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Quantifying search effort of moving animals at several spatial scales using first-passage time analysis: effect of the structure of environment and tracking systems
使用首次通过时间分析量化多个空间尺度上移动动物的搜索工作：环境结构和跟踪系统的影响
首次发布：2007 年 9 月 5 日 https://doi.org/10.1111/j.1365-2664.2007.01370.x 引用次数：73
Summary 概括
- 1
How and at what spatial scale(s) animals change their movements in relation to their environment is central to several topics in ecology and conservation, including foraging ecology, habitat selection and dispersal. A method (first-passage time analysis, FPT) has recently been proposed to measure changes in movements through the landscape, as an index of search effort at the pertinent spatial scales. This method seems largely applicable to an increasing number of studies using satellite, radio-tracking or global positioning system (GPS), but its limits have not yet been assessed.
动物如何以及在何种空间尺度上改变其相对于环境的运动是生态学和保护领域几个主题的核心，包括觅食生态学、栖息地选择和扩散。最近提出了一种方法（首次通过时间分析，FPT）来测量景观中运动的变化，作为相关空间尺度搜索工作的指标。这种方法似乎在很大程度上适用于越来越多使用卫星、无线电跟踪或全球定位系统（GPS）的研究，但其局限性尚未得到评估。 - 2
Here I used several movement simulations to examine the ability of FPT analysis to detect area-restricted search (ARS) according to different changes in movements, different patch structures and tracking accuracy.
这里我使用了几次运动模拟来检验FPT分析根据不同的运动变化、不同的patch结构和跟踪精度来检测区域限制搜索（ARS）的能力。 - 3
FPT analysis was able to detect changes in movements when both speed and sinuosity changed, or when the animal reacted to patch boundaries. It was also able to detect ARS within the same path at several spatial scales in patches (nested or not) of different sizes.
FPT 分析能够检测速度和蜿蜒度变化时或动物对斑块边界做出反应时的运动变化。它还能够在不同大小的补丁（嵌套或非嵌套）的多个空间尺度上检测同一路径内的 ARS。 - 4
Tracking accuracy affected the detection of ARS by FPT analysis. With the widely used Argos system, a minimum of 13 locations in effective ARS was necessary to detect this behaviour; seven when velocity filtering was applied. Similarly, spatial error in location affected the estimation of the ARS scale value, but the application of velocity filtering reduced this effect.
跟踪精度影响 FPT 分析对 ARS 的检测。对于广泛使用的 Argos 系统，有效 ARS 中至少需要 13 个位置才能检测到这种行为；当应用速度过滤时为七。同样，位置的空间误差影响了ARS尺度值的估计，但速度滤波的应用减少了这种影响。 - 5
Comparisons between a real GPS track and pathways simulating the Argos error showed that the time-sampling rate of locations (due to satellite-pass frequency) decreased the probability of detecting ARS at small scales (<10 km), while the spatial error decreased this probability by >50% across the whole range of scales. A velocity filter enabled significant reductions in this effect.
真实 GPS 轨迹与模拟 Argos 误差的路径之间的比较表明，位置的时间采样率（由于卫星通过频率）降低了小尺度（<10 km）检测到 ARS 的概率，而空间误差则降低了这种概率。在整个尺度范围内概率>50%。速度滤波器可以显着减少这种影响。 - 6
Synthesis and application. Within limits, FPT analysis is highly suitable for animal movement analysis, either to quantify habitat use, or to determine the scale most relevant for describing an ecological system or factors affecting movement decisions. In anticipation of increasing applications of FPT analysis in applied ecology, I provide recommendations for the use of the technique with several tracking methods.
合成与应用。在一定范围内，FPT 分析非常适合动物运动分析，可以量化栖息地的使用，或者确定与描述生态系统或影响运动决策的因素最相关的尺度。预计 FPT 分析在应用生态学中的应用会越来越多，我提供了将该技术与多种跟踪方法一起使用的建议。
Introduction 介绍
Understanding how organisms explore and exploit their environment is a central topic in ecology, and the assessment of factors affecting their movements and habitat use is of great value for conservation. Since the early 1990s there has been an exponential increase in animal-borne satellite-tracking studies using the Argos system (Coyne & Godley 2005) and, more recently, global positioning systems (GPS). Data sets produced using these technologies are autocorrelated in time and space, and pose some analytical problems when studying habitat use (White & Garrott 1990). Rather than eliminating some information about animal movement contained in these data sets (for example, by subsampling every x hours), recent methods enable this dynamic aspect to be accounted for fully. These methods consider changes in animal movement as a response to heterogeneity in the environment resulting from the interaction between animal decisions and landscape properties (Morales et al. 2005), and enable the assessment of underlying ecological mechanisms. Fully accounting for movement is crucial to understanding the links between the behaviour of individuals and landscape-level problems in fundamental ecology (Lima & Zollner 1996), and is essential for conservation and population management (Rushton, Ormerod & Kerby 2004). Furthermore, this approach enables the definition of pertinent scales of interaction between animals and the environment, at which ecological processes operate (Fortin & Agrawal 2005), indicating ecologically meaningful management units in fragmented landscapes.
了解生物体如何探索和利用其环境是生态学的一个中心主题，评估影响其运动和栖息地利用的因素对于保护具有重要价值。自 20 世纪 90 年代初以来，使用 Argos 系统 (Coyne & Godley 2005) 以及最近的全球定位系统 (GPS) 进行的动物卫星跟踪研究呈指数增长。使用这些技术产生的数据集在时间和空间上是自相关的，并且在研究栖息地利用时提出了一些分析问题（White & Garrott 1990）。最近的方法并没有消除这些数据集中包含的有关动物运动的一些信息（例如，通过每 x 小时进行二次采样），而是能够充分考虑这一动态方面。这些方法将动物运动的变化视为对环境异质性的反应，这种异质性是由动物决策和景观特性之间的相互作用产生的（Morales 等人，2005 年），并能够评估潜在的生态机制。充分考虑运动对于理解基础生态学中个体行为和景观水平问题之间的联系至关重要（Lima & Zollner 1996），对于保护和种群管理也至关重要（Rushton, Ormerod & Kerby 2004）。此外，这种方法能够定义动物与环境之间相互作用的相关尺度，生态过程在该尺度上运行（Fortin＆Agrawal 2005），表明支离破碎的景观中具有生态意义的管理单元。
Analysing animal movement follows naturally the development of tracking technology combined with the use of geographic information system tools. It is expected that this new ‘toolbox’ will be used increasingly in ecological and conservation studies, especially because it leads to quantitative understanding of the connection between moving animals and increasingly fragmented landscapes, as well as, ultimately, the consequences of fragmentation for populations (Morales et al. 2005). Analyses of movements are based on the premise that, as the environment is not spatially uniform, animals should react to habitat features and spend more time in areas where resources are more abundant. When resources are distributed in patches (sensu Fauchald 1999), the searching activity of foragers should be concentrated in these high-density areas (e.g. Kareiva & Odell 1987). Thus movements of animals should follow the structure of the environment, exhibiting, for example, a behaviour called area-restricted search (ARS). ARS might arise where an animal increases its turning rate and/or decreases its speed, or where it reacts to changes in resource density (i.e. patch boundary) to stay in the patch (Benhamou & Bovet 1989; Fauchald & Tveraa 2003).
