Dispersal is a critical life history trait that has important consequences for populations from both an ecological and genetic perspective. The dynamics and persistence of populations are strongly influenced by dispersal strategies. Genetically, patterns of gene flow are clearly dependent on forms of dispersal. The great diversity of patterns of dispersal observed in different environments and species is staggering.

Investigation of dispersal patterns has been extensive but can be broadly split into theoretical and empirical studies. Historically, most ecologists and modelers have assumed that dispersal is unconditional in both rate and directionality. This is especially true with regard to a majority of the theoretical literature (e.g. many ESS models and several group selection models of dispersal). Empirical work has largely dealt with ecological parameters that may select for certain dispersal strategies (e.g. polygyny in ants). Despite the great amount of attention paid to dispersal by scientists, very little exchange of ideas has occurred between modelers and those working with empirical data. As a consequence, we still know very little about why we see different dispersal strategies in various species and environments. Recently, increased attention has been paid to patterns of dispersal in response to spatially heterogeneous environments.

This paper will attempt to synthesize the theoretical and empirical literature surrounding dispersal. In particular, I will focus on evolutionary mechanisms that have been hypothesized to select for dispersal, especially in spatially and temporally heterogeneous environments. There is a wealth of modeling on this topic that I will summarize and then try to bring together with the existing experimental studies.

The pattern of dispersal in organisms is a life history trait that pervades virtually all facets of ecological and evolutionary biology. Almost all organisms show some form of dispersal whether it occurs at a gametic, larval, or adult stage. Dispersal encompasses many different types of movement patterns and many definitions exist. Generally, dispersal can be defined as the movement of an individual from one place to another. For the purposes of this paper, dispersal will be considered as the movement of any individual away from its natal population to another population for the purposes of breeding. This more restricted definition excludes patterns of annual migration like those seen in certain species of the Lepidoptera or Odonata.

The impressive diversity of contemporary dispersal strategies belies the fact that dispersal is a critical part of a species' life history strategy. Given this, what evolutionary mechanisms have led to the evolution of dispersal? This is a complex question where biologists have only touched the tip of the proverbial iceberg. Monitoring the movement patterns of megafuana such as large herbivores has proven very difficult due to the time and spatial scale over which they move. For instance, long term study of Acorn Woodpeckers (Melanerpes formicivorus) has demonstrated a "right censoring" problem where the scale over which dispersal is measured is smaller than the scale over which the organisms are actually dispersing. Thus, despite almost thirty years of population data almost nothing can be said about woodpecker dispersal (Dieckmann 1999, Koenig and Mumme 1987). Other biologists have turned to monitoring the movements of insects in an attempt to examine important questions of dispersal at a manageable scale. However, this has proven just as difficult for various reasons, making solid empirical data on dispersal hard to find. Thus, a lot of the work exploring the evolution of dispersal has focused on theoretical models of dispersal.

The historical progression of these models has been, like many areas of science, strongly influenced by our increased ability to create complex models using computers. Dispersal models initially assumed that dispersal was a process that was uniform across space and varied solely across time. With the introduction of game theory and evolutionary stable strategies (Maynard Smith, 1982) payoff matrices were used to model dispersal strategies. This approach also assumed that systems were at equilibrium or evolved towards equilibrium. Unfortunately, payoff matrices overly simplify the tradeoffs between dispersal strategies (Dieckmann, 1999). Group selection was invoked by Van Valen (1971) as an important force in promoting dispersal. This has never been demonstrated. More recently, landscape heterogeneity has begun to enter into models of dispersal as well as non-equilibrium systems. This movement has led to the theory of adaptive dynamics (Metz et al. 1996). Adaptive dynamics theory moves beyond the use of payoff matrices and models the intricate interactions of dispersing individuals in a population with a spatially heterogeneous environment and the resulting ecological feedback.

In general, models developed over the last 30-35 years have identified five major mechanisms that seem to be very important in selecting for or against dispersal. These include competition among kin, costs of inbreeding, unstable habitats, temporal and spatial variability of habitat, and cost of dispersal (Dieckmann, 1999).

-Competition among kin is easy to understand. If a given patch is occupied by individuals that have a greater relatedness than the population wide value, it may be advantageous to disperse. Dispersal in such a situation is predicted by the theory of kin selection, competition with closely related individuals could lead to reduced inclusive fitness (Hamilton and May, 1977).

-Inbreeding can seriously decrease the fitness of offspring. This is clearly tied to the first mechanism mentioned, competition with kin, but the mechanism selecting for dispersal is tied to direct fitness, not considerations of inclusive fitness.

-Unstable habitats are often used to explain the evolution of dispersal. If a given individual disperses there may be a significant chance of offsetting the cost of moving with increased reproductive output (Roff, 1994).

