Ecological network analysis: forgotten?

A new [preprint article](http://dx.doi.org/10.1016/j.ecolmodel.2009.07.012) pop up in *Ecological Modelling*'s RSS feed today, showing a case study using ecological network analysis in the functional assessment of an estuary ecosystem. I was wondering what is ecological network analysis, and how it assesses a system's function, so I read on.

It turns out that the technical details of ecological network analysis involves food web and information theory. The former I have some understanding, but the latter is too complex for me as a newcomer to dwell in the late night. [Here](http://www.fisheries.ubc.ca/files/ECOPATH%20IISoftwareForEcosystemModels%20_SmallerFileSize.pdf) is the paper describing the ECOPATH II model used by the preprint article. Judging from its number of being cited, many people must have used it successfully in their studies. However, the authors of the model acknowledged that it is based on a steady-state assumption, which arguably hardly exist in any real ecosystem, thus they recommend it used only in snapshot descriptions of ecosystems.

I doubt such a model can be used to describe ecosystem functions, considering that ecosystem functions do not present themselves in full in a "snapshot". The authors of the preprint article seem confident that this method at least identify ecosystem functions based on the goal of management defined by researchers and decision makers. But I think the role of artifacts and stochasticity in this is too significant to let pass.

In preliminary studies, I think this method has its use. If researchers can establish the food web structure and nutrient dynamics in a system, we may use this method to identify some key species or functions of the system. However, its results must be iteratively put back to our picture of the system, to check whether it conforms the dynamics and management goals. The method seems to work only with "pure" ecosystems, while many researchers have moved on to study social-ecological complex systems. I wonder if this is the reason why the method has been silent for all these years.

Christian, R., Brinson, M., Dame, J., Johnson, G., Peterson, C., & Baird, D. (2009). Ecological network analyses and their use for establishing reference domain in functional assessment of an estuary Ecological Modelling DOI: 10.1016/j.ecolmodel.2009.07.012

Christensen, V., & Pauly, D. (1992). ECOPATH II — a software for balancing steady-state ecosystem models and calculating network characteristics Ecological Modelling, 61 (3-4), 169-185 DOI: 10.1016/0304-3800(92)90016-8

Bodélé: "More or Less" a major dust source

Image via Wikipedia

Recently I am help doing a study on dust transport and deposition
concerning central and northern Libya. [A geochemical study](http://dx.doi.org/10.1016/j.atmosenv.2006.02.020) by my mentors suggest
that some of the dust in Hun and Sebha, even some in the coastal
areas, may be from the Bodélé, which is the largest source of dust in
Libya. [This preprint article on
PNAS](http://dx.doi.org/10.1073/pnas.0711850106), therefore, is of
special interest to me.

However, if the authors of the paper are right about the transport
mode of dust from Bodélé, our story may prove wrong. The authors
claim that the prevailing direction of the dust transport from this
area is towards the west in winter, which is also the maximum of dust
output in a year in the area. But our study area shows a constrasting
trend: lowest dust deposition both by ground data and remote sensing,
in winter, and it is to the north of Bodélé. The summer
transportation, if any, may contribute very little to our study area,
limited both by transport and production.

The MODIS brightness temperature difference (BTD) data is being
derived, which can provide us a picture of dust plumes for major dust
events. We are also looking at the geochemical properties and
meteorological data around the area. Combining these data, hopefully,
can provide more information on the transport mode in our study.

In the PNAS paper, the authors point out that the Bodélé area may be a
"tipping element" in the context of climate change, due to its
dominant position in the output of dust and its location. Some
climate models suggest that the area may become wetter, yet the wind
will be strengthened. As a result, it is really difficult to tell how
the dust output will be influenced by climate change at the moment.
Will we have more or less dust from Bodélé? This will be an
interesting problem, as dust from this area interacts with many
large-scale systems. It is a wonder, considering that the Bodélé
Depression is so small. The difficulty is that we only have inaccurate
model and incomplete data for this area, and for the North Africa.
New remote sensing technology such as
[SEVIRI](http://www.esa.int/esapub/bulletin/bullet111/chapter4_bul111.pdf)
(imagine quasi-MODIS resolution images every 15 minutes, very cool) may partly solve
the problem, but more geochemical and meteorological data are
essential to answer the complex dust question.

Washington, R., Bouet, C., Cautenet, G., Mackenzie, E., Ashpole, I., Engelstaedter, S., Lizcano, G., Henderson, G., Schepanski, K., & Tegen, I. (2009). Tipping Elements in Earth Systems Special Feature: Dust as a tipping element: The Bodele Depression, Chad Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.0711850106

OHARA, S., CLARKE, M., & ELATRASH, M. (2006). Field measurements of desert dust deposition in Libya Atmospheric Environment, 40 (21), 3881-3897 DOI: 10.1016/j.atmosenv.2006.02.020

Some like it hot ... or variable

I have the impression that someone on researchblogging.org has already used a similar title to describe the link between rising temperature and vectors of contagious diseases. But [this article](http://dx.doi.org/10.1073/pnas.0903423106) has pointed out another layer of complexity existing in the temperature-disease connection. Turns out that malaria does not necessarily need hot weather, a reasonably warm mean temperature with high diurnal temperature range (DTR) will do.

