The relationship between sediment mobilisation and the entry of Baetis mayflies into the water column in a laboratory flume

Mass bedload movement is thought to play a key role in initiating stream invertebrate drift during extreme flood events. However, little is known of the importance of the shear of invertebrates from stone surfaces relative to their entrainment along with bed material at different discharges. In particular, it is unclear whether so-called catastrophic drift only occurs once mass bedload movement, and hence entrainment of invertebrates, occurs. We investigated the relationship between the mobilisation and transport of bed sediments and the entry of Baetis mayflies into the water column in a laboratory flume. Experiments quantified the percentage of Baetis drifting at a range of discharges that mobilised between 0 and 95% of the flume-bed sediments. Control experiments quantified drift losses from sediment fixed to the bed of the flume, such that sediments were immobile even at the highest discharges. Drift losses increased with increasing discharge and velocity in the flume. Sediment mobility contributed significantly to drift (ANCOVA, p < 0.001), with consistently greater drift losses in mobile sediment experiments than in those with fixed sediment. The discharge which resulted in a loss of 100% of Baetis from the mobile sediment bed (discharge 30 l s^–1) resulted in a loss of approximately 50% of individuals from the fixed bed. Results indicate that once bed sediments are mobilised, entry of Baetis into the drift is greater than expected from the shear of animals from stone surfaces alone. Thus, entrainment of animals along with sediment contributes significantly to drift at high flows. This implies that differences in bed stability between sites or streams, or temporal changes in sediment characteristics within a site, could influence patterns of drift.     

The evolution of an 'intelligent' dispersal strategy: biased, correlated random walks in patchy landscapes

Theoretical work exploring dispersal evolution focuses on the emigration rate of individuals and typically assumes that movement occurs either at random to any other patch or to one of the nearest‐neighbour patches. There is a lack of work exploring the process by which individuals move between patches, and how this process evolves. This is of concern because any organism that can exert control over dispersal direction can potentially evolve efficiencies in locating patches, and the process by which individuals find new patches will potentially have major effects on metapopulation dynamics and gene flow. Here, we take an initial step towards filling this knowledge gap. To do this we constructed a continuous space population model, in which individuals each carry heritable trait values that specify the characteristics of the biased correlated random walk they use to disperse from their natal patch. We explore how the evolution of the random walk depends upon the cost of dispersal, the density of patches in the landscape, and the emigration rate. The clearest result is that highly correlated walks always evolved (individuals tended to disperse in relatively straight lines from their natal patch), reflecting the efficiency of straight‐line movement. In our models, more costly dispersal resulted in walks with higher correlation between successive steps. However, the exact walk that evolved also depended upon the density of suitable habitat patches, with low density habitat evolving more biased walks (individuals which orient towards suitable habitat at quite large distances from that habitat). Thus, low density habitat will tend to develop individuals which disperse efficiently between adjacent habitat patches but which only rarely disperse to more distant patches; a result that has clear implications for metapopulation theory. Hence, an understanding of the movement behaviour of dispersing individuals is critical for robust long‐term predictions of population dynamics in fragmented landscapes.     

Evidence for upstream dispersion of adult CAD disflies (Trichoptera: Hydropsychidae) in the Columbia River

The radioisotope ⁶⁵Zn, introduced to the Columbia River in discharges of the U.S. Atomic Energy Commission's Hanford reactors, was used to test the hypothesis that adult caddis flies migrate upstream after emerging from the aquatic environment. The larval stages living downstream of the effluents are known to accumulate appreciable levels of ⁶⁵Zn. The radioisotope was found in levels above background in shoreline swarms of adult caddis flies as far as 16 km above the uppermost reactor effluent. Whether movement was only upstream and the precise distances flown remain unclear. The upstream movement is important for understanding the biology of riverine aquatic insects and for evaluating the upstream dispersal of radioactive contaminants.     

