Correlated Random Walk Research Articles

Absolute direction in organelle movement.

In movement analysis, correlated random walk (CRW) models often use so-called turning angles, which are measured relative to the previous movement direction. To segregate between different movement modes, hidden Markov models (HMMs) describe movements as piecewise stationary CRWs in which the distributions of turning angles and step sizes depend on the underlying state. This typically allows for the segregation of movement modes that show different movement speeds. We show that in some cases, it may be interesting to investigate absolute angles, that is, biased random walks (BRWs) instead of turning angles. In particular, while discrimination between states in the turning angle setting can only rely on movement speed, models with absolute angles can be used to discriminate between sections of different movement directions. A preprocessing algorithm is provided that enables the analysis of absolute angles in the existing R package moveHMM. In a data set of movements of cell organelles, models using not the turning angle but the absolute angle could capture interesting additional properties. Goodness-of-fit was increased for HMMs with absolute angles, and HMMs with absolute angles tended to choose a higher number of states, suggesting the existence and relevance of prominent directional changes in the present data set. These results suggest that models with absolute angles can provide important information in the analysis of movement patterns if the existence and frequency of directional changes is of biological importance.

Tracking and modeling the movement of Queensland fruit flies, Bactrocera tryoni, using harmonic radar in papaya fields

Determining movement parameters for pest insects such as tephritid fruit flies is critical to developing models which can be used to increase the effectiveness of surveillance and control strategies. In this study, harmonic radar was used to track wild-caught male Queensland fruit flies (Qflies), Bactrocera tryoni, in papaya fields. Experiment 1 continuously tracked single flies which were prodded to induce movement. Qfly movements from this experiment showed greater mean squared displacement than predicted by both a simple random walk (RW) or a correlated random walk (CRW) model, suggesting that movement parameters derived from the entire data set do not adequately describe the movement of individual Qfly at all spatial scales or for all behavioral states. This conclusion is supported by both fractal and hidden Markov model (HMM) analysis. Lower fractal dimensions (straighter movement paths) were observed at larger spatial scales (> 2.5 m) suggesting that Qflies have qualitatively distinct movement at different scales. Further, a two-state HMM fit the observed movement data better than the CRW or RW models. Experiment 2 identified individual landing locations, twice a day, for groups of released Qflies, demonstrating that flies could be tracked over longer periods of time.

Caterpillar movement mediates spatially local interactions and determines the relationship between population density and contact.

While interactions in nature are inherently local, ecological models often assume homogeneity across space, allowing for generalization across systems and greater mathematical tractability. Density-dependent disease models are a prominent example of models that assume homogeneous interactions, leading to the prediction that disease transmission will scale linearly with population density. In this study, we examined how the scale of larval butterfly movement interacts with the resource landscape to influence the relationship between larval contact and population density in the Baltimore checkerspot (Euphydryas phaeton). Our study was inspired by the recent discovery of a viral pathogen that is transmitted horizontally among Baltimore checkerspot larvae. We used multi-year larvae location data across six Baltimore checkerspot populations in the eastern U.S. to test whether larval nests are spatially clustered. We then integrated these spatial data with larval movement data in different resource contexts to investigate whether heterogeneity in spatially local interactions alters the assumed linear relationship between larval nest density and contact. We used Correlated Random Walk (CRW) models and field observations of larval movement behavior to construct Probability Distribution Functions (PDFs) of larval dispersal, and calculated the overlap in these PDFs to estimate conspecific contact within each population. We found that all populations exhibited significant spatial clustering in their habitat use. Subsequent larval movement rates were influenced by encounters with host plants and larval age, and under many movement scenarios, the scale of predicted larval movement was not sufficient to allow for the "homogeneous mixing" assumed in density dependent disease models. Therefore, relationships between population density and larval contact were typically non-linear. We also found that observed use of available habitat patches led to significantly greater contact than would occur if habitat use were spatially random. These findings strongly suggest that incorporating larval movement and spatial variation in larval interactions is critical to modeling disease outcomes in E. phaeton. Epidemiological models that assume a linear relationship between population density and larval contact have the potential to underestimate transmission rates, especially in small populations that are already vulnerable to extinction.