The malaria parasites will need to develop to a certain stage before it can actually infect people. And this takes time. Researchers already know that the length of the period depends on the environmental temperature, and accordingly they predict that the risk of malaria epidemics will increase, as the mean temperatures in many areas rise. It takes less time for the parasite to develop, and the carrier -- mosquitoes -- has more time to bite and infect people before it dies. If the period of development is so long that it almost equals or even exceeds the mosquito's life expectancy, very little harm is done.

The authors of the PNAS paper find that the period of development depends not only on daily mean temperature, but also on the temperature range through the day. In areas with relatively low temperature, given the same mean temperature, malaria parasites in areas with higher temperature variation in a day need significantly shorter time to develop. Similarly, high DTR in areas with high temperature may slow down the development. Thus the authors say the picture of malaria and similar epidemic in a global climate change context may be more complex than we previously think.

The immediate lesson is that we may have overestimated the additional risk in some tropical areas, and underestimated that in some temperate regions. But exactly what are these areas asks for studies at local scale.

Paaijmans, K., Read, A., & Thomas, M. (2009). Understanding the link between malaria risk and climate Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.0903423106

北美蝴蝶物种多样性的统计研究

今天在学校听了来自 UC Irvine 的 [Bradford A. Hawkins 教授](http://www.faculty.uci.edu/profile.cfm?faculty_id=4562)的一个讲座。 据说Hawkins 是生物地理学和宏观生态学方面的大牛，可惜听讲前自己没有做足功课，虽然讲座是近期少见的信息量大、富启发意义的题目，却没有听得太明白。 好在回来搜论文找到了 Hawkins 等即将发表的关于同一个研究的[论文](http://dx.doi.org/10.1111/j.1365-2699.2009.02119.x)。

Hawkins 等人使用了墨西哥以北的北美地区夏季和冬季的蝴蝶物种丰度资料，将蝴蝶亚科按照分布范围分成热带和非热带两部分进行讨论。从物种丰度在纬度方向上的梯度看，热带类型的蝴蝶物种明显地表现出夏季向北迁徙或者 recolonize 的趋势；而非热带类型的蝴蝶则很少表现出有长距离的迁移。而以亚科在包括弄蝶总科 Hesperioidea 和凤蝶总科 Papilionoidea 的整个谱系树上的遗传距离（Mean Root Distance, MRD）来看，北美地区靠近热带的南部物种间的距离较短。 如果蝴蝶起源于热带的假设成立，这说明非热带物种多是适应了较寒冷气候的进化支。

根据对 8 个可能因素的回归分析，热带物种的丰度跟温度正相关，与热带地区的距离成负相关。非热带物种丰度与温度的关系更复杂一些。虽然夏季温度还是与物种丰度正相关，冬季温度较高的地区物种丰度却不一定更高。作者提出的解释是对于适应了较寒冷环境的蝴蝶物种，冬季温度有一个最适范围，高于这个范围的温度可能会扰乱休眠期的蝴蝶的生理活动，导致其数量减少甚至局部灭绝。一些对北半球气候变化造成的物种向北迁移的现象可以作为这个观点的一个注脚。

作者在文末指出形成北美蝴蝶多样性梯度的根本原因在于蝴蝶的热带起源和第三纪中期以来的长期气候变化模式。Hawkins 今天在讲座中进一步指出在欧洲、澳大利亚、智利、南非等地区也都发现了类似的梯度分布，可见他的观点具有相当强的解释力。这一研究不仅能用来解释北美现有的蝴蝶多样性梯度，也有可能被用来进一步研究蝴蝶各亚科和物种的进化和迁徙模式。这种研究方法理论上说也应该可以应用于其它起源于热带的物种，但对于蝶科的生活史、习性和物种分布的完整研究是做出这样研究的前提条件，不知道在无脊椎动物中还有哪些物种有这样完整的研究记录。

这一研究也揭示了气候变化引起的冬季温度变化将会给非热带蝴蝶物种带来的问题。从北美地区来看，热带物种可能不会仅仅因为温度上升就迁往更朝北的地区，但非热带物种聚集的地带可能会向北移动，欧洲也是如此，甚至有可能在热带和非热带物种区之间形成一个空白地带，也许会对这些地区的农业和林业产生影响。

Hawkins, B., & DeVries, P. (2009). Tropical niche conservatism and the species richness gradient of North American butterflies Journal of Biogeography DOI: 10.1111/j.1365-2699.2009.02119.x

Capturing cross-scale interactions

People studying ecological resilience talk about cross-scale interactions a lot. Yet people often claim that cross-scale interaction is in play without quantitative evidence. [Researchers from Argentina](http://dx.doi.org/10.1007/s10021-005-0091-9) in 2005 proposed to use regression on data sets collected in different years to identify the existence of cross-scale interactions.

The approach cannot tell what really is cross-interacting with other variables, yet. And being a statistical method, it requires a huge amount of data. Perhaps by regression of multiple series and types of data, and with the aid of conceptual models, this approach can bring more insight into the system.

Crowd-Sourced Science

In [an article](http://dx.doi.org/10.1016/j.tree.2009.03.017) published on TREE, J. Silvertown from the Open University, UK notes a trend that various ecological and evolution studies are engaging non-scientists in a unique way: by letting them collect and analyze data these projects are turning "lay people" into "citizen scientists".

