On the possibility of identifying human subjects using behavioural complexity analyses

Background: Identification of human subjects using a geometric approach to complexity analysis of behavioural data is designed to provide a basis for a more precise diagnosis leading towards personalised medicine. Methods: The approach is based on capturing behavioural time-series that can be characterized by a fractional dimension using non-invasive longer-time acquisitions of heart rate, perfusion, blood oxygenation, skin temperature, relative movement and steps frequency. The geometry based approach consists in the analysis of the area and centroid of convex hulls encapsulating the behavioural data represented in Euclidian index spaces based on the scaling properties of the self-similar normally distributed behavioural time-series of the above mentioned quantities. Results: An example demonstrating the presented approach of behavioural fingerprinting is provided using sensory data of eight healthy human subjects based on approximately fifteen hours of data acquisition. Our results show that healthy subjects can be factorized to different similarity groups based on a particular choice of a convex hull in the corresponding Euclidian space. One of the results indicates that healthy subjects share only a small part of the convex hull pertaining to a highly trained individual from the geometric comparison point of view. Similarly, the presented pair-wise individual geometric similarity measure indicates large differences among the subjects suggesting the possibility of neuro-fingerprinting. Conclusions: Recently introduced multi-channel body-attached sensors provide a possibility to acquire behavioural time-series that can be mathematically analysed to obtain various objective measures of behavioural patterns yielding behavioural diagnoses favouring personalised treatments of, e.g., neuropathologies or aging.     

LoCoH: nonparameteric kernel methods for constructing home ranges and utilization distributions

Parametric kernel methods currently dominate the literature regarding the construction of animal home ranges (HRs) and utilization distributions (UDs). These methods frequently fail to capture the kinds of hard boundaries common to many natural systems. Recently a local convex hull (LoCoH) nonparametric kernel method, which generalizes the minimum convex polygon (MCP) method, was shown to be more appropriate than parametric kernel methods for constructing HRs and UDs, because of its ability to identify hard boundaries (e.g., rivers, cliff edges) and convergence to the true distribution as sample size increases. Here we extend the LoCoH in two ways: "fixed sphere-of-influence," or r-LoCoH (kernels constructed from all points within a fixed radius r of each reference point), and an "adaptive sphere-of-influence," or a-LoCoH (kernels constructed from all points within a radius a such that the distances of all points within the radius to the reference point sum to a value less than or equal to a), and compare them to the original "fixed-number-of-points," or k-LoCoH (all kernels constructed from k-1 nearest neighbors of root points). We also compare these nonparametric LoCoH to parametric kernel methods using manufactured data and data collected from GPS collars on African buffalo in the Kruger National Park, South Africa. Our results demonstrate that LoCoH methods are superior to parametric kernel methods in estimating areas used by animals, excluding unused areas (holes) and, generally, in constructing UDs and HRs arising from the movement of animals influenced by hard boundaries and irregular structures (e.g., rocky outcrops). We also demonstrate that a-LoCoH is generally superior to k- and r-LoCoH (with software for all three methods available at http://locoh.cnr.berkeley.edu).     

The analysis of space use patterns.

In this paper we describe and test a new method for characterizing the space use patterns of individual animals on the basis of successive locations of marked individuals. Existing methods either do not describe space use in probabilistic terms, e.g. the maximum distance between locations or the area of the convex hull of all locations, or they assume a priori knowledge of the probabilistic shape of each individual's use pattern, e.g. bivariate or circular normal distributions. We develop a method for calculating a probability of location distribution for an average individual member of a population that requires no assumptions about the shape of the distribution (we call this distribution the population utilization distribution or PUD). Using nine different sets of location data, we demonstrate that these distributions accurately characterize the space use patterns of the populations from which they were derived. The assumption of normality is found to result in a consistent and significant overestimate of the area of use. We then describe a function which relates probability of location to area (termed the MAP index) which has a number of advantages over existing size indices. Finally, we show how any quantities such as the MAP index derived from our average distributions can be subjected to standard statistical tests of significance.     

