One common way to quantify vulnerability is via environmental or plant physiological thresholding studies. Often some force of stress, whether related to climate change or other anthropogenic activities, can increase for some time and to a certain limit before having negative consquences. Past this 'threshold' the ecosystem's resistance and ability to recover is overcome and detrimental effects compound. I've used thresholding concepts in both drought stress studies related to climate change ecotone shifts and also on air pollution impacts, both related to conifer forest health, with success.

I suggest you define a process that you consider most important for your particular ecosystem and how this process can be quantified (we usually use some measure for decomposition). You then stress your system and measure this process before versus after (or in parallel, depending on your experimental design). These studies might alos include ecophysiological studies on single species to get a first idea of the reasons of the vulnerability found...

You can use ecosystem processes, such as productivity, or nutrient cycling. I was involved in research on vulnerability of grassland ecosystems to land-use change (extensification/cessation of grazing regimes) and our approach used community-level values of functional plant traits, and linked them to ecosystem processes.

As others mention, you need to firstly define what ecosystem is of interest to you, then select or identify specific processes, look at the variables that influence the process, and then see how these variables may be affected by climate change, keeping in mind some of the seasonal, interannual and interdecadal variability seen in the past couple decades may also be influenced by changing climatic patterns. For example, flow in a stream can change with land use as well as precipitation variability arising from climate change. One can then look at what different flows may mean to oxygen levels, nutrient spiralling, decomposition, biotic composition etc. and also carry out a scenario analysis at diff levels of precip to see how that affects flow. One can then select a suite of vulnerability indicators (such as dissolved oxygen in a stream) and quantify the variability in DO as a response to flow.

There is a good model for evaluating ecosystems here: http://science.nature.nps.gov/im/units/sfcn/monitoring.cfm

As Amartya points out, understanding cause-effect linkages are essential for identifying key indicators to observe systematically. I would add that Hubbell's neutral theory of biodiversity appears to be a simple, effective way to identify vulnerability of patch-level extirpation or invasion from non-native species. A relevant article can be found here: http://userwww.sfsu.edu/parker/bio840/pdfs/neutral/Hubbell05.pdf

Remember, a system can be vulnerable to change from a variety of drivers. Nutrients, hydrology, fire risk, disease processes, and exotic species can all drive degradation processes, and each driver operates in a unique way.

Have a look at our 2012 report on Climate Change Impacts and Vulnerability on Canada's Pacific marine ecosystems for an example of an expert-based and habitat-based spatial assessment of climate change vulnerability. This may give you some ideas.

Kind colleagues, thank you very much for your great ideas, comments, suggestions, and examples.

The specific ecosystems of interest are irrigated cropland system and dry cold grassland system. I understand there are two methods to identify the vulnerability: one is based on processes such as water and nutrition cycles, as commented by Amartya Saha, Carly Golodets, and Martin Zimmer; the other is based on the cause-effect linkage, as commented by Jed Redwine. Both of two methods could generate some indicators and indexes, but both of them need thresholds to identify the vulnerability, then the question comes: how to reasonably determine the desirable thresholds? For example, grassland will fail to grow during one or several dry years when drought index is out of a certain threshold. This threshold may work for short-term. However, the grassland will recover when wet year(s) returns. Then, does this selected threshold still work?

In a word, I am confused about how to quantitatively identify the resilience range of an ecosystem? Out of the resilience range is vulnerability. If you have such ideas, methods, or experiences to share, please kindly let me know. Thanks again.

You could look at the variability in your measured index, and determine a threshold for vulnerability based on this variability. I have been working on vulnerability of rangeland productivity (from desert to Mediterranean) to climate change (reduced and more variable rainfall). We looked at the ratio of biomass CV to rainfall CV to get an indication of the vulnerability of our different studied rangelands.