-Temporal and spatial heterogeneity has been extensively modeled with respect to dispersal. This realistic condition of heterogeneity is thought to be an important mechanism selecting for high dispersal rates (McPeek, 1992).

-Cost of dispersal may often may a major factor in determining dispersal strategies. Not surprisingly, a high dispersal cost may lead to lower levels of immigration than predicted. Models have also indicated that a higher cost of dispersal may reduce dispersal polymorphisms in a population (Doebeli et al. 1997).

These five mechanisms can be divided into two main categories: interactions with individuals (kin competition and inbreeding) and interactions with the environment (unstable habitats and temporal and spatial heterogeneity). The cost of dispersal is, obviously, closely linked to both categories and reflects the relative importance of the other four mechanisms in a given situation. The relationship between environmental conditions and dispersal strategies is the primary subject of interest. Thus, interactions between individuals will be left largely neglected.

Southwood (1962) advanced the following hypothesis: "the prime evolutionary advantage of migratory movement lies in its enabling a species to keep pace with the changes in the locations of its habitats." Since then, copious amounts of papers have been published that examine this relationship in a theoretical framework (Van Valen 1971, Roff 1990, McPeek et al. 1992). To create a general picture of this literature, consider a simplified version of models presented by Roff (1990) and McPeek (1992). The landscape consists of one patch that persists from generation to generation with probability, p (0<p<1). If we want to calculate the probability of patch persistence for t generations, the simple relationship is given by p^t. It is clear that the probability of persistence drops in a patch as t increases. Now consider a two-patch system given two different scenarios. In one scenario dispersal occurs between patches whereas no dispersal occurs in the other scenario. The likelihood of extinction in the zero dispersal scenario is certain if p<1, it's only a matter of time. However, in the model with dispersal, both patches would have to simultaneously go extinct in order for the overall population to become extinct. Roff (1990) used a similar model to calculate that, given a p=0.95, the scenario without dispersal was 66 times more likely to go extinct within the first t=100 generations. This increased likelihood increases to 6890 when p=0.90. The dramatic difference in extinction probability underscores the importance of dispersal between groups of individuals. Of course there is no cost to dispersal in this hypothetical example which is extremely unrealistic and represents a major tradeoff for dispersing individuals. One last point with this model is that, given dispersal across a landscape, as the number of patches increases, the probability of extinction drops. Therefore, unstable habitats (e.g. lower values of p) should contain species with higher dispersal rates than those existing in stable habitats (p~1).

The empirical evidence of this simple relationship can be generally considered in the context of island biogeography. Islands (e.g. patches) that are far away and thus have a lower probability of dispersal tend to have fewer species (MacArthur and Wilson 1968). Without an exchange of individuals between populations, stochastic events such as fires or floods can totally wipe out an isolated population. Additionally, isolated populations can suffer serious reductions in fitness due to genetic drift and founder effects over time.

An obvious way to examine the strength of selection for dispersal in unstable environments is to look for situations where species have either gained or lost the ability to disperse in unstable or stable environments. Roff (1990) examined the evolution of flightlessness in insects. He tested for an association between flightlessness and environmental heterogeneity, geographic variables, gender, alternate modes of migration, and taxonomic variation. Roff's detailed and well substantiated findings, for the most part, bore out the hypothesis that stable conditions will lead to flightlessness.

It is important to remember that flightlessness has evolved because there is a substantial cost to flying. For insects, the muscle tissue required for flight can be substantial (up to 70% of body mass in some insects but averaging 10-20% for most insects -Greenewalt 1962). Other investigators have shown a negative correlation between fecundity and flight ability in species of wing dimorphic insects (Roff 1986). Roff took two major monographs on North American Orthoptera (Blatchley 1920, Vickery and Kevan 1983) and analyzed the frequency of flightless species with respect to habitat type. He found that winged species tended to predominate (p<0.01) in pastures, meadows, scrubland, prairies, borders of swamps lakes and streams outside of woods, arboreal habitats, and open dry areas. Flightless species composed a majority of the orthopteran species in woodlands away from water, under logs and stones, in burrows, caves, ant nests, and alpine and tundra. Flightless species definitely seem to occur in what appears to be a predictable and stable environment.

Other environments identified by Roff (1990) to have a high degree of flightless species include the surface of the ocean (water striders and midges), snow surfaces (some Mecoptera and Diptera), and endotherm body surfaces (ectoparasites). All of these environments provide exceptional opportunities to look at rates of dispersal between patches. Unfortunately the analysis does not move much beyond simple comparisons of habitat types and numbers of flightless species. Snowfields seem especially fertile for research since they certainly appear to be more ephemeral yet still possess a high abundance of flightless insects. The examination of patch dynamics in the context of spatial and temporal heterogeneity would represent a good empirical test of the existing models.

