Science responses to IUCN Red Listing

Method for detecting effects of IUCN listing

We test for the effect of IUCN listing on publication rate under the following statistical model. Consider a group of J species with the same listing category. We assume that over the observation period (0, T) publications on species j follow a Poisson process with rate function: (1)${\displaystyle {\mu }_j\left(t\right)=\left\{\begin{array}{ccc}{\mu }_j\hfill & \hfill & 0<t\le {\tau }_j\hfill \\ \beta {\mu }_j\hfill & \hfill & {\tau }_j<t\le T\hfill \end{array}\right.}$ where μ_j is the unknown pre-listing publication rate for species j, τ_j is the known listing time for species j, and β is the unknown multiplicative listing effect that is assumed to be common for all species in the group. Under this model, the number B_j of publications prior to listing has a Poisson distribution with mean μ_jτ_j and the number A_j of publications following listing has a Poisson distribution with mean βμ_j (T − τ_j). It is a property of the Poisson distribution that, conditional on the total number n_j of publications during the observation period, B_j has a binomial distribution with n_j trials and success probability: (2)${\displaystyle p_j=\frac{{\tau }_j}{{\tau }_j+\beta \left(T-{\tau }_j\right)}.}$ Inference about β can be based on the log likelihood function: (3)${\displaystyle logL\left(\beta \right)=\sum _{j=1}^J{b}_{j}log{p}_j+\left(n_j-b_j\right)log\left(1-p_j\right)}$ where b_j is the observed value of B_j. In particular, the maximum likelihood estimate $\hat{\beta }$ of β is found by maximizing Eq. (3) over β.

This model has two obvious limitations. First, it assumes that any publication effect occurs immediately after listing when, in reality, such an effect would appear only after a delay due to the time lag in funding application, research activity and publication. It is straightforward to extend the model to incorporate a common delay δ between the time of listing and the time at which the listing effect is manifested. We therefore included δ and compared the model output with and without it. As the results are insensitive to δ, for convenience, we present only those for the simpler model.

A more serious problem is that the model assumes that both the pre- and post-listing publication rates are constant. As a consequence, even in the absence of a listing effect, a steadily increasing publication rate would be reflected in a positive estimate of β. By the same token, a steadily decreasing publication rate could obscure a publication effect. To control for this, we based inference about a listing effect for DD and CR species groups on the differences: (4)${\displaystyle D_{DD}={\hat{\beta }}_{DD}-{\hat{\beta }}_{LC}}$ (5)${\displaystyle D_{CR}={\hat{\beta }}_{CR}-{\hat{\beta }}_{LC}}$ where, for example, ${\hat{\beta }}_{DD}$ is the maximum likelihood estimate of β for species in the DD group. The idea here is that the LC group serves as a control, in the sense that ${\hat{\beta }}_{LC}$ reflects any common trend in publication rate independent of a listing effect (Larsen & Von Ins, 2010).

Briefly, we tested the null hypothesis of no DD listing effect against the one-sided alternative hypothesis of a positive listing effect by repeatedly randomizing the assignment of the pooled DD and LC species and re-calculating the value of D_DD. The observed significance level (or p value) was approximated by the proportion of randomized data sets for which D_DD exceeded the observed value. An analogous procedure was used to test for a positive CR listing effect.

In the next step, we applied the method outlined above to species with at least one publication. Strictly speaking, this means that the statistical method should condition on this event. While this conditioning could create a significant technical problem, as the random variables B_j and A_j are no longer independent, the randomization remains a fully valid test.