A class of statistical models for the motion of Daphnia over small time scales

A common question in the aquatic sciences is that of how zooplankter movement can be modeled. It is well-established in the literature that there exists a randomness to this movement, but the question is how to characterize this randomness. The most common methods for doing this involve the random walk and correlated random walk (CRW) models. Here, we present a time series model that allows a better description the randomness in Daphnia motion when the amount of time that elapses between observations of their position is small. Our approach is adaptable to description of tracks of a multitude of animal species through re-estimation of model parameters. The model we propose uses information about how the animal moved during the previous two time intervals to explain how it moves currently. We demonstrate that the proposed model provides better predictive accuracy and fit than do the CRW and random walk models.

Brain-localized CD4 and CD8 T cells perform correlated random walks and not Levy walks

Background. For survival of the organism, T cells must efficiently control pathogens invading different peripheral tissues but whether such control (and lack of thereof) is achieved by utilizing different movement strategies remains poorly understood. Liver-localized CD8 T cells perform correlated random walks (CRWs)— a type of a Brownian walk – in liver sinusoids but in some conditions, these T cells may also perform Levy flights – rapid and large displacements by floating with the blood flow. CD8 T cells in lymph nodes or skin also undergo Brownian walks. A recent study suggested that brain-localized CD8 T cells, specific to Toxoplasma gondii, perform generalized Levy walks (LWs) – a walk type in which T cells alternate pausing and displacing long distances — which may indicate that brain is a unique organ where T cells exhibit movement strategies different from other tissues. Methods. We quantified movement patterns of brain-localized Plasmodium berghei-specific CD4 and CD8 T cells by using well-established statistical and computational methods. Results. We found that T cells change their movement pattern with time since infection and that CD4 T cells move faster and turn less than CD8 T cells. Importantly, both CD4 and CD8 T cells move in the brain by CRWs without long displacements challenging previous observations. We have also re-analyzed movement data of brain-localized CD8 T cells in T. gondii-infected mice from a previous study and found no evidence of LWs. We hypothesize that the previous conclusion of LWs of T. gondii-specific CD8 T cells in the brain was reached due to missing timeframes in the data that create an impression of large displacements between assumed-to-be sequential movements. Conclusion. Our results suggest that movement strategies of CD8 T cells are largely similar between LNs, liver, and the brain and consistent with CRWs and not LWs.

Evidence for a consistent use of external cues by marine fish larvae for orientation

The larval stage is the main dispersive process of most marine teleost species. The degree to which larval behavior controls dispersal has been a subject of debate. Here, we apply a cross-species meta-analysis, focusing on the fundamental question of whether larval fish use external cues for directional movement (i.e., directed movement). Under the assumption that directed movement results in straighter paths (i.e., higher mean vector lengths) compared to undirected, we compare observed patterns to those expected under undirected pattern of Correlated Random Walk (CRW). We find that the bulk of larvae exhibit higher mean vector lengths than those expected under CRW, suggesting the use of external cues for directional movement. We discuss special cases which diverge from our assumptions. Our results highlight the potential contribution of orientation to larval dispersal outcomes. This finding can improve the accuracy of larval dispersal models, and promote a sustainable management of marine resources.

Species' movement influence responses to habitat fragmentation

AbstractAimHuman conversion of land leads to habitat loss and fragmentation. The effects of habitat loss are well‐established, but the effects of fragmentation beyond those of habitat loss, “fragmentation per se” (FPS), are intensely debated. One area of debate is how different species might respond to FPS. We will answer whether FPS have more negative effects on species that spend more time in the matrix and less on species with higher potential patch encounter rates.LocationVirtual landscapes.MethodsWe simulated the effects of FPS on multiple species with different movement characteristics. All species moved with a random walk (RW), a correlated RW (CRW), or a habitat‐dependent walk (HDW). Species also had increasing habitat bias which caused individuals to have a higher probability of moving into a more suitable habitat. The walk type modified the rate at which species encountered habitat patches. Increased bias caused individuals to spend more time in suitable habitats and less time in the matrix between patches. All species experienced higher mortality in less suitable habitats. We analysed FPS effects on species for whom the fragmented focal habitat was the most suitable.ResultsWith bias, the species diversity of RW species declined with FPS, while FPS had little effect on the species diversity of species moving by CRW. For HDW species, spending less time in the matrix (moderate movement bias) caused species diversity to increase with FPS, but to decline with high bias.Main conclusionsThese results suggest that even for species that are dependent on fragmented habitat, FPS does not have a unidirectional effect. FPS can have a positive effect on species with high patch encounter rates (HDW with moderate bias) as their functional connectivity increases. These results help to explain why different studies show contradictory effects of FPS on biodiversity.

