Skip to main content
Log in

Bayesian inference to partition determinants of community dynamics from observational time series

  • Published:
Community Ecology Aims and scope Submit manuscript

Abstract

Ecological communities are shaped by a complex interplay between abiotic forcing, biotic regulation and demographic stochasticity. However, community dynamics modelers tend to focus on abiotic forcing overlooking biotic interactions, due to notorious challenges involved in modeling and quantifying inter-specific interactions, particularly for species-rich systems such as planktonic assemblages. Nevertheless, inclusive models with regard to the full range of plausible drivers are essential to characterizing and predicting community response to environmental changes. Here we develop a Bayesian model for identifying, from in-situ time series, the biotic, abiotic and stochastic factors underlying the dynamics of species-rich communities, focusing on the joint biomass dynamics of biologically meaningful groups. We parameterize a multivariate model of population co-variation with an explicit account for demographic stochasticity, density-dependent feedbacks, pairwise interactions, and abiotic stress mediated by changing environmental conditions and resource availability, and work out explicit formulae for partitioning the temporal variance of each group in its biotic, abiotic and stochastic components. We illustrate the methodology by analyzing the joint biomass dynamics of four major phytoplankton functional types namely, diatoms, dinoflagellates, coccolithophores and phytoflagellates at Station L4 in the Western English Channel using weekly biomass records and coincident measurements of environmental covariates describing water conditions and potentially limiting resources. Abiotic and biotic factors explain comparable amounts of temporal variance in log-biomass growth across functional types. Our results demonstrate that effective modelling of resource limitation and inter-specific interactions is critical for quantifying the relative importance of abiotic and biotic factors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Abbreviations

AR model:

Autoregressive model

BUGS:

Bayesian inference Using Gibbs Sampling

LASSO:

Least Absolute Shrinkage and Selection Operator

MCMC:

Markov Chain Monte Carlo

PSU:

Practical Salinity Unit

VAR model:

Vector Autoregressive model

References

  • Araújo, M.B. and M. Luoto. 2007. The importance of biotic interactions for modelling species distributions under climate change. Global Ecol. Biogeogr. 16:743–753.

    Article  Google Scholar 

  • Boalch, G.T., D.S. Harbour and E.I. Butler. 1978. Seasonal phytoplankton production in the western English Channel 1964–1974. J. Mar. Biol. Assoc. UK 58:943–953.

    Article  Google Scholar 

  • Brook, B.W. and C.J.A. Bradshaw. 2006. Strength of evidence for density dependence in abundance time series of 1198 species. Ecology 87:1445–1451.

    Article  PubMed  Google Scholar 

  • Brooks, C. and C. Tasman. 2018. Density and biotic interactions modify the combined effects of global and local stressors. Oikos 127:1746–1758.

    Article  Google Scholar 

  • Clark, N.J., K. Wells and O. Lindberg 2018. Unravelling changing interspecific interactions across environmental gradients using Markov random fields.. Ecology 99:1277–1283.

    Article  PubMed  Google Scholar 

  • Cooper, G.J. 2003. The Science of the Struggle for Existence. Cambridge University Press, Cambridge, UK.

    Book  Google Scholar 

  • Davis, A.J., J.H. Lawton, B. Shorrocks and L.S. Jenkinson. 1998a. Individualistic species responses invalidate simple physiological models of community dynamics under global environmental change.. J. Anim. Ecol. 67:600–612.

    Article  Google Scholar 

  • Davis, A., L.S. Jenkinson, J.H. Lawton, B. Shorrocks and S. Wood. 1998b. Making mistakes when predicting shifts in species range in response to global warming.. Nature 391:783–786.

    Article  CAS  PubMed  Google Scholar 

  • De Baar, H.J.W. 1994. Von Liebig law of the minimum and plankton ecology (1899–1991). Prog. Oceanogr. 33:347–386.

    Article  Google Scholar 

  • Delean, S., B.W. Brook and C.J.A. Bradshaw. 2013. Ecologically realistic estimates of maximum population growth using informed Bayesian priors. Methods Ecol. Evol. 4:34–44.

    Article  Google Scholar 

  • Doney, S.C., 2006. Phytoplankton in a warmer world.. Nature 444:695–696.

    Article  CAS  PubMed  Google Scholar 

  • Field, C.B., M.J. Behrenfeld, J.T. Randerson and P. Falkowski. 1998. Primary production of the biosphere: integrating terrestrial and oceanic components. Science 281:237–240.