分析动物运动自然伴随着跟踪技术的发展并结合地理信息系统工具的使用。预计这个新的“工具箱”将越来越多地用于生态和保护研究，特别是因为它可以定量了解移动的动物与日益破碎的景观之间的联系，以及最终对种群造成的破碎化后果。莫拉莱斯等，2005）。运动分析的前提是，由于环境在空间上不均匀，动物应该对栖息地特征做出反应，并在资源更丰富的地区花费更多的时间。当资源呈斑块分布时（Fauchald 1999 意义），觅食者的搜寻活动应集中在这些高密度区域（例如 Kareiva & Odell 1987）。因此，动物的运动应该遵循环境的结构，例如表现出一种称为区域限制搜索（ARS）的行为。当动物增加其转向速率和/或降低其速度时，或者当动物对资源密度（即斑块边界）的变化做出反应以留在斑块中时，可能会出现 ARS（Benhamou & Bovet 1989；Fauchald & Tveraa 2003）。
Considering that resources can be distributed in a nested patch hierarchy (Johnson 1980; Kotliar & Wiens 1990), animals should be able to respond to patches at several spatial scales (Fauchald 1999). To understand habitat selection and how organisms exploit their environment, it is crucial to identify the scales of environment–animal interactions (Johnson 1980; Levin 1992), particularly in nested scale systems where large-scale patterns tend to mask fine-scale ones (Fauchald, Erikstad, & Skarsfjord 2000). Novel methods have been used recently to study scale-dependent movements (Johnson et al. 2002; Fauchald & Tveraa 2003; Fritz, Saïd & Weimerskirch 2003; Nams 2005). First-passage time analysis (FPT; Fauchald & Tveraa 2003) has allowed the description of search effort at scales where an animal adopts an ARS behaviour in interaction with a patchy environment. This analysis is based on calculation of the time taken by an animal to cross a circle with a given radius. This circle is moved along the path of the animal with increasing radii as a scale-dependent measure of search effort. FPT analysis has been used successfully on various species in many ecosystems, using different tracking techniques. These include satellite-tracked seabirds (Fauchald & Tveraa 2003; Pinaud & Weimerskirch 2005; Suryan et al. 2006), GPS-collared elks (Frair et al. 2005), and theodolite-tracked bottlenosed dolphins (Bailey & Thompson 2006). It is expected that FPT analysis will be increasingly used, especially for highly migratory, endangered species (Suryan et al. 2006); however, the limits of the technique have yet to be fully explored.
考虑到资源可以在嵌套的斑块层次结构中分布（Johnson 1980；Kotliar & Wiens 1990），动物应该能够在多个空间尺度上对斑块做出反应（Fauchald 1999）。为了了解栖息地选择以及生物体如何利用其环境，确定环境与动物相互作用的尺度至关重要（Johnson 1980；Levin 1992），特别是在嵌套尺度系统中，大尺度模式往往会掩盖小尺度模式（Fauchald） 、埃里克斯塔和斯卡斯峡湾 2000）。最近使用了新方法来研究与尺度相关的运动（Johnson et al. 2002；Fauchald & Tveraa 2003；Fritz, Saïd & Weimerskirch 2003；Nams 2005）。首次通过时间分析（FPT；Fauchald & Tveraa 2003）可以描述动物在与斑驳环境相互作用时采取 ARS 行为的规模的搜索工作。该分析基于动物穿过给定半径的圆所需时间的计算。这个圆圈沿着动物的路径移动，半径不断增加，作为搜索工作量的尺度相关度量。 FPT 分析已使用不同的跟踪技术成功应用于许多生态系统中的各种物种。其中包括卫星追踪的海鸟（Fauchald & Tveraa 2003；Pinaud & Weimerskirch 2005；Suryan et al. 2006）、GPS项圈麋鹿（Frair et al. 2005）和经纬仪追踪的宽吻海豚（Bailey & Thompson 2006）。预计 FPT 分析将得到越来越多的应用，特别是对于高度迁徙的濒危物种（Suryan 等人，2006 年）；然而，该技术的局限性尚未得到充分探索。
Despite their potential value for ecologists and conservationists, the efficiency of techniques including FPT analysis is still under debate, and there remains a need to understand better the limits of their application (Johnson et al. 2006; Nams 2006). Here I present results of different movement simulations to test the limits of FPT analysis. Animals can modify their searching behaviour in different ways, or encounter patches of different sizes, resulting in heterogeneous ARS at different spatial scales during the same movement path (Fauchald 1999). Using different movement simulations, I test (i) the ability of FPT analysis to detect different modes of animal searching behaviour; (ii) the ability to detect ARS behaviour in an environment presenting patches of different sizes; and (iii) the effect of tracking accuracy and time-sampling rate on ARS detection by FPT analysis, especially with the Argos system. As an applied example, FPT analysis is applied to a GPS path of an at-sea, foraging black-browed albatross, Thalassarche melanophris (Temminck), a highly migratory, endangered seabird species (IUCN 2006). Finally, I provide recommendations for the use of FPT analysis in studies using different tracking systems.
尽管它们对生态学家和自然资源保护主义者具有潜在价值，但包括 FPT 分析在内的技术的效率仍然存在争议，并且仍然需要更好地了解其应用的局限性（Johnson 等人，2006 年；Nams 2006）。在这里，我展示了不同运动模拟的结果，以测试 FPT 分析的极限。动物可以以不同的方式修改它们的搜索行为，或者遇到不同大小的斑块，从而导致在同一运动路径中不同空间尺度的异质ARS（Fauchald 1999）。使用不同的运动模拟，我测试了 (i) FPT 分析检测不同动物搜索行为模式的能力； (ii) 在呈现不同大小斑块的环境中检测 ARS 行为的能力； (iii) FPT 分析跟踪精度和时间采样率对 ARS 检测的影响，尤其是 Argos 系统。作为一个应用示例，FPT 分析应用于海上觅食的黑眉信天翁 Thalassarche melanophris (Temminck) 的 GPS 路径，这是一种高度迁徙的濒临灭绝的海鸟物种 (IUCN 2006)。最后，我提供了在使用不同跟踪系统的研究中使用 FPT 分析的建议。
Materials and methods 材料和方法
FPT analysis FPT分析
First-passage time analysis is based on calculating the time taken by an animal to cross a circle with a given radius. Calculations of FPT are repeated along the path of the animal by moving the circle at distance d and for increasing radii r. The relative variance S(r) in FPT is then calculated for the whole path, given by var[log(FPT)], where t(r) is FPT for circle of radius r, and is log-transformed to make the variance S(r) independent of the magnitude of the mean FPT (Fauchald & Tveraa 2003). Maxima in the plot of S(r) in relation to r will suggest the presence of ARS behaviour and indicate the scale, r, at which the animal increased its search effort (Fauchald & Tveraa 2003). FPT analysis can then be used as a scale-dependent measure of search effort, with high FPT values corresponding to high effort.
首次通过时间分析基于计算动物穿过给定半径的圆所花费的时间。通过将圆移动距离 d 并增加半径 r，沿着动物的路径重复 FPT 的计算。然后计算整个路径的 FPT 中的相对方差 S(r)，由 var[log(FPT)] 给出，其中 t(r) 是半径为 r 的圆的 FPT，并进行对数变换以使方差 S (r) 与平均 FPT 的大小无关（Fauchald & Tveraa 2003）。 S(r) 图中与 r 相关的最大值将表明 ARS 行为的存在，并指示动物增加搜索努力的规模 r (Fauchald & Tveraa 2003)。然后，FPT 分析可用作搜索工作量的尺度相关度量，高 FPT 值对应于高工作量。
detection of different search modes by FPT analysis
通过 FPT 分析检测不同的搜索模式
In order to test whether FPT analysis is sensitive to different modes of searching, I simulated a virtual animal moving in an environment with circular patches of a given size. When outside a patch, the animal adopted a relatively straight correlated random walk (CRW) with two spatial units (2 km) moved per time unit (10 min, with a constant speed of 12 km h−1) and a distribution of turning angles between successive moves taken from a Von Mises distribution with K = 250. The Von Mises distribution is a circular normal distribution, with larger K values representing straighter movement paths (Fisher 1993). The simulation started with the animal outside a patch. Once in a patch, the animal adopted a searching behaviour. I tested four different modes of searching within a patch: (i) REFL: the animal was reflected by the boundaries of the patch with a probability of 0·9; (ii) SIN: the animal adopted a tortuous CRW with an increase in sinuosity (K = 5); (iii) SP: the animal adopted a slow CRW by decreasing its speed with a step length of 0·5 km; and (iv) SINSP: the animal changed both its speed (slow CRW with a step length of 0·5 km) and its sinuosity (tortuous CRW with K = 5).
