Biotic interactions and jSDM – report from a workshop at the Ecology Across Borders conference in Ghent, Dez 2017

This guest post by Carsten F. Dormann, with inputs from Casper Kraan and the panel (see below) summarises the results from the short workshop “Biotic interactions and joint species distribution models” at the Ecology Across Borders BES/GfÖ/NEVECOL/EEF-meeting 2017 in Ghent, Belgium. The purpose of this event was to exchange thoughts and questions about joint Species Distribution Models (jSDMs) and their ecological interpretation, in particular as indicators of biotic interactions.

1 The Panel

The workshop was organised and moderated by Carsten Dormann and Casper Kraan (who regrettably was ill and could not attend). A panel of five people using/developing jSDMs answered questions (or comment on points of views) expressed by the workshop participants (“audience”): Heidi Mod (Uni Lausanne, CH), Jörn Pagel (Uni Hohenheim, D), Melinda de Jonge (Radboud Uni, NL), Florian Hartig (Uni Regensburg, D) and Nick Golding (Uni Melbourne, AUS).

2 Introduction (CFD & CK)

In the workshop, we implicitly expected some familiarity with jSDMs, either passively (as readers of some of those recent papers), or actively (as users of the various available softwares). For novices, who want to get an idea of what jSDMs are, how they may be constructed and applied, we provide here a short introduction that was not part of the workshop.

2.1 Separating biotic interactions and environment

Attempts to fit/plot/understand associations among species is, of course, much older than jSDMs. For example, Braun-Blanquet (1964) called consistently occurring plant communities “associations”, and vegetation scientists have used ordination to depict such associations. In this wider sense, a rich literature of methods exists to identify associations among species (Fig. 1).

Acr38025488515202857988.png
Figure 1. Approaches to detect associations among species, and some of their characteristics. From Dormann et al., in revision. See also Nieto-Lugilde et al. (2017).

If we want to interpret species co-occurrences as positive/negative associations, it is crucial to separate the species-species signal from environmental effects on occurrence/abundance, instead of analysing “raw” co-occurrence data directly, e.g. through correlation analysis (Harris 2016). Figure 2 shows, on the left, a correlation matrix for some dozen soft-sediment marine organisms in New Zealand seagrass meadows resulting from a jSDM, and, on the right, the same correlations based on per-species residuals after accounting for environmental preferences in a jSDM. Clearly, most associations in the raw data can easily be explained by similar environmental preferences (“niches”).

Acr38025488515201658686.png
Figure 2. Correlations in raw abundance data (left) and in model residuals, after removing the influence of environment in driving occurrences (right). Data and analyses by Casper Kraan, unpublished.

The idea of jSDMs is therefore to simultaneously estimate the environmental niches and species associations, where associations (“interactions”) mean residual covariation in species occurrences, after accounting for environmental effects. A good introductory review to the field is provided by Warton et al. (2015). The more recent review by Ovaskainen et al. (2017) is (even) more technical. Both share the same fundamental outlook, but emphasise different details differently. Historically, Latimer et al. (2009) were probably the first to use the “modern” form of jSDMs (i.e. linking individual regressions through their residuals), but similar approaches soon followed from other groups. Pollock et al. (2014) were the first to use the term “joint SDMs”.

2.2 Technical definitions

Technically, there are two ways in which independent SDMs can be “joined”. The first is linking their parameters, which leads to so-called multispecies models, and the second is estimating residual (after environment) species covariances, which leads to “real” jSDMs.

  • Multispecies models: The idea here is using data on multiple species simultaneously for better parameter estimation. (“joint estimation”), e.g. mixed-effect models with species as random effect (see Ovaskainen & Soininen 2011, Ovaskainen et al. 2017). In a somewhat uncommon formulation, we could write that as a set of single regressions connected through hyperparameters on their parameter estimates (i.e., the random effect):
    Screen Shot 2018-04-06 at 5.31.20 PM.png
  • Joint species distribution models: unlike multi-species models, which use the multiple species only to inform each other on their parameter values, a “real” jSDM looks at species associations. It can thus be defined as  “A parametric statistical model for the abundance of multiple taxa (usually species), accounting for correlation between taxa as well as response to predictor variables” (from Warton et al. 2015). In a simplified notation we could write this as:

Screen Shot 2018-04-06 at 5.30.42 PM.png

For example, BayesComm fits this (type of) jSDM, while Pollock et al. (2014) combine both parts and have both parameters and errors drawn from a multivariate normal distribution. It should also be noted that the multivariate normal distribution MNV in the formulae is the traditional choice, but this assumption could of course be relaxed to include other distributions as well.

