Dynamics of populations with individual variation in dispersal on bounded domains

Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates and patterns may vary among different individuals. A simple way to capture variation in dispersal that has been suggested in the ecological literature is to allow individuals to switch between two distinct dispersal modes. We study models for populations whose members can switch between two different nonzero rates of diffusion and whose local population dynamics are subject to density dependence of logistic type. The resulting models are reaction–diffusion systems that can be cooperative at some population densities and competitive at others. We assume that the focal population inhabits a bounded region and study how its overall dynamics depend on the parameters describing switching rates and local population dynamics. (Traveling waves and spread rates have been studied for similar models in the context of biological invasions.) The analytic methods include ideas and results from reaction–diffusion theory, semi-dynamical systems, and bifurcation/continuation theory.     

Evaluating hypotheses about dispersal in a vulnerable butterfly

Sound management of species requires reliable estimates of dispersal. Indeed, dispersal of individuals among local populations is a key factor in the biology and persistence of local populations and metapopulations. Here, the small-scale dispersal pattern of a vulnerable species, the endemic Sardinian chalk hill blue butterfly, was studied by applying capture–recapture multistate models and a model selection based on AIC values. Model parameters were survival, capture and movement probabilities. The model selection showed that (a) survival probability of individuals varied between sexes, (b) capture probability varied between sexes and among patches, and (c) movement probability varied with direction. The probability of movement among adjacent local populations was generally low and ranged from 0.009 to 0.212. Movement probabilities were subsequently modeled using data on interpatch distance and donor patch population size or area. The ultrastructural biology-based models turned out to be the most appropriate models for inference, showing that dispersal decreases with increasing interpatch distance and increasing donor patch population size or area, and suggesting that butterfly dispersal is affected by patch geometry and the presence of conspecifics. The application of multistate models, the model selection approach, and ultrastructural modeling allowed testing the validity of some general hypotheses related to dispersal in metapopulations and helped elucidate the butterfly small-scale dispersal pattern.     

Death odour changes movement pattern of a Collembola

We used video-tracking of individuals of a Collembola, Protaphorura armata, on a clay surface in a petri dish to analyse their movement pattern in an environment with attractive and repellent cues. An area with dead conspecifics was repellent whilst live conspecifics made the area attractive. An area which had been occupied for 24 hours by the predatory mite, Hypoaspis aculeifer, was avoided only if the mite had preyed upon P. armata before it was placed in the area. P. armata lost their looping behaviour, moved faster and more straightened out (decreased turning rate) in the presence of attractive or repellent odours. The resulting net squared displacement was faster than in the control and best described as a correlated random walk. Our results emphasise the importance of considering varying movement pattern in response to environmental cues when predicting dispersal and spatial distribution of an animal.     

Characteristics of dispersal in the eastern mosquitofish Gambusia holbrooki

The demographic and genetic characteristics of dispersing Gambusia holbrooki were examined relative to changes in stream flow velocity, flow direction, and rapid saltwater inundation. Dispersal of all G. holbrooki sex classes decreased as flow velocity increased, dispersal for a given flow velocity being greater in female, than male and juvenile fish respectively. Juveniles and males dispersed at low (9 mm s⁻¹) but not high (109 mm s ¹) flow. Females dispersed at both flow rates. Dispersing adults were not larger than non-dispersing adults of the same sex. Direction of dispersal was sex and size dependent, but independent of flow velocity. Larger females (>22 mm) moved preferentially downstream, while smaller females (17–22 mm) remained stationary or moved in the upstream direction. Males dispersed equally in both directions. No relationship was found between dispersal characteristics and the presence of high salt concentrations. Movement patterns at high flow were independent of glucose-6-phosphate isomerase ( GPI-2* ) alleles carried by dispersing individuals. Significant non-random dispersal of sex or size cohorts, and the interaction of dispersal with flow velocity have significant implications for the maintenance of genetic diversity in stream ecosystems, particularly where localized selection or genetic drift may alter the genetic constitution of specific sex or size cohorts. The applicability of these results to field populations is discussed.     