为了测试 FPT 分析是否对不同的搜索模式敏感，我模拟了一个虚拟动物在具有给定大小的圆形斑块的环境中移动。当在斑块之外时，动物采用相对直接的相关随机游走（CRW），每个时间单位（10 分钟，以 12 公里/小时的恒定速度 −1 ）移动两个空间单位（2 公里），并且连续移动之间的转向角度分布，取自 K = 250 的 Von Mises 分布。Von Mises 分布是圆形正态分布，K 值越大表示移动路径越直（Fisher 1993）。模拟从一块区域外的动物开始。一旦进入一块土地，动物就会采取搜索行为。我测试了斑块内四种不同的搜索模式： (i) REFL：动物以 0·9 的概率被斑块的边界反射； (ii) SIN：动物采用曲折的 CRW，蜿蜒度增加 (K = 5)； (iii) SP：动物采用缓慢的 CRW，以 0·5 km 的步长降低速度； (iv) SINSP：动物改变了速度（步长为 0·5 km 的慢速 CRW）和蜿蜒度（K = 5 的曲折 CRW）。
In order to test the influence of patch size (relative to step length), this simulation was performed for each search mode with five different patch radii: 5, 10, 20, 30 and 50 km (2·5, 5, 10, 15 and 25 times the step length), with each path simulated for 400, 500, 600, 800 and 1000 steps, respectively. Patches were distributed regularly in the environment, with an interpatch distance of four times the radius to avoid interference between patches. For each combination of search mode and patch radius, 200 paths were simulated. FPT was calculated every 0·5 km for r varying from 2 to 100 km.
为了测试斑块大小（相对于步长）的影响，对具有五种不同斑块半径的每种搜索模式进行了模拟：5、10、20、30 和 50 km（2·5、5、10、15和25倍步长），每条路径分别模拟400、500、600、800和1000步。斑块在环境中规则分布，斑块间距为半径的四倍，以避免斑块之间的干扰。对于搜索模式和补丁半径的每种组合，模拟了 200 条路径。对于 r 从 2 公里到 100 公里的范围，每 0·5 公里计算一次 FPT。
detection of ARS for different patch sizes
检测不同补丁大小的 ARS
To explore the scale dependencies in S(r) in an environment with patches of different sizes, I simulated ARS associated with circular patches of two different radii (10 and 30 km). As these dependencies in FPT variance could differ in a nested patch structure (Fauchald 1999; Fauchald & Tveraa 2003), two different patterns were simulated. In the exclusive patch structure (ES) simulation, small patches were located strictly outside large patches, with a minimal distance of 90 km between centres. In the nested structure (NS), each small patch was included completely in a large patch, with a minimal distance of 90 km between the centres of large patches (to avoid interference between patches). In each type of simulation, 1000 paths (of 700 steps each) were simulated according to Fauchald & Tveraa (2003): an organism performed CRW and ARS behaviour (REFL mode, K = 15) when visiting a patch. This strategy allowed the animal to search across the whole patch area, keeping the correspondence between the patch radius values and those observed in ARS scale with FPT analysis. FPT was calculated every 0·5 km for r varying from 2 to 100 km.
为了探索具有不同大小斑块的环境中 S(r) 的尺度依赖性，我模拟了与两个不同半径（10 公里和 30 公里）的圆形斑块相关的 ARS。由于 FPT 方差中的这些依赖性在嵌套补丁结构中可能有所不同（Fauchald 1999；Fauchald & Tveraa 2003），因此模拟了两种不同的模式。在独家斑块结构（ES）模拟中，小斑块严格位于大斑块之外，中心之间的最小距离为 90 公里。在嵌套结构（NS）中，每个小斑块完全包含在一个大斑块中，大斑块中心之间的最小距离为90公里（以避免斑块之间的干扰）。在每种类型的模拟中，根据 Fauchald & Tveraa (2003) 模拟了 1000 条路径（每条 700 个步骤）：有机体在访问补丁时执行 CRW 和 ARS 行为（REFL 模式，K = 15）。这种策略允许动物搜索整个斑块区域，保持斑块半径值与通过 FPT 分析在 ARS 尺度中观察到的值之间的对应关系。对于 r 从 2 公里到 100 公里的范围，每 0·5 公里计算一次 FPT。
effect of argos tracking accuracy, filtering and ARS intensity
argos 跟踪精度、过滤和 ARS 强度的影响
I simulated a ‘theoretical’ path with an ARS and added spatial noise due to measurement error to generate a typical observed path according to the error of the tracking system. First, I took parameter values from a study on seabirds using the Argos system as a reference, then extended this approach to take into account spatial errors from other systems.
我使用 ARS 模拟了一条“理论”路径，并添加了由于测量误差而产生的空间噪声，以根据跟踪系统的误差生成典型的观测路径。首先，我使用 Argos 系统作为参考，从海鸟研究中获取参数值，然后扩展此方法以考虑其他系统的空间误差。
First, the theoretical path simulated a virtual animal moving in a straight line (500 km in total). The animal started at a constant speed of 30 km h−1. At the mid-point of the trip (250 km), it stopped for a variable duration (see below) and then moved again at 30 km h−1. This stop simulated an ARS behaviour at very small scale (where r→ 0 km), meaning that, after adding a simulated spatial error in location, the apparent movement around this position was wholly due to the error of the tracking system. The stop (ARS behaviour) duration was set to 1, 2, 3, 5, 7, 10 and 15 h, increasing the number of fixes involved in ARS. Then I simulated typical results obtained from an Argos satellite-tracking study by applying an ‘Argos noise’ to these paths. This procedure was simulated 1000 times for each ARS duration, generating 7 × 1000 paths. Argos noise was considered with two components (Argos 1996): (i) a satellite-pass frequency giving an expected number of locations per day with a different proportion for each localization class (LC) given by Argos; (ii) a spatial error according to each LC, following a normal distribution in longitude and latitude (Vincent et al. 2002; Jonsen, Flemming & Myers 2005). In these simulations, parameter values (see Appendix S1 in Supplementary Material) were chosen according to a mid-latitude data set (n = 234 locations) on wandering albatross Diomedea exulans (L.) in Kerguelen Island (Pinaud & Weimerskirch 2007). Locations were chosen randomly to obtain an average of 16 locations per day (1·5 locations per hour), corresponding to a survey situated at a latitude of 45° (Argos 1996). The spatial error was applied to each location simulating the Argos accuracy: co-ordinates in longitude and latitude of the Argos location were taken from a normal distribution centred at the true location with a standard deviation set for each LC (given in Appendix S1). To study the effect of removing locations with low accuracy, I applied an iterative forward/backward averaging filter to all locations in the focal path (McConnell, Chambers & Fedak 1992). A velocity Vi was associated with the ith location:
首先，理论路径模拟虚拟动物直线移动（总共500公里）。动物以 30 公里/小时的匀速出发 −1 。在行程的中点（250 公里），它停了一段可变的持续时间（见下文），然后再次以 30 公里/小时的速度移动 −1 。该停止点模拟了非常小尺度的 ARS 行为（其中 r→ 0 km），这意味着在添加模拟位置空间误差后，该位置周围的明显运动完全是由于跟踪系统的误差造成的。停止（ARS 行为）持续时间设置为 1、2、3、5、7、10 和 15 小时，增加了 ARS 涉及的修复数量。然后，我通过对这些路径应用“Argos 噪声”来模拟从 Argos 卫星跟踪研究中获得的典型结果。对于每个 ARS 持续时间，该过程被模拟 1000 次，生成 7 × 1000 条路径。 Argos 噪声被认为有两个组成部分（Argos 1996）：（i）卫星通过频率给出了每天的预期位置数量，其中 Argos 给出的每个定位类别（LC）具有不同的比例； (ii) 根据每个 LC 的空间误差，遵循经度和纬度的正态分布（Vincent 等人，2002 年；Jonsen、Flemming 和 Myers，2005 年）。在这些模拟中，参数值（参见补充材料中的附录 S1）是根据凯尔盖朗岛流浪信天翁 Diomedea exulans (L.) 的中纬度数据集（n = 234 个位置）选择的（Pinaud & Weimerskirch 2007）。随机选择位置，平均每天获得 16 个位置（每小时 1·5 个位置），对应于位于纬度 45° 的调查（Argos 1996）。 将空间误差应用于模拟 Argos 精度的每个位置：Argos 位置的经度和纬度坐标取自以真实位置为中心的正态分布，并为每个 LC 设置标准差（在附录 S1 中给出）。为了研究去除低精度位置的效果，我对焦点路径中的所有位置应用了迭代前向/后向平均滤波器（McConnell、Chambers & Fedak 1992）。 速度 V 与第 i 个位置相关：
(eqn 1) （等式1）where vi,j is the velocity between successive locations i and j. This velocity filtering was applied to the 7000 paths. Locations with Vi > 100 km h−1 (value for wandering albatross, Weimerskirch, Salamolard & Jouventin 1992) were rejected. FPT was then calculated every 0·5 km for radius r varying from 1 to 200 km.