Effects of Point Pattern Shape on Home-Range Estimates

Abstract: Home-range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home-range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home-range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space-use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home-range estimation: 1) KDE with reference bandwidths, 2) KDE with least-squares cross-validation, 3) KDE with plug-in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home-range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home-range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home-range estimation.     

Minimum convex hull mass estimations of complete mounted skeletons

Body mass is a critical parameter used to constrain biomechanical and physiological traits of organisms. Volumetric methods are becoming more common as techniques for estimating the body masses of fossil vertebrates. However, they are often accused of excessive subjective input when estimating the thickness of missing soft tissue. Here, we demonstrate an alternative approach where a minimum convex hull is derived mathematically from the point cloud generated by laser-scanning mounted skeletons. This has the advantage of requiring minimal user intervention and is thus more objective and far quicker. We test this method on 14 relatively large-bodied mammalian skeletons and demonstrate that it consistently underestimates body mass by 21 per cent with minimal scatter around the regression line. We therefore suggest that it is a robust method of estimating body mass where a mounted skeletal reconstruction is available and demonstrate its usage to predict the body mass of one of the largest, relatively complete sauropod dinosaurs: Giraffatitan brancai (previously Brachiosaurus) as 23200 kg.     

A scaled line-based kernel density estimator for the retrieval of utilization distributions and home ranges from GPS movement tracks

Utilization distributions (UDs) can be used to describe the intensity with which an animal or human has used a certain geographical location. Within the domain of wildlife ecology, a density distribution model represents one way to describe an animals' home range. Several methods have been developed to derive UDs, and subsequently home ranges. Most of these methods, e.g. kernel density estimation (KDE), and local convex hull methods, have been developed with point-based datasets in mind, and do not utilize additional information that comes with GPS-based tracking data (e.g., temporal information). To employ such additional information we extend the point-based KDE approach to work with sequential GPS-point tracks, the outcome of which is a line-based KDE. We first describe the design criteria for the line-KDE algorithm. Then we introduce the basic modeling approach and its refinement through the introduction of a scaling function. This scaling function modifies the utilization distribution so that a bone-like probability distribution for a single GPS track segment is obtained. Finally we compare the estimated utilization distributions and home ranges for two datasets derived using our line-KDE approach with those obtained using the point-KDE and Brownian Bridge (BB) approaches. Advantages of the line-based KDE by design are (i) a better representation of utilization density near GPS points when compared against the BB approach, and (ii) the ability to model and retain movement corridors when compared against point-KDE.     

Estimating utilization distributions with kernel versus local convex hull methods

Estimates of utilization distributions (UDs) are used in analyses of home-range area, habitat and resource selection, and social interactions. We simulated data from 12 parent UDs, representing 3 series of increasingly intense space-use patterns (clustering of points around a home site, restriction of locations to a network of nodes and corridors, and dominance of a central hole in the UD) and compared the ability of kernel density estimation (KDE) and local convex hull (LCH) construction to reconstruct known UDs from samples of 10, 50, 250, and 1,000 location points. For KDE, we considered 4 bandwidth selectors: the reference bandwidth, least-squares cross-validation (LSCV), direct plug-in (DPI), and solve-the-equation (STE). For the sample sizes and UD patterns tested here, KDE achieved significantly higher volume-of-intersection (VI) scores with known parent UDs than did LCH; KDE also provided less biased home-range area estimates under many conditions. However, LCH minimized the UD volume that occurred outside the true home range boundary (V_out). Among the KDE bandwidth estimators, relative performance depended on the type and intensity of space use patterns, sample size, and the metric used to evaluate performance. Biologists should use KDE for UD and home range estimation within a probabilistic context, unless their objective is to exclude potentially unused areas by defining the area delimited by data. © 2011 The Wildlife Society.     