2.3 Biotic interactions interpretation

Most discussions about jSDMs center about the association matrix, which some interpret (with qualifying statements) as hinting towards biotic interactions. This is an ecological interpretation of a so far purely statistical matrix that describes species-species associations after accounting for environmental effects.

Note that most jSDM-papers are very cautiously worded and refer to the correlations of the residuals as “associations”, rather than interactions. Indeed, Harris (2016) showed for simulated interacting communities that the compared approaches (except his mistnet approach) may easily detect spurious associations and hence would incorrectly infer biotic interactions. This conclusion seems to be corroborated by simulations of Laura Pollock, as presented the day after our workshop at the meeting, which showed that strong competitive interactions are reliably detected, but errors are high for weak or facilitative interactions.

2.4 Software

While the first approaches to jSDMs were coded in JAGS or even C, there is currently a wider selection of R-packages that can be used for this purpose. Some promising approaches are

3 Notes from the panel discussion

The following questions were collected from the audience, and then passed on to the panel. Panel responses are given in italics. Due to the shortness of time, and complexity of the topic, we could only address a few questions. Questions that were not addressed during the discussion are still listed here, but stand unanswered. Feel free to address them in the comment section. (Many thanks to Florian Hartig for his dual role of taking notes and addressing questions!)

3.1 What are the goals/possible applications of jSDMs?

  • Do we have examples where jSDMs have contributed new knowledge?
    • Currently, jSDMs have generated new interpretations of the data, but also due to the difficulties of interpretation (see below), they have probably not (yet) created fundamentally new knowledge in ecology. In the future, jSDMs may eventually be used mainly as a hypothesis-generator / pattern synthesizer, possibly to be followed up by more direct / experimental investigations of detected interactions / species associations.
  • When can we clearly interpret co-occurrence as a signal of ecological interactions?
    • Rarely, see also discussion below. jSDMs highlight co-occurrence patterns that deviate from environment-only expectations. There are several explanations for such a pattern, of which a true biotic interaction is only one possibility. Moreover, a positive signal at a particular scale (e.g. 10km grid) does not necessarily mean that a biotic interaction is positive / facilitative. Also with a predator-prey interaction, one might find both species more likely close to each other than expected from pure environment. 

3.2 Technical questions

  • How to do model selection with jSDMs?
    • Standard AIC etc. in principle possible, but the usual problems with counting df in mixed models and poorly supported by most packages. Also, runtimes are typically prohibitive to dredge jSDMs.
    • In Bayesian approaches, regularisation priors may be a good alternative to model selection.
  • Can we account for spatial and temporal autocorrelation in jSDMs?
    • For spatially structured associations see Ovaskainen et al. (2016); for spatio-temporal jSDMs see Schliep et al. (2017). Also Thorson et al. (2016; Global Ecology & Biogeography 25, 1144-1158)
  • What are the benefits for prediction, and can jSDMs be extrapolated?
    • Prediction may benefit from jSDMs, compared to multispecies models, but it depends on the context, e.g. on how important BIs are. Also, it must be noted that the interaction part increases model complexity and thus may increase predictive errors if the data is not sufficient to constrain these additional degrees of freedom (bias-variance trade-off)
    • Whether predictions are improved also depends on what we mean by predictions and extrapolation. There are at least three types of jSDM-based predictions: (1) conditional, i.e. providing abundances/occurrence information for all but the target species; (2) unconditional, i.e. estimating abundances/occurrences from XX alone, for all species; and (3) marginal, by integrating over all non-target species.
    • As usual, we can test predictive power and estimate predictive errors by using process-based models as references (truth), or by cross-validation if sufficiently large datasets are available.