There have been some long-standing projects (starting from early 20th century) that has managed to help scientists collect a huge set of data, most of which related to bird observation. It is pointed out that more data collection projects aided by improved field and software tools are on the horizon to help scientists better understand ecology and evolution of various systems in Europe and North America.

But it is important to note that although collecting data is an important scientific activity, merely doing so hardly qualifies one as a scientist. Arguably, the real meaning of "citizen science" can only be recognized when non-professional people actually take part in proposing hypotheses and analysis of data. The [Evolution MegaLab](http://www.evolutionmegalab.org/) project seems promising enough in this aspect.

The author also mentioned the potential of mobile devices as an instrument for collecting data and as a field guide. The camera and GPS functions of many of today's cellphone, for instance, should be extremely helpful if citizen scientists want to collect species distribution data.

Unfortunately the author did not mention any such project in other parts of the world, nor can I find any in short time. Given the history and experience of some of the citizen science projects, many countries in Asia, to say the least, should now have the capability to establish an environmental/ecological data collecting network. It will both benefit the professional scientists' studies and the science education of thousands of people.

Silvertown, J. (2009). A new dawn for citizen science Trends in Ecology & Evolution DOI: 10.1016/j.tree.2009.03.017

Serious Play, blog 与酸葡萄

Serious Play 是2008年[美国艺术中心设计会议](http://www2.artcenter.edu/designconference/)的主题词，在这次会议上艺术家 [Paula Scher](http://www.paulascher.com/) 专门做了以 Great Design is Serious (not solemn) 为题的[演讲](http://www.ted.com/index.php/talks/paula_scher_gets_serious.html)。她在演讲当中强调了 Serious 与 Solemn 两个概念的区别，我在这里姑且将其分别译为“认真”和“肃穆”。她说，许多孩子都是以玩耍的方式开始认识世界的，而且ta们对待玩耍的态度都是认真的。类似地，刚开始职业生涯的成年人在他们20来岁的时候最有可能取得巨大的进步，在30来岁、40来岁、50来岁……的时候取得的进步越来越小，如这个[职业生涯阶梯](http://www.youtube.com/watch?v=atn22-bmTPU#t=3m29s)所示。Paula 说，这是因为人们变得肃穆了。变得肃穆很容易，只要别人对我的工作有所期望，随着年龄的增长我自然会变得肃穆。但维持认真的态度却是非常不容易的事情，很多时候我们以为自己的态度是认真的，但其实只是肃穆的。而 Paula 认为，对于艺术家来说，有价值的作品来自于认真的玩耍。认真的玩耍代表着反叛、创新和改变的态度，其产物在肃穆的眼光中看来并不完美，但完善是交给肃穆的人的工作。

Paula 回顾了她职业生涯中4次“认真”之后变得肃穆的经历，并指出她认真地玩耍的机会都是来自于那些她刚刚接触的，完全“不够格”去做的工作。而当她的作品被主流开始接受以后，她不自觉地开始对主流的反应有所期待，而且她的风格也被其它人模仿，于是这时候的玩耍就变成了肃穆的工作。为了保持创作的生命力，Paula 的选择是不断尝试那些她“不会做”的项目。

我们的传统更多地强调务实和肃穆，小学生们进学校的第一堂课就是学习如何把手背在身后肃穆地听老师讲课，为了高考这个肃穆的目的，学生可以不用认真地思考上了大学以后何去何从的问题，只需要肃穆地应付考试；好不容易进了大学，毕业设计的时候一大任务就是肃穆地保证论文格式100%服从教务处一年一变的格式要求，至于论文写作的过程和背后的结论是否认真，倒是显得次要。在这种肃穆的氛围中成长起来的我们，在离开学校和发现了互联网这个无与伦比的玩具之后，选择了变本加厉地玩耍。以前有各种“恶搞”，现在有各种对文化和社会现象的山寨化。这些玩耍的主动者，动机无从知晓，他们也许是认真的，这些玩耍也确实传达了一些信息，强过那些肃穆却言之无物的所谓作品，但对于大部分被动地参与这些玩耍的人，他们的玩耍也许既不是肃穆的也不是认真的。有些玩耍是反叛的，但是它们都是建立在迎合大部分受众（网民）的口味，以及创作者熟悉的理论和工具的基础上，因而不构成认真的创新，也不构成对创作者自身的挑战和反叛。“嫦娥”撞月的新闻是肃穆的，网友们 PS 的探测器撞向美国国旗的玩耍是恶搞的，而计算嫦娥应该在哪里以怎样的变轨动作开始下降才能撞向那面美国国旗，或者撞向[伽利略环形山](http://en.wikipedia.org/wiki/Galileo_Galilei)来纪念伽利略开创天文观测400周年，这样的玩耍是认真的。

你也许会说，那是 Rocket Science，没几个人能算对。别忘了认真地玩耍的要素就是尝试“不会做”“不够格做”的事情，而且没人要求我们算得完美。我一直是一个肃穆的人，但现在我想我有理由尝试认真地玩耍的态度，因为科学虽然常常被看作是一个肃穆地在前人研究的基础上研究的过程，但不能否认往往是那些将其它领域的，别人认为“不够格”去谈论的成果带进自己研究领域，质疑现有状况的科学家才做出了开创性的工作，创造了新的经典。是的，我想科学甚至应该允许人们以玩耍的态度向她提出问题，甚至是质疑。而像[搞笑诺贝尔奖](http://improbable.com/)这样的玩耍，其意义之一也在于它以认真的态度鼓励看似不务正业，实际上最体现科学和玩耍精神的研究。