Random movement pattern of the sea urchin Strongylocentrotus droebachiensis

We describe the fine-scale movement of the sea urchin Strongylocentrotus droebachiensis based on analyses of video recordings of undisturbed individuals in the two habitats which mainly differed in food availability, urchin barrens and grazing front. Urchin activity decreased as urchin density increased. Individuals alternated between moving and being stationary and their behaviour did not appear to be affected by either current velocity (within the range from 0 to 15 cm s^− 1) and temperature (2.3 to 6.0 °C). Movement of individuals at each location was compared to that predicted by a random walk model. Mean move length (linear distance between two stationary periods), turning angle and net squared displacement were calculated for each individual. The distribution of turning angles was uniform at each location and there was no evidence of a relationship between urchin density and either move length or urchin velocity. The random model predicted a higher dispersal rate at locations with low urchin densities, such as barrens habitats. However, the movement was sometimes greater or less than predicted by the model, suggesting the influence of local environmental factors. The deviation of individual paths from the model revealed that urchins can be stationary or adopt a local (displacement less than random), random or directional movement. The net daily distance displaced on the barrens, predicted by a random walk model, was similar to the observed movement recorded in our previous study of tagged urchins at one site, but less than that observed at a second site. We postulate that the random dispersal of urchins allows individuals on barrens to reach the kelp zone where food is more abundant although the time required to reach the kelp zone may be considerable (months to years). Urchins decrease their rate of dispersal once they reach the kelp zone so that they likely remain close to this abundant food sources for long periods.     

Drift and settlement of stream insects in a complex hydraulic environment

1. The hydraulic and geomorphic characteristics of stream patches are often associated with distinctive assemblages or densities of stream invertebrates, and it is routinely presumed that these patterns reflect primarily species‐specific habitat requirements. An alternative hypothesis is that such patterns may be influenced by constraints on movement, such as the results of departure and settlement processes. We describe a manipulative experiment that examined how the hydraulic environments created by topographic bedforms influenced the drift behaviour and potential settlement sites for two species of mayfly (Baetis rhodani and Ecdyonurus torrentis). These species are common in the drift and often co‐occur in streams, but differ in their small‐scale distribution patterns, body shape and movement behaviour. 2. Flume experiments were carried out to determine how the hydraulic environments conditioned by a step bedform influence the behaviour of mayflies in the drift (swimming, posturing, tumbling), and the consequences of those behaviours (drift distance and time), compared to drift over a plane bed. The ramped step in the flume mimicked step bedforms that are common in coarse‐grained, high‐gradient streams. In contrast to the plane bed, a zone of recirculating flow was created downstream of the step, above which flow was faster and more turbulent. Uniform flows are used in most flume studies of drift; our approach is novel in recreating a complex hydraulic environment characteristic of stream channels. 3. Both species had some behavioural control over drift, and drift distances and times were shorter for live larvae than for dead larvae over the plane bed. The step had no impact on drift time or distance for live Baetis, but dead larvae were trapped in the flow separation eddy and drift time increased accordingly. Some Ecdyonurus also became trapped in the eddy, but live larvae drifted farther than dead larvae, and farther over the step than the plane bed. 4. Whilst in the drift, larvae altered their behaviour according to the ambient hydraulic environment, but in a species‐specific manner. Over the plane bed, Baetis had occasional swimming bursts, but primarily postured (maintained a stable body orientation), whereas Ecdyonurus spent roughly equal time posturing and swimming. In the more turbulent flows generated by the step, Baetis spent proportionately more time swimming, whereas Ecdyonurus spent more time posturing and often tumbling as body orientation became unstable. 5. In a high‐gradient stream, Baetis was more abundant close to steps than in plane bed patches with less complex flow, whereas the opposite pattern held for Ecdyonurus. Thus, the small‐scale distribution patterns of these species within streams correspond to their drift behaviours and ability to access various hydraulic patch types in our flume. These results are consistent with the hypothesis that constraints on movement and settlement may be important driver of distribution patterns within streams.     

Animal space use: distinguishing a two‐level superposition of scale‐specific walks from scale‐free Lévy walk

How to differentiate between scale‐free space use like Lévy walk and a two‐level scale‐specific process like composite random walk (mixture of intra‐ and inter‐patch habitat movement) is surrounded by controversy. Composite random walk may under some parameter conditions appear Lévy walk‐like from the perspective of the path’s distribution of step lengths due to superabundance of very long steps relative to the expectation from a classic (single‐level) random walk. However, a more explicit focus on the qualitative differences between studying movement at a high resolution mechanistic (behavioral) level and the more coarse‐grained statistical mechanical level may contribute to resolving both this and other issues related to scaling complexity. Specifically, a re‐sampling of a composite random walk at larger time lags than the micro‐level unit time step for the simulation makes a Lévy‐look‐alike step length distribution re‐shaping towards a Brownian motion‐like pattern. Conversely, a true Levy walk maintains its scaling characteristics upon re‐sampling. This result illustrates how a confusing pattern at the mechanistic level may be resolved by changing observational scale from the micro level to the coarser statistical mechanical meso‐ or macro‐scale. The instability of the composite random walk pattern under rescaling is a consequence of influence of the central limit theorem. I propose that a coarse‐graining test – studying simulated animal paths at a coarsened temporal scale by re‐sampling a series – should be routinely performed prior to comparing theoretical results with those patterns generated from GPS data describing animal movement paths. Fixes from terrestrial mammals are often collected at hourly intervals or larger, and such a priori coarse‐grained series may thus comply better with the statistical mechanical meso‐ or macro‐level of analysis than the behavioral mechanics observed at finer resolutions typically in the range of seconds and minutes. If fixes of real animals are collected at this high frequency, coarse graining both the simulated and real series is advised in order to bring the analysis into a temporal scale domain where analytical methods from statistical mechanics can be applied.     