Spatial and temporal heterogeneity are clearly important to dispersal strategies as evidenced by our initial model. Models of dispersal in environments with temporal and spatial variance have focused on the effect of this variance on the strength of selection for dispersal and changes in overall fitness. The fitness of an individual is the product of its genotype and its interaction with the environment and thus, will vary across the landscape with regard to space and time. Dispersal can then be regarded as a "bet-hedging" strategy (McPeek and Holt 1992). The predictions of these models have been quite interesting. Holt (1985) showed that spatial heterogeneity by itself was not enough to select for dispersal. Only when occupied habitat patches were temporally unstable did dispersal evolve. McPeek and Holt (1992) demonstrated that given constant rates of dispersal and density-dependence in two patches, temporal variation in growth rates across patches selected for dispersal. It was also shown that polymorphisms in dispersal strategies could be maintained by spatial heterogeneity. These models represent the precursors to adaptive dynamics, the latest category of dispersal models.

Adaptive dynamics is an enhanced extension of evolutionarily stable strategy (ESS) modeling that uses population dynamics to derive selective pressures and adaptive responses of populations. This is in contrast to ESS models that stipulate selective pressures through the use of payoff matrices. Previously, phenotypes were considered in a black and white fashion, they were either an ESS or not. This new approach takes a broader approach. For example, interactions between individuals are taken into account by acknowledging that these interactions can alter the probability of invasion by a mutant phenotype. Adaptive dynamics also represents an attempt to take the spatial structure of a population into account. When an invader phenotype is presented to the resident phenotype, its status as a neighbor is considered as well as its similarity to other neighboring phenotypes. Invading phenotypes are also allowed to coexist with resident and other invading phenotypes in this class of models. Situations where an invader phenotype does not immediately exclude the resident phenotype can lead to evolutionary branching (e.g. polymorphisms in dispersal strategies). Though not of focal interest here, the natural question that follows the discovery of maintenance of polymorphisms is whether these are genetically isolated. If so, this could eventually become a mechanism for speciation.

Evolutionary cycling, the observation of regular fluctuations in dispersal rates has also been observed in models using adaptive dynamics. This reflects one of the great strengths of adaptive dynamics theory; systems can be chaotic and evolve away from equilibrium. Work by Doebeli and Ruxton (1997) goes beyond previous work (Holt and McPeek 1996, Metz et al. 1996) that demonstrated evolutionary cycling as simply fluctuations in a set number of dispersal phenotypes between generations. They show that it is strongly dependent on the cost of dispersal and is much more likely in non-equilibrium systems.

Unfortunately, little empirical data exist that represent an explicit test of adaptive dynamics theory. However, an earlier test of spatial and temporal heterogeneity on patch dynamics in a wing dimorphic planthopper by Roff (1994) and an investigation of dispersal strategies for queen leptothoracine ants (Bourke and Heinze 1994) both represent interesting tests of these models.

Wing dimorphism is a well-documented phenomenon in insects (Roff 1986). As stated above, it has been shown that there is a trade-off in flying ability and fecundity. Better flyers are less fecund and visa versa. Taking the data of Denno et al (1991), Roff attempted to assess three parameters: the proportion of macropterous, m, (winged) individuals which migrate, the proportion, s, of these migrating individuals that survive and locate a patch, and the cost, c, of dispersal expressed in terms of reduced fecundity in 35 species of planthoppers. The cost of reduced fecundity was the most important factor determining the pattern of observed dispersal. The greater the cost of being macropterous determines the frequency of dispersing individuals in a population. Also of importance is the patch persistence probability, a lower persistence probability selects for increased rates of dispersal (higher m).

Another system that represents a useful empirical test of these models is leptothoracince ants. It is quite common for these species to exhibit polygynous nests. Bourke and Heinze (1994) reviewed observed dispersal strategies in the reproductive females (e.g. queens) in several species of ants in the genus Leptothorax. In this case, the queens are very poor dispersers and thus, the cost of dispersal is very high. Queens sharing a nest are usually more closely related to one another than predicted by chance. This creates a situation where mechanisms of dispersal are operating in opposite directions. The cost of dispersal and the stability of the next (recall Roff 1990) should select against dispersal. However, competition with kin and possibly, inbreeding should select for dispersal. In this case it seems that the costs of kin competition and inbreeding have been somewhat circumvented by the creation of a dominance and thus, reproductive hierarchy among polygyne queens. Bourke and Heinze demonstrate that in environments with plentiful nest sites and a low cost of dispersal, monogyne colonies are found. This lends considerable support to the idea that the cost of dispersing from the stable environment of the nest is substantial.

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