I fully agree with the response from Amartya. You can see some examples for marine waters in my profile. For instance, a recent paper on macroalgae, but also others on coastal vulnerability

Please (re) consider what you mean by vulnerability and resilience. These concepts are often used without being properly conceptualized. Which means that you have to define them carefully and translate them into operational units. Climate change (and which aspect exactly, temperature increase, temp variability, precipitation changes..) affects both production and man-made cause-and-efffect chains. So, figuring out the causal links you want to investigate is essential. There is no discrepancy between searching for the relevant causal links, and the process-based approach. One of the aspects you have to consider is the parameter's spatial and temporal variability, linking to the time and geographical scale of the effects you are interested in. However, this is not as straightforward as it looks. Why should any time frame or spatial scale be relevant, and for whom? Maybe policy-based or stakeholder consultation may inform you about what is thought of being relevant (apart from you having your own idea about what should be studies of course).

So, finding the right parameters to study is one thing, but finding thresholds for vulnerability is looking for the holy grail. Setting up the 'right' indicators and thresholds is no objective ecological search for the truth; they are heavily laden with normative (personal, cultural, political) concepts. A threshold should indicate any border you (as a society) would not want to cross because of the negative impact it has on the goods and services it provides. There simply is no objective level of 'good' ecosystem functioning. Involve what is being valued by stakeholders, within the borders of what an ecosystem may provide (its carrying capacity). If biodiversity is more valued than productivity (as an example), then management focus may need to shift from productive systems to diverse systems (this is just an example, not my personal opinion). But, the essence is that you have to be transparent about why you want to estimate a specific parameter for vulnerability. Without that, the whole use of this word is meaningless.

Hi, dear Dr. Boon

I really appreciate your answers. I agree with what you have said. Finding right parameter, indicator, or index, and then identifying thresholds is the only way to evaluate the vulnerability of ecosystem. In applications, cause-effect analysis may help to find right parameter or index, but it is very hard to find thresholds. Your comments inspire me. Scenario analysis for stakeholders may work to find suitable borders.

Dear Zhigang Sun / all, - indeed a relevant and important issue that you are discussing please have

Article Assessment of climate change impacts on the quantity and qua...

sorry - I pushed send b too fast :-) - in the two attached papers you will find some considerations on the issue -especially in the paper by Hinsby et al.

- I'm apparently not used to Research Gate - here is the paper that you may find interesting and relevant...

Article Threshold values and management options for nutrients in a c...

I agree that identifying thresholds is the key aspect for defining vulnerability of an ecological system for change. An example of the process of defining thresholds, and then using these in a long-term simulation model to identify the likelihood that an ecological community will be present is found here: http://www.evergladesplan.org/pm/recover/recover_docs/perf_measures/ge_slough_veg_pm_final_092611.pdf

The thresholds were identified using experiments. And then a 3.5 decade long pattern of observed hydrological conditions is summarized with four metrics, and each metric is visualized with a return period plot. This approach could be easily adapted to drought intensity or temperature metrics. And if you can access downscaled climate model data, then it is easy to compare the recent history of conditions with a set of climate change scenarios.

Ultimately, choosing contrasting summary variables helps a lot, because no one metric (or driver) determines the health of a grassland. Instead a healthy grassland occurs when it is not too dry, not too wet, not too hot, and not too cold. So using the thresholds of metrics defining different types of "extreme events" can help recognize the proportion of years when a healthy system occurs versus the proportion of years that a compromised system occurs.

Also, there are different degrees of resilience. The amount of aboveground biomass in a year can be affected by temperature and moisture conditions. The ability to recover aboveground biomass following a disturbance event is affected by a different set of temperature and moisture patterns. The ability of a grassland community to recover from a seedbank is affected by a different set of temperature and moisture patterns.

This is a similar point to Dr. Boon's post. I think the good part of the performance measure that we developed is that it clearly identifies the rationale for which metrics were developed.

Zhigang, thanks for this stimulating question. In my opinion, the best way to assess ecosystem vulnerability and resilience is to evaluate effects of multiple stressors (either pulse or constant exposure) within a quantitative ecosystem modeling exercise. For cropland and grassland systems, this approach is more of a challenge than for freshwater systems, but it is still feasible. Even when data are very limited, it can help one identify key species and strong interactions within the biological community that control community structure, potential trophic cascades, alternative system states, and tipping points. All of these affect vulnerability and resilience.

I think this paper will be very useful to you. It contains methodology for mapping ecosystem vulnerability and risks and is based on vulnerable species and habita mapping techniques

The paper is Bianchi et al., 2012, Diversity, 4: 419-452.

open access journal site : www.mdpi.com/journal/diveristy

That is a very broad question with many potential approaches. I think you need to clarify your question and refine a specific focus- as stated the question is to broad/vague to be easily answered.

