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Formal modelling of predator preferences using molecular gut-content analysis

Abstract

The literature on modelling a predator’s prey selection describes many intuitive indices, few of which have both reasonable statistical justification and tractable asymptotic properties. Here, we provide a simple model that meets both of these criteria, while extending previous work to include an array of data from multiple species and time points. Further, we apply the expectation–maximisation algorithm to compute estimates if exact counts of the number of prey species eaten in a particular time period are not observed. We conduct a simulation study to demonstrate the accuracy of our method, and illustrate the utility of the approach for field analysis of predation using a real data set, collected on wolf spiders using molecular gut-content analysis.

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References

  • Agustí N, Shayler S, Harwood JD, Vaughan I, Sunderland K, Symondson WOC (2003) Collembola as alternative prey sustaining spiders in arable ecosystems: prey detection within predators using molecular markers. Mol Ecol 12(12):3467–3475

    Article  PubMed  Google Scholar 

  • Chesson J (1978) Measuring preference in selective predation. Ecology 59(2):211–215

    Article  Google Scholar 

  • Chesson J (1983) The estimation and analysis of preference and its relationship to foraging models. Ecology 64(5):1297–1304

    Article  Google Scholar 

  • Clements HS, Tambling CJ, Hayward MW, Kerley GI (2014) An objective approach to determining the weight ranges of prey preferred by and accessible to the five large african carnivores. PloS ONE 9(7):e101,054

    Article  Google Scholar 

  • Core Team R (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/

  • Davey JS, Vaughan IP, King RA, Bell JR, Bohan DA, Bruford MW, Holland JM, Symondson WO (2013) Intraguild predation in winter wheat: prey choice by a common epigeal carabid consuming spiders. J Appl Ecol 50(1):271–279

    Article  Google Scholar 

  • Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodological) 39(1):1–38

    Google Scholar 

  • Eitzinger B, Unger EM, Traugott M, Scheu S (2014) Effects of prey quality and predator body size on prey DNA detection success in a centipede predator. Mol Ecol 23(15):3767–3776

    CAS  Article  PubMed  Google Scholar 

  • Givens GH, Hoeting JA (2012) Computational statistics, vol 708. Wiley, Hoboken

    Book  Google Scholar 

  • Greenstone MH, Payton ME, Weber DC, Simmons AM (2013) The detectability half-life in arthropod predator-prey research: what it is, why we need it, how to measure it, and how to use it. Mol Ecol 23(15):3799–3813

    Article  PubMed  Google Scholar 

  • Hansen AG, Beauchamp DA (2014) Effects of prey abundance, distribution, visual contrast and morphology on selection by a pelagic piscivore. Freshw Biol 59(11):2328–2341

    Article  Google Scholar 

  • Hellström P, Nyström J, Angerbjörn A (2014) Functional responses of the rough-legged buzzard in a multi-prey system. Oecologia 174(4):1241–1254

    Article  PubMed  Google Scholar 

  • Ivlev VS (1964) Experimental ecology of the feeding of fishes. Yale University Press, New Haven

    Google Scholar 

  • Jacobs J (1974) Quantitative measurement of food selection. Oecologia 14(4):413–417

    Article  Google Scholar 

  • King RA, Vaughan IP, Bell JR, Bohan DA, Symondson WO (2010) Prey choice by carabid beetles feeding on an earthworm community analysed using species-and lineage-specific PCR primers. Mol Ecol 19(8):1721–1732

    CAS  Article  PubMed  Google Scholar 

  • Lechowicz MJ (1982) The sampling characteristics of electivity indices. Oecologia 52(1):22–30

    Article  Google Scholar 

  • Luo ZQ, Tseng P (1992) On the convergence of the coordinate descent method for convex differentiable minimization. J Optim Theory Appl 72(1):7–35

    Article  Google Scholar 

  • Lyngdoh S, Shrotriya S, Goyal SP, Clements H, Hayward MW, Habib B (2014) Prey preferences of the snow leopard (Panthera uncia): regional diet specificity holds global significance for conservation. PloS ONE 9(2):e88,349

    Article  Google Scholar 

  • Madduppa HH, Zamani NP, Subhan B, Aktani U, Ferse SC (2014) Feeding behavior and diet of the eight-banded butterflyfish Chaetodon octofasciatus in the Thousand Islands, Indonesia. Environ Biol Fish 97:1–13

    Article  Google Scholar 

  • Manly B, McDonald L, Thomas D, McDonald T, Erickson W (2002) Resource selection by animals: statistical analysis and design for field studies. Kluwer, Nordrecht

    Google Scholar 

  • McLachlan G, Krishnan T (2007) The EM algorithm and extensions, vol 382. Wiley, Hoboken

    Google Scholar 

  • Raso L, Sint D, Mayer R, Plangg S, Recheis T, Brunner S, Kaufmann R, Traugott M (2014) Intraguild predation in pioneer predator communities of alpine glacier forelands. Mol Ecol 23(15):3744–3754