The effect of conspecifics on individual male movement in Roesel's bush cricket, Metrioptera roeseli

Abstract.  1. Individual movement behaviours of male Roesel's bush crickets were compared between individuals experimentally released with or without conspecifics.
2. Differences in movement behaviour were recorded between the groups, with individuals released with conspecifics moving faster and further.
3. The study shows that behavioural interactions between individuals need to be considered in population modelling. Empirical movement data derived from lone individuals would result in a significant underestimation of both population expansion (−38.1%) and inter-patch movement (−35.8%).     

Resource-dependent dispersal and the speed of biological invasions

Many mobile organisms exhibit resource-dependent movement in which movement rates adjust to changes in local resource densities through changes in either the probability of moving or the distance moved. Such changes may have important consequences for invasions because reductions in resources behind an invasion front may cause higher dispersal while simultaneously reducing population growth behind the front and thus lowering the number of dispersers. Intuiting how the interplay between population growth and dispersal affects invasions is difficult without mathematical models, yet most models assume dispersal rates are constant. Here we present spatial-spread models that allow for consumer-resource interactions and resource-dependent dispersal. Our results show that when resources affect the probability of dispersal, then the invasion dynamics are no different than if resources did not affect dispersal. When resources instead affect the distance dispersed, however, the invasion dynamics are strongly affected by the strength of the consumer-resource interaction, and population cycles behind the wave front lead to fluctuating rates of spread. Our results suggest that for actively dispersing invaders, invasion dynamics can be determined by species interactions. More practically, our work suggests that reducing invader densities behind the front may be a useful method of slowing an invader's rate of spread.     

Determinants and costs of natal dispersal in a lekking species

Avoidance of competition and inbreeding have been invoked as the major ultimate causes of natal dispersal, but proximate factors such as sex, body condition or birth date can also be important. Natal dispersal is expected to be of particular importance to understanding the ecological and evolutionary implications of dispersal strategies, since 1) numerous evidences suggest that individual differences in dispersal strategies are expressed early in life (i.e. at the onset of dispersal movement), 2) ultimate and proximate factors are more likely to act during this stage and 3) this stage is associated with the highest mortality rates in most vertebrates. We analysed the natal dispersal (hereafter, dispersal) behaviour in 100 marked individuals of a lekking species, the North African houbara bustards Chlamydotis undulata undulata, during four years. We investigated the effects of proximate factors on dispersal pattern and distance, as well as the mortality cost associated with movement using multievent models, allowing uncertainty in sex assignment and mixture of live recaptures and dead recoveries. Overall, males exhibited longer dispersal distances than females, contrary to the common pattern in birds. Moreover, males in poorer body condition moved further than those in better condition, whereas distance was independent of body condition in females. Finally, survival rates during dispersal were lower for females than for males and were negatively correlated with the distances covered with a similar distance‐survival slope in the two sexes. Collectively, our results suggest that 1) there is substantial dispersal cost in both sexes, 2) dispersal is strongly male‐biased, 3) this bias is unlikely to be explained by differential movement costs of each sex, and 4) dispersal differences found across different categories of individuals are in broad agreement with both the inbreeding avoidance and intraspecific competition mechanisms for dispersal.     

A field test of simple dispersal models as predictors of movement in a cohort of lake-dwelling brook charr