Random movement pattern of fed and unfed adult Colorado potato beetles in bare‐ground habitat

• 1 Although the successful management of the Colorado potato beetle Leptinotarsa decemlineata (Say) depends on the prevention of its dispersal, its walking pattern in the landscape remains poorly understood. In the present study, post‐diapause, early summer, late summer and colony adult beetles, both fed and unfed before release, were tracked with a harmonic radar to establish their walking movement pattern in a bare‐ground field.
• 2 The random walk model successfully described the dispersal of all beetle types, whether fed or unfed.
• 3 The diverse life history of this species was manifested by an increased distance travelled and deviations of individual paths from the random model. Starved post‐diapause beetles travelled furthest and individual paths deviating from random were both local and directed, probably aiming to maximize opportunities for host colonization. Starved early summer beetles also travelled further than fed beetles but relied more on random movement to disperse in the habitat. Starving had little impact on the distance travelled or the path deviations of late summer beetles that are searching for overwintering site rather than hosts.
• 4 The increased displacement of starving beetles over fed beetles corresponded with an increased walking step and index of straightness.
• 5 The impact of starvation on travel distance was greater than expected from laboratory tests.
• 6 In conclusion, the results obtained in the present study suggest a random walking pattern to search arable land until host volatile or visual impulses trigger a more directed walk or flight.

     

ESTIMATION OF SINGLE GENERATION MIGRATION DISTANCES FROM GEOGRAPHIC VARIATION IN ANIMAL MITOCHONDRIAL DNA

A new approach is introduced for the analysis of dispersal from the geographic distributions of mtDNA lineages. The method is based on the expected spatial distributions of lineages arising under a multigeneration random walk process. Unlike previous methods based on the predicted equilibria between genetic drift and gene flow, this approach is appropriate for non-equilibrium conditions, and yields an estimate of dispersal distance rather than dispersal rate. The theoretical basis for this method is examined, and an analysis of mtDNA restriction site data for Peromyscus maniculatus is presented as an example of how this approach can be applied to empirical data.     

Behavior underpins the predictive power of a trait‐based model of butterfly movement

1. Dispersal ability is key to species persistence in times of environmental change. Assessing a species' vulnerability and response to anthropogenic changes is often performed using one of two methods: correlative approaches that infer dispersal potential based on traits, such as wingspan or an index of mobility derived from expert opinion, or a mechanistic modeling approach that extrapolates displacement rates from empirical data on short‐term movements.
2. Here, we compare and evaluate the success of the correlative and mechanistic approaches using a mechanistic random‐walk model of butterfly movement that incorporates relationships between wingspan and sex‐specific movement behaviors.
3. The model was parameterized with new data collected on four species of butterfly in the south of England, and we observe how wingspan relates to flight speeds, turning angles, flight durations, and displacement rates.
4. We show that flight speeds and turning angles correlate with wingspan but that to achieve good prediction of displacement even over 10 min the model must also include details of sex‐ and species‐specific movement behaviors.
5. We discuss what factors are likely to differentially motivate the sexes and how these could be included in mechanistic models of dispersal to improve their use in ecological forecasting.