    Article  CAS  PubMed  Google Scholar 

  • Finkel, Z.V., A.J. Irwin and O. Schofield. 2004. Resource limitation alters the 3/4 size scaling of metabolic rates in phytoplankton. Mar. Ecol. Prog. Ser. 273:269–279.

    Article  Google Scholar 

  • Finkel, Z.V., 2001. Light absorption and size scaling of light-limited metabolism in marine diatoms.. Limnol. Oceanogr. 46:86–94.

    Article  CAS  Google Scholar 

  • Finkel, Z.V. and A.J. Irwin. 2000. Modelling size-dependent photosynthesis: light absorption and the allometric rule. J. Theor. Biol. 204:361–369.

    Article  CAS  PubMed  Google Scholar 

  • Gelman, A., J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari and D.B. Rubin. 2013. Bayesian Data Analysis 3r Ed. Chapman and Hall, London, England.

    Book  Google Scholar 

  • George, E.I. and R.E. McCulloch. 1993. Variable selection via Gibbs sampling. J. Am. Stat. Assoc. 85:398–409.

    Google Scholar 

  • Gilks, W.R., S. Richardson and D.J. Spiegelhalter (eds.), 1996. Markov Chain Monte Carlo in Practice. Chapman and Hall, London, UK.

    Google Scholar 

  • Gilman, S.E., M.C. Urban, J. Tewksbury, G.W. Gilchrist and R.D. Holt. 2010. A framework for community interactions under climate change. Trends Ecol. Evol. 25:325–331.

    Article  PubMed  Google Scholar 

  • Giraudeau, J. and G.W. Bailey. 1995. Spatia1 dynamics of cocco1ithophore communities during an upwelling event in the Southern Bengue1a system. Cont. Shelf Res. 15:1825–1852.

    Article  Google Scholar 

  • Götzenberger, L., F. de Bello, K.A. Bråthen, J. Davison, A. Dubuis, A. Guisan, et al. 2012. Ecological assembly rules in plant communities –approaches, patterns and prospects. Biol. Rev. 87:111–127.

    Article  PubMed  Google Scholar 

  • Hampton, S.E., E.E. Holmes, L.P. Scheef, M.D. Scheuerell, S.L. Katz, D.E. Pendleton and E.J. Ward. 2013. Quantifying effects of abiotic and biotic drivers on community dynamics with multivariate autoregressive (MAR) models. Ecology 94:2663–2669.

    Article  PubMed  Google Scholar 

  • Hampton, S.E., M.D. Scheuerell and D.E. Schindler. 2006. Coalescence in the Lake Washington story: interaction strengths in a planktonic food web. Limnol. Oceanogr. 51:2042–2051.

    Article  Google Scholar 

  • Hartman, S.E., M.C. Hartman, D.J. Hydes, D. Smythe-Wright, F. Gohin, F. and P. Lazure. 2014. The role of hydrographic parameters, measured from a ship of opportunity, in bloom formation of Karenia mikimotoi in the English Channel. J. Mar. Syst. 140:39–49.

    Article  Google Scholar 

  • Heikkinen, R.K., M. Luoto, R. Virkkala, R.G. Pearson and J.-H. Körber. 2007. Biotic interactions improve prediction of boreal bird distributions at macro-scales. Glob. Ecol. Biogeogr. 16:754–763.

    Article  Google Scholar 

  • Hoerl, A. E. and R. W. Kennard. 1970. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12(1):55–67.

    Article  Google Scholar 

  • Holligan, P.M. and D.S. Harbour. 1977. The vertical distribution and succession of phytoplankton in the western English Channel in 1975 and 1976. J. Mar. Biol. Assoc. U.K. 57:1075–1093.

    Article  CAS  Google Scholar 

  • Irwin, A.J. and Z.V. Finkel. 2018. Phytoplankton functional types: a trait perspective. In: Kirchman, D.M. and Gasol, J.M. (eds), Microbial Ecology of the Ocean. Wiley. Chapter 11, pp. 435–465.

  • Ives, A.R., B. Dennis, K.L. Cottingham and S.R. Carpenter. 2003. Estimating community stability and ecological interactions from time-series data. Ecol. Monogr. 73:301–330.