3.3 What are the assumptions, and what are the statistical properties of these estimators?

  • Statistical: are confidence intervals reliable?
    • As always in statistics – yes, when the model assumptions are met.
  • Structural assumptions/confounders, how can we safeguard against missing predictors, could BIs confound environmental effects?
    • Associations are assumed to be constant, i.e. independent of the environment (but see Tikhonov et al. 2017 for a relaxation of this assumption).
    • Very difficult to safeguard against missing environmental, which are in principle always an alternative explanation for signals in the association matrix.
  • How broad taxonomically and functionally/trophically should a jSDM be?
  • What about asymmetric/trophic interactions? (Note: Current jSDMs fit a symmetric association matrix; thus, the effect of A on B is the same as B on A. This is rarely ecologically plausible. For an exception, see packages mistnet, referenced above and Schliep et al. 2017.)
    • Complicated. Technically, it could certainly be done, and has been done in special cases (e.g. Schliep et al 2017 GEB), but it might be computationally very costly. As argued earlier, it is anyway difficult to directly interpret association patterns between species as measures of ecological interaction strength or direction. It is therefore questionable if it is useful to invest excessive amount of energy in making these “non-interactions” ecologically realistic.

3.4 Data properties

  • Detection probability, possibly variable across species, possibly interacting with other factors (also biotic).
  • How to deal with very rare or very common species?
    • Could increase uncertainty, but also improve fit. In doubt, keep in the analysis.
  • Are occurrence data suitable at all for inferring BIs?
    • These are ecological questions, irrespective of jSDM. Is it sensible to interpret BI at this spatial/temporal scale? Data are often not points in space/time, but aggregates over years and hundreds of square kilometers. Remember that interactions are between individuals, not species, i.e. at very small scales.
    • Is the environmental data quality high enough and does it contain important predictors?
    • Is an interaction a priori sensible, e.g. expected from experimental evidence of these species?
  • Can biotic interactions drive range margins?
  • Data problems: are species maps/records uncorrelated? For example, if plant distribution data originate from vegetation releves, we actually have point-co-occurrence data. After turning them into (single-species) range maps, this information is lost, and co-occurrences in the original data may disappear after range mapping.
    • Indeed, this points to a problem in data handling. Detection probabilities may not be independent: if I expect a species in a certain vegetation, I will be on the look-out for it, thereby biasing detection probabilities and invalidating the independence among species (see Beissinger et al. 2016, Warton et al. 2016).
  • How to accommodate different spatial scales of species/BIs? For example, a lynx will interact at much larger spatial extents than its prey.
  • Combining data from different sources/scales?

3.5 Metacommunity analysis with jSDMs

  • How to include traits and phylogeny? For an example see Abrego et al. (2017).
    • On environmental predictors (as random slope across species, e.g. by making the effect of temperature being dependent on the body size of the species)
    • As a strategy to test the plausibility of biotic interaction-interpretation.
    • Post-hoc, after the actual jSDM analysis (see talk by Jörn Pagel on the day after the workshop)
    • Possibly as a constraint on covariance-matrix.

4 Conclusions

From the comments we received on this mini-workshop, both panel and audience enjoyed the exchange of thoughts and ideas. Also, realising that many people seem to all struggle with similar issues was deemed to be very helpful.

JSDMs are a young and rapidly moving field, and both audience and panel felt that jSDMs offer many promises for ecology, but that also many challenges in application and interpretation remain. Moreover, computing times can be prohibitive for large data sets with many species. For unlimited data, we would expect jSDMs to reduce prediction errors and therefore benefit science and conservation applications, but when this approach’s benefits actually starts to outweigh its costs (increased model flexibility) requires further investigations. Interpreting associations in jSDMs as biotic interactions is risky, as it requires eliminating all other drives of co-occurrence. Ideally, jSDM results should therefore more often followed up by traditional, causal approaches such as manipulative experiments.

5 References

Abrego, N., Norberg, A., & Ovaskainen, O. (2017). Measuring and predicting the influence of traits on the assembly processes of wood-inhabiting fungi. Journal of Ecology, 105(4), 1070–1081. doi:10.1111/1365-2745.12722

Beissinger, S. R., Iknayan, K. J., Guillera-Arroita, G., Zipkin, E. F., Dorazio, R. M., Royle, J. A., & Kéry, M. (2016). Incorporating Imperfect Detection into Joint Models of Communities: A response to Warton et al. Trends in Ecology & Evolution, 31(10), 736–737. doi:10.1016/j.tree.2016.07.009

Braun-Blanquet, J., 1964. Pflanzensoziologie. Springer, Berlin, New York, 865 pp.

Harris, D.J. (2016) Inferring species interactions from co-occurrence data with Markov networks. Ecology, 97, 3308–3314.