     

From random walks to informed movement

The analysis of animal movement is a large and continuously growing field of research. Detailed knowledge about movement strategies is of crucial importance for understanding eco‐evolutionary dynamics at all scales – from individuals to (meta‐)populations. This and the availability of detailed movement and dispersal data motivated Nathan and colleagues to published their much appreciated call to base movement ecology on a more thorough mechanistic basis. So far, most movement models are based on random walks. However, even if a random walk might describe real movement patterns acceptably well, there is no reason to assume that animals move randomly. Therefore, mechanistic models of foraging strategies should be based on information use and memory in order to increase our understanding of the processes that lead to animal movement decisions. We present a mechanistic movement model of an animal with a limited perceptual range and basic information storage capacities. This ‘spatially informed forager’ constructs an internal map of its environment by using perception, memory and learned or evolutionarily acquired assumptions about landscape attributes. We analyse resulting movement patterns and search efficiencies and compare them to area restricted search strategies (ARS) and biased correlated random walks (BCRW) of omniscient individuals. We show that, in spite of their limited perceptual range, spatially informed individuals boost their foraging success and may perform much better than the best ARS. The construction of an internal map and the use of spatial information results in the emergence of a highly correlated walk between patches and a rather systematic search within resource clusters. Furthermore, the resulting movement patterns may include foray search behaviour. Our work highlights the strength of mechanistic modelling approaches and sets the stage for the development of more sophisticated models of memory use for movement decisions and dispersal.     

Linking movement behaviour to dispersal and divergence in plethodontid salamanders

To better understand the evolutionary and ecological effects of dispersal, there is growing emphasis on the need to integrate direct data on movement behaviour into landscape-scale analyses. However, little is known about the general link between movement behaviour and large-scale patterns of dispersal and gene flow. Likewise, although recent studies suggest that nonrandom, directionally biased movement and dispersal can promote evolutionary divergence, the generality of this mechanism is unknown. We test the hypothesis that directionally biased movement and dispersal by plethodontid salamanders interact with the topography of headwater areas to affect genetic and phenotypic divergence. Movements by Gyrinophilus porphyriticus and Eurycea bislineata show contrasting directional biases: upstream bias in G. porphyriticus and downstream bias in E. bislineata. Consistent with predictions of how these biases interact with slope to affect dispersal and gene flow, genetic distance increased with slope in G. porphyriticus and decreased with slope in E. bislineata over a standardized distance of 1 km along six headwater streams. In both species, phenotypic divergence in relative trunk length was positively related to genetic divergence. These results indicate that landscape-scale patterns of dispersal and gene flow are closely related to movement behaviour in G. porphyriticus and E. bislineata, and underscore the value of information on movement behaviour for predicting and interpreting patterns of dispersal and gene flow in complex landscapes. This study also provides new evidence that directionally biased movement and dispersal can be important sources of intra- and interspecific variation in population divergence, and highlights the value of explicit, a priori predictions in landscape genetic studies.     

Effect of body length and temperature on the crawling speed of Protophormia terraenovae larvae (Robineau-Desvoidy) (Diptera Calliphoridae)

This work investigates variation in the crawling speed of Protophormia terraenovae larvae (Robineau-Desvoidy) (Diptera Calliphoridae) as a function of body length and ambient temperature. A video-tracking system was used to follow the movement of larvae in an experimental arena, and to estimate their average crawling speed. Recordings were carried out at various temperatures using larvae of different developmental stages. As temperature increased, the larvae crawled at a faster speed. Furthermore, speed increased as a function of body length. We present a general allometric relationship to express the average crawling speed of larvae as a combined function of temperature and body length, expressed in the following equation: speed (cm/min)=5.45 x log[length (mm)]+0.66 x temperature (degrees C)-12.8. These results are particularly useful in forensic entomology for estimating the time that elapsed following the larva's departure from the corpse. This information can provide more accuracy for post-mortem interval estimations and a better comprehension of larvae behaviour and displacement.     

Short-term responses of macroinvertebrate drift following experimental sediment flushing in a Japanese headwater channel

We examined short-term responses of macroinvertebrate drift associated with experimental sediment flushing in a headwater. Increases in the drifting abundances of Ephemeroptera and Plecoptera coincided with increases in bed load yield rather than peaks in discharge or suspended sediment concentrations. The approach and arrival of a sediment wave may provide a physical cue that initiates the escape of benthic macroinvertebrates. Because fine bed load sediments, with diameters <4 mm, tended to accumulate on and in the substrate matrix, such sedimentation affected the benthic macroinvertebrates residing on and in the substrate, increasing the number of macroinvertebrates in the drift. Therefore, the decreases observed in the densities of most macroinvertebrate taxa following sediment flushing were probably associated with sediment deposition and the resulting escape of macroinvertebrates from benthic habitats. The magnitudes of the decreases in macroinvertebrate density were lower at sites located 200 m downstream from the sediment sources than at sites located 20 m downstream. The results from this experimental flushing study suggest that bed load movement and resulting sediment accumulation alter macroinvertebrate drift patterns and cause decreases in the abundances of benthic macroinvertebrates in headwater streams.     