其中 v i,j 是连续位置 i 和 j 之间的速度。此速度过滤应用于 7000 个路径。 V > 100 km h −1 的位置（流浪信天翁的值，Weimerskirch、Salamolard & Jouventin 1992）被拒绝。然后，半径 r 从 1 公里到 200 公里不等，每 0·5 公里计算一次 FPT。
To generalize the effect of location accuracy on estimation of ARS scale by FPT analysis, I created a second set of simulations of a virtual animal moving in a straight line (speed 30 km h−1) for 200 km with a stop of 10 h in the middle. Locations were taken every 30 min. Normal error was applied to these locations, with a standard deviation (mimicking the location accuracy of various tracking systems) ranging from 20 m to 20 km (60 simulations in total). FPT analysis was then applied.
为了概括位置精度对通过 FPT 分析估计 ARS 规模的影响，我创建了第二组模拟，模拟虚拟动物以直线（速度 30 km h −1 ）移动 200 公里，中间停10小时。每 30 分钟采集一次位置。对这些位置应用了正态误差，标准偏差（模仿各种跟踪系统的定位精度）范围为 20 m 到 20 km（总共 60 次模拟）。然后应用FPT分析。
application of argos noise to an albatross path
argos 噪声在信天翁路径上的应用
In order to detect the effect of Argos accuracy on FPT analysis using real movement data, I applied FPT analysis (i) to a real path obtained from a GPS tracking study on a seabird; and (ii) to this real GPS path with Argos noise added by simulation. In early January 2004, during the brooding period, a breeding black-browed albatross at Kerguelen Island was fitted with a GPS logger (GPS receiver with an integrated antenna and 1-Mb flash memory, Newbehavior company; Steiner et al. 2000). The GPS path, with locations and instantaneous speed recorded every 10 s with a precision of few metres, was taken to be the ‘theoretical’ path (Appendix S2), and FPT was calculated every 1 km for radius r varying from 1 to 100 km.
为了使用真实运动数据检测 Argos 精度对 FPT 分析的影响，我将 FPT 分析 (i) 应用于从海鸟 GPS 跟踪研究中获得的真实路径； (ii) 通过模拟添加 Argos 噪声的真实 GPS 路径。 2004 年 1 月上旬，在育雏期间，凯尔盖朗岛的一只繁殖黑眉信天翁安装了 GPS 记录仪（带有集成天线和 1 Mb 闪存的 GPS 接收器，Newbehavior 公司；Steiner 等人，2000）。 GPS 路径，每 10 秒记录一次位置和瞬时速度，精度为几米，被视为“理论”路径（附录 S2），并且每 1 公里计算一次 FPT，半径 r 从 1 到 100 公里不等。 。
In a second step, an Argos noise was applied to the subsampled GPS path to reproduce 200 typical Argos paths, using the same procedure and parameters as described previously. To detect the effect of each Argos component on ARS detection (effect of an infrequent satellite pass, effect of spatial error and effect of velocity filtering), FPT analysis was applied to these 200 paths at different steps of the simulation (see an example in Appendix S3): (i) corresponding to the path with Argos time-sampling rate only (with GPS accuracy but 1·5 locations h−1 on average); (ii) corresponding to the path with both Argos time-sampling rate and spatial error (typical Argos track); and (iii) the same as (ii) but with the application of velocity filtering (filtered Argos track). FPT was calculated every 1 km for scales from 1 to 100 km.
第二步，使用与前面所述相同的程序和参数，将 Argos 噪声应用于二次采样的 GPS 路径，以重现 200 条典型的 Argos 路径。为了检测每个 Argos 组件对 ARS 检测的影响（卫星不频繁通过的影响、空间误差的影响和速度滤波的影响），在模拟的不同步骤对这 200 条路径应用了 FPT 分析（参见附录中的示例） S3)：(i)仅对应于Argos时间采样率的路径（具有GPS精度，但平均有1·5个位置h −1 ）； (ii) 对应于同时具有Argos时间采样率和空间误差的路径（典型的Argos航迹）； (iii) 与 (ii) 相同，但应用了速度滤波（滤波后的 Argos 航迹）。从 1 公里到 100 公里的范围内，每 1 公里计算一次 FPT。
statistics 统计数据
Each simulated path was inspected to confirm that ARS behaviour in patches was effectively present and that high FPT values (indicating ARS) matched with presence in patches. With this inspection I was able to make the distinction between two kinds of error (type I and II) that one can make using FPT analysis: identifying wrong ARS scales (e.g. one scale when there is none) or missing existing scales (for example 0 instead of 1). Normality and homoscedasticity were tested when using parametric tests, and non-parametric statistics were used when appropriate. Unless stated otherwise, values are reported as means ± 1 SD and statistical significance was considered to be P < 0·05. All statistics and programming used r ver. 2.1.1 (R Development Core Team 2005).
检查每个模拟路径，以确认补丁中的 ARS 行为有效存在，并且高 FPT 值（指示 ARS）与补丁中的存在相匹配。通过这次检查，我能够区分使用 FPT 分析可能产生的两种错误（类型 I 和 II）：识别错误的 ARS 量表（例如，没有量表时有一个量表）或缺少现有量表（例如 0而不是 1)。使用参数检验时检验正态性和方差齐性，适当时使用非参数统计。除非另有说明，数值报告为平均值±1 SD，统计显着性被认为是P < 0·05。所有统计和编程都使用 r 版本。 2.1.1（R 开发核心团队 2005 年）。
Results 结果
detection of different search modes by FPT analysis
通过 FPT 分析检测不同的搜索模式
In 202 of 4000 initial simulations, the animal did not enter the patch, thus showing no effective ARS behaviour. FPT analysis revealed a peak of variance in 34 of these 202 cases with an average ARS scale of 76·5 ± 17·3 km, indicating a false detection of ARS of 16·8%.
在 4000 次初始模拟中，有 202 次动物没有进入斑块，因此没有表现出有效的 ARS 行为。 FPT 分析显示，这 202 个案例中有 34 个出现了方差峰值，平均 ARS 规模为 76·5 ± 17·3 km，表明 ARS 误检率为 16·8%。
The ability of FPT analysis to detect ARS behaviour was significantly dependent on the searching mode adopted by the animal, but not on the patch radius (anova, proportion of ARS detected as dependent variable with arcsine transformation, effect of SearchMode: F3,12 = 299·9, P < 0·001; PatchRadius: F1,12 = 1·07, P = 0·32; interaction: F3,12 = 2·31, P = 0·12). On paths presenting effective ARS behaviour, the REFL mode showed more efficient detection: FPT analysis detected at least one peak in variance on 99·0% of cases, with 99·9% of these paths matching between the effective and the observed ARS. For the other searching modes, these values were for mode SIN, 59·9 and 85·5%; for mode SP, 4·6 and 79·5%, and for mode SPSIN, 93·8 and 97·6%, respectively.