A local nearest-neighbor convex-hull construction of home ranges and utilization distributions

We describe a new method for estimating the area of home ranges and constructing utilization distributions (UDs) from spatial data. We compare our method with bivariate kernel and α-hull methods, using both randomly distributed and highly aggregated data to test the accuracy of area estimates and UD isopleth construction. The data variously contain holes, corners, and corridors linking high use areas. Our method is based on taking the union of the minimum convex polygons (MCP) associated with the k−1 nearest neighbors of each point in the data and, as such, has one free parameter k. We propose a "minimum spurious hole covering" (MSHC) rule for selecting k and interpret its application in terms of type I and type II statistical errors. Our MSHC rule provides estimates within 12% of true area values for all 5 data sets, while kernel methods are worse in all cases: in one case overestimating area by a factor of 10 and in another case underestimating area by a factor of 50. Our method also constructs much better estimates for the density isopleths of the UDs than kernel methods. The α-hull method does not lead directly to the construction of isopleths and also does not always include all points in the constructed home range. Finally we demonstrate that kernel methods, unlike our method and the α-hull method, does not converges to the true area represented by the data as the number of data points increase.     

Density dependence,territoriality, and divisibility of resources: from optimality models to population processes

Species differ enormously in their territorial systems. Some species defend only small areas surrounded by undefended space, while others defend large contiguous territories. Using an optimization approach, we show that this variation can be explained from the density of two types of resources: divisible and nondivisible. We assume that benefits of territories are monotonously related to the defended amount of divisible resources (hereafter called food). In contrast, no benefits are obtained without a nondivisible resource (hereafter called nest site) in the territory, while more than one nest site does not further increase the benefits. The optimal territory size depends on the relative abundance of these resources. With a low density of nest sites, the optimal territory size is small and includes only the nest site. If the density of nest sites is relatively large, the optimal territory size is high, and territories are contiguous. Competition for these different resources yields contrasting patterns of how populations are regulated. If there is mainly competition for nest sites, we expect density-dependent exclusion through territoriality and no density-dependent reproduction. When competition is mainly for food, we expect density-dependent reproduction because optimal territory size will be compressed at higher densities, resulting in lower reproductive success. These predicted patterns indeed are observed in some well-studied passerine species for which both the territorial system and the occurrence of density dependence is known.     

Assessing the influence of environmental heterogeneity on bird spacing patterns: a case study with two raptors

Testing for aggregation or regularity in point patterns is difficult in the presence of spatial variation in abundance due to environmental heterogeneity. Using a recently developed method generalizing Ripley's K function for non homogeneous point patterns, we test the aggregation of the nests in two species of birds (little owl and Montagu's harrier) exhibiting heterogeneous distributions in response to landscape structure. We compare the results obtained under different null models accounting for environmental heterogeneity at large and/or small spatial scales.
Whereas both species were initially found to form clusters at some scale, taking spatial heterogeneity into account revealed that 1) territorial little owls showed no clustering of territories when habitat availability was considered; 2) semi-colonial harriers still formed significant clusters, but part of the aggregation in this species could be explained by landscape structure alone. Our results highlight that it is feasible and highly recommended to account for non-stationarity when testing for aggregation. Further, provided that sufficient knowledge of the study system is available, this approach helps to identify behavioural and environmental components of spatial variation in abundance. Additionally, we demonstrate that accounting for large or small-scale heterogeneity affects the perception of spacing behaviours differently, so that both need to be considered.     

Comparing amber fossil assemblages across the Cenozoic

To justify faunistic comparisons of ambers that differ botanically, geographically and by age, we need to determine that resins sampled uniformly. Our pluralistic approach, analysing size distributions of 671 fossilized spider species from different behavioural guilds, demonstrates that ecological information about the communities of two well-studied ambers is retained. Several lines of evidence show that greater structural complexity of Baltic compared to Dominican amber trees explains the presence of larger web-spinners. No size differences occur in active hunters. Consequently, we demonstrate for the first time that resins were trapping organisms uniformly and that comparisons of amber palaeoecosystem structure across deep time are possible.     