A Characteristic Polynomial for the Transition Probability Matrix of Correlated Random Walks on a Graph

We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW by using a determinant expression for the generalized weighted zeta function of $G$. As an application, we give the spectrum of the transition probability matrices for the CRWs induced from the Grover matrices of regular graphs and semiregular bipartite graphs. Furthermore, we consider another type of the CRW on a graph.

Simulation experiment to test strategies of geomagnetic navigation during long-distance bird migration

BackgroundDifferent theories suggest birds may use compass or map navigational systems associated with Earth’s magnetic intensity or inclination, especially during migratory flights. These theories have only been tested by considering properties of the Earth’s magnetic field at coarse temporal scales, typically ignoring the temporal dynamics of geomagnetic values that may affect migratory navigational capacity.MethodsWe designed a simulation experiment to study if and how birds use the geomagnetic field during migration by using both high resolution GPS tracking data and geomagnetic data at relatively fine spatial and temporal resolutions in comparison to previous studies. Our simulations use correlated random walks (CRW) and correlated random bridge (CRB) models to model different navigational strategies based on underlying dynamic geomagnetic data. We translated navigational strategies associated with geomagnetic cues into probability surfaces that are included in the random walk models. Simulated trajectories from these models were compared to the actual GPS trajectories of migratory birds using 3 different similarity measurements to evaluate which of the strategies was most likely to have occurred.Results and conclusionWe designed a simulation experiment which can be applied to different wildlife species under varying conditions worldwide. In the case of our example species, we found that a compass-type strategy based on taxis, defined as movement towards an extreme value, produced the closest and most similar trajectories when compared to original GPS tracking data in CRW models. Our results indicate less evidence for map navigation (constant heading and bi-gradient taxis navigation). Additionally, our results indicate a multifactorial navigational mechanism necessitating more than one cue for successful navigation to the target. This is apparent from our simulations because the modelled endpoints of the trajectories of the CRW models do not reach close proximity to the target location of the GPS trajectory when simulated with geomagnetic navigational strategies alone. Additionally, the magnitude of the effect of the geomagnetic cues during navigation in our models was low in our CRB models. More research on the scale effects of the geomagnetic field on navigation, along with temporally varying geomagnetic data could be useful for further improving future models.

A bio-inspired localization-free stochastic coverage algorithm with verified reachability

Dependence on constant availability to an external localization service is often unreliable and infeasible in mobile robots. In this paper, we take inspiration from a continuous fish motion model, the persistent turning Walker (PTW), to devise a strategy which is able to achieve 2D and 3D coverage in an unknown environment in the absence of a localization service, such as a global positioning system (GPS). This is achieved by converting the continuous-time dynamical system into a discrete-time Markov chain which is then shown to exhibit strongly connected properties that are verifiable through numerical methods. The aforementioned proposed framework can also be used to study the continuous-time dynamics of other biological systems and evaluate their properties. The performance of the PTW model is also compared with two existing random search strategies, simple random walks (SRW) and correlated random walks (CRW) by using analytical bounds, simulation results, and statistical tests. The simulation results show that the proposed PTW algorithm covers a given search-space at a faster rate compared to the CRW and SRW models. Hence, the PTW may be effectively used as a coverage strategy by mobile robots in underwater or underground environments where the availability of a GPS cannot be guaranteed at all times.

Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps. We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency. We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion. Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Moving infections: individual movement decisions drive disease persistence in spatially structured landscapes

Understanding host–pathogen dynamics requires realistic consideration of transmission events that, in the case of directly transmitted pathogens, result from contacts between susceptible and infected individuals. The corresponding contact rates are usually heterogeneous due to variation in individual movement patterns and the underlying landscape structure. However, in epidemiological models, the roles that explicit host movements and landscape structure play in shaping contact rates are often overlooked.We adapted an established agent‐based model of classical swine fever (CSF) in wild boar Sus scrofa to investigate how explicit representation of landscape heterogeneity and host movement between social groups affects invasion and persistence probabilities. We simulated individual movement both phenomenologically as a correlated random walk (CRW) and mechanistically by representing interactions of the moving individuals with the landscape and host population structure.The effect of landscape structure on the probability of invasion success and disease persistence depended remarkably on the way host movement is simulated and the case fatality ratio associated with the pathogen strain. The persistence probabilities were generally low with CRW which ignores feedbacks to external factors. Although the basic reproduction number R0, a measure of the contagiousness of an infectious disease, was kept constant, these probabilities were up to eight times higher under mechanistic movement rules, especially in heterogeneous landscapes. The increased persistence emerged due to important feedbacks of the directed movement on the spatial variation of host density, contact rates and transmission events to distant areas.Our findings underscore the importance of accounting for spatial context and group size structures in eco‐epidemiological models. Our study highlights that the simulation of explicit, mechanistic movement behaviour can reverse predictions of disease persistence in comparison to phenomenological rules such as random walk approaches. This can have severe consequences when predicting the probability of disease persistence and assessing control measures to prevent outbreaks.

Examining the relative influence of animal movement patterns and mortality models on the distribution of animal transported subsidies

Active subsidies are animal-transported consumption (e.g., predators, pathogens, parasites) and resources (e.g., prey, detritus, nutrients) moved between ecosystems. Animal movement behavior has the potential to mediate the extent and intensity of active subsidies and corresponding ecosystem responses. Animal movement behaviors could interact with mortality risk to affect active subsidy distributions and ecosystem impacts but have rarely been examined in existing ecosystem models of spatial subsidies. Movement ecologists typically simulate animal dispersal and foraging movements using stochastic random walk models such as correlated random walk (CRW) and Lévy walk (LW) models. Movement models generally implement mortality as an instantaneous mortality rate (i.e., probability of death per step). Variation in CRW and LW movement patterns, in combination with mortality rate level and model, can likely change emergent subsidy distributions and impact. Using a spatially explicit individual-based model (IBM), we quantify how variation in the straightness (i.e., CRW) and step length (i.e., LW) of animal movement patterns with variation in mortality rate and model (i.e., distance-dependent versus time-dependent function) alter the intensity and extent of consumer and nutrient subsidy distributions. Movement pattern was a dominant determinant of subsidy displacement with more pronounced effects on consumer (i.e., living) subsidy (e.g., predators) patterns. Mortality rate and mortality model (i.e., distance-dependent versus time-dependent on LW) strongly predicted subsidy density with stronger effects on nutrient (i.e., dead) subsidy (e.g., feces) patterns. Consumer subsidies were deposited farther and at lower densities than nutrient subsidies. Given lower mortality rate, movements with more variable step lengths displaced both nutrient and consumer subsidies farther and at lower densities than straighter movements. Movements with more variable step lengths also resulted in greater nutrient subsidy numbers at lower densities with higher mortality rate in distance-dependent compared to time-dependent mortality models. We conclude that ecosystem modeling frameworks that incorporate interaction between animal movement behavior and mortality conditions will enhance insights into active subsidy distributions.

Correlated random walks inside a cell: actin branching and microtubule dynamics.

Correlated random walks (CRW) have been explored in many settings, most notably in the motion of individuals in a swarm or flock. But some subcellular systems such as growth or disassembly of bio-polymers can also be described with similar models and understood using related mathematical methods. Here we consider two examples of growing cytoskeletal elements, actin and microtubules. We use CRW or generalized CRW-like PDEs to model their spatial distributions. In each case, the linear models can be reduced to a Telegrapher's equation. A combination of explicit solutions (in one case) and numerical solutions (in the other) demonstrates that the approach to steady state can be accompanied by (decaying) waves.

Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

Abstract The most reliable estimates of the population abundance of ground‐dwelling arthropods are obtained almost entirely through trap counts. Trap shape can be easily controlled by the researcher, commonly the same trap design is employed in all sites within a given study. Few researchers really try to compare abundances (numbers of collected individuals) between studies because these are heavily influenced by environmental conditions, e.g. temperature, habitat structure and food sources available, directly affecting insect movement activity. We propose that useful insights can be obtained from a theoretical‐based approach. We focus on the interplay between trap shape (circle, square, slot), the underlying movement behaviour and the subsequent effect on captures. We simulate trap counts within these different geometries whilst considering movement processes with clear distinct properties, such as Brownian motion (BM), the correlated random walk (CRW) and the Lévy walk (LW). (a) We find that slot shaped traps are far less efficient than circular or square traps assuming same perimeter length, with differences which can exceed more than two‐fold. Such impacts of trap geometry are only realized if insect mobility is sufficiently large, which is known to significantly vary depending on type of habitat. (b) If the movement pattern incorporates localized forward persistence then trap counts accumulate at a much slower rate, and this rate decreases further with higher persistency. (c) If the movement behaviour is of Lévy type, then fastest catch rates are recorded in the case of circular trap, and the slowest for the slot trap, indicating that trap counts can strongly depend on trap shape. Lévy walks exacerbate the impact of geometry while CRW make these differences more inconsequential. In this study we reveal trap efficiencies and how movement type can alter capture rates. Such information contributes towards improved trap count interpretations, as required in ecological studies which make use of trapping systems.

Stopped Dead in Their Tracks: The Impact of Railways on Gopher Tortoise (Gopherus polyphemus) Movement and Behavior

Habitat fragmentation is one of the leading causes of biodiversity decline and most commonly results from urbanization and construction of transportation infrastructure. Roads are known to negatively impact species, but railways can often cause similar effects. Certain taxa, such as turtles and tortoises, are more vulnerable to railways than others due to limitations in mobility. We studied the impact of rails on the movement and behavior of Gopher Tortoises (Gopherus polyphemus), a threatened, highly terrestrial species likely in frequent contact with railways. First, we used radio-telemetry to determine the frequency of railway crossings and compared this to correlated random walk (CRW) simulations to assess if tortoises were crossing the rails less frequently than is expected by unconstrained movement. Second, we placed tortoises into the railway and measured behavior for one hour to assess crossing ability. Lastly, we tested whether trenches dug underneath the rails could allow safe passage for tortoi...

Auto-correlated directional swimming can enhance settlement success and connectivity in fish larvae

Larvae of coastal-marine fishes have been shown repeatedly to swim directionally in the pelagic environment. Yet, biophysical models of larval dispersal typically impose a Simple Random Walk (SRW) algorithm to simulate non-directional movement in the open ocean. Here we investigate the use of a Correlated Random Walk (CRW) algorithm; imposing auto-correlated directional swimming onto simulated larvae within a high-resolution 3D biophysical model of the Gulf of Aqaba, the Red Sea. Our findings demonstrate that implementation of auto-correlated directional swimming can result in an increase of up to ×2.7 in the estimated success rate of larval-settlement, as well as an increase in the extent of connectivity. With accumulating empirical support for the capacity for directional-swimming during the pelagic phase, we propose that CRW should be applied in biophysical models of dispersal by coastal marine fish-larvae.

Movements and Inferred Foraging by Bowhead Whales in the Canadian Beaufort Sea during August and September, 2006–12

