species’ initial parasitism rates was not sufficient to predict their changes in abundance (Fig. 5f, Supplementary Table 10), but rather the predictions based on apparent competition were necessary. Summary of most important results We found that for each host species in the community, we could predict both the final parasitism rate, and with even greater accuracy, the change in abundance between time steps for that species. This prediction required information on the initial parasitism rate for that species, the ‘normal’ extent to which that host species shares parasitoids with all other host species in the region, plus the change in abundance between time steps of other host species. These predictions could equally be made for hosts in either native forest or adjacent exotic plantation forest, and for large or small changes in abundances of other host species in the system. These predictions even held when they were made for hosts in one habitat, but based only on data from the other habitat, regardless of whether the host’s habitat was native or plantation forest. Discussion Our finding that apparent competition is a structuring force strong enough to determine up to 31% of the variation in forest herbivore abundances has great potential utility in biological control and invasive species management, which often face poor predictive ability due to indirect effects among species26. Both these fields face the challenge of predicting potential impacts of introduced species or control agents before their arrival or release30,31. Our results show that apparent competition is an important
(2) diAjB is the proportion of parasitoids attacking species i in habitat A that were reared from species j in habitat B. A is the habitat of host species i, B is the habitat of host species j, Hq is the total number of host species from the total pool of q habitats producing parasitoids. For all calculations with Equation 2 in this study, q includes both the native and plantation forests. All other variables are as defined in Equation 1. The first part of Equation 2 represents the fraction of attacks by parasitoid species k on host species i in habitat A out of the total number of attacks by all of the P species of parasitoid on host i in habitat A. This is then multiplied by the number of parasitoids of species k that were reared out of host species j in habitat B during the same sampling period, divided by the total number of individuals of parasitoid species k that were reared out of all of the H host species in either of the habitats considered. In the case A = B, diAjB measures within-habitat shared parasitism, and when A ≠ B, diAjB measures cross-habitat shared parasitism. However, in both of these cases q = 2, since even for parasitism within only one of the habitats, both habitats will contribute to the total pool of parasitoids. If the total pool of parasitoids occurs in only one habitat, Equation 2 simplifies to Equation 1 (when A = B and q = 1). When i = j, diAjB measures the proportion of parasitoids attacking species i that recruit from species i in the same (A = B) or different (A ≠ B) habitat (i.e. the intraspecific contribution of i to its own parasitoid pool). Expected, observed and initial parasitism rates
We tested whether we could use knowledge of the proportions of shared parasitoids (diAjB values) between host species in our training metaweb (Fig. 1e), as well as initial attack rates from (pre-treatment) time t at our validation sites (Fig. 1g), to predict parasitism rates at (post-treatment) time t + 1 at the validation sites (Fig. 1h), given known changes in host abundances (Fig. 1g, h). Parasitism rate refers to the number of parasitism events divided by the number of hosts sampled. We first calculated the expected parasitism rate at time t + 1 of host species i in habitat A using: (3) where n is host abundance, t is a time step (before or after sampling dates), and all other variables are defined as in Equation 2. Here, when q = 2, B can take values of either habitat. When q = 1, B is limited to being either one habitat or the other (here plantation or native forest). That is, when q = 2, this equation calculates the expected parasitism rate of host i in habitat A based on potential apparent competition with hosts in the same and the adjacent habitat. When q = 1 it calculates the expected parasitism rate of host i in habitat A based on potential apparent competition with hosts either in plantation or in native forest. In both cases, A can take values of either habitat. We calculated diAjB from the metaweb (transect plus extra sampling data for maximum resolution on interactions) from our training sites (Fig. 1d, e), and αiAl(t) (transect plus extra sampling data) and njB(t) (transect data only, for a standardized measure of abundance) from our validation sites in the pre-herbivore-reduction (time t) samples (in both reduction and control sites; Fig. 1g). We calculated njB(t+1) (transect data only) and niA(t+1) (transect plus extra sampling data, since αiAl(t) was calculated from transect plus extra sampling data) from the post-herbivore-reduction samples (also in both reduction and control sites; Fig. 1h).
Equation 3 calculates, for every host j (in either habitat) that shares parasitoids with host i in habitat A, the expected per capita attack rate on host i of parasitoids that were reared from host j. This expected per capita attack rate on host i due to parasitoids from host j is then multiplied by the t + 1 abundance of species j to convert the rate to a number of parasitism events. When summed over all H, this gives the expected number of attacks (not rate) on species i at time t + 1, which can then be divided by the abundance of species i at time t + 1 to give the expected parasitism rate (Fig. 1i). In cases where more attacks were predicted than hosts were collected in the t + 1 collection, expected parasitism rates were greater than one. We reduced these expected parasitism rates to 1 in our analysis because our definition of parasitism rate was parasitized hosts / total hosts (i.e. host centric), so rates greater than one are not possible. Equation 3 is written such that the expected parasitism rate of host i increases in proportion to the abundance of host j. Thus, it assumes apparent competition between hosts that share parasitoids, rather than apparent mutualism. A positive correlation between expected and observed parasitism rate would therefore suggest that apparent competition is more important than apparent mutualism, whereas a negative correlation would suggest that apparent mutualism is more important than apparent competition. For the entire herbivore assemblage, we tested whether this expected parasitism rate significantly predicted the observed parasitism rate of each host species i at time t + 1, which was calculated as: (4) where all variables are defined and calculated as in equation 3 (Fig. 1j).
is largely due to its prediction of within-habitat effects. For this analysis we included only cases in which parasitism was observed at t+1, because zero-values (no parasitism) could not be attributed to either within- or cross-habitat hosts. We separated the expected parasitism rates into the expected attacks based on cross-habitat versus within-habitat host abundances. To calculate cross-habitat vs. within-habitat expected parasitism rates, we set q equal to 1 in Equation 3, and first set B (the habitat of host j) to be plantation forest. These settings allowed us to calculate expected parasitism rates for host i in both plantation and native forest based on apparent competition with hosts in plantation forest. For host i in plantation forest, this would produce within-habitat expected parasitism rates, and for host i in native forest, this would produce cross-habitat expected parasitism rates. We then set B to be native forest, and again calculated EiA(t+1) for host i. For host i in plantation forest, this produced cross-habitat expected parasitism rates, and for host i in native forest, this produced within-habitat expected parasitism rates. This process produced both within- and cross-habitat expected parasitism rates for each host species i in plantation forest, and each host species i in native forest. To test whether cross-habitat expected parasitism rates predicted observed parasitism rate, and whether they predicted a component of the variation in observed parasitism rate beyond that predicted by expected parasitism rate, we used a GLMM with a binomial distribution and OiA(t+1) as the response variable. Within-habitat and cross-habitat expected parasitism rates were included as separate fixed predictors, and forest within site within block were included as nested random factors in the full model, before selection of the best random and then fixed effect structure. Expected parasitism rates were log-transformed to achieve a more even distribution of values and improve linear model fit (but results were not