distances than adults (de Jong & Kindvall 1991; With 1994; Mason et al. 1995). On the other hand, population densities of young nymphs of Orthoptera species are much higher than adult densities (Cherrill & Brown 1990; Kindvall 1993). The model assumption, that movement parameters remain constant over the whole active period of one generation, can only be a approximation of the real situation if the two aspects mentioned counteract each other.

The simplified description of landscape composition in the natural distribution area of M. bicolor may impose serious biases on model predictions. Habitats were classified in just two categories, i.e. suitable habitat patches and unprofitable matrix habitats. Inter-patch dispersal of M. bicolor may be affected by various landscape elements in the matrix and by habitat heterogeneity within suitable patches (Gustafson & Gardner 1996). If individuals are aggregated within patches, emigration will be more likely in certain directions.

Despite the ambiguity of the present attempts to model inter-patch dispersal in the Swedish M. bicolor system, model predictions gave several realistic and important insights for metapopulation theory. Earlier models of metapopulation dynamics have without exception assumed emigration rates to be independent of patch size (e.g. Hanski, Kuussaari & Nieminen 1994; Hanski & Thomas 1994). Simulations of a structured model of metapopulation dynamics, with constant emigration rates, predict a negative relationship between population density and patch area, which is not consistent with empirical data on M. bicolor. Unless average emigration rates are substantially lower than predicted from present data, the hypothesis of patch independent emigration rates has to be rejected. Obviously, constant emigration rates close to zero can give rise to observed patterns.

When patch independent emigration rates are assumed, immigration will exceed emigration on smaller patches and the reverse will be true for larger patches. Thus, the number of individuals will exceed the carrying capacity on smaller patches, while larger patches will become unsaturated. With increasing emigration rates, greater deviations from local carrying capacities are expected. Natural selection is expected to counteract such patterns (McPeek & Holt 1992).

When individuals chose habitats according to an ideal free distribution (Fretwell & Lucas 1970), a perfect fit between population densities and local carrying capacities is expected. Structured models of metapopulation dynamics that assume patch independent emigration rates predict distribution patterns that are clearly distinguished from an ideal free distribution. However, if animals move according to the present movement model, the spatial distribution of individuals may become similar to an ideal free distribution. Thus, it is expected that such a movement strategy can be evolutionarily stable, even if habitat configuration changes.

It was demonstrated that patches observed to be colonized by M. bicolor are expected to receive more immigrants than patches that were not colonized. However, if the model predictions are quantitatively correct, successful colonization must be achieved by usually less than three individuals of each sex in a period of 5 years. This is only possible if a single mated female of M. bicolor has the potential of initiating a new population. Whether this is probable has yet to be confirmed by field experiments.

One interesting consequence of patch-dependent emigration, is the way dispersal may affect extinction probabilities of local populations. Local extinction risks are expected to increase with increasing isolation of habitat patches because local populations living on patches that are situated close to other local populations may become rescued by immigration. This phenomenon, i.e. the ‘rescue effect’ (Brown & Kodric-Brown 1977), has been demonstrated in several metapopulation studies (e.g. Smith 1980; Hanski et al. 1994; Sjögren Gulve 1994). The results from this study suggest that patches where local populations became extinct received approximately the same amount of immigrants as patches with surviving local populations. Thus, the range of isolation distances occurring within the Swedish metapopulation of M. bicolor, is expected to be too small to impose effects of inter-patch distance on local extinction risks. This is consistent with previous analyses (Kindvall & Ahlén 1992; Kindvall 1996).

Earlier studies have demonstrated that local extinction probability of M. bicolor is negatively associated with patch size (e.g. Kindvall & Ahlén 1992). This observation was interpreted as an effect of demographic and environmental stochasticity that is expected to affect smaller populations more than larger ones (Shaffer 1987). However, from this study it is apparent that patch size can affect local extinction risks by its impact on emigration. This phenomenon is also suggested by Hill et al. (1996), and further discussed by Thomas & Hanski (1997). Local populations living on small patches are expected to lose more individuals than are compensated by immigration. Thus, in the metapopulation of M. bicolor, inter-patch dispersal seems to be high enough to compensate losses by emigration on large patches, while small patches receive too little immigration to be rescued.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References

This project was supported by the Swedish Council for Forestry and Agricultural Research and the World Wildlife Fund in Sweden. I thank, Annika Kindvall, Susanne Godow and Johan Ahlén for helping me with the field work and Ingemar Ahlén, Allan Carlson, Ilkka Hanski, Lennart Hansson, Tomas Pärt, Chris Thomas and an anonymous referee for their comments on the manuscript.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Modelling animal movement
  5. Material and methods
  6. Results
  7. Discussion
  8. Acknowledgements
  9. References
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Received 19 January 1998;revisionreceived 8 May 1998