FPT 分析检测 ARS 行为的能力显着依赖于动物采用的搜索模式，但不依赖于斑块半径（方差分析、反正弦变换检测为因变量的 ARS 比例、SearchMode 的效果：F 3,12 = 1·07，P = 0·32；交互：F 3,12 = 2·31， P = 0·12）。在呈现有效 ARS 行为的路径上，REFL 模式显示出更有效的检测：FPT 分析在 99·0% 的情况下检测到至少一个方差峰值，其中 99·9% 的这些路径在有效 ARS 与观察到的 ARS 之间匹配。对于其他搜索模式，这些值为模式 SIN、59·9 和 85·5%；对于 SP 模式，分别为 4·6 和 79·5%；对于 SPSIN 模式，分别为 93·8 和 97·6%。
For paths where a match was observed between the effective and observed ARS, the observed ARS scales differed significantly according to searching mode (anova, F3,2320 = 564·6, P < 0·001) and patch radius (F1,2320 = 607·1, P < 0·001) with a significant effect of the interaction (F3,2320 = 216·0, P < 0·001). The estimation of ARS scale by FPT analysis when the animal was reflected by the patch boundary was particularly relevant, with observed ARS scales close to the diameter of the patch radii (Fig. 1). Considering the other searching modes, this correspondence between the ARS scale and patch radius was unclear (with a large variance in ARS scale), especially when considering the mode with a change in both speed and sinuosity.
对于在有效 ARS 和观察到的 ARS 之间观察到匹配的路径，观察到的 ARS 尺度根据搜索模式（方差分析，F 3,2320 = 564·6，P < 0·001）和斑块半径（ F 1,2320 = 607·1，P < 0·001），交互作用显着（F 3,2320 = 216·0，P < 0·001）。当动物被斑块边界反射时，通过 FPT 分析对 ARS 尺度的估计尤其相关，观察到的 ARS 尺度接近斑块半径的直径（图 1）。考虑到其他搜索模式，ARS 尺度和斑块半径之间的对应关系不清楚（ARS 尺度变化很大），特别是在考虑速度和蜿蜒度都发生变化的模式时。
The results of simulations to estimate area-restricted search (ARS) scales by first-passage time (FPT) analysis according to different patch radii and different modes of searching movement (see text for details). Dotted line indicates a perfect match between patch radius and value of ARS scale given by FPT analysis.
根据不同的斑块半径和不同的搜索运动模式，通过首次通过时间（FPT）分析来估计区域限制搜索（ARS）规模的模拟结果（详见正文）。虚线表示斑块半径与 FPT 分析给出的 ARS 尺度值之间的完美匹配。
simulating ARS in different patch structures
模拟不同补丁结构中的 ARS
283 (28·3%) and 821 (82·1%) paths in ES and NS arenas, respectively, presented an effective ARS behaviour in both patch sizes for the same path (two examples of each structure shown in Appendix S4). Using these paths, I assessed the detection of ARS behaviour by FPT analysis when the animal visited several patches that differed in size. FPT analysis clearly showed peaks of variance in FPT (see examples in Appendix S4) related to ARS behaviour in around 50% of cases (Table 1). This relationship can be illustrated by plotting FPT (at the scale corresponding to each peak of variance) as a function of time elapsed since departure (Fauchald & Tveraa 2003), as shown in Appendix S5. Changes in FPT can be related to the occurrence of ARS behaviour and presence in patch, indicated by an increase and large values of FPT. This correspondence was found for simulated paths in both ES and NS structures and also when several small patches (up to four) were nested in one large patch. Simulations with different radius ratios between the small and large patches (30 and 5 km or 30 and 20 km, for example), showed that the distinction between the two peaks of variance was not perceptible for a radius ratio from 2 : 1 to 1 : 1 (in this simulation for small patches of radius >15 km).
ES 和 NS 领域中的 283 (28·3%) 和 821 (82·1%) 条路径分别在同一路径的两种补丁大小中呈现出有效的 ARS 行为（附录 S4 中显示了每种结构的两个示例）。使用这些路径，当动物访问几个大小不同的斑块时，我通过 FPT 分析评估了 ARS 行为的检测情况。 FPT 分析清楚地显示了大约 50% 的案例中与 ARS 行为相关的 FPT 方差峰值（参见附录 S4 中的示例）（表 1）。这种关系可以通过绘制 FPT（在对应于每个方差峰值的比例）作为自出发以来经过的时间的函数来说明（Fauchald & Tveraa 2003），如附录 S5 所示。 FPT 的变化可能与 ARS 行为的发生和斑块中的存在有关，这由 FPT 的增加和较大值表明。在 ES 和 NS 结构中的模拟路径中，以及在多个小补丁（最多四个）嵌套在一个大补丁中时，都发现了这种对应关系。小斑块和大斑块之间不同半径比（例如，30 和 5 公里或 30 和 20 公里）的模拟表明，对于从 2:1 到 1 的半径比，两个方差峰值之间的区别是不可察觉的： 1（在此模拟中，半径 > 15 公里的小斑块）。
表 1. 在不同斑块结构中使用有效区域限制搜索对模拟路径进行首次通过时间分析的结果，表明显示一个和两个方差峰值的模拟路径的百分比以及这些峰值的比例
| Number of detected peak of variance 检测到的方差峰值数 |
Exclusive patch structure 独家贴片结构 |
Nested structure 嵌套结构 | ||
|---|---|---|---|---|
| One | Two | One | Two | |
| Walks with detected peak (%) 行走时检测到峰值 (%) |
39·6 | 53·8 | 46·2 | 51·3 |
| Scale of detected peak (km) 检测峰值规模（km） |
31·9 ± 15·4 31·9 ± 15·4 | 22·6 ± 7·0 | 37·2 ± 12·0 37·2 ± 12·0 | 22·9 ± 5·3 22·9 ± 5·3 |
| 53·6 ± 9·3 53·6 ± 9·3 | 48·0 ± 8·8 | |||
effect of location accuracy, ARS intensity and argos filtering
定位精度、ARS 强度和 argos 过滤的影响
When Argos noise was added to the path of a moving animal, the probability with which ARS behaviour was detected increased with the number of Argos fixes during the period of ARS behaviour (logistic regression with non-filtered locations: d.f.1,6998 = 2163·1, P < 0·001; Fig. 2a). To detect ARS behaviour with a probability of 0·95, at least 13 locations were required during the ARS. Using filtered locations, this value decreased, reaching a minimum of seven locations in ARS (logistic regression with filtered locations: d.f.1,6998 = 2883·7, P < 0·001; Fig. 2b). For paths with only one peak of variance before filtering (with an effective ARS, n = 1671), the peak of variance occurred at a spatial scale of 23·89 ± 25·31 km. Filtering reduced this noise by 8·11 ± 24·27 km (paired comparison without and with filtering, Wilcoxon signed rank test, V = 5707·5, P < 0·001). Simulations for a larger range of location error values indicated that the estimation of ARS scale from FPT analysis was significantly dependent on the location accuracy (linear model, F1,58 = 8148, P < 0·001, adjusted-R2 = 0·993; Fig. 3).
当Argos噪声添加到移动动物的路径中时，检测到ARS行为的概率随着ARS行为期间Argos修复的数量而增加（未过滤位置的逻辑回归：d.f. 1,6998 = 2163·1，P < 0·001；图 2a)。为了以 0·95 的概率检测 ARS 行为，ARS 期间至少需要 13 个位置。使用过滤后的位置，该值下降，达到 ARS 中至少 7 个位置（过滤位置的逻辑回归：d.f. 1,6998 = 2883·7，P < 0·001；图 2b）。对于滤波前只有一个方差峰值的路径（有效 ARS，n = 1671），方差峰值出现在 23·89 ± 25·31 km 的空间尺度上。滤波将噪声降低了 8·11 ± 24·27 km（无滤波和有滤波的配对比较，Wilcoxon 符号秩检验，V = 5707·5，P < 0·001）。对较大范围定位误差值的模拟表明，FPT 分析对 ARS 尺度的估计显着依赖于定位精度（线性模型，F 1,58 = 8148，P < 0·001，调整后的 R 2 = 0·993；图 3)。
Effect of the number of Argos locations gained during an area-restricted search (ARS) bout on the probability with which a peak of variance is detected using first-passage time (FPT) analysis (a) without and (b) with location filtering. Solid lines indicate results of logistic models. Diameters of circles are proportional to the number of tracks. Dotted line indicates a probability of 0·95.