Latimer, A.M., Banerjee, S., Sang, H., Mosher, E.S. & Silander, J.A. (2009) Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern United States. Ecology Letters, 12, 144–54.

Nieto-Lugilde, Diego, Kaitlin C. Maguire, Jessica L. Blois, John W. Williams, and Matthew C. Fitzpatrick. (2017) Multiresponse algorithms for community-level modelling: Review of theory, applications, and comparison to species distribution models. Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210X.12936.

Ovaskainen, O. & Soininen, J. (2011) Making more out of sparse data: hierarchical modeling of species communities. Ecology, 92, 289–295.

Ovaskainen, O., Roy, D.B., Fox, R. & Anderson, B.J. (2016) Uncovering hidden spatial structure in species communities with spatially explicit joint species distribution models. Methods in Ecology and Evolution, 7, 428–436.

Ovaskainen, O., Gleb Tikhonov, Norberg, A., Blanchet, F.G., Duan, L., Dunson, D., Roslin, T. & Abrego, N. (2017) How to make more out of community data? A conceptual framework and its implementation as models and software. Ecology Letters, 20, 561–576.

Pollock, L.J., Tingley, R., Morris, W.K., Golding, N., O’Hara, R.B., Parris, K.M., Vesk, P. a. & McCarthy, M. a. (2014) Understanding co-occurrence by modelling species simultaneously with a Joint Species Distribution Model (JSDM). Methods in Ecology and Evolution, 5, 397–406.

Schliep, E.M., Lany, N.K., Zarnetske, P.L., Schaeffer, R.N., Orians, C.M., Orwig, D.A. & Preisser, E.L. (2017) Joint species distribution modelling for spatio-temporal occurrence and ordinal abundance data. Global Ecology and Biogeography, 27, 142–155.

Tikhonov, G., Abrego, N., Dunson, D., & Ovaskainen, O. (2017). Using joint species distribution models for evaluating how species-to-species associations depend on the environmental context. Methods in Ecology and Evolution, 8, 443–452. doi:10.1111/2041-210X.12723

Warton, D.I., Blanchet, F.G., Hara, R.B.O., Ovaskainen, O., Taskinen, S., Walker, S.C. & Hui, F.K.C. (2015) So many variables: joint modeling in community ecology. Trends in Ecology and Evolution, 30, 766–779.

Warton, D. I., Blanchet, F. G., O’Hara, R., Ovaskainen, O., Taskinen, S., Walker, S. C., & Hui, F. K. C. (2016). Extending Joint Models in Community Ecology: A Response to Beissinger et al. Trends in Ecology & Evolution, 31(10), 737–738. doi:10.1016/j.tree.2016.07.007

Wisz, M. S., Pottier, J., Kissling, W. D., Pellissier, L., Lenoir, J., Damgaard, C. F., … Svenning, J.-C. (2013). The role of biotic interactions in shaping distributions and realised assemblages of species: implications for species distribution modelling. Biological Reviews, 88, 15–30.

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AK Computational Ecology Spring Cleaning Message

Dear AK members,

I hope you are enjoying the longed-for arrival of spring while periodically looking up from your keyboards!

It’s been too long since you have heard from us too, so here are a few random items about the recent past and future of our group:

Report from the Ecology Across Borders (#EAB2017) meeting in Ghent

  • General impressions: the EAB started a bit sluggish due to the weather, which had many attendees and speakers stranded at various airports, but then everything got rolling and I had the feeling we had an exceptionally nice and social meeting. A big thank you to all the organizers!
  • AK Events: as explained in an earlier post, the AK was involved in three activities at the EAB, the Ecology Hackathon, a joint mixer (with the YoMos and the SIG Quantitative Ecology) and a session “Are we any good at simulating ecology? Success and future challenges in ecological simulation models” (again, joint with the YoMos and the SIG Quantitative Ecology). All of these worked out great, and we were very pleased and grateful for the collaboration with our “partner groups”, something to be continued in the future.
  • AK Name / Status: you might have noticed: I’m writing AK instead of IK. This is because we are now officially an AK of the GFÖ. The decision was approved during the general assembly of the GFÖ during the EAB meeting.
  • Other things: AK members were also involved in a lunch session on using jSDMs to identify biotic interactions. A summary of this session will be posted as an extra guest post on this blog.