    Article  Google Scholar 

  • Jeffreys, H., 1961. The Theory of Probability (3rd ed.). Oxford University Press, Oxford, UK

  • Kissling, W.D., C.F. Dormann, J. Groeneveld, T. Hickler, I. Kühn, G.J. McInerny, J.M. Montoya, C. Römermann, K. Schiffers, F.M. Schurr, A. Singer, J.-C. Svenning, E.Z. Niklaus, and R.B. O’Hara. 2012. Towards novel approaches to modelling biotic interactions in multispecies assemblages at large spatial extents. J. Biogeogr. 39:2163–2178.

    Article  Google Scholar 

  • Lande, R., S. Engen and B-E. Saether. 2003. Stochastic Population Dynamics in Ecology and Conservation. Oxford University Press, Oxford.

    Book  Google Scholar 

  • Lany, N.K., P.L. Zarnetske, T.C. Gouhier and B.A. Menge. 2017. Incorporating Context Dependency of Species Interactions in Species Distribution Models. Integr. Comparat. Biol. 57:159–167, https://doi.org/10.1093/icb/icx057.

  • Laws, E.A. 2013. Evaluation of in situ phytoplankton growth rates: A synthesis of data from varied approaches. Ann. Rev. Mar. Sci. 5:247–268.

    Article  PubMed  Google Scholar 

  • Le Quéré, C., S.P. Harrison, P.I. Colin, E.T. Buitenhuis, et al. 2005. Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models. Glob. Change Biol. 11:2016–2040.

    Google Scholar 

  • Litchman, E., C.A. Klausmeier, J.R. Miller, O.M. Schofield and P.G. Falkowksi. 2006. Multi-nutrient, multi-group model of present and future oceanic phytoplankton communities. Biogeosciences 3:585–606.

    Article  CAS  Google Scholar 

  • Loreau, M. and C. de Mazancourt. 2008. Species synchrony and its drivers: neutral and nonneutral community dynamics in fluctuating environments. Am. Nat. 172:E48–E6.

    Article  PubMed  Google Scholar 

  • Lunn, D.J., A. Thomas, N. Best and D. Spiegelhalter. 2000. WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility.. Stat. Comput. 10:325–337.

    Article  Google Scholar 

  • McCarthy, M. 2007. Bayesian Methods in Ecology. Cambridge University Press, New York.

    Book  Google Scholar 

  • Menden-Deuer, S. and E.J. Lessard. 2000. Carbon to volume relationships for dinoflagellates, diatoms, and other protest plankton. Limnol. Oceanogr. 45:569–579.

    Article  CAS  Google Scholar 

  • Mutshinda, C.M., Z.V. Finkel, C.E. Widdicombe and A.J. Irwin. 2017. Phytoplankton traits from long-term oceanographic time-series. Mar. Ecol. Prog. Ser. 576:11–25.

    Article  CAS  Google Scholar 

  • Mutshinda, C.M., Z.V. Finkel, C.E. Widdicombe and A.J. Irwin. 2016. Ecological equivalence of species within phytoplankton functional groups. Funct. Ecol. 30:1714–1722.

    Article  Google Scholar 

  • Mutshinda, C.M., Z.V. Finkel and A.J. Irwin. 2013. Which environmental factors control phytoplankton populations? A Bayesian variable selection approach. Ecol. Model. 269:1–8.

    Article  Google Scholar 

  • Mutshinda, C. M. and M. J. Sillanpää 2011. Bayesian shrinkage analysis of QTLs under shape-adaptive shrinkage priors, and accurate re-estimation of genetic effects.. Heredity 107:405–412.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Mutshinda, C.M. and M.J. Sillanpää. 2012. A decision rule for quantitative trait locus detection under the extended Bayesian LASSO model. Genetics 192:1483–1491.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Mutshinda, C.M., R.B. O’Hara and I.P. Woiwod. 2011. A multispecies perspective on ecological impacts of climatic forcing. J. Anim. Ecol. 80:101–107.

    Article  PubMed  Google Scholar 

  • Mutshinda, C.M. 2010. Bayesian Analysis of Community dynamics. PhD thesis, University of Helsinki, Helsinki, Finland.

  • Mutshinda, C.M. and M.J. Sillanpää. 2010. Extended Bayesian LASSO for multiple quantitative trait loci mapping and unobserved phenotype prediction. Genetics 186:1067–1075.