但是像气候变化否定论（Denial）和生物的“智能设计”这样的理论是否能在认真的玩耍的旗帜下，对科学界现有的理论发起质疑呢？我认为它们没能满足两个重要的条件：其一，它们可能是肃穆的，但不是认真的。翻开像 Roy Spencer 这样的全球变暖否定者和“智能设计”鼓吹者的文章，你可以看到ta们从遣词造句到表格图表，无不尽庄严肃穆之能事，但ta们从未表现出对既有理论的认真反驳；其二，它们不是玩耍的产物，玩耍要求涉足未知的领域，而这两种意识形态（实在不能称之为“理论”）的鼓吹者却都是固守着自己的知识和看法，对新进展和新学科如基因学提出的证据选择性失明。

关于我的 blog，我知道它既不像和菜头的 blog 那样引人入胜，也不像闾丘露薇的那样关心国计民生，更不像李淼和松鼠会的 blog 那样充满了专业的科学洞见，这里的绝大多数帖子对于绝大多数人来说都没有什么实用价值。它只是一个连自己学的是什么都没有搞得太清楚的人出于好奇心试图对自己相对熟悉的东西和不那么熟悉的东西都记录和评论一番，它不完美甚至不美。每次我看到 Google Analytics 里本来就少的访问量仅集中于几篇“实用”的帖子就觉得很囧，但容我酸葡萄一下，我认为这个 blog 作为一个没有确定完成期限的 project，完全符合 Serious 和 Play 两大要素，而当有太多的人真的关心它说了些什么，它就变成一个 solemn 的工作了，我宁愿这一天到得晚一些。

生态拓扑学：新瓶旧酒

Image via Wikipedia

1999年美国的 NSF 在[一篇论文](http://www.ingentaconnect.com/content/aibs/bio/2001/00000051/00000001/art00005)中提出生态拓扑学应该成为未来生态学研究的四大前沿之一（另外三个是地区物种池产生的复杂社群发展，生态记忆在生态过程中的作用，以及复杂系统的涌现特性）。这篇论文在[这里](http://www.planta.cn/forum/viewtopic.php?t=7256)有中文的简介。

最近在 Ecological Complexity 上发表的一篇论文则对生态拓扑学这个概念的应用进行了[综述](http://dx.doi.org/10.1016/j.ecocom.2008.11.001)。作者指出，生态拓扑学虽然被作为研究的前沿，但其理论和方法事实上至少已经被生态学家们应用了超过半个世纪。拓扑学的两大奠基人物 Euler 和 Poincaré 分别确立了这门学科的两大分支，Euler 提出了图论和网络拓扑学，而 Poincaré 则提出了用几何方法抽象动态系统的概念。这两种基本的拓扑学方法在生态学研究中都得到了应用。网络拓扑学促进了食物网等概念的研究，以及多种系统模型的建立；Poincaré 的流型概念则推动了 bifurcation 和跨比例作用等概念的出现和非线性生态模型的发展。

在今天，这些研究领域仍然是生态学中的热门问题。综述的作者指出，生态学中的许多数学方法本质上都代表了拓扑学的思想，深入对拓扑学的研究，有助于更好地评估对生态过程的跨比例理解，更好地定义系统的因果性边界，建立连接不同尺度的形式结构，通过系统结构研究物种互动，以及帮助人们理解那些不易直接观察的“高阶现象”。Panarchy 等研究系统不连续性的方法也与拓扑学概念有直接的联系。综述的作者认为，以更为规范的形式讨论拓扑学在生态学中的作用，将有助于更深入和广泛地理解复杂生态系统。将拓扑学与空间统计、GIS 等其它手段结合应用将帮助我们更好地理解自然。

当然，作者也认为将自身就是两个分开的部分的拓扑学显式地引入生态学研究中，会有一些概念定义和与现有方法整合的困难。也许我们不需要作为生态学分支的拓扑学，但引入拓扑学的方法是一个可能的研究方向。

Prager, S., & Reiners, W. (2009). Historical and emerging practices in ecological topology Ecological Complexity, 6 (2), 160-171 DOI: 10.1016/j.ecocom.2008.11.001

Yet another use of ice record

Today's ScienceDaily [reported](http://www.sciencedaily.com/releases/2008/12/081231131813.htm) a new possibility of ice core sample analysis, this time using bacteria frozen in the ice.

It was found that in ice core sample collected from Mountain Geladaindong, the abundance of bacteria is in accordance with $$\delta ^{18}\text{O}$$, which can serve as an indicator of temperature. It is already known that higher $$\delta ^{18}\text{O}$$ level implies higher temperature, now it seems bacteria abundance also increases with $$\delta ^{18}\text{O}$$, therefore it is possible to use bacteria numbers as an indicator of historical temperature change.