在区域限制搜索 (ARS) 回合中获得的 Argos 位置数量对使用首次通过时间 (FPT) 分析（a）不使用位置过滤和 (b) 使用位置过滤检测到方差峰值的概率的影响。实线表示逻辑模型的结果。圆的直径与轨道的数量成正比。虚线表示概率为 0·95。
Effect of location accuracy (log scale) on the estimation of area-restricted search (ARS) scale by first-passage time (FPT) analysis (log scale), as revealed by 60 simulated paths with different location accuracy.
通过首次通过时间 (FPT) 分析（对数尺度），定位精度（对数尺度）对区域限制搜索 (ARS) 尺度估计的影响，如 60 条具有不同定位精度的模拟路径所示。
comparison between GPS and argos paths
GPS 和 argos 路径之间的比较
FPT analysis of the albatross GPS path revealed the presence of ARS behaviour at three spatial scales (Fig. 4a): 3, 14 and 80 km. Search effort was quantified at precisely the correct spatial scales in relation to the environment (Fig. 5). First, this individual moved rapidly from the colony and increased its search effort at a scale of 80 km on the edge of the Kerguelen plateau, 120 km away from the colony. In this area it increased its search effort in four areas at a scale of 14 km and two areas at a spatial scale of 3 km.
对信天翁 GPS 路径的 FPT 分析揭示了在三个空间尺度上存在 ARS 行为（图 4a）：3、14 和 80 公里。搜索工作在与环境相关的正确空间尺度上进行了精确量化（图 5）。首先，该个体迅速离开聚居地，并在距离聚居地120公里的凯尔盖朗高原边缘，以80公里的范围加大了搜索力度。在该地区，它增加了四个14公里尺度的区域和两个3公里空间尺度的区域的搜索力度。
Variance in spatial scale indicated by first-passage time (FPT) analysis of (a) a GPS path of black-browed albatross from Kerguelen Island; (b) the same GPS path where Argos noise is simulated with different components: solid line, time-sampling rate component only; dashed line, time-sampling rate and spatial error components; dotted line, time-sampling rate and spatial error components with velocity filtering.
通过对 (a) 凯尔盖朗岛黑眉信天翁 GPS 路径的首次通过时间 (FPT) 分析表明的空间尺度变化； (b) 使用不同分量模拟 Argos 噪声的相同 GPS 路径：实线，仅时间采样率分量；虚线、时间采样率和空间误差分量；虚线、时间采样率和带有速度滤波的空间误差分量。
GPS path of a black-browed albatross from Kerguelen Island (top left) and corresponding search effort as revealed by first-passage time (FPT) analysis (Fig. 4a) at different spatial scales: 3 km (top right), 14 km (below left) and 80 km (below right). Grey triangle indicates colony on the coast of Kerguelen Island (grey). Bathymetry isolines (–2000, –1500, –1000, –500, –200 m) are represented by dotted lines. Grey intensity on the track refers to search effort: darker grey, the more intensive search effort.
凯尔盖朗岛黑眉信天翁的 GPS 路径（左上）以及首次通过时间 (FPT) 分析显示的相应搜索工作（图 4a）在不同空间尺度：3 公里（右上）、14 公里（左下）和 80 公里（右下）。灰色三角形表示凯尔盖朗岛（灰色）海岸的殖民地。测深等值线（–2000、–1500、–1000、–500、–200 m）用虚线表示。轨道上的灰色强度指的是搜索工作量：灰色越深，搜索工作量越强。
Taking the GPS path as a basis for comparison (see example in Appendix S3), the time-sampling rate due to Argos satellite passes introduced a biased detection in ARS (see example in Fig. 4b), with a lower proportion of simulations with an ARS detected at the 3-km scale (Fig. 6a). The spatial error introduced by the Argos system decreased the proportion of ARS detected at the three spatial scales by more than 50% (Fig. 6a). Velocity filtering attenuated this effect by retrieving 75% of ARS detected.
以 GPS 路径作为比较的基础（参见附录 S3 中的示例），由于 Argos 卫星经过而导致的时间采样率在 ARS 中引入了偏差检测（参见图 4b 中的示例），具有较低比例的模拟ARS 在 3 公里范围内检测到（图 6a）。 Argos系统引入的空间误差使在三个空间尺度上检测到的ARS比例下降了50%以上（图6a）。速度过滤通过检索检测到的 75% 的 ARS 减弱了这种影响。
Results of first-passage time (FPT) analysis of the black-browed albatross GPS path [with initial area-restricted search (ARS) at scales of 3, 14 and 80 km], where Argos noise is simulated with different components: white bars, time-sampling rate; left-hatched, time-sampling rate and spatial error; right-hatched, time-sampling rate and spatial error with a velocity filtering. (a) Proportion of ARS events detected by FPT analysis at different simulation steps; (b) detected ARS scales at different simulation steps. In (b), horizontal, hatched lines indicate true ARS scales detected from the GPS path.
黑眉信天翁 GPS 路径的首次通过时间 (FPT) 分析结果 [在 3、14 和 80 km 尺度上进行初始区域限制搜索 (ARS)]，其中使用不同的组件模拟 Argos 噪声：白条，时间采样率；左阴影线、时间采样率和空间误差；右阴影线、时间采样率和空间误差以及速度滤波。 (a) FPT 分析在不同模拟步骤检测到的 ARS 事件的比例； (b) 在不同的模拟步骤中检测到的 ARS 尺度。 (b) 中，水平阴影线表示从 GPS 路径检测到的真实 ARS 比例。
The ARS scale identified by FPT in the presence of simulated Argos noise was compared with the true value of ARS scale from the GPS path. Infrequent time-sampling rate from Argos introduced a noise in the estimation of the ARS scale value, especially for ARS performed at small scales relative to the accuracy of the tracking system, <10 km here (Fig. 6b). On average, values of the ARS scale detected after the application of spatial noise reproducing the Argos time-sampling rate were lower than those detected after application of the Argos spatial error, but were still close to the true ARS scale given from FPT analysis on the GPS path. At the 3-km scale, the effect of spatial error introduced by the Argos system was more important, leading to an overestimation of ARS scale (for spatial error, 11·00 ± 11·63 km; after filtering, 9·16 ± 3·76 km; anova, F2,20 = 3·81, P = 0·04).
将 FPT 在存在模拟 Argos 噪声的情况下识别的 ARS 尺度与来自 GPS 路径的 ARS 尺度的真实值进行比较。 Argos 的不频繁时间采样率在 ARS 尺度值的估计中引入了噪声，特别是对于相对于跟踪系统的精度而言在小尺度上执行的 ARS，这里 <10 km（图 6b）。平均而言，应用再现 Argos 时间采样率的空间噪声后检测到的 ARS 标度值低于应用 Argos 空间误差后检测到的值，但仍接近 FPT 分析给出的真实 ARS 标度。 GPS 路径。在3公里尺度上，Argos系统引入的空间误差影响更为重要，导致ARS尺度高估（空间误差为11·00±11·63 km；滤波后为9·16±3） ·76 公里；方差分析，F 2,20 = 3·81，P = 0·04)。
Discussion 讨论
The results of this study show that FPT analysis is an efficient method of studying animal movement with various systems like Argos and GPS. FPT analysis can reveal changes in movement, suggesting spatial scales of important interactions of the animal and its environment. FPT analysis can also quantify search effort as an index of habitat use by animals tracked in the wild, even if patches differ in size or are present in a nested structure.
