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
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.
Download figure to PowerPoint
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.