However, $$\delta ^{18}\text{O}$$ can also serve as an indicator of precipitation, with higher level in low-precipitation years. It has also been noted that in the ice core higher bacteria level concurs with higher amount of dust. So here's my speculation: it may well be that in dry years the dust activity is more pronounced, leading to more dust and bacteria precipitate on the glacier. In that case, bacteria itself is not a useful indicator of either temperature nor precipitation.

It is also interesting to note that the lowest bacteria level was found in 1938 and the highest in 1997. According to [Desert Research Institute](http://www.wrcc.dri.edu/enso/ensodef.html), 1938 was a strong La Niña year, while 1997 was a strong El Niño year. So there is possibility that the effect of El Niño/La Niña may have so strong signals that the actual trend due to climate change is harder to observe. Moreover, if the bacteria abundance is proved more correlated to El Niño/La Niña, it suggests the increased possibility that bacteria level is linked with precipitation rather than temperature, as [earlier research](http://ecosystems.wcp.muohio.edu/studentresearch/climatechange03/elnino/Ice%20core%20records.pdf) argued that precipitation is more correlated to El Niño than $$\delta ^{18}\text{O}$$ does.

On the other hand, if this method is proved feasible, it would mean that scientists have get hold of another relatively cheap way of deriving historical climate data, and do not have to deal with expensive isotope analysis. Similar method may also be used in lake sediment or peat analysis. But to validate this method, "we need more data".

Progress

Recently I have managed to derive a dynamic model for my research area, imitating a model proposed by Ludwig et al. (2002) [3.   D. Ludwig, B. H. Walker, and C. S. Holling. Resilience and the Behavior of Large-Scale Systems, chapter 2 Models and metaphors of sustainability, stability, and resilience. Island Press, Washington, D.C., 2002] for a rangeland.  Now I find that it is producing a range of interesting results.  More importantly, I think I can defy accusation that the model is manipulated to produce domains of attractions.  The hysteric behaviour and the appearance of domains of attraction/resilience are emerging from classic dynamic model functions, this is what I call fascinating.

The next step would be setting a range of scenarios, with different sets of parameters, see the behaviour and resilience of the system in these settings.

Furthermore, combining it with what I derived from remote sensing images collected for the last few decades, the model can go spatial to some extent.  Use the remote sensing image to determine the initial state for each pixel, run the model on them, with a specified parameter set for each type of pixels, the result may be very interesting.  Of course the computation would also be intense.  I need also to think about a) how do I verify the model and b) how do I parametrise the different situations for different pixels.

深搜索引擎

ReadWriteWeb 介绍了一个名叫 Infovell 的深度搜索引擎，据称作用是索引那些没有被主流搜索引擎如 Google 抓过的网页，包括各大学术出版商如 Oxford University Press, SAGE, Taylor & Francis, Annual Reviews 等等。Infovell 自己的定义也是 "Research engine"。我这里由于网络质量不佳只能看到 ReadWriteWeb 上的截图，看起来 Infovell 主要的特色是结合了 Web of Knowledge 将搜索结果按学科分类的功能并提供了方便的关键词修改系统，还有些提高可用性的改进例如高亮含有搜索词的句子和显示有同一关键词的不同主题文档之间的关系。

虽然 Google Scholar 现在并不是一个好用的搜索引擎，这个 Infovell 貌似也不是特别让人激动。它在描述自己使用的技术时提到了关键词搜索的一些固有缺点，例如关键词越多，得到的结果越少而且很可能相关程度反而不高。Infovell 宣称它索引了每一段话中各种可能的词语和短语的组合，而且没有网页语言的限制，这似乎说明它使用的不是语义的方法。现在像 Google Scholar 这样的搜索引擎的问题在于它不能搞懂关键词之间的语义关系，而且只会用文章被引用次数等等指标来排序搜索结果，用户可能很难找到含有特定信息的文档。比如我想找一篇关于澳大利亚北部降水对沙漠影响的文章，Google Scholar 给出的第一页结果中可能就有澳大利亚的学者研究纳米比亚沙漠的文章，而 "precipitation" 这个词只是在其参考文献中出现了一次。对于非语义的搜索引擎能把这个问题解决到什么程度，我持相当的怀疑态度。

Infovell 将在9月22日正式上线，按收费方式提供服务，并提供了30天的免费试用。目前的数据库似乎以生物科学期刊和文献为主。这个搜索引擎是否比 Scholar + Web of Knowledge 更有价值要到下周才知道了。

生态/环境研究的新挑战

Holling (1973)[1. Holling, C. S. Resilience and stability of ecological systems. Annual Review of Ecology and Systematics, 4:1–23, 1973.] 这样定义生态系统的 resilience：系统在发生重构和功能变化之前能够接受的最大扰动。而 Pimm (1984)[2. Pimm, S. L. The complexity and stability of ecosystems. Nature, 307:321–326, 1984. ] 在十年之后才提出 resilience 的另一个定义：系统受到扰动后回到初始状态所需的时间。虽然 Pimm 的定义提出较晚，但却得到了广泛得多的应用。而对于 Holling 的定义，虽然研究者往往会提及，却很少有人将其应用到实际研究中，以致到现在这个概念的研究者和实践者似乎已经成了一个不为人注意的学派。为什么 Holling 的想法应者如此寥寥？