Each spring, most bowhead whales of the Bering-Chukchi-Beaufort (BCB) population migrate to the southeast Beaufort Sea and summer in Canadian waters. In August and September, they form aggregations, which are known to occur mainly in the shallow, shelf waters when oceanographic conditions promote concentration of their zooplankton prey. The movements of individual bowheads while they occupy these late summer habitats are less well known; our knowledge is based on photographic evidence and limited tagging studies conducted from 1982 to 2000. In this study, 85% (17) of the 20 satellite-tagged whales that could have spent some time in the Canadian portion of the Beaufort Sea during late summer 2006 to 2012 spent all or part of August and September there. We analyzed location data for 16 whales, using a two-state switching correlated random walk (CRW) behavioural model, and classified locations in the Canadian waters as associated with lingering behaviour (inferred foraging) or directed travel. We found that these whales spent the greatest proportion of their time lingering (59%), followed by traveling (22%), and transitioning between lingering and traveling (19%). Using only lingering locations for these tagged whales in all study years pooled, we calculated kernel densities and defined five areas within the 75% density contour as aggregation areas. Together, the five aggregation areas we defined comprised 25 341 km2, 14.1% of the total area used by these tagged whales in Canadian waters during August and September of the deployment years. Three aggregation areas were located in shallow waters of the Beaufort Sea Shelf and were used almost exclusively by immature tagged whales in our sample. Two other aggregation areas were observed, one in Darnley Bay and one in Viscount Melville Sound in the Canadian Arctic Archipelago. Each of these was used by one mature whale. Tagged whales were observed to use one or two aggregation areas in a single season, and rarely more. The proportion of lingering time spent in each aggregation area was highly variable among individuals. The largest aggregation area (10 877 km2), located over the Beaufort Shelf north of the Tuktoyaktuk Peninsula (5 – 52 m depth), was used by 13 of the 16 tagged whales, almost exclusively by the immature whales, including three of four that were tracked in two consecutive summers. The Beaufort Shelf overall (and possibly the Tuktoyaktuk Shelf, including the Outer Shelf, in particular) was especially important for immature bowhead whales, while mature whales used habitats beyond the Beaufort Shelf during late summer. Findings may be important to inform both decisions on management and mitigative actions relating to bowhead whale use of the Beaufort Shelf and studies that aim to improve our understanding of the prey base of BCB bowhead whales in the Canadian Beaufort Sea region.

Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection.

The advent of two-photon microscopy now reveals unprecedented, detailed spatio-temporal data on cellular motility and interactions in vivo. Understanding cellular motility patterns is key to gaining insight into the development and possible manipulation of the immune response. Computational simulation has become an established technique for understanding immune processes and evaluating hypotheses in the context of experimental data, and there is clear scope to integrate microscopy-informed motility dynamics. However, determining which motility model best reflects in vivo motility is non-trivial: 3D motility is an intricate process requiring several metrics to characterize. This complicates model selection and parameterization, which must be performed against several metrics simultaneously. Here we evaluate Brownian motion, Lévy walk and several correlated random walks (CRWs) against the motility dynamics of neutrophils and lymph node T cells under inflammatory conditions by simultaneously considering cellular translational and turn speeds, and meandering indices. Heterogeneous cells exhibiting a continuum of inherent translational speeds and directionalities comprise both datasets, a feature significantly improving capture of in vivo motility when simulated as a CRW. Furthermore, translational and turn speeds are inversely correlated, and the corresponding CRW simulation again improves capture of our in vivo data, albeit to a lesser extent. In contrast, Brownian motion poorly reflects our data. Lévy walk is competitive in capturing some aspects of neutrophil motility, but T cell directional persistence only, therein highlighting the importance of evaluating models against several motility metrics simultaneously. This we achieve through novel application of multi-objective optimization, wherein each model is independently implemented and then parameterized to identify optimal trade-offs in performance against each metric. The resultant Pareto fronts of optimal solutions are directly contrasted to identify models best capturing in vivo dynamics, a technique that can aid model selection more generally. Our technique robustly determines our cell populations’ motility strategies, and paves the way for simulations that incorporate accurate immune cell motility dynamics.

The Correlated Random Walk and the Rise of Movement Ecology

Understanding why, how, and when animals move is essential to many areas of ecology and related fields. Indeed, key aspects of animal behavior, population genetics, biological control, predator–prey dynamics, ecosystem engineering, and conservation biology all hinge upon knowing what critters are moving from where to where in a landscape, including information on how quickly, how regularly, and by what route they travel. The complexities involved in such processes have spawned tremendous efforts in both field research (where goals include measuring and characterizing such movements) and theoretical research (where goals include exploring the nature and potential consequences of movement). Ecologists today routinely receive some training in both empirical and theoretical research, and in the role of statistical analyses and model fitting as a way of linking the two perspectives. However, that has not always been the case. Spatial questions in ecology were long an area where the gulf between theory and reality was particularly wide. In part, this was due to the additional mathematical challenges of spatial models, but it also due to the perhaps greater technological challenges of measuring and contextualizing animal movements.