1. Dispersal can be a major determinant of the distribution and abundance of animals, as well as a key mechanism linking behaviour to population dynamics, but progress in understanding dispersal has been hampered by the lack of a general framework for modelling dispersal. 2. This study tested the capacity of simple models to summarize and predict the lake-wide dispersal of an emerging cohort of young-of-the-year brook charr Salvelinus fontinalis, over 12 surveys conducted during a 2-month period. 3. The models are based on two types of dispersal kernel, the normal distribution from a simple diffusion process, and a Laplace distribution depicting exponential decay of the frequency of dispersers away from the point of origin. In all, four models were assessed: one-group diffusion (D1S) and exponential (E1S) models assuming homogeneous dispersal behaviour within the cohort, and two-group diffusion (D2S) and exponential (E2S) models accounting for intrapopulation differences in dispersal between sedentary and mobile individuals. 4. A rigorous cross-validation, based on calibrating the models to the distributions from the first two surveys only and then validating them on the remaining 10 distributions, was used to compare model predictions with observed values for five properties of the dispersal distributions: counts in individual shoreline sections; mean lateral displacement, variance and kurtosis of displacements; and the percentage of long-distance dispersers. 5. Substantial intrapopulation heterogeneity in dispersal behaviour was apparent: 83% of all individuals were estimated to be sedentary and the remainder mobile. Remarkably, the two-group exponential model E2S - calibrated to data from only two surveys conducted 3.5 and 8.5 days after the beginning of emergence - predicted reasonably well all properties of the spatial distribution of the cohort until the end of the study, 7 weeks later. 6. Standardized measures of mobility derived from simple models may lead to better understanding of population dynamics and improved management. Specifically, the ability to accurately predict long-distance dispersal may be critical to assessing population persistence and cohort strength whenever key habitats, such as refugia or productive areas supporting a large proportion of the cohort, are sparsely distributed or distant from the point of origin.     

Effects of an Ecosystem Engineer on Belowground Movement of Microarthropods

Ecosystem engineers affect other species by changing physical environments. Such changes may influence movement of organisms, particularly belowground where soil permeability can restrict dispersal. We investigated whether earthworms, iconic ecosystem engineers, influence microarthropod movement. Our experiment tested whether movement is affected by tunnels (i.e., burrows), earthworm excreta (mucus, castings), or earthworms themselves. Earthworm burrows form tunnel networks that may facilitate movement. This effect may be enhanced by excreta, which could provide resources for microarthropods moving along the network. Earthworms may also promote movement via phoresy. Conversely, negative effects could occur if earthworms alter predator-prey relationships or change competitive interactions between microarthropods. We used microcosms consisting of a box connecting a “source” container in which microarthropods were present and a “destination” container filled with autoclaved soil. Treatments were set up within the boxes, which also contained autoclaved soil, as follows: 1) control with no burrows; 2) artificial burrows with no excreta; 3) abandoned burrows with excreta but no earthworms; and 4) earthworms (Lumbricus rubellus) present in burrows. Half of the replicates were sampled once after eight days, while the other half were sampled repeatedly to examine movement over time. Rather than performing classical pairwise comparisons to test our hypotheses, we used AIC_c to assess support for three competing models (presence of tunnels, excreta, and earthworms). More individuals of Collembola, Mesostigmata, and all microarthropods together dispersed when tunnels were present. Models that included excreta and earthworms were less well supported. Total numbers of dispersing Oribatida and Prostigmata+Astigmata were not well explained by any models tested. Further research is needed to examine the impact of soil structure and ecosystem engineering on movement belowground, as the substantial increase in movement of some microarthropods when corridors were present suggests these factors can strongly affect colonization and community assembly.     

Lack of sex‐specific movement patterns in an alien species at its invasion front – consequences for invasion speed

Efficient targeting of actions to reduce the spread of invasive alien species relies on understanding the spatial, temporal, and individual variation of movement, in particular related to dispersal. Such patterns may differ between individuals at the invasion front compared to individuals in established and dense populations due to differences in environmental and ecological conditions such as abundance of conspecifics or sex‐specific dispersal affecting the encounter rate of potential mates. We assessed seasonal and diurnal variation in movement pattern (step length and turning angle) of adult male and female raccoon dog at their invasion front in northern Sweden using data from Global Positioning System (GPS)‐marked adult individuals and assessed whether male and female raccoon dog differed in their movement behavior. There were few consistent sex differences in movement. The rate of dispersal was rather similar over the months, suggesting that both male and female raccoon dog disperse during most of the year, but with higher speed during spring and summer. There were diurnal movement patterns in both sexes with more directional and faster movement during the dark hours. However, the short summer nights may limit such movement patterns, and long‐distance displacement was best explained by fine‐scale movement patterns from 18:00 to 05:00, rather than by movement patterns only from twilight and night. Simulation of dispersing raccoon dogs suggested a higher frequency of male–female encounters that were further away from the source population for the empirical data compared to a scenario with sex differences in movement pattern. The lack of sex differences in movement pattern at the invasion front results in an increased likelihood for reproductive events far from the source population. Animals outside the source population should be considered potential reproducing individuals, and a high effort to capture such individuals is needed throughout the year to prevent further spread.     