Resilience and the Behavior of Large-Scale Systems（以下 RBLSS）这本书可以看作是这个久被忽视的学派争取学界注意的又一次努力，书中文章的主要作者包括 L. H. Gunderson，C. S. Holling，G. D. Peterson，B. H. Walker，S. R. Carpenter 和 D. Ludwig 等人，事实上他们就是仅有的几位我们通过一般的期刊搜索能比较容易地找到的，主张利用 Holling 的 resilience 定义研究社会-生态复合系统的学者。在书中他们重申了自己的想法，即 Pimm 的 resilience 的前提是不成立的，复杂系统并没有一个唯一、恒定、稳固的均衡（equilibrium）状态，相反系统可能有多个均衡状态，外力可以导致系统在这些状态间转换。在一个均衡状态附近（称为均衡域或吸引域），系统的变化是连续而接近线性的，可以用方程描述，但一旦变化超过了一定范围，系统的转变就是突然、非线性的。定义或者评价一个系统的 resilience，就是要找出均衡域的范围和其它可能的均衡状态。

这样的说法比较抽象，所以 Holling 的追随者们使用盆中的小球这个概念来说明：小球相当于系统，放在一个盆（均衡域）当中，盆的宽度就是 resilience 的强弱程度，而小球一旦越出盆沿，就会落入另一个盆，即一个性质、结构、功能都可能完全不同的系统状态。在数学上，他们则利用二分点这个概念来说明系统是如何离开均衡域的：类似我们熟悉的量变引起质变的思想，系统某些变量的取值会使类似下面方程的性质在这个取值附近发生巨大的改变：

$$\frac{dx}{dt} = -x(x^{2} - \alpha)$$

这类变量称为系统中的“慢变量”，变化往往较慢，却对系统的性质和功能有根本性的影响。到这里我们已经可以看到 Holling 的定义固然比 Pimm 的定义更能把握生态系统的非均衡本质，同时也避免了过度的还原论思想，但其实践比起 Pimm 的仅仅通过经验性的观察就可以测量的方法要困难许多，要求研究者对于系统的全面性质和各种内外影响因素都有较全面的了解，这在大的生态和社会经济系统中是难以做到的，难怪许多人望而却步。

也许正是因为这一点，RBLSS 这本脱胎于 workshop 的书将重点放在对大型系统的具体案例研究上。其研究的系统包括了主要的陆地生态系统如森林、湿地和草原，以及水生生态系统如湖泊和珊瑚礁群，研究方法也是多种多样，包括情境分析，数学建模，实地观测和地理信息科学等等。这些案例确实体现了 resilience 这个概念的普适性，但也暴露了它的一个重大不足，就是对于不同的生态系统缺乏一个一致的方法体系。即使在同类的生态系统中，由于物种和扰动因素的不同，研究者也往往不能套用书中给出的分析结果，而要自己从概念模型开始分析。在整个体系中缺乏“可重用”的部分，无疑也限制了这一概念像环境影响评价那样成为工业和学界中通行的做法。

当然，仅从框架来说，这本书也提供了一个可供套用的模式，包括概念模型的建立，跨比例过程和慢变量的识别等等，可供有意利用这个概念进行研究的人参考。但我认为这本书更大的意义在于指出了一条有可能让生态学研究从目前的还原主义研究方法飞跃到真正综合性的，把“人”这一因素纳入研究范围的研究的途径，向传统的研究方法提出了挑战。同时，相对于基于 Pimm 概念的，以某一特定状态为目标、要求保持和固守的环境管理，Holling 的 resilience 概念使得他能够提出新的生态/环境管理思想，即适应性的管理，承认生态和社会系统的变化和非均衡性，这比 resilience 这个概念本身有更大的实践意义，已经在一些具体的环境管理方案中得到应用。在 resilience 的评估当中，又要求研究者对现有的生态模型进行检验，并研究和归纳具体生态系统当中的各种主体和相互作用，这在一定程度上也促进了传统生态学理论和方法论的发展。从这个意义上说，这本书和 resilience 概念本身，对于生态和环境科学的研究者来说具有超越直接价值的意义。

How will statistics go spatial

摘要：讨论空间统计的元素和面临的困难以及可能的发展方向。

When I consider the organisation of my thesis I want to boast that my study has used free software GIS -- Grass GIS as well as free statistics software package/language R to achieve spatial statistics capacity where even many commercial software packages are handicapped, as the two champions in the free software world can cooperate almost seamlessly, processing map and data back and forth and providing convicing statistics on a map.  However after a second thought I realised that "statistics on a map" is not the equivalent of "spatial statistics".

Although Geographic Information Systems were designed and built with statistics in mind, geographical data in its early days only were included as a context for other data such as census or measurement.  From an early GIS-generated map we can obtain information such as the total number of cars in UK and their distribution in various cities whose population is larger than x.  This is of course useful information but is insufficient now that people have more demands on geographical data itself, partly thanks to Google Maps/Earth and all those mash-up applications.  Therefore the statistics ability of GIS needs to be enhanced, allowing it to be able to process geographical data both as an explanatory variable and a dependent variable, instead of just as a context.