    Article  PubMed  PubMed Central  Google Scholar 

  • Mutshinda, C.M., R.B. O’Hara and I.P. Woiwod. 2009. What drives community dynamics? Proc. R. Soc. London, Ser. B 276:2923–2929.

    Article  Google Scholar 

  • Mutshinda C.M. 2009. Cutting across discipline boundaries: Statistical prospects in disclosing and handling the workings of natural biodiversity. Intl. J. Biol. 1:101–103.

    Article  Google Scholar 

  • Nicholson, A.J. 1933. The balance of animal populations. J. Anim. Ecol. 2:131–178.

    Article  Google Scholar 

  • O’Hara R.B. and M.J. Sillanpää. 2009. A review of Bayesian variable selection methods: what, how and which? Bayesian Analysis 4:85–115.

    Article  Google Scholar 

  • Ovaskainen, O., J. Hottola and J. Siitonen. 2010. Modeling species co-occurrence by multivariate logistic regression generates new hypotheses on fungal interactions. Ecology 91:2514–2521.

    Article  PubMed  Google Scholar 

  • Ovaskainen, O, G. Tikhonov, D. Dunson, V. Grøtan, S. Engen, B.-E. Sæther and N. Abrego. 2017. How are species interactions structured in species-rich communities? A new method for analysing time-series data. Proc. R. Soc. London, Ser. B 284:20170768.

    Article  Google Scholar 

  • Park, T. and G. Casella. 2008. The Bayesian LASSO. J. Amer. Stat. Assoc. 2008:103:681–686.

    Article  CAS  Google Scholar 

  • Plummer, M., et al. 2003. Jags: A program for analysis of Bayesian graphical models using gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing, volume 124. Vienna, Austria.

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

    Article  Google Scholar 

  • Porzig, E.L., N.E. Seavy, J.M. Eadie, D.L. Humple, G.R. Geupel and T. Gardali. 2016. Interspecific interactions, population variation, and environmental forcing in the context of the community. Ecosphere 7(6), e01349. 10.1002/ecs2.1349.

    Article  Google Scholar 

  • Saether, B.-E., J. Tufto, S. Engen, K. Jerstad, O.W. Rostad and J.E. Skátan. 2000. Population dynamical consequences of climate change for a small temperate songbird. Science 287:854–856.

    Article  CAS  PubMed  Google Scholar 

  • Stachowicz, J.J. 2001. Mutualism, facilitation, and the structure of ecological communities. Bioscience 51:235–246.

    Article  Google Scholar 

  • Stan Development Team. 2018. Stan modelling language user’s guide and reference manual, version 2.18.0. http://mc-stan.org/.

  • Tibshirani, R. 1996. Regression shrinkage and selection via LASSO. J. Roy. Stat. Soc. B 58:267–288.

    Google Scholar 

  • Thomas, A., R.B. O’Hara, U. Ligges and S. Sturtz. 2006. Making BUGS Open. R News 6:12–17.

    Google Scholar 

  • van der Ploeg, R.R. and M. Kirkham. 1999. On the origin of the theory of mineral nutrition of plants and the law of the minimum. Soil Sci. Soc. Am. J. 63:1055–1062.

    Article  Google Scholar 

  • Widdicombe, C.E., D. Eloire, D. Harbour, R.P. Harris and P.J. Somerfield. 2010a. Long-term phytoplankton community dynamics in the Western English Channel.. J. Plankton Res. 32:643–655.

    Article  Google Scholar 

  • Widdicombe, C.E., D. Eloire, D. Harbour, R.P. Harris and P.J. Somerfield. 2010b. Time series of phytoplankton abundance and composition at station L4 in the English Channel from 1988 to 2009. PANGAEA, https://doi.org/10.1594/PANGAEA.754335, In supplement to: Widdicombe, C.E. et al. (2010) Long-term phytoplankton community dynamics in the Western English Channel. J. Plankton Res. 32:643–655, https://doi.org/10.1093/plankt/fbp127.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. M. Mutshinda.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mutshinda, C.M., Finkel, Z.V., Widdicombe, C.E. et al. Bayesian inference to partition determinants of community dynamics from observational time series. COMMUNITY ECOLOGY 20, 238–251 (2019). https://doi.org/10.1556/168.2019.20.3.4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1556/168.2019.20.3.4

Keywords

Navigation