Lasting effects of maternal behaviour on the distribution of a dispersive stream insect

1. Predicting population dynamics at large spatial scales requires integrating information about spatial distribution patterns, inter-patch movement rates and within-patch processes. Advective dispersal of aquatic species by water movement is considered paramount to understanding their population dynamics. Rivers are model advective systems, and the larvae of baetid mayflies are considered quintessential dispersers. Egg laying of baetids along channels is patchy and reflects the distribution of oviposition sites, but larvae are assumed to drift frequently and far, thereby erasing patterns created during oviposition. Dispersal kernels are often overestimated, however, and empirical tests of such assumptions are warranted because of the pivotal role distribution patterns can have on populations. 2. We tested empirically whether the egg distribution patterns arising from oviposition behaviours persisted and were reflected in the distribution patterns of larval Baetis rhodani. In field surveys, we tested for associations between egg mass and larval densities over 1 km lengths of four streams. A control species, the mayfly Ephemerella ignita, was employed to test for covarying environmental factors. We estimated drift rates directly to test whether larvae dispersed between riffles (patches of high egg mass density) and whether drift rates were density-dependent or density-related - expected outcomes if drift erases patterns established by maternal behaviours. 3. Positive associations between egg masses and larval benthic densities were found for neonate and mid-stage larvae of Baetis, but not the control species, suggesting persistence of the patchy distribution patterns established at oviposition. Drift rates were high, and riffles were net exporters of neonate and mid-stage larvae, but drift rates were unrelated to benthic densities and few drifters reached the next riffle. Riffles were sinks for large larvae, suggesting ontogenetic shifts in habitat use, but little long-distance dispersal. 4. Overall, the results suggest that most neonate and mid-stage larvae of B. rhodani remain close to the natal riffle, and late-stage larvae disperse shorter distances than routinely assumed. The persistence of maternal effects on distribution patterns well into juvenile life of an allegedly iconic disperser suggests that traditional models of how dispersal influences the population dynamics of many lotic invertebrates may be incorrect.     

Modelling dispersal of a temperate insect in a changing climate

We construct a novel individual-based random-walk model to assess how predicted global climate change might affect the dispersal rates of a temperate insect. Using a novel approach we obtained accurate field measurements of daily movements for individuals over time to parameterize our model. Males were found to move significantly further on average than females. Significant variation in movement was evident among individuals; the most dispersive individuals moved up to five (females) and seven (males) times as far on average as the least dispersive individuals. Mean relative daily movement of both males and females were exponentially related to maximum daily temperature recorded within the grass sward. Variability, both within and among individuals, in relative daily movement was incorporated into the model using gamma probability distributions. Resultant dispersal functions for seasonal movement are predicted to be highly leptokurtic, which agrees well with observations from the field. Predictions of the model suggest that for populations at the polewards edge of the current range an increase of 3-5 degrees C in daily maximum temperature may increase the proportion of long-distance dispersers (those characterized as comprising the top 0.1% of furthest dispersing individuals under local conditions experienced during the 1963-1990 period) by up to 70%.     

Evolutionary stability of ideal free nonlocal dispersal

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium. We find that the property of producing ideal free distributions is necessary and often sufficient for evolutionary stability. Our results extend those already developed for discrete diffusion models on finite patch networks to the case of nonlocal dispersal models based on integrodifferential equations. The analysis is based on the use of comparison methods and the construction of sub- and supersolutions.     

Evolutionary stability of ideal free nonlocal dispersal

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium. We find that the property of producing ideal free distributions is necessary and often sufficient for evolutionary stability. Our results extend those already developed for discrete diffusion models on finite patch networks to the case of nonlocal dispersal models based on integrodifferential equations. The analysis is based on the use of comparison methods and the construction of sub- and supersolutions.     