Asymmetric dispersal structures a riverine metapopulation of the freshwater pearl mussel Margaritifera laevis

Unidirectional water flow results in the downstream‐biased, asymmetric dispersal of many riverine organisms. However, little is known of how asymmetric dispersal influences riverine population structure and dynamics, limiting our ability to properly manage riverine organisms. A metapopulation of the freshwater pearl mussel Margaritifera laevis may be sensitive to river currents because mussels are repeatedly exposed to downstream drift during floods—a parasitic life stage is the only, limited period (~40 days) during which larvae (glochidia) can move upstream with the aid of host fish. We hypothesized that water‐mediated dispersal would overwhelm upstream dispersal via host fish, and therefore, that upstream subpopulations play a critical role as immigrant sources. To test this hypothesis, we examined the effects of both up‐ and downstream immigrant sources on the size of target subpopulations in the Shubuto River system, Hokkaido, Japan. We found that target subpopulation size was dependent on the upstream distribution range of reproductive subpopulations and the number of upstream tributaries, which are proxies for the number of potential immigrants moving downstream. In contrast, little influence was observed of downstream immigrant sources (proximity to downstream reproductive subpopulations). These results were consistent even after accounting for local environments and stream size. Our finding suggests that upstream subpopulations can be disproportionately important as immigrant sources when dispersal is strongly asymmetric.     

Field experiments on the mobility of benthic invertebrates in a southern English stream

1. In each of twenty-six week-long experiments, the colonization by macroinvertebrates of boxes of natural sediment in a stony stream was measured. The experiments took place between February and November 1992 and environmental conditions prevailing during the weeks (particularly discharge and temperature) differed widely.
2. Colonization rate also varied widely between the weekly experiments and was sensitive to discharge, temperature and background benthic density, depending on the taxa considered.
3. A 'mobility index' measured colonization rate independently of background benthic density. This index was most strongly and positively correlated with discharge for the abundant stonefly Leuctra nigra, the net-spinning caddis Plectrocnemia conspersa and the Chironomidae, perhaps indicating that their mobility is physically driven by the influence of flow on drift.
4. Mobility in a second stonefly ( Nemurella pictetii ) was greatest in summer, when flows were low but temperature was high. Peak mobility in this species occurred during an ochreous bloom on the stream bed. It is likely the mobility of N. pictetii is more active than the other taxa.
5. There were thus differences among taxa in their mobility at baseflow and in their susceptibility to flow fluctuations. The population consequences of differences in mobility among taxa are discussed.     

When is stream invertebrate drift catastrophic? The role of hydraulics and sediment transport in initiating drift during flood events

1. The term ‘catastrophic drift’ is used to describe the large‐scale displacement of invertebrates that occurs during periods of increased river discharge. However, the physical processes that lead to animals entering the water column at such times remain poorly understood. Specifically, the hypothesis that the movement of bed sediments during floods triggers a large increase in drift has lacked a rigorous field test. 2. Using a portable flume, the hydraulic conditions and rates of bedload transport associated with small, frequent floods were created in situ within a reach of a gravel bed river. Experiments focussed on the patches of fine sediment which are the dominant source of bed material transported during small floods. The flume produced near bed velocities of up to 2 m s^?1 over the patches, increasing shear stress, initiating sediment transport and causing invertebrates to enter the drift. 3. The total number of individuals lost from the bed, as well as the taxonomic composition of the drift, were influenced strongly by shear stress and bedload. The rate of loss from the bed was low at shear stresses <9 dynes cm^?2 (0–4 individuals min^?1 from the 0.5 m² flume bed area). Once shear stress exceeded 9 dynes cm^?2, the threshold that resulted in consistent bedload transport from the patches, the rate of loss of animals increased to a maximum of 56 individuals min^?1. When bedload transport rates were at their highest, the taxonomic composition of the drift was more similar to the benthos than it was to the drift observed when bed material was stable. 4. Absolute rates of bedload transport created by the manipulations were extremely low (<7 g m^?1 s^?1) and typical of those measured during small, frequent floods. Events of this magnitude do not break up the armour layer across the reach as a whole and so exposed patches of fine sediment are the principal source of bedload material. Consequently, discharge events not considered as disturbances in geomorphic terms may initiate frequent episodes of so‐called ‘catastrophic drift’ from patches of stream bed.     