这项研究的结果表明，FPT 分析是利用 Argos 和 GPS 等各种系统研究动物运动的有效方法。 FPT 分析可以揭示运动的变化，表明动物与其环境之间重要相互作用的空间尺度。 FPT 分析还可以将搜索工作量量化为野外追踪动物栖息地使用的指数，即使斑块大小不同或存在于嵌套结构中。
effect of searching mode and structure of the environment
搜索模式和环境结构的影响
In their initial simulations to test the ability of FPT analysis to detect ARS behaviour, Fauchald & Tveraa (2003) considered ARS only in patches of the same size, with an animal being reflected by patch boundaries. My results show that FPT analysis is also able to detect changes in different movement parameters (speed and sinuosity). In the same movement path, ARS behaviour in patches of different sizes can be detected. It has been shown empirically that, while searching, animals change both their speed and sinuosity in contact with a high density of resource, or react to the patch boundary when perceiving it (Benhamou 1992). FPT analysis is able to detect changes in movements in these two search modes. A clear correspondence exists between the ARS scale and the patch radius when the animal adopts a ‘patch-boundary reflectance’ search mode (Fauchald & Tveraa 2003), but this was not true when the animal changed both speed and sinuosity, because the patch area is not necessarily covered totally with this mode. Caution is thus essential when trying to relate scale of search to patch size in this case.
在测试 FPT 分析检测 ARS 行为的能力的最初模拟中，Fauchald 和 Tveraa (2003) 只考虑了相同大小的斑块中的 ARS，并且斑块边界反映了动物。我的结果表明，FPT 分析还能够检测不同运动参数（速度和蜿蜒度）的变化。在相同的运动路径中，可以检测到不同大小的斑块中的ARS行为。经验表明，在搜索时，动物在接触高密度资源时会改变其速度和蜿蜒度，或者在感知到斑块边界时会做出反应（Benhamou 1992）。 FPT 分析能够检测这两种搜索模式下的运动变化。当动物采用“斑块边界反射”搜索模式时，ARS 尺度和斑块半径之间存在明显的对应关系（Fauchald & Tveraa 2003），但当动物同时改变速度和蜿蜒度时，情况并非如此，因为斑块面积此模式不一定完全覆盖。因此，在这种情况下尝试将搜索规模与补丁大小联系起来时必须小心谨慎。
In my simulations, peaks of variance were observed at values close to the diameter of simulated patches in >50% of cases. Results were similar when small patches were nested in large ones. Peaks of variance in both patch sizes were not detected in all cases (≈50%), mainly because of differences in ARS intensity. In fact, the probability with which ARS behaviour is detected depends on the number of locations recorded during this behaviour (see below), and could explain the inability of FPT to detect all ARS events. As this method is based on the detection of clear peaks in variance plotted against spatial scale, definition of the ARS scale is less accurate when the search effort increased at several spatial scales close in magnitude. Here, large patches were three times larger than small ones, allowing a clear detection of peaks of variance. In the case of patches of different sizes but closer in diameter (ratio from 2 : 1 to 1 : 1), this detection was less effective with less obvious peaks of variance.
在我的模拟中，在 > 50% 的情况下，在接近模拟斑块直径的值处观察到方差峰值。当小补丁嵌套在大补丁中时，结果相似。在所有情况下均未检测到两种斑块大小的方差峰值（约 50%），这主要是由于 ARS 强度的差异。事实上，检测到 ARS 行为的概率取决于在此行为期间记录的位置数量（见下文），并且可以解释 FPT 无法检测所有 ARS 事件的原因。由于该方法基于检测针对空间尺度绘制的方差中的清晰峰值，因此当搜索工作在几个数量级接近的空间尺度上增加时，ARS 尺度的定义不太准确。在这里，大斑块比小斑块大三倍，可以清楚地检测方差峰值。对于大小不同但直径较接近的斑块（比例从 2:1 到 1:1），这种检测效果较差，方差峰不太明显。
effect of tracking system accuracy
跟踪系统精度的影响
Simulations demonstrated that location spatial error and, to a lesser extent, sampling time interval affected the detection and quantification of ARS behaviour. These effects were also related to the duration of ARS behaviour: longer bouts of ARS behaviour and higher numbers of locations increased detection by FPT analysis. ARS events had a lower probability of detection at small scales relative to the tracking system accuracy (e.g. <10 km for Argos) because of their short duration (which leads to less-efficient description by the tracking system). Nevertheless, small spatial-scale events can be detected if their duration is long enough to enable sufficient locations during the bout. The effect of velocity filtering can be interpreted as a reduction in spatial noise (Vincent et al. 2002), leading to a clearer distinction between travel (higher speed and lower turning rate) and search (lower speed and higher turning rate). This increases the probability of ARS detection by FTP analysis.
模拟表明，位置空间误差以及采样时间间隔在较小程度上影响了 ARS 行为的检测和量化。这些影响还与 ARS 行为的持续时间有关：较长的 ARS 行为发作和较多的位置数量增加了 FPT 分析的检测率。相对于跟踪系统的精度（例如，Argos <10 km），ARS 事件在小尺度上的检测概率较低，因为它们的持续时间较短（这导致跟踪系统的描述效率较低）。然而，如果小空间尺度事件的持续时间足够长以在比赛期间提供足够的位置，则可以检测到它们。速度过滤的效果可以解释为空间噪声的减少（Vincent et al. 2002），从而使行进（较高的速度和较低的转弯速率）和搜索（较低的速度和较高的转弯速率）之间的区别更加清晰。这增加了 FTP 分析检测到 ARS 的概率。
Estimating ARS scale using FPT analysis depends significantly on location accuracy (see equation in Fig. 3). The relationship derived here (Fig. 3) is helpful only where accuracy remains relatively constant for each location (the same error distribution with the same parameters); this is not the case for the Argos system, where accuracy depends on the location class (Argos 1996; Vincent et al. 2002). For Argos-derived paths, I found that the resolution of FPT analysis was, on average, 24 km, which was close to the higher spatial error of Argos system in the study. This finding seems consistent with studies providing information about error measurements (Fauchald & Tveraa 2003; Frair et al. 2005; Pinaud & Weimerskirch 2005; Bailey & Thompson 2006). This means that an affective ARS at a smaller scale (say 5 or 10 km) could be detected, but ARS scale will be overestimated at an average value of 24 km.
使用 FPT 分析估计 ARS 规模在很大程度上取决于位置精度（参见图 3 中的方程）。仅当每个位置的精度保持相对恒定（具有相同参数的相同误差分布）时，此处得出的关系（图 3）才有用； Argos 系统的情况并非如此，其精度取决于位置类别（Argos 1996；Vincent 等人 2002）。对于Argos导出的路径，我发现FPT分析的平均分辨率为24公里，接近研究中Argos系统的较高空间误差。这一发现似乎与提供误差测量信息的研究一致（Fauchald & Tveraa 2003；Frair et al. 2005；Pinaud & Weimerskirch 2005；Bailey & Thompson 2006）。这意味着可以检测到较小尺度（例如 5 或 10 公里）的情感 ARS，但在 24 公里的平均值处 ARS 尺度将被高估。
The simulated example was based on an animal searching in a marine environment, but conclusions can be applied easily to terrestrial animals, for example with a study employing radio tracking with a spatial error of 50 m. In fact, organisms face heterogeneity at several scales in both marine and terrestrial ecosystems, and tracking techniques (such as radio tracking, Argos or GPS) are shared by these ecosystems to study animal movements in response to environmental heterogeneity. The simulations presented here show that FPT analysis can be applied using these tracking techniques.
模拟示例基于海洋环境中的动物搜索，但结论可以轻松应用于陆地动物，例如一项采用空间误差为 50 m 的无线电跟踪的研究。事实上，海洋和陆地生态系统中的生物体都面临着多个尺度的异质性，这些生态系统共享跟踪技术（例如无线电跟踪、Argos 或 GPS）来研究动物运动对环境异质性的反应。此处的模拟表明，可以使用这些跟踪技术来应用 FPT 分析。
recommendations when assessing search effort using FPT analysis
使用 FPT 分析评估搜索工作时的建议
Growing technological developments for wild-animal tracking provide important information about habitat use, which can be applied to conservation problems in both terrestrial and marine ecosystems (for example the migration of the white-napped crane, Higuchi et al. 1996; or the definition of at-sea protected areas for albatrosses, BirdLife International 2004). In the latter example, Kernel estimation was used on Argos data sets to quantify habitat utilization at sea, which is based on location density only (Worton 1989). Undoubtedly this approach is of great conservation value, but it could lead to overestimation of the importance of areas very close to breeding colonies (Wood et al. 2000). By considering fully the behaviour of the animal, FPT analysis can solve this problem and allow important foraging areas to be defined at several spatial scales (see example for black-browed albatross in Fig. 5) in relation to environment and fisheries (Pinaud & Weimerskirch 2005, 2007).