Three ways of assessing metapopulation structure in the butterfly Plebejus argus

1. Three independent methods were used to investigate population structure in the butterfly Plebejus argus . First, migration and dispersal ability were measured by mark–release–recapture in seven adjacent habitat patches, and by release of butterflies in unoccupied habitat. Secondly, colonization of newly created habitat was observed over 7 years. Finally, genetic differentiation of local populations within a metapopulation was investigated. Sampled local populations included parts of the mark–release–recapture study area.
2. Plebejus argus is relatively sedentary: the maximum movement detected was 395 m, and only 2% of individuals moved further than 100 m between recaptures on different days. None the less, adjacent local populations in the mark–release–recapture study area were linked by occasional migration, with ≈ 1.4% of individuals moving between patches separated by 13–200 m.
3. Despite low mobility, observed colonizations occurred rapidly over distances of 1 km. Because P. argus occurs at high population densities, 1.4% migration can generate enough migrants to colonize newly suitable habitat quickly at this spatial scale.
4. Mark–release–recapture data were used to predict that there would be limited genetic differentiation through drift between local populations at this spatial scale. The prediction was supported by allele frequency data for the same local populations.
5. Genetic differentiation often indicates higher levels of migration than are revealed by the movements of marked individuals. This study shows that when experimental releases and extensive marking are undertaken in areas that are large relative to most movements, indirect measures of gene flow and direct measures of dispersal can concur.
6. Evidence from the three different approaches was complementary, indicating that P. argus occurs as metapopulations within the study area.     

Natal dispersal in great bustards: the effect of sex, local population size and spatial isolation

1. We investigated the causes of natal dispersal in four Spanish areas where 35 breeding groups of the polygynous great bustard Otis tarda were monitored intensively. A total of 392 juveniles were radio-tracked between 1991 and 2006 by ground and via aeroplane to avoid potential biases derived from the non-detection of long-distance dispersers. 2. We explored 10 explanatory variables that were related to individual phenotypic features, habitat and conspecific traits in terms of group size and breeding performance, and spatial distribution of available breeding groups. Probability of group change and natal dispersal distances were investigated separately through multifactorial analyses. 3. Natal dispersal occurred in 47.8% of the birds and median natal dispersal distance of dispersers was 18.1 km (range 4.97-178.42 km). Sex largely determined the dispersal probability, with 75.6% of males being dispersers and 80.0% of females being philopatric, in contrast to the general pattern of female-biased dispersal found in most avian species. 4. Both the frequency of natal dispersal and dispersal distances were affected by the spatial distribution of breeding groups. More isolated groups showed a higher proportion of philopatric individuals, the effect being more evident in males than in females. This implies a reduction in gene flow in fragmented populations, as most genetic exchange is achieved through male dispersal. Additionally, dispersers hatched in more isolated groups tended to exhibit longer dispersal distances, which increases the associated energetic costs and mortality risks. 5. The dispersal decision was influenced by the number of conspecifics in the natal group. The individual probability of natal dispersal was related inversely to the size of the natal group, which supports the balanced dispersal model and the conspecific attraction hypothesis. 6. Overall, our results provide a good example of phenotypic plasticity and reinforce the current view that dispersal is an evolutionary complex trait conditioned by the interaction of individual, social and environmental causes that vary between individuals and populations.     

The effect of landscape structure on dispersal distances of the Eurasian red squirrel

Landscape structure can affect dispersal and gene flow in a species. In urban areas, buildings, roads, and small habitat patches make the landscape highly fragmented and can inhibit movement and affect dispersal behavior. Similarly, in rural forested areas, large open areas, such as fields, may act as barriers to movement. We studied how landscape structure affects natal dispersal distances of Eurasian red squirrels (Sciurus vulgaris) in an urban area and a rural area in Finland, by monitoring juvenile red squirrels with radio telemetry. We observed extremely long dispersal distances—up to 16 km—in the rural study area, but shorter distances—on average only half a kilometer—in the urban study area. The landscape structure affected the eventual dispersal paths; in the rural landscape, dispersers favored spruce dominated areas and avoided fields along their dispersal route, although they occasionally even crossed wide fields. In the urban landscape, squirrels preferred areas with deciduous or coniferous trees. The movement steps made by dispersers were longer in the more hostile landscape compared to forested areas. Despite these effects on movement path, the landscape structure only had a minor effect on straight line dispersal distances moved from the natal nest. In other words, individuals moved longer distances and were likely to circumvent barriers in their path, but this did not affect how far they settled from their natal home. This result indicates that, although landscape structure has obvious effects on movement, it still may have only a small effect on other aspects of the population, for example, gene flow.     