If you are looking for pragmatic approaches on the issue, here is a methodology (Loidi et al., 2007) based on phytosociology which I have used and find useful: https://www.researchgate.net/publication/233817400_Vegetation_Science_and_the_implementation_of_the_Habitat_Directive_in_Spain_up-to-now_experiences_and_further_development_to_provide_tools_for_management?ev=prf_pub

The 1994 proposal from the same author (Loidi J., 1994 - see above article references for full reference) mentioned vulnerability as one of the considered criteria, but in this more recent proposal the adopted term for this criteria was resilience.

Article Vegetation Science and the implementation of the Habitat Dir...

For social-ecological sistems like those you are dealing with perhaps few papers in my profile can be of interest to you like "indicating fragility .....; "indicating retrospective resilience of real habitats in a landscape..." (dealing also with thresholds); and "highlighting order and disorder...." (addressing also weather extremes).

Best

Have you ever heard of the Millennium Ecosystem Assessment project? Check their website for more info http://millenniumassessment.org/en/Framework.html

I agree with Saha. is is difficult to isolate one responsible factor for ecosystem vulnerability. It's depend on the ecosystem. eg. addition of nitrogen fixing plant to nitrogen poor ecosystem will increase the n content of that ecosystem. Then what will happen to biota adapted to live under poor nitrogen. So which character that we can used for vulnerability determination.

Sena

We have conducted several approaches on this and they are used by authorities. It could not be perfect, but has been vaildated by experts and local communities and at the end help to decision makers, some examples: http://www.ciifen.org/index.php?option=com_content&view=article&catid=69&id=511&Itemid=83

Hi Rodney, thank you very much for your comments. I would appreciate if you could recommend some related materials in English because I don`t know Spanish.

Hi Zhigang, these publications can help, although are not specific enough as the spanish ones: http://www.hks.harvard.edu/var/ezp_site/storage/fckeditor/file/pdfs/centers-programs/centers/cid/publications/student-fellows/wp/010.pdf

http://www.unep.org/maweb/documents/bridging/papers/metzger.marc.pdf

http://www.eldis.org/go/display&type=Document&id=60494?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+eldis-cdkn+%28CDKN%29&loclang=en_gb#.UfkGC9I9-Lo

Many thanks, Rodneg. I am going to browse the websites you recommended.

I am pleased that Alessandro immediately considers this to be a problem in applied math - specifically numerical analysis. However, I would like to hear it from Zhigang Sun that he expects a quantitative solution. If quantitative, has he any experience with simulators and would a computer simulation with a simplified model be adequate. I am a little uncomfortable with the notion of "keeping it linear". It strikes me that the system is probably highly nonlinear and probably does exhibit many "interesting" nonlinear phenomena. (I recognize that the victims of catastrophes may not find them so interesting.) I am a rank amateur when it comes to ecology; but, I can't help wondering if it might be better to model non-linearity in a eco-sub-system than to linearize the entire system.

I don't have the answer, but you might wish to to look at the work coming out of an IUCN working group on coming up with a Red List for Ecosystems. You'll note that because there is an explicit aim for comparability between systems, some niceties get swept under the carpet. In a particular case study, one can be more detailed. Recent paper here:

http://www.plosone.org/article/info:doi/10.1371/journal.pone.0062111

One interesting problem in forestry ecosystem is discussed in one of paper:

"Mathematical analysis of a delayed stage-structured predator–prey model with impulsive diffusion between two predators territories"

http://www.sciencedirect.com/science/article/pii/S1476945X12000657

If the ecosystem you are interested in contains microorganisms, you can study the changes of biomass as affected by human activities. Beside that you can study microbial activities such as nitrification, denitrification, organic oxidation, oxygen uptake rate...etc.

It is not necessary to know the actual dynamics of ecosystems to pinpoint their vulnerable links. These can be determined from a weighted network of exchanges among the compartments. See (http://people.biology.ufl.edu/ulan/pubs/Cnp.pdf).

I fully agree with Alessandro. What an expert solution ! At the same time bio-economics modeling can also be thought of.