Developing Children’s Observation Skills Using a Fractal Pattern from Nature

Abstract

This study aimed to support the development of the scientific observation skills of children at an early age using a pattern selected from nearby nature. For this purpose, a simple, innovative and authentic observation activity was designed using thorny burnet (Sarcopoterium spinosum L.), a plant unique to the Mediterranean region. The activity was conducted in a preschool institution with six-year-old children in the class hours of a weekly science course in three different environments (in-class, out-of-class, and out-of-school), and seven stages. In this activity, which aimed to transform children’s natural/spontaneous observation skills into scientific observation skills, patterns were revealed through systematic and sequential observation and drawings. At the end of the activity, it was found that the children had developed skills related to breaking a whole into its parts and putting the parts together according to patterns, making detailed observations, and systematic data collection, and they successfully implemented these skills outside the classroom and school.     

北美车前(Plantago Virginica)和车前(P.asiatica)分布格局的分形分析

北美车前 (ＰｌａｎｔａｇｏｖｒｉｇｉｎｉｃａＬ .)是我国东南地区的一种外来杂草 ,该杂草在浙江、江苏、上海、江西等省区有分布 ,多见于田梗路边、住宅四周、抛荒地、公路两侧等人畜出没频繁的地段 ,其种群生长迅速 ,呈现出生态爆发态势 ,是一种典型的生态入侵种。分形理论已被广泛地应用于自然科学、社会科学中的众多领域。在生态学领域 ,应用分形维数能够客观地表达种群的分布式样 ,同时也能反映种群占有空间、资源利用的能力[1～ 6 ] 。本研究以新入侵种北美车前为对象 ,并与我国境内分布较广的杂草车前 (Ｐ .ａｓｉａｔｉｃａ)作比…     

What's your move? Movement as a link between personality and spatial dynamics in animal populations

Recent studies have established the ecological and evolutionary importance of animal personalities. Individual differences in movement and space‐use, fundamental to many personality traits (e.g. activity, boldness and exploratory behaviour) have been documented across many species and contexts, for instance personality‐dependent dispersal syndromes. Yet, insights from the concurrently developing movement ecology paradigm are rarely considered and recent evidence for other personality‐dependent movements and space‐use lack a general unifying framework. We propose a conceptual framework for personality‐dependent spatial ecology. We link expectations derived from the movement ecology paradigm with behavioural reaction‐norms to offer specific predictions on the interactions between environmental factors, such as resource distribution or landscape structure, and intrinsic behavioural variation. We consider how environmental heterogeneity and individual consistency in movements that carry‐over across spatial scales can lead to personality‐dependent: (1) foraging search performance; (2) habitat preference; (3) home range utilization patterns; (4) social network structure and (5) emergence of assortative population structure with spatial clusters of personalities. We support our conceptual model with spatially explicit simulations of behavioural variation in space‐use, demonstrating the emergence of complex population‐level patterns from differences in simple individual‐level behaviours. Consideration of consistent individual variation in space‐use will facilitate mechanistic understanding of processes that drive social, spatial, ecological and evolutionary dynamics in heterogeneous environments.     

The Quasi-Fractal Structure of Fish Brain Neurons

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.     

Evolution of African mole-rat sociality: burrow architecture, rainfall and foraging in colonies of the cooperatively breeding Fukomys mechowii

African mole rats (Bathyergidae) offer an excellent system with which to test theories relating to the evolution and maintenance of sociality in mammals. The aridity food distribution hypothesis (AFDH) suggests that, within the bathyergids, sociality has evolved in response to patterns of rainfall, its effects on food distribution, and the subsequent costs and risks of foraging and dispersal. Here, in the first detailed study of burrow architecture in a social mole-rat species, with data from 32 burrows, we show that in the giant mole-rat Fukomys mechowii burrow fractal dimension increases with colony size and is higher during the rainy season than during the dry season. The mass of food in the burrow increases with fractal dimension and is higher during the rainy season than during the dry season. These results link for the first time colony size, burrow architecture, rainfall and foraging success and provide support for two assumptions of the AFDH, namely that (1) in arid conditions burrowing may be severely constrained by the high costs of digging; and (2) the potential risks of failing to locate food may be mitigated by increases in colony size.     