By geographical data I mean the following attributes:

Vicinity	Direction
Gradient	Visibility
Fragmentation	Shape
Spatial correlation	Accessibility
Anomalies	Agents and behaviour

This is, of course, just a non-exhaustive list.  At present most GIS can only process a few of these attributes at a not very satistying level.  To enhance the ability of GIS, there are some hurdles that have to be overcome first.  The biggest one may be the problem of describing.  The nature of GIS and its supporting technology determine that GIS use mathematic-based, reductionist approaches to store and express data in a discrete way, however geography is continuous, with some concepts that are difficult to quantify.  How do we state "the habitat is located around the intersection of a footpath and a main highway bridge near Baxton, with a thinner canopy in the northern part providing more favourable conditions for lower storey plants" to a computer?  A promising direction of development seems lies in semantics and cognition science.

Another problem is the model used.  In geography everything is linked, then how does one represent such link with mathematical models?  Besides, statistics in its traditional sense is the aggregation of measurements, which can bring unexpected results in geographical studies.  This is especially a prominent problem if social processes are involved.  At least, the simple aggregation based on descriptive statistics will have a more limited role.  New techniques such as fractal mathematics and trend analysis may have more contribution to the solution to the problem in the future.

The more developed spatial statistics perhaps also will put a demand on more sophisticated spatial data, although the improvement of methodology can alleviate such demand.  When statisticians and geographers look at more subtle aspects of natural and social interactions going on on the ground, they will need more data such as the heteogeneity within a "patch" and individual behaviour.  In return GIS fed on these data may provide some insights in design of public spaces, priority of conservation, and so on.

I decide to wait and try to contribute to the (r)evolution of new spatial statistics.  Before that takes place my thesis will be "using GIS technology and simple statistics with a spatial concern".

Many of the ideas in this entry comes from or are inspired by this slide by Michael F.Goodchild in University of California, Santa Barbara.

Emergence, or merely a mistake?

When I conduct DFA on my NDVI data, I found some interesting behaviour of the result.  Apparently the system behaves differently in different spatial scales, which is reflected in the fluctuation-temporal scale correlation and the slope of $$\text{log}F(L)/\text{log}L$$ (i.e. $$\alpha$$).

The DFA result for the whole map is like the picture below, $$\alpha$$ is between 0.5 and 1, indicating a correlation between fluctuation and time.  But the pixel results are seemingly random (this is expected), and all have $$\alpha << 0.5$$ (this is quite unexpected), indicating anti-correlations.

After examined the scripts and data in question I believe the design of the experiment has no fault that I could find.  I have also considered the possibility that nonstationarity and trend may have effects on the result, but the NDVI data I used have already had seasonal trend eliminated, while nonstationarity is not likely to cause such dramatic change in $$\alpha$$.  The result, if not a technical failure, will suggest that the system's behaviour at 8km (single pixel) and regional scales are different.  At the fine-grained scale, the fluctuation reduces as temporal scale increases, i.e. a fluctuation is likely to cause smaller and smaller fluctuations in the distant future.  But at coarser scale the behaviour is inversed, a fluctuation may cause larger and larger fluctuations at long intervals.

It is possible that the system's behaviour at coarser scales is the result of relatively simpler interactions at finer scales, creating a phenomenon known as emergence.  But the question is, if it is really emergence, what is the critical scale that such behaviour shift takes place.  Besides, what I have now is at best correlation, are there any intrinsic mechanism that determine such emergence?  In ecology, has there been similar emergence taking place in the shift from community to biome scale?

The system I'm studying is a pastoral socio-ecosystem.  If there is really emergence like this, does it suggest that the system at the farm scale is resilient but as a whole is not [1. There are some resilience researchers noted the problem of emergence, such as

Allen, C.R., Gunderson, L. & Johnson, A.R., 2005. The Use of Discontinuities and Functional Groups to Assess Relative Resilience in Complex Systems. Ecosystems, 8(8), 958-966. and

Folke, C., 2006. Resilience: The emergence of a perspective for social-ecological systems analyses. Global Environmental Change, 16(3), 253-267.]?  This is a really intriguing question.  I just hope it is not raised from a false observation.

Find underlying fluctuation using DFA

We often have to deal with NDVI time series like this.  What does it tell on earth?  Very little information can be identified from this figure and its subsets.  However, techniques like DFA allow us to dig some information on the fluctuation and its cause.

Detrended Fluctuation Analysis (DFA) was first used in DNA analysis to identify whether the purine and pyrimidine base's distubution is scalable, or fractal.  Later it has been used by many to examine whether a bounded time series has fractal characteristics and is self-similar.  First of all the time series has to be converted to a random walk series using equation:

$$X_{t} = \sum_{i=1}^{t}(x_{i}-\langle x_{i} \rangle)$$

Where $$\langle x_{i} \rangle$$ is a value within the range of the time series, or a variable that changes with the element in the time series according to certain rule.  This is the "detrending" step.  Once the series has been converted, one can split the whole series into a number of non-overlapping "windows", each with a equal number of samples or length $$n$$.