Territorial intrusion risk and antipredator behaviour: a mathematical model

In territorial animals that hide to avoid predators, a predatory attack creates a conflict because a hiding animal cannot defend its territory from conspecific intruders. When intruders are persistent, a past conspecific intrusion informs a territorial resident that future intrusions by the same animal are likely. Using a mathematical model, I examine the effects that past territorial intrusions can have on antipredator behaviour. Past territorial intrusions rarely affect a resident animal's time to hide (the optimal behaviour is to hide as soon as the predator initiates its attack). In contrast, past intrusions should shorten the length of time during which territory holders remain in hiding, with the magnitude of this effect depending on the time of the predator's attack, the re-intruder's pattern of return, and the intrusion rates of other conspecifics. The results of the model show that we need more information on patterns of re-intruders' behaviour, and emphasize that a similar functional explanation could underlie other behavioural changes following territorial and/or aggressive encounters (such as winner/loser effects or changes in display frequency and territorial vigilance). Differences between my findings and those from previous studies suggest that the trade-off between antipredator behaviour and territorial defence can involve different costs from the trade-off between antipredator behaviour and foraging.     

The Effect of Variability on the Optimal Size of a Feeding Territory

Previous empirical and theoretical work has focused on how feedingterritory size is governed by average levels of food availabilityand intrusion pressure; the potentially important effects ofvariability have not yet been studied in detail. Here I incorporatevariation in food availability and intrusion pressure in somesimple optimality models of territory size. The results showthat the possible effects of variability are diverse, includingboth increase and decrease in territory size. And in some cases,variation in food availability produces qualitatively differenteffects than variation in intrusion pressure.     

The ideal hydrodynamic form of the concavo‐convex productide brachiopod shell

Shiino, Y & Suzuki, Y. 2011: The ideal hydrodynamic form of the concavo‐convex productide brachiopod shell. Lethaia, Vol. 44, pp. 329–343. Water‐flume experiments were performed to determine whether the concavo‐convex Permian brachiopod Waagenoconcha imperfecta was hydrodynamically adapted for feeding. The generation of passive currents inside the valves was observed experimentally. The use of four transparent, hollow polyhedron models, each differing in a single morphological feature, permitted observation of the currents inside the valves and allowed evaluation of the hydrodynamic significance of the ears and the prominent geniculated trail. Regardless of the direction of ambient flow, only the approximate‐imitation model generated a stable flow pattern consisting of inhalation from the ear gapes and exhalation from the anterior trail gape; models lacking or with small changes in these morphological features failed to generate stable flow patterns. The stable flow pattern was probably maintained by a pressure difference between the posterior lower ear gapes (maximum pressure) and the anterior trail gape (minimum pressure). Notably, bilaterally rotating internal currents formed parallel to the brachial ridges; such flow patterns would facilitate the capture of food particles by the animal via tentacles on its lophophore, which is most likely were located on the brachial ridges. Our results demonstrate that the immobile brachiopod W. imperfecta, an animal incapable of widely opening its valves, probably fed on the passive internal currents generated by its shell form. This unique valve morphology appears to be perfectly adapted from a hydrodynamic point of view. □Biomechanics, ecomorphology, evolution, morphological disparity, Productidina, suspension feeder.     