Contribution of Ca2+ calmodulin-dependent protein kinase II and mitogen-activated protein kinase kinase to neural activity-induced neurite outgrowth and survival of cerebellar granule cells

In this report we describe our studies on intracellular signals that mediate neurite outgrowth and long-term survival of cerebellar granule cells. The effect of voltage-gated calcium channel activation on neurite complexity was evaluated in cultured cerebellar granule cells grown for 48 h at low density; the parameter measured was the fractal dimension of the cell. We explored the contribution of two intracellular pathways, Ca2+ calmodulin-dependent protein kinase II and mitogen-activated protein kinase kinase (MEK1), to the effects of high [K+ ]e under serum-free conditions. We found that 25 mm KCl (25K) induced an increase in calcium influx through L subtype channels. In neurones grown for 24-48 h under low-density conditions, the activation of these channels induced neurite outgrowth through the activation of Ca2+ calmodulin-dependent protein kinase II. This also produced an increase in long-term neuronal survival with a partial contribution from the MEK1 pathway. We also found that the addition of 25K increased the levels of the phosphorylated forms of Ca2+ calmodulin-dependent protein kinase II and of the extracellular signal-regulated kinases 1 and 2. Neuronal survival under resting conditions is supported by the MEK1 pathway. We conclude that intracellular calcium oscillations can triggered different biological effects depending on the stage of maturation of the neuronal phenotype. Ca2+ calmodulin-dependent protein kinase II activation determines the growth of neurites and the development of neuronal complexity.     

Tunnel geometry of the subterranean termite Reticulitermes grassei （Isoptera： Rhinotermitidae）in response to sand bulk density and the presence of food

The cryptic habits of subterranean termites restricts detailed analysis of their foraging patterns in situ, but the process is evidently dominated by tunnel constructions connecting the nest with woody resources discovered within the territory of each colony. In this study, tunnel formation and orientation were studied experimentally in the termite Reticulitermes grassei （Clement）, using 2-dimensional laboratory foraging arenas con- taining fine sand as the substratum. The building of exploratory tunnels over a 10-day period and the geometry of the resulting network are described. Fractal analysis showed that tunnel geometry had a fractal dimension, regardless of the total length tunnelled whether foragers encountered the food source or not. The bulk density of the sand in the arenas affected the distances tunnelled, with higher density reducing construction, but did not affect tunnel geometry. Tunnels were not discernibly orientated with respect to the positioning of the food source, even in a situation where termites had failed to find the food source at a distance of less than 50 mm, suggesting that volatiles from wood are not attractants.     

Power scaling of ammonitic suture patterns from Cretaceous Ancyloceratina: constraints on septal/sutural complexity

The spatial scaling of 77 hemisutures from 65 species of Cretaceous heteromorphic ammonites was quantified with the fractal box‐counting method. Fractal dimensions within Baculites compressus did not significantly differ between adult hemisutures; however, the juvenile suture of this species did exhibit a significantly lower fractal dimension. This suggests that variation in sutural complexity between explicitly adult ontogenetic stages may not contribute to significant noise in comparisons between other species/morphotypes. High‐spired, three‐dimensionally coiled heteromorphs with a larger degree of septal asymmetry exhibit higher fractal dimensions in outer whorl hemisutures than inner whorl hemisutures due to their elongation and improved space occupation over a larger whorl surface. Three‐dimensionally coiled ammonites also have higher fractal dimensions on average (mean D_b = 1.45) with respect to their 2‐D coiled counterparts (mean D_b = 1.38). All ammonites in this study exhibit a positive trend between sutural complexity and shell size (proxied by whorl height). These relationships suggest that septal frilling is constrained by shell morphology and whorl section geometry during septal morphogenesis. This, in turn, influences the scaling, space‐filling properties and scaling limits of ammonitic suture patterns. Sutural/septal complexity is also found to positively influence the amount of liquid retained in marginal septal recesses. However, as these septa approach larger scales, less cameral liquid is retained per septal mass. This may further explain the positive relationship between sutural complexity and shell size.     

青海云杉(Picea crassifolia)种群格局的分形特征及其影响因素

应用计盒维数、信息维数和关联维数对祁连山主要森林类型青海云杉(Picea crassifolia)种群空间格局进行的研究表明:青海云杉种群格局计盒维数在0.992～1.938之间,平均值为1.716,信息维数在0.996～1.860之间,平均值为1.632, 关联维数在1.418～1.759之间,平均值为1.568.计盒维数与样地海拔和土壤水分含量呈显著的负相关,与样地坡向呈显著的正相关,信息维数与样地海拔呈显著负相关而与坡向呈显著的正相关,关联维数与样地坡度呈显著的负相关,主成分分析表明,海拔和土壤含水量是影响青海云杉种群格局分形维数第一主成分,坡向是第二主成分,坡度是第三主成分,这3个主成分累计解释率为87.6%.