Future events

  • GFÖ Vienna: we have not organized a session at the GFÖ in Vienna, but of course we hope to see you there, and there will be an AK meeting during the general AK slot.
  • AK Meeting: apart from the GFÖ, it would be nice to have again an extra AK meeting this year. Given the advanced time, this must most likely be in summer. We are currently looking at options. If you want to help / have suggestions, please get in touch!

AK Organization

  • Emanuel and I am thinking of putting the AK organization onto a bit wider (i.e. more) shoulders. If you are interested in participating in internal discussions / take over a few tasks, please get in touch!

 

 

IK Computational Ecology activities at the #EAB2017 in Ghent

Dear all,

the joint meeting of the GFÖ / BES / NECOV and EFF in Ghent is around the corner, and we are all very excited. Here’s a final heads up about activities you should not miss if you want to meet with your fellow computational ecologists next week:

  • Hack R at the Ecology Hackathon on Monday (if you have signed up for that)
  • Mix with us at the joint mixer (with the YoMos and the SIG Quantitative Ecology), Tuesday, 19.00 Baekelandzaal 3
  • Get inspired by our session (again, joint with the YoMos and the SIG Quantitative Ecology) “TT10: Are we any good at simulating ecology? Success and future challenges in ecological simulation models”, Thursday, 9.45 Casinozaal 1

Also, as announced, we will bring forward a motion to convert the IK status of our group into a more permanent AK status during the general assembly of the GFÖ, Wednesday, 17.15.

See you in Ghent,

Emanuel and Florian

IK activities at the joint GFÖ / BES / NECOV / EFF meeting in Ghent

Dear IK members,

we are looking forward to seeing many of you at the joint meeting of the GFÖ / BES / NECOV and EFF in December in Ghent.

We wanted to update you about the activities of the AK during the meeting:

  1. Pre-conference Hackathon: The IK is co-organizing a pre-conference workshop “Ecology Hackathon: Developing R Packages for Accessing, Synthesizing and Analysing Ecological Data”, sponsored by the journal “Methods in Ecology and Evolution“, together with the BES Quantitative Ecology Special Interest Group and the NeCov Ecological Informatics SIG. The idea of this event is to jointly implement some useful R code / packages in teams made up by the people that join the workshop. We hope this will be a great opportunity to learn new things, make useful contacts, and contribute something to the community. So, remember to sign up for the Hackathon when you register for the conference, and regardless of whether you will join or not, you may suggest topics the group could work on here.
  2. IK session: Are we any good at simulating ecology? Success and future challenges in ecological simulation models. As announced earlier, together with the YoMos and the SIG QE of the BES, we have organized a session to reflect on the status and future of simulation models in ecology. The time of the session is not yet fixed, but what we know is that we have a fantastic list of speakers from different areas of ecology, so look out for the session and we hope to see you there. Note also that we are planning to connect the session with a walk-around in the poster area, focusing on posters of early-stage researchers with IK-related interests.
  3. IK meeting:  The IK meeting will be held together with the SIG QE of the BES and the YoMos at the conference center. The plan is to follow the BES SIG tradition and make this a bit more of a social mixer with a few drinks and snacks. The positive side of this is that there will be more room for meeting people, the negative is obviously that this doesn’t allow for a structured discussion on future activities and the like. However, all in all we had the feeling that we are better off using the context of the joint meeting to socialize a bit, and move discussions online or to our “normal” GFÖ meeting next year, where we are among ourselves again. If you think that there are urgent things that need to be discussed within the AK, please let us known though.
  4. IK / AK: Finally, a heads up that we will propose at the GFÖ assembly to transform the IK (Interessenskreis) into a normal AK (Arbeitskreis). For people that have no idea what we are talking about – this is the normal procedure in the GFÖ for establishing a permanent interest group, the IK is a kind of “test phase”.

All the best, and see you in Ghent

Emanuel and Florian (AK speakers)

 

 

 

 

 

 

Report from the first IK Computational Ecology Meeting

Dear all,

with apologies for the massive delay in posting this, we are pleased to confirm that our first AK meeting in May did indeed take place, as announced, at the Waldschlösschen in Göttingen. We had a great time, discussing science, sitting in the sun, and catching up with old friends.