野生动物追踪技术的不断发展提供了有关栖息地利用的重要信息，这些信息可应用于陆地和海洋生态系统的保护问题（例如白枕鹤的迁徙，Higuchi et al. 1996；或定义信天翁海上保护区，国际鸟盟 2004 年）。在后一个例子中，在 Argos 数据集上使用核估计来量化海上栖息地的利用，这仅基于位置密度（Worton 1989）。毫无疑问，这种方法具有很大的保护价值，但它可能会导致对非常接近繁殖群的区域的重要性的高估（Wood et al. 2000）。通过充分考虑动物的行为，FPT 分析可以解决这个问题，并允许在与环境和渔业相关的多个空间尺度上定义重要的觅食区域（参见图 5 中的黑眉信天翁示例）（Pinaud & Weimerskirch） 2005 年、2007 年）。
Despite the increasing availability of spatial data on animal movement, a quantitative understanding of factors affecting animal movements and distribution is still limited, especially in relation to providing predictive models in response to changing environments (Jonsen et al. 2003). The development of analytical approaches such as FPT will help to fill this gap. Changes in patterns of movement at biologically relevant scales can indicate appropriate spatial scale(s) for conservation guidelines (Nams, Mowat & Panian 2006). In fact, it is possible to relate and map variations in FPT as a function of habitat variables to identify pertinent factors affecting movement decisions and habitat use (Frair et al. 2005; Pinaud & Weimerskirch 2005, 2007).
尽管动物运动的空间数据越来越多，但对影响动物运动和分布的因素的定量理解仍然有限，特别是在提供响应不断变化的环境的预测模型方面（Jonsen et al. 2003）。 FPT 等分析方法的发展将有助于填补这一空白。生物相关尺度上运动模式的变化可以为保护指南指明适当的空间尺度（Nams、Mowat 和 Panian 2006）。事实上，可以将 FPT 的变化作为栖息地变量的函数进行关联和映射，以识别影响迁移决策和栖息地利用的相关因素（Frair 等人，2005 年；Pinaud & Weimerskirch，2005 年，2007 年）。
This study provides several recommendations for successful application of FPT analysis to data sets originating from different tracking methods. First, the intensity of ARS behaviour affects the probability of its detection, with small scales/duration events relative to the tracking system error less detectable. Using Argos, a very good estimation is reached with 13 locations describing the ARS behaviour. This sample can be reduced to seven locations after application of velocity filtering (reduction of spatial error). Second, the resolution of FPT is dependent on the spatial resolution of the system, with an equation given in Fig. 3. When the location accuracy is not constant (for example with Argos), the FPT resolution is dependent on the larger error in location (in this example, class B). This effect implies that an ARS event occurring at a smaller scale than the larger location error can be detected by FPT analysis, but will be overestimated: its observed value will be close to the larger location error. Third, the frequency at which locations are obtained affects the detection of fine-scale ARS events; more regular fixes are better. Argos (the most widely used individual tracking system) enables detection of scale-dependent movements at scales >20 km in a heterogeneous structure (patches of different sizes), and I recommend the application of velocity filtering (following, for example, McConnell et al. 1992).
这项研究为成功地将 FPT 分析应用于源自不同跟踪方法的数据集提供了一些建议。首先，ARS 行为的强度会影响其检测的概率，相对于跟踪系统误差的小规模/持续时间事件较不易检测。使用 Argos，通过描述 ARS 行为的 13 个位置达到了非常好的估计。应用速度滤波（减少空间误差）后，该样本可以减少到七个位置。其次，FPT 的分辨率取决于系统的空间分辨率，其方程如图 3 所示。当定位精度不恒定时（例如 Argos），FPT 分辨率取决于较大的定位误差（在本例中为 B 类）。这种效应意味着，FPT 分析可以检测到比较大定位误差更小规模发生的 ARS 事件，但会被高估：其观测值将接近较大定位误差。第三，获取位置的频率影响小尺度ARS事件的检测；定期修复越多越好。 Argos（使用最广泛的个体跟踪系统）能够检测异质结构（不同大小的斑块）中 >20 km 尺度的依赖于尺度的运动，我建议应用速度过滤（例如，McConnell 等人） 1992）。
Depending on the latitude of the study (satellite passes are more frequent around the poles, providing more locations per day) and characteristics of platform terminal transmitters (PTT, influencing location accuracy), some limitations affect the detection and quantification of ARS behaviour by FPT analysis. In the case of very infrequent satellite passes, some fitting techniques such as curvilinear interpolations of tracking data (Tremblay et al. 2006) could improve this estimation. Many tracking studies use PTTs integrating a duty cycle timer (succession of ‘on’ and ‘off’ periods of various durations in order to save power, resulting in a bimodal distribution of time intervals between successive locations). This can limit ARS detection by FPT analysis, and the resolution will be given by the longest interval between consecutive locations (the duration of ‘off’ mode). To isolate this problem, I recommend running FPT in two stages. The first step is to run FPT analysis on the whole path in order to detect large-scale ARS. To obtain similar time intervals between consecutive locations along the path, some locations in the ‘on’ mode session can be randomly removed. The second step is to run FPT analysis on each ‘on’ mode session in order to detect small scale events. This two-step procedure was the same as that used by Fauchald & Tveraa (2003) to detect small, nested scale ARS within intensively searched areas at large scale.
根据研究的纬度（卫星在两极周围通过更频繁，每天提供更多位置）和平台终端发射机的特性（PTT，影响定位精度），一些限制会影响 FPT 分析对 ARS 行为的检测和量化。在卫星通过的情况非常罕见的情况下，一些拟合技术，例如跟踪数据的曲线插值（Tremblay 等人，2006 年）可以改进这种估计。许多跟踪研究使用集成占空比计时器的 PTT（连续不同持续时间的“开”和“关”周期以节省电量，从而导致连续位置之间时间间隔的双峰分布）。这可以限制 FPT 分析的 ARS 检测，并且分辨率将由连续位置之间的最长间隔（“关闭”模式的持续时间）给出。为了隔离此问题，我建议分两个阶段运行 FPT。第一步是在整个路径上运行 FPT 分析，以检测大规模 ARS。为了获得沿路径的连续位置之间的相似时间间隔，可以随机删除“开启”模式会话中的一些位置。第二步是对每个“开启”模式会话运行 FPT 分析，以检测小规模事件。这个两步程序与 Fauchald 和 Tveraa (2003) 用于在大规模密集搜索区域内检测小型嵌套规模 ARS 的程序相同。
Acknowledgements 致谢
I thank H. Weimerskirch for use of the GPS data set on black-browed albatross and for comments on the manuscript. Protocols and procedures for field work were approved by the Ethical Committee of the Institut Paul-Emile Victor. I also thank those people involved in GPS deployment, L. Dubroca for help in spatial analysis and programming, N. G. Yoccoz, M. Nevoux and two anonymous referees with the editors for constructive comments. Finally, I thank K. Poitras and J. Hobson for their improvements.
我感谢 H. Weimerskirch 使用黑眉信天翁 GPS 数据集以及对手稿的评论。现场工作的方案和程序得到了保罗·埃米尔·维克多研究所伦理委员会的批准。我还要感谢那些参与 GPS 部署的人，L. Dubroca 在空间分析和编程方面提供的帮助，N. G. Yoccoz、M. Nevoux 以及两位匿名审稿人以及编辑提供的建设性意见。最后，我感谢 K. Poitras 和 J. Hobson 的改进。