Individual and spatio-temporal variations in the home range behaviour of a long-lived, territorial species

Despite the fact that investigations of home range behaviour have exponentially evolved on theoretical, analytical and technological grounds, the factors that shape animal home range behaviour still represent an unsolved question and a challenging field of research. However, home range studies have recently begun to be approached under a new integrated conceptual framework, considering home range behaviour as the result of the simultaneous influences of temporal, spatial and individual-level processes, with potential consequences at the population level. Following an integrated approach, we studied the influence of both external and internal factors on variations in the home range behaviour of 34 radiotagged eagle owl (Bubo bubo) breeders. Home range behaviour was characterised through complementary analysis of space use, movement patterns and rhythms of activity at multiple spatio-temporal scales. The effects of the different phases of the biological cycle became considerably evident at the level of movement patterns, with males travelling longer distances than females during incubation and nestling periods. Both external (i.e. habitat structure and composition) and internal (i.e. sex and health state) factors explained a substantial amount of the variation in home range behaviour. At the broader temporal scale, home range and core area size were negatively correlated with landscape heterogeneity. Males showed (1) smaller home range and core area sizes, (2) more complex home range internal structure and (3) higher rates of movement. The better the physiological condition of the individuals, the simpler the internal home range structure. Finally, inter- and intra-individual effects contributed to shaping space use and movement patterns during the biological cycle. Because of the plurality of behavioural and ecological processes simultaneously involved in home range behaviour, we claim that an integrative approach is required for adequate investigation of its temporal and spatial variation.     

Role of demographic dynamics and conflict in the population-area relationship for human languages

Many patterns displayed by the distribution of human linguistic groups are similar to the ecological organization described for biological species. It remains a challenge to identify simple and meaningful processes that describe these patterns. The population size distribution of human linguistic groups, for example, is well fitted by a log-normal distribution that may arise from stochastic demographic processes. As we show in this contribution, the distribution of the area size of home ranges of those groups also agrees with a log-normal function. Further, size and area are significantly correlated: the number of speakers p and the area a spanned by linguistic groups follow the allometric relation a proportional to p2, with an exponent z varying accross different world regions. The empirical evidence presented leads to the hypothesis that the distributions of p and a, and their mutual dependence, rely on demographic dynamics and on the result of conflicts over territory due to group growth. To substantiate this point, we introduce a two-variable stochastic multiplicative model whose analytical solution recovers the empirical observations. Applied to different world regions, the model reveals that the retreat in home range is sublinear with respect to the decrease in population size, and that the population-area exponent z grows with the typical strength of conflicts. While the shape of the population size and area distributions, and their allometric relation, seem unavoidable outcomes of demography and inter-group contact, the precise value of z could give insight on the cultural organization of those human groups in the last thousand years.     

Home range size estimates of red deer in Germany: environmental,individual and methodological correlates

Home range size (HRS) is the fundamental measure of space use by animals. Despite the importance of the home range concept, there is no consensus on how to estimate the HRS of animals. Assessments of the performance of commonly applied HRS estimators have largely been based on simulated data or on location data of few sample individuals occupying one study area. To empirically evaluate the impact of supplementary feeding, habitat composition, red deer sex, and estimation method (minimum convex polygon (MCP), kernel density estimator (KDE) and α-local convex hull (α-LoCoH)) on HRS, we analysed the data of 183 annual red deer home ranges using a mixed modelling approach. Red deer HRSs were smallest in areas with substantial supplementary feeding, intermediate in areas with closed forest cover but no supplementary feeding, and largest in fragmented landscapes where supplementary feeding rarely occurs. Consistently, male HRSs were larger than female HRSs. While MCP- and KDE-HRS estimates were roughly similar, estimates from the α-LoCoH method were substantially smaller than those of MCP and KDE. Analyses of 342 seasonal HRS largely reflected patterns of annual HRS. However, seasonal HRS differed between seasons and red deer sex. In areas with no or little feeding, red deer adjusted HRS seasonally, whereas red deer supplied with supplementary food during winter did not alter their HRS seasonally. Our study suggests that supplementary feeding and habitat configuration strongly affect the spatial ecology of red deer; this might have considerable sanitary and ecological implications. We suggest that sex differences in annual space use extent are proportional along a resource gradient but are mediated by seasons. Finally, method-related variation in space use studies of animals needs to be considered more cautiously.     

