test_interactions function

Compare observed interaction strengths in a network to those estimated from a null model

Takes the result of running a null model with generate_null_net and tests whether the observed interactions between consumer species and resource species differ those expected under the null model.

test_interactions(nullnet, signif.level = 0.95)

Arguments

• nullnet: An object of class "nullnet" from generate_null_net
• signif.level: An optional value specifying the threshold used for testing for 'significant' deviations from the null model. Defaults to 0.95

Returns

Returns a data frame listing all possible consumer and resource species combinations with the following column headings:

• Consumer: The name of the consumer species

• Resource: The name of the resource species

• Observed: The 'strength' of the observed interaction (e.g. total number of interactions summed across the individual consumers)

• Null: The mean strength of the interaction across the iterations of the null model

• Lower: Lower confidence limit for the interaction strength

• Upper: Upper confidence limit for the interaction strength

• Test: Whether the observed interaction is significantly stronger than expected under the null model, weaker

   or consistent with the null model (ns )
  

• SES: The standardised effect size for the interaction

Details

Statistical significance is determined for each consumer-resource interaction according to whether the observed interaction strength falls outside the confidence limits calculated across the iterations of the null model. Confidence limits are calculated as the 1 -- alpha/2 percentiles from the frequency distribution (Manly 2006).

The observed and expected interactions strengths are also compared by calculating the standardised effect size (Gotelli & McCabe 2002):

test_interactions will issue warnings when:

1. The number of iterations of the null model was small <100, as the confidence intervals are unlikely to be reliable
2. The number of tests >50, due to the increasing risk of Type I errors (incorrectly denoting an interaction as significantly different from the null model). Many networks will contain many more than 100 potential interactions, so the significance of individual interactions should be treated with caution. Some form of false discovery rate correction may be valuable (e.g. the local false discovery rate; Gotelli & Ulrich 2010).

Examples

null.1 <- generate_null_net(WelshStreams[, 2:18], WelshStreams.prey[, 2:17],
                            sims = 10, c.samples = WelshStreams[, 1],
                            r.samples = WelshStreams.prey[, 1])
test_interactions(null.1, 0.95)

References

Gotelli, N.J. & McCabe, D.J. (2002) Species co-occurrence: a meta-analysis of J. M. Diamond's assembly rules model. Ecology, 83 , 2091--2096.

Gotelli, N.J. & Ulrich, W. (2010) The empirical Bayes approach as a tool to identify non-random species associations. Oecologia, 162 , 463--477.

Manly, B.F.J. (2006) Randomization, Bootstrap and Monte Carlo Methods in Biology (3rd edn). Chapman & Hall, Boca Raton.

Vaughan, I.P., Gotelli, N.J., Memmott, J., Pearson, C.E., Woodward, G. & Symondson, W.O.C. (2018) econullnetr: an R package using null models to analyse the structure of ecological networks and identify resource selection. Methods in Ecology and Evolution, 9 , 728--733.

See Also

generate_null_net, plot_preferences