Karels et al. (2008) present a re-examination of data analysed in an earlier paper by ourselves (Blackburn et al., 2004) that addressed relationships between features of oceanic islands and the numbers of extinct and threatened species in the avifaunas of those islands. Our paper used a generalized linear mixed modelling (GLMM) approach to explore, amongst other things, correlates of the probability of historical extinction in island avifaunas. The best multivariate model for extinction probability in our analysis included strong effects of the number of exotic mammal predator species on an island and island area. Our results showed that bird species were more likely to go extinct from smaller islands (note that the statement by Karels et al. (2008) that our analysis shows that extinction probability is greater on larger islands is incorrect), and from islands with more mammal predator species.
In contrast, Karels et al. (2008) used a causal analysis approach with structural equation modelling to explore correlates of the number of extinct bird species on a slightly expanded set of islands. They found, amongst other things, that island area, isolation, number of introduced mammal species, and size of the original avifauna all have significant positive effects on the number of bird extinctions. The effect of island area was largely indirect, acting by means of positive direct effects of area on the size of the original bird and introduced mammal predator faunas. They concur with the conclusions of Blackburn et al. (2004) that mammal predator richness is an important determinant of island bird extinctions, but argue that biogeographical variables, notably island area, are likely to be as or more important.
The key difference between our analyses (Blackburn et al., 2004) and those in Karels et al. (2008) is not the use of structural equation models in the former, but rather the fact that they analyse a different response variable: we analysed the probability of extinction whereas Karels et al. (2008) analysed the number of extinctions. Given that the two sets of analyses consider different response variables, it is not unduly surprising that different explanatory variables emerge as important. The main point is thus not whether Karels et al.’s results differ from ours (we would expect them to), but whether their results provide any additional insights into the extinction process. Here, we explain why we believe that they do not.
Karels et al. (2008) emphasize that physical attributes of islands (area and isolation) are equally as or more important than introduced predators as determinants of the number of birds driven extinct from islands. As noted above, Blackburn et al. (2004) also found strong effects of island physical attributes on the probability of extinction, so the point that such attributes affect extinctions is not contentious. What may be contentious is which physical attributes are important and their interpretation. The primary finding of Karels et al. (2008) was that island area had the strongest influence on number of extinctions. The effect of island area was largely indirect: island area strongly influenced the total number of species on islands (as is well known: Rosenzweig, 1995), and the more species on an island, the greater the number of extinctions. However, if extinctions occurred at random, so that the probability of extinction was the same for all islands, we would expect to observe a greater number of extinctions on larger islands that have more species. Because this outcome is what would a priori be expected from a null model in which nothing of interest happens (random extinction), observing this outcome provides no insight into the causes of extinction.
We pointed out this problem to Karels et al. (personal communications and Blackburn et al., 2008), and their response follows our suggestion to consider the correlation that would be expected under a null model of random extinction. Karels et al. (2008) showed that the observed path correlation is significantly lower than would be expected if extinctions had occurred at random and claim that this provides a new insight: extinctions did not occur at random, with some islands being hit harder than others. However, this is not a new insight: it is obvious from Fig. 1A in Blackburn et al. (2004) that extinction probability differs among islands, and that some have suffered more than others. Indeed, it is exactly such variation that our original analysis (Blackburn et al., 2004) was designed to explain.
Karels et al. (2008) suggest that the positive effect of island area on number of extinctions may be because larger islands support larger human populations, with their associated greater environmental impact. However, a correlation lower than expected under a null model of random extinction implies that the effect of island area is unexpectedly weak. This may well occur because extinctions were non-random, but it then makes no sense to consider explanations for why island area has a strong effect on number of extinctions. Stated correctly, Karels et al.’s results show that there is no evidence for an effect of island area as a driver of number of extinctions: the indirect effect of area on the number of extinctions is weaker than expected by chance alone, whereas the direct effect is non-significant (see their table 1). This is not surprising, given that extinction probability is negatively related to island area (Blackburn et al., 2004).
The fact that the model presented by Karels et al. (2008) fails to incorporate the appropriate null hypothesis into the calculation of their path coefficients also complicates the interpretation of their other findings. Thus, although Karels et al. argue that there is a positive effect of isolation on number of extinctions, it is difficult to know whether this is a stronger or a weaker effect than that expected by chance. The issue is further complicated by the fact that isolation and number of extinctions are negatively related in our data (Fig. 1), contradicting their significant positive direct path. Whatever the relationship between isolation and number of extinctions, however, we question Karels et al.’s interpretation that the lack of a rescue effect on distant islands is responsible for their higher number of extinctions. If more isolated islands did have more extinctions, this pattern would be unlikely to be generated by a reduced rescue effect on isolated islands, as 77% of the extinctions in these data refer to island endemic species for which rescue from the mainland is impossible. A more likely interpretation is that species on isolated islands have been separated from mammal predators for a greater period of evolutionary time, giving them more chance to have lost anti-predator behaviours (Duncan & Blackburn, 2004).
In conclusion, Karels et al. (2008) argue that their paper provides new insights into island bird extinctions: that island bird extinctions have not occurred at random, and that island area has a strong influence on the number of extinctions. We show that the first of these insights is not new, and that the second is not correct. Thus, although the structural equation modelling approach adopted by Karels et al. can potentially yield insights into avian assemblages that are not revealed by linear modelling (see, for example, Rompréet al., 2007), it does not do so in this case. Finally, we note that the structural equation model used by Karels et al. assumes a normally distributed response variable. The number of extinctions, however, is dominated by zeroes, and even a log + 1 transformation does not bring this variable close to normality. A more appropriate model for these data would include a negative binomial error structure. Better still would be to model the probability of extinction using a binomial distribution, as Blackburn et al. (2004) did in the first place.