Status-dependent behavioural sex change in a polygynous coral-reef fish, Halichoeres melanurus

To examine how a change in an individual's social status could influence its behavioural sex, we conducted male "removal-and-return" experiments in the polygynous wrasse, Halichoeres melanurus. This coral-reef fish is a protogynous hermaphrodite: the largest female (LF) living in a male's territory typically completes functional sex change within 2–3 weeks after the male's disappearance. In this experiment we removed males from their territories just prior to spawning time, about 1 h before sunset. In 12 of 30 trials, the resident LF spawned in the male role with smaller females, 21–98 min after male removal. Previous research suggests the LF should readily adopt male sexual behaviour to retain smaller females as future mates. However, the LFs of smaller body size were less likely to immediately perform male-role behaviour. This could be related to females' preference for larger mates: smaller LFs would be less likely to be chosen by other females, even if they could complete sex change and defend a territory. When a male was returned immediately after an occurrence of female–female spawning, the LF subsequently spawned in the female role with the returned male (6 of 12 trials). It could be adaptive for the LFs to accept a larger male as a mate rather than to fight against it. Thus, behavioural sex is reversible in H. melanurus, changing rapidly with social status. Electronic Publication     

Sample Size in the Study of Behaviour

The choice of an appropriate sample size for a study is a notoriously neglected topic in behavioural research, even though it is of utmost importance and the rules of action are more than clear – or are they? They may be clear if a formal power analysis is concerned. However, with the educated guesswork usually applied in behavioural studies there are various trade‐offs, and the degrees of freedom are extensive. An analysis of 119 original studies haphazardly chosen from five leading behavioural journals suggests that the selected sample size reflects an influence of constraints more often than a rational optimization process. As predicted, field work involves greater samples than studies conducted in captivity, and invertebrates are used in greater numbers than vertebrates when the approach is similar. However, it seems to be less important for determining the number of subjects if the study employs observational or experimental means. This is surprising because in contrast to mere observations, experiments allow to reduce random variation in the data, which is an essential precondition for economizing on sample size. By pointing to inconsistent patterns the intention of this article is to induce thought and discussion among behavioural researchers on this crucial issue, where apparently neither standard procedures are applied nor conventions have yet been established. This is an issue of concern for authors, referees and editors alike.     

Song matching in a long-lived,sedentary bird with a low song rate: The importance of song type,song duration and intrusion

Territorial songbirds often match the song features or singing patterns of rivals, commonly as an aggressive signal. Most studies of song matching have been on Northern Hemisphere species with short lifespans and high song rates, but vocal matching is predicted to be affected both by longevity and territorial stability. We studied song matching in males of the white-browed scrubwren, Sericornis frontalis, a long-lived, sedentary, territorial Australian songbird. We quantified natural song rate and diversity, and then conducted three playback experiments to test: (a) whether males match by song type; (b) how they respond physically and vocally to territorial intrusion; and (c) whether they match by song length, and use it as an agonistic signal. Males naturally had very low song rates, singing on average less than three times per hour, and moderate repertoires, with an estimated mean of 17.5 song types for individual males. Males did not engage in extended counter-singing bouts. The first experiment showed that males matched the song type of immediate neighbours almost 90% of the time, if that type was in their repertoire. The remaining experiments revealed that song-type matching was an aggressive signal; males responded more aggressively to, and were more likely to match, playback simulating a neighbour's territorial intrusion than song from their shared boundary. Males did not match songs by length, but they produced longer songs after simulated intrusion. Males also responded more aggressively to playback of longer songs that simulated intrusion, but less aggressively to longer songs from the territory boundary. Overall, we show that sedentary, long-lived songbirds with low song rates, can use song-type matching as an aggressive signal to communicate with neighbours and intruders. Song length had a different role in communication, possibly related to individual quality or territory ownership.