Least Square fit is done to each of the windows to get the local trend.  The root-mean-squared deviation from the trend is called fluctuation:

$$F(L) = \[\frac{1}{L}\sum_{i=1}^{L}(X_{i} - ai -b)^{2}\]^{\frac{1}{2}}$$

For different window size $$L$$ we can obtain different $$F(L)$$.  On a log$$F(L)$$ vs. log$$L$$ plot, we have a straight line whose slope is $$\alpha$$ if the random walk has self-affinity.  The values of $$\alpha$$ have different meanings.  $$\frac{1}{2} < \alpha < 1$$ indicates that the fluctuation is correlated with time; while $$\alpha$$ close to 0.5 indicates white noise [1. Detrended fluctuation analysis. (2007, October 31). In Wikipedia, The Free Encyclopedia. Retrieved 13:15, August 1, 2008, from http://en.wikipedia.org/w/index.php?title=Detrended_fluctuation_analysis&oldid=168313780].

This technique is further used to identify whether there is identifiable trend in the variation of NDVI throughout years.  Telesca et al. (2005)[2. Luciano Telesca, Rosa Lasaponara, Antonio Lanorte, 1/f* fluctuations in the time dynamics of Mediterranean forest ecosystems by using normalized difference vegetation index satellite data, Physica A: Statistical Mechanics and its Applications, Volume 361, Issue 2, 1 March 2006, Pages 699-706.] has utilised the technique and identified positive feedbacks and reduced adaptability in Italian forest ecosystem.  Note that NDVI has natural periodic fluctuation due to seasonality, before DFA is applied, one should first reduce this fluctuation from the data.

This technique may also be applied in my study as I am also looking at NDVI trends.  Some spatial analysis may be added by using the technique on single pixels and/or "windows".

再看 Contact

Contact (1997)

首先表示对小p同学的感谢，感谢他从 Sheffield 把 DVD 带给我。

不太记得上次看这个片子是什么时候了，不过可以确定的是那时候我已经有了电脑，同时还没有从高中毕业，因为我看完电影以后不久就下载了 SETI@Home 的客户端，然后问我的一位同学有没有看这个片子。那位同学高中毕业后就很少联系，直到不久以前才在北京又见到。这样算来，我上次看 Contact 已经是至少6-7年前的事了。

对于这部电影，我想我这样一个工科生的语言并不能表达它是怎样带给我兴奋和长期的激励──关于科学和理想主义的激励。借用女主角的一句话：“Poetry....They should send a poet!”它提醒了我们，习惯于在家购物，网上冲浪，足不出户的现代人，还有一些东西是“out there”，有一些东西是“above us”的。我们所受的关于科学的教育告诉我们，不要好高鹜远，要在前人的基础上慢慢前进，但这部影片对我的作用，无异于在泥沼中缓慢前行时头顶的星空，它提醒我，在单调重复的科学研究背后，永远都有值得追求的美丽的“Truth”。

六七年过去了，我电脑里运行的分布式计算程序已经从 SETI@Home 变成了更加 practical，也许甚至更加 profitable 的 Folding@Home，我身上的理想主义色彩也早已淡去不少。但是重新看到 Ellie 这个角色，仍然让我兴奋。电影里她也面临着寻求经费的压力，同行的排挤，来自社会各界的怀疑和反对，她缺少的是其他电影里科学家都有的先进的设备，花不完的经费，还有聪明又性感的助手──当然她的助手是很聪明的──而她的理想主义，或者说她的信念，始终支撑着她。我们在老一辈科学家的故事里也常能看到这种理想主义的存在，而科学界的现实也许是排斥这种理想主义的，但我确实相信科学发现的背后，必须要有独立于 Practicality 和 Profitability 之外的动机。所以我喜欢 Ellie 这个角色，喜欢她代表的理想主义精神。

除了“信念”，影片的第二个主题，关于科学与宗教的关系，几乎每篇关于 Contact 的影评都会提到。我在这里不想深入。当看到电影里 Ellie 被问到是否相信上帝时，我也试图帮她回答。做为一个受科学教育长大的人，我不相信人造的宗教，也不相信做为人类创造物而反过来主宰宇宙命运的上帝──那只是一种人类沙文主义的 delusion。但我确实相信这个复杂的世界是被一些更高的原则所决定的，为了方便理解，我们可以称其为上帝，但它肯定不是我们所创造出来用来膜拜的偶像，住在九天之上俯瞰众生。相反，它可能只是一些可以从量子力学方向试图理解的“弦”，或者其他更渺小而基本的东西，组成了我们，组成了世界。但是，纯粹地从科学的角度理解这些原则可能也是危险的，至少从我们现在的认识，我们知道像“爱”“信仰”这样的东西不能被分析，不能被量化，所以我们在科学之外还需要 humanity 来帮助我们更好地理解自己。对于影片的这个主题，我认为与其说它是科学与宗教的共存与和解，不如说是科学与人性的共存与和解。可能唯有如此，我们才能认识自己和宇宙，成为宇宙大家庭中成熟的一员。

生活的压力让我们需要面对现实，对于科学家来说也是如此，但 Contact 在生动地刻画了科学家所面临的现实的同时，也提醒了我们还存在着一个广袤而美丽的宇宙，我们每一个普通人都是它的 small and trivial, yet unique and precious 的一分子，这足以引起我们的许多思考。也许有人认为这不过是畅销小说改编的好莱坞科幻片，但在我看来，它是一些真正有创造力的人对于人类的自省，是我们走向启蒙的一小步，也许这一小步会引领我们去接触智慧，接触未来。

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