The Weierstrassian movement patterns of snails

Foraging in heterogeneous landscapes: variation in movement patterns of a tropical sand-bubbler crab

Acquiring food in heterogeneous landscapes presents a challenge to many foragers, as searching for food in an optimal manner is difficult in spatially and temporally variable environments. Investigating individual foraging patterns can elucidate how environmental variations at different scales constrain or select for energy-optimizing movements, which can inform conservation and management strategies by identifying spatio-temporal variations in species’ habitat use. To test how such movements vary with environmental conditions, we investigated foraging patterns of the deposit-feeding sand-bubbler crab, Scopimera intermedia Balss, 1934 at multiple spatial and temporal scales on soft sediment shores in Hong Kong. On a broad, annual, scale the crabs produced foraging tracks of different length and foraged over different areas around their burrows between hot and cool seasons. Although foraging movements of the crabs were slower and more restricted during the cool season, probably due to low environmental temperatures, foraging areas during the hot season were larger but limited by increasing conspecific interactions. Over a smaller scale at which the crabs make movement decisions, parameters such as turning angle and speed were variable, even within individual foraging excursions. Such variations appeared to be responses to small-scale variations in sediment food patches, which resulted in the crabs employing multiple movement modes. This context-dependent foraging strategy enables the crabs to feed for a longer time in food-rich patches compared with a fixed strategy and is, therefore, critical for species living in environments such as intertidal sediments, where food distribution is heterogeneous and foraging time is constrained by the tide.

On the mean path length invariance property for random walks of animals in open environment

Random walks are common in nature and are at the basis of many different phenomena that span from neutrons and light scattering to the behaviour of animals. Despite the evident differences among all these phenomena, theory predicts that they all share a common fascinating feature known as Invariance Property (IP). In a nutshell, IP means that the mean length of the total path of a random walker inside a closed domain is fixed by the geometry and size of the medium. Such a property has been demonstrated to hold not only in optics, but recently also in the field of biology, by studying the movement of bacteria. However, the range of validity of such a universal property, strictly linked to the fulfilment of equilibrium conditions and to the statistical distributions of the steps of the random walkers, is not trivial and needs to be studied in different contexts, such as in the case of biological entities occupied in random foraging in an open environment. Hence, in this paper the IP in a virtual medium inside an open environment has been studied by using actual movements of animals recorded in nature. In particular, we analysed the behaviour of a grazer mollusc, the chiton Acanthopleura granulata. The results depart from those predicted by the IP when the dimension of the medium increases. Such findings are framed in both the condition of nonequilibrium of the walkers, which is typical of animals in nature, and the characteristics of actual animal movements.

Rethinking the Prevalence and Relevance of Chaos in Ecology

Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.

Establishing a High-Throughput Locomotion Tracking Method for Multiple Biological Assessments in Tetrahymena

Protozoa are eukaryotic, unicellular microorganisms that have an important ecological role, are easy to handle, and grow rapidly, which makes them suitable for ecotoxicity assessment. Previous methods for locomotion tracking in protozoa are largely based on software with the drawback of high cost and/or low operation throughput. This study aimed to develop an automated pipeline to measure the locomotion activity of the ciliated protozoan Tetrahymena thermophila using a machine learning-based software, TRex, to conduct tracking. Behavioral endpoints, including the total distance, velocity, burst movement, angular velocity, meandering, and rotation movement, were derived from the coordinates of individual cells. To validate the utility, we measured the locomotor activity in either the knockout mutant of the dynein subunit DYH7 or under starvation. Significant reduction of locomotion and alteration of behavior was detected in either the dynein mutant or in the starvation condition. We also analyzed how Tetrahymena locomotion was affected by the exposure to copper sulfate and showed that our method indeed can be used to conduct a toxicity assessment in a high-throughput manner. Finally, we performed a principal component analysis and hierarchy clustering to demonstrate that our analysis could potentially differentiate altered behaviors affected by different factors. Taken together, this study offers a robust methodology for Tetrahymena locomotion tracking in a high-throughput manner for the first time.

Weierstrassian Lévy walks are a by-product of crawling

Weierstrassian Lévy walks are one of the simplest random walks which do not satisfy the central limit theorem and have come to epitomize scale invariance even though they were initially regarded as being a mathematical abstraction. Here, I show how these Lévy walks can be generated intrinsically as a by-product of crawling, a common but ancient form of locomotion. This may explain why Weierstrassian Lévy walks provide accurate representations of the movement patterns of a diverse group of molluscs-certain mussels, mud snails and limpets. I show that such movements are not specific to molluscs as they are also evident in Drosophila larvae. The findings add to the growing realization that there are many idiosyncratic, seemingly accidental pathways to Lévy walking. And that the occurrence of Lévy walks need not be attributed to the execution of an advantageous searching strategy.

Intermittent inverse-square Lévy walks are optimal for finding targets of all sizes

Lévy walks are random walk processes whose step lengths follow a long-tailed power-law distribution. Because of their abundance as movement patterns of biological organisms, substantial theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous. However, despite extensive research, there is currently no mathematical proof indicating that Lévy walks are, in any manner, preferable strategies in higher dimensions than one. Here, we prove that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely efficient at finding sparse targets of arbitrary size and shape. Moreover, this holds even under the weak model of intermittent detection. Conversely, any other intermittent Lévy walk fails to efficiently find either large targets or small ones. Our results shed new light on the Lévy foraging hypothesis and are thus expected to affect future experiments on animals performing Lévy walks.

Lévy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long "flights". Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for "reprogramming" the Lévy walks into either diffusive or ballistic movements.