About the science: apart from short talks from all participants, we had structured the meeting around a number of discussion groups, proposed and led by some of the meeting participants. Those were

  • Synthesis and predictions in ecological models (Carsten Dormann, Lionel Hertzog)
  • Interactions in modelling species distribution: What could be next? (Heike Lischke)
  • Next generation movement models (Ulrike Schlaegel, Stephanie Kramer-Schadt)
  • Hybrid model designs to merge individual-based (bottom-up) with equation-based (top-down) processes (Gudrun Wallentin)
  • Mini-workshop: Machine Learning Bootcamp for Beginners (Masahiro Ryo)
  • Infections on the move (Cédric Scherer & Stephanie Kramer-Schadt)
  • Eco-evolutionary simulation approaches for macroecology (Mikael Pontarp)
  • Advanced Methods for species distribution modelling (Bogdan Caradima)
  • Simulation models and coexistence theory (Felix May)
  • Cooperation between IK Computational Ecology + Young Modellers in Ecology YoMos (Theresa Stratmann)

We may post some of the results of these groups in the next weeks, but if you are particularly interested in one of the topics, you may want to contact the group facilitator directly to hear what was going on.

To end with an organizational note: from what I could gather, people liked the venue a lot, but we were at capacity with 33 participants. Our apologies to the people that couldn’t join for lack of space. We’ll have to see how the demand develops over the next years, but we will try to see if we can get a larger venue in the next year (the alternative would be to meet at a university and get hotels in town, but this is of course less social).

20170518_144304b.jpg
The inevitable group photo

 

 

Status update IK Computational Ecology

Dear IK members,

it’s been a while since you last heard from us, so we wanted to share a few items of information with you about the current status of the IK.

IK Meeting in Göttingen: first of all, we were very glad that there was so much interest in our first IK meting. The unfortunate side effect is that we are by now booked out (33 participants), and had to create a waiting list. We are still hopeful, however, that we will be able to accommodate most people that wanted to join. In any case, we are very much looking forward to seeing so many of you at an exciting first IK meeting in Göttingen.

Activities at the BES / GFÖ: secondly, we wanted to inform you that, together with the YOMOs and the SIG Quantitative Ecology of the BES, the IK will convene a session “Are we any good at simulating ecology? Success and future challenges in ecological simulation models” at this year’s Joint Annual Meeting being organised by the British Ecological Society (BES), NecoV and Gesellschaft für Ökologie (GfÖ), in association with the European Ecological Federation (EEF), between 11th and 14th December 2017 in Ghent, Belgium. Apart from the interest in the session as such, we think it’s great that the computational groups in the BES and GFÖ are organizing something together, and we certainly hope there will be similar joint activities in the future. Also, there is talk about the IK supporting a hackaton organized by the MEE journal at the meeting, but this is not decided yet.

IK Members: we have by now around 120 people that have signed up for the IK. This is great! Nevertheless, there may still be many people that haven’t heard about the IK, so please do feel free to spread the word and forward the IK website or our sign-up link to potentially interested colleagues.

Mailing list: a comment on the use of the mailing list: if you are on the list, you can write directly to the list, you don’t have to write to us with the request to forward job / conference announcements! Also, remember that you can tweet us to retweet @AKCompEcol.

And finally, please to let us know if you have any comments / suggestions for the IK!

 

Register now for the first IK Computational Ecology meeting 17.5. – 19.5. 2017 in Göttingen, Germany

It is our great pleasure to invite you to the first meeting of the GFÖ special interest group for computational ecology

  • When: Wed, 17.5. (evening) – Fr. 19.5. 2017 (lunch time)
  • Where: in the Waldschlösschen close to Göttingen, Germany

Program

The meeting will start on Wednesday evening  (17th of May) and last until Friday, lunchtime (19th of May). In line with the discussion during our inaugural meeting at last year’s GFÖ, the program of the meeting will consist of

  • Short talks (5 min) of all participants to introduce their research interests
  • Mini-excursion
  • Discussion groups on subjects related to computational ecology, organized and lead by the participants

The goal of all activities is to get to know each other,  and develop new collaborations or research questions between IK members.

Accommodation and registration

The Waldschlösschen provides lodgings (2 nights in single rooms) and full board (3 meals a day) for a price of 132 EUR per person. We have reserved a sufficient number of rooms, but to confirm them, we require a definite confirmation of your attendance before the 7th of February.

Please register for the meeting here.

With many hopes for an inspiring first IK meeting at this great location

Florian Hartig, Emanuel A. Fronhofer, Alexander Kubisch (AK speakers), Johannes Signer (local organizer)

ps: if you want to print / post this invitation, you can find a pdf here.