    Article  PubMed  PubMed Central  Google Scholar 

  • Roualdes EA, Bonner S (2014) spiders: fits predator preferences model. R package version 1

  • Schmidt JM, Barney SK, Williams MA, Bessin RT, Coolong TW, Harwood JD (2014) Predator–prey trophic relationships in response to organic management practices. Mol Ecol 23(15):3777–3789

    Article  PubMed  Google Scholar 

  • Serfling RJ (2001) Approximation theorems of mathematical statistics. Wiley, Hoboken

    Google Scholar 

  • Sint D, Raso L, Traugott M (2012) Advances in multiplex PCR: balancing primer efficiencies and improving detection success. Methods Ecol Evolut 3(5):898–905

    Article  Google Scholar 

  • Strauss RE (1979) Reliability estimates for Ivlev’s electivity index, the forage ratio, and a proposed linear index of food selection. Trans Am Fish Soc 108(4):344–352

    Article  Google Scholar 

  • Uetz GW, Halaj J, Cady AB (1999) Guild structure of spiders in major crops. J Arachnol 27(1):270–280

    Google Scholar 

  • Vanderploeg H, Scavia D (1979) Two electivity indices for feeding with special reference to zooplankton grazing. J Fish Board Can 36(4):362–365

    Article  Google Scholar 

  • Wilks SS (1938) The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Stat 9(1):60–62

    Article  Google Scholar 

Download references

Acknowledgments

The information reported in this paper (No. 15-08-008) is part of a project of the Kentucky Agricultural Experiment Station and is published with the approval of the Director. Support for this research was provided by the University of Kentucky Agricultural Experiment Station State Project KY008055 and the National Science Foundation Graduate Research Fellowship Program.

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Correspondence to Edward A. Roualdes.

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Handling Editor: Bryan F. J. Manly.

Appendix: Varying trap efficiency

Appendix: Varying trap efficiency

When there is concern about trap efficiency varying across time, we recommend the following reparameterization of \(c_{st} = \lambda _{st}/\gamma _{st}\). Let

$$\begin{aligned} k_{st}d_t = \frac{\lambda _{st}}{\gamma _{st}}, \end{aligned}$$

such that \(\sum _{s=1}^S k_{st} = 1\), for all t. The parameter \(d_t\) allows for changes in trap efficiency or in actual abundance over time. If such changes are believed to be present, this reparameterization allows for a more natural interpretation. The parameter \(k_{st}\) models relative consumption to encounter rates, as expected.

Since this reparameterization amounts to a linear transformation of the parameters, the asymptotic distribution for \(\hat{d}_t\) can be evaluated directly. Because of the constraint \(\sum _{s=1}^S k_{st} = 1\), we find that \(d_t = \sum _{s=1}^S c_{st}\) or written in matrix notation \(\mathbf {d} = \mathbf {1}' \mathbf {c}\), where \(\mathbf {d} \in \mathbb {R}^T\). The asymptotic distribution of \(\hat{\mathbf {d}}\) follows immediately, \(\hat{\mathbf {d}} \mathop {\sim }\limits ^{\cdot } \mathcal {N}(\mathbf {1}'\mathbf {d}, \mathbf {1}'\varSigma \mathbf {1})\), where \(\varSigma \) is the covariance matrix of the asymptotic distribution of \(\hat{\mathbf {c}}\).

More importantly, we can find the asymptotic distribution of \(\hat{\mathbf {k}}_t = (k_{1t}, \ldots , k_{St})' \in \mathbb {R}^S\). We make use of the delta method (Serfling 2001). The asymptotic variance relies on the derivatives, \(d k_{rt} / d c_{st}\). Let \(c_{\cdot t} = \sum _{s=1}^S c_{st}\). Because \(k_{st} = c_{st}/ c_{\cdot t}\), we can find the necessary derivatives in two cases

$$\begin{aligned} \frac{d k_{rt}}{d c_{st}} = {\left\{ \begin{array}{ll} \frac{-c_{rt}}{c_{\cdot t}^2}, &{} r \ne s \\ \frac{c_{\cdot t} - c_{st}}{c_{\cdot t}^2}, &{} r = s. \end{array}\right. } \end{aligned}$$

Thus, the asymptotic distribution of \(\hat{\mathbf {k}}_{t}\) is \(\mathcal {N}(\frac{c_{st}}{c_{\cdot t}}, (\frac{d \mathbf {k}_t}{d \mathbf {c}_t}) \varSigma (\frac{d \mathbf {k}_t}{d \mathbf {c}_t})')\).

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Roualdes, E.A., Bonner, S.J., Whitney, T.D. et al. Formal modelling of predator preferences using molecular gut-content analysis. Environ Ecol Stat 23, 317–336 (2016). https://doi.org/10.1007/s10651-016-0341-3

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  • DOI: https://doi.org/10.1007/s10651-016-0341-3

Keywords

  • Electivity
  • Expectation–maximisation
  • Food web analysis
  • Generalist predators
  • Predator–prey interactions