Dispersal mood revealed by shifts from routine to direct flights in the meadow brown butterfly Maniola jurtina

A comprehensive mechanistic approach to dispersal requires the translation of the whole mobility register of the target organism into movement rules that could subsequently be used to model its displacements. According to the optimality paradigm, this procedure implies a cost–benefit analysis of mobility patterns taking into account not only movements, but also their external context and the internal state of the moving individuals. Using this framework, we detected a ‘dispersal mood’ in some individuals of the meadow brown butterfly Maniola jurtina. These adopted a direct flight strategy, which was topologically different from the previously documented foray search strategy. Those individuals that used the direct flight strategy moved straighter as soon as they left the habitat and avoided heading back to their patch of origin, which is the best inter‐patch search strategy when dispersal risks and costs are high. The direct flight strategy was conditional to sex: females used it twice as much as males. We suggest that this sex bias was due to female investment in offspring, which is maximized by male avoidance and spatial bet hedging. Inter‐patch dispersal of gravid females is crucial for the persistence of M. jurtina populations in spatially and temporally unpredictable environments.     

Hybridization and introgression during density‐dependent range expansion: European wildcats as a case study

Interbreeding between historically allopatric species with incomplete reproductive barriers may result when species expand their range. The genetic consequences of such hybridization depend critically on the dynamics of the range expansion. Hybridization models during range expansion have been developed but assume dispersal to be independent from neighboring population densities. However, organisms may disperse because they are attracted by conspecifics or because they prefer depopulated areas. Here, through spatially explicit simulations, we assess the effect of various density‐dependent dispersal modes on the introgression between two species. We find huge introgression from the local species into the invasive one with all dispersal modes investigated, even when the hybridization rate is relatively low. This represents a general expectation for neutral genes even if the dispersal modes differ in colonization times and amount of introgression. Invasive individuals attracted by conspecifics need more time to colonize the whole area and are more introgressed by local genes, whereas the opposite is found for solitary individuals. We applied our approach to a recent expansion of European wildcats in the Jura Mountains and the hybridization with domestic cats. We show that the simulations explained better the observed level of introgression at nuclear, mtDNA, and Y chromosome markers, when using solitary dispersal for wildcats instead of random or gregarious dispersal, in accordance with ecological knowledge. Thus, use of density‐dependent dispersal models increases the predictive power of the approach.     

Individual-level personality influences social foraging and collective behaviour in wild birds

There is increasing evidence that animal groups can maintain coordinated behaviour and make collective decisions based on simple interaction rules. Effective collective action may be further facilitated by individual variation within groups, particularly through leader–follower polymorphisms. Recent studies have suggested that individual-level personality traits influence the degree to which individuals use social information, are attracted to conspecifics, or act as leaders/followers. However, evidence is equivocal and largely limited to laboratory studies. We use an automated data-collection system to conduct an experiment testing the relationship between personality and collective decision-making in the wild. First, we report that foraging flocks of great tits (Parus major) show strikingly synchronous behaviour. A predictive model of collective decision-making replicates patterns well, suggesting simple interaction rules are sufficient to explain the observed social behaviour. Second, within groups, individuals with more reactive personalities behave more collectively, moving to within-flock areas of higher density. By contrast, proactive individuals tend to move to and feed at spatial periphery of flocks. Finally, comparing alternative simulations of flocking with empirical data, we demonstrate that variation in personality promotes within-patch movement while maintaining group cohesion. Our results illustrate the importance of incorporating individual variability in models of social behaviour.