Species traits and channel architecture mediate flow disturbance impacts on invertebrate drift

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Directional movement in response to altered flow in six lowland stream Trichoptera

Understanding the trait adaptations associated with mobility in Trichoptera larvae under different flow conditions would enhance the understanding of survival mechanisms under flow stress induced by spates. In stream mesocosms, we mimicked a lowland stream spate by suddenly increasing current velocity above an organic habitat patch from 10 to 30 or 50 cm/s. Subsequently, we investigated whether short-term, small-scale movements in six Trichoptera species were not random but directional and whether the type of movement was related to the magnitude of flow increase. Main types of response distinguished were as follows: (1) resistance, in which the species remained in the habitat patch, (2) upstream or downstream crawling, and (3) being dislodged from the streambed and drift downstream (vulnerability). The type of response observed was related to the species’ ecological preferences and morphological traits. The experiment showed that movement in Trichoptera larvae was directional and flow-dependent. Drift was the main mechanism observed with an increase in current velocity, but upstream crawling and aggregation in the habitat patch were observed as well. The type and magnitude of the response were highly species specific. It appeared that each combination of morphological and behavioral adaptations developed individually for each species under niche-specific conditions.     

Ontogenetic shifts in drift periodicity and benthic dispersal in elmid beetles

1. There is a paucity of information on ontogenetic changes in the dispersal of benthic invertebrates, which is an important aspect of their ecology. This study quantifies ontogenetic changes in diel periodicity in drift, and in upstream–downstream dispersal on the substratum for Elmis aenea, Oulimnius tuberculatus, Esolus parallelepipedus and Limnius volkmari (Coleoptera: Elmidae). Three drift nets were emptied every 3 h over 24 h in each month (October 1965–December 1968) at two contrasting sites: one in a deep section with abundant macrophytes, the other in a shallow stony riffle. Comparisons of periodicity between life‐stages of the same species were limited to months when numbers in the drift were highest. Dispersal was evaluated in six experimental stream channels, placed above the stream, with initial numbers of each life‐stage varying from 20 to 80. 2. Drift numbers were always highest at night with few or no animals in the day samples. Ontogenetic shifts in diel periodicity were similar for all four species. Drift catches were similar throughout the night for the early and intermediate larval instars and for mature adults, but were highest in the early hours of the night with a gradual decline thereafter for later larval instars and immature adults. These patterns were unaffected by a severe spate, even though drift numbers increased considerably. 3. Dispersal was density‐independent; the number of dispersing animals was a constant proportion of the initial number for each life‐stage. The relationship between dispersal distance and the number of animals travelling that distance was well described by an inverse power function. Median and maximum distances (m day^?1) were estimated for each life‐stage. 4. Ontogenetic shifts in dispersal in the stream channels matched those shown in diel drift periodicity. For all four species, the later larval instars and immature adults showed little movement in either direction, whereas early and intermediate larval instars and mature adults dispersed predominantly upstream, adults travelling further than any other life‐stage. 5. Ontogenetic shifts in diel drift periodicity and dispersal were related to seasonal changes in drift density and critical periods in the life cycle. Such shifts have not been quantified in other stream invertebrates, but should be considered when evaluating the role of dispersal in their population dynamics and their colonization ability.     

Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Computational models have shown that biophysical stimuli can be correlated with observed patterns of tissue differentiation, and simulations have been performed that predict the time course of tissue differentiation in, for example, long bone fracture healing. Some simulations have used a diffusion model to simulate the migration and proliferation of cells with the differentiating tissue. However, despite the convenience of the diffusion model, diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. In this paper, a random-walk model (i.e., a stochastic model), with and without a preferred direction, is studied as an approach to simulate cell proliferation/migration in differentiating tissues and it is compared with the diffusion model. A simulation of tissue differentiation of gap tissue in a two-dimensional model of a bone/implant interface was performed to demonstrate the differences between diffusion vs. random walk with a preferred direction. Results of diffusion and random-walk models are similar with respect to the change in the stiffness of the gap tissue but rather different results are obtained regarding tissue patterning in the differentiating tissues; the diffusion approach predicted continuous patterns of tissue differentiation whereas the random-walk model showed a more discontinuous pattern-histological results are not available that can unequivocally establish which is most similar to experimental observation. Comparing isotropic to anisotropic random walk (preferred direction of proliferation and cell migration), a more rapid reduction of the relative displacement between implant and bone is predicted. In conclusion, we have shown how random-walk models of cell dispersal and proliferation can be implemented, and shown where differences between them exist. Further study of the random-walk model is warranted, given the importance of cell seeding and cell dispersal/proliferation in many mechanobiological problems.