‘On being the right size’ – Do aliens follow the rules?

To assess whether mammalian species introduced onto islands across the globe have evolved to exhibit body size patterns consistent with the ‘island rule,’, and to test an ecological explanation for body size evolution of insular mammals.

Perhaps the most compelling patterns of evolutionary transformations in native insular vertebrates are those in body mass, known as the 'island rule' which describes a graded trend from gigantism in small species to dwarfism in large species (Foster, 1964;Lomolino, 1985Lomolino, , 2005Van Valen, 1973). Based on our earlier studies of native insular mammals (Lomolino, Sax, Palombo, & van der Geer, 2012;Lomolino et al., 2013;, we hypothesized that the island rule pattern results from reversals in selective pressures from ecological displacement in high diversity communities on the mainland (which drive diversification in fundamental traitsbody size in particular) to ecological release and convergence in body size (gigantism in small-sized species and dwarfism in large-sized species) on species-poor islands, especially in the absence of other mammals.
Despite the pervasive nature and generality of the island rule pattern across a diversity of taxa, regions and time periods (e.g. Burns, 2016;Lomolino, Riddle, & Whittaker, 2017:503-513;Lomolino et al., 2012Lomolino et al., , 2013Lyras, van der Geer, & Rook, 2010;McClain, Boyer, & Rosenberg, 2006;van der Geer et al., 2013van der Geer et al., , 2016, there exists much variation about the general trend for native insular mammals. This variation has sometimes led to rejection of the island rule pattern for mammals (e.g. Meiri, Cooper, & Purvis, 2008;Meiri, Dayan, & Simberloff, 2004;Raia, Carotenuto, & Meiri, 2010). However, our analysis of body size variation of 385 insular populations of mammals from 98 species across 248 islands indicated that this residual variation was attributable to differences in functional characteristics (e.g. diet, 'bauplan') among the species and to variation among islands in their geographical and ecological characteristics, in particular latitude, topographic and environmental diversity, and diversity of insular communities, especially co-occurring mammals (Lomolino et al., 2012). Insular relative body size (S i ) of small mammals increased with latitude, consistent with Bergmann's rule (Bergmann, 1847), but as S i was standardized for body size of the mainland populations, this trend indicates that the Bergmann's rule pattern may be more intensified on islands. This study on native insular mammals also indicated that, for small mammals, gigantism was more pronounced for populations inhabiting smaller and more isolated islands, and those of more limited topographic complexity. Insular body size of mammals (both small and large species) also tended to be larger on islands with fewer mammalian competitors.
Our complementary study on temporal shifts in body size of small mammals inhabiting Mediterranean islands from the late Miocene to the early Holocene provided further evidence for the influence of ecological interactions on body size evolution of native insular mammals . Small mammals (e.g. mice, shrews and pikas) tended to increase in body size following colonization of these islands, but these trends towards gigantism ceased or were reversed following colonization of the islands by mammalian competitors or predators. A study on palaeo-insular rodent populations from 58 species across 32 islands worldwide also indicated the influence of climatewith gigantism in rodents being much less pronounced during cold phases of the Pleistocene in the Mediterranean (van den Hoek Ostende, van der Geer, & Wijngaarden, 2017).
Here, we capitalize on the thousands of unplanned experiments of introductions of mammals onto islands to further investigate the generality and causality of body size evolution. Our purpose is to assess whether mammalian species introduced onto islands across the globe have evolved to exhibit body size patterns consistent with the island rule, and to test our ecological explanation for body size evolution of insular mammals; that is, body size evolution should be dependent on the presence of ecologically relevant competitors and predators (Lomolino et al., 2012). To evaluate this hypothesis on the ecology of evolution, we test its predictions that body size evolution of introduced mammals (1) is more pronounced (i.e. greater degree of gigantism and dwarfism) for populations with longer residence times on islands; (2) is influenced by characteristics of the islands, including latitude (with body size of small mammals increasing with latitude, consistent with Bergmann's rule) and maximum elevation of the islands (with body size evolution being more pronounced on low elevation islands because of their lower habitat diversity); and (3) is more pronounced on ecologically simple islands, that is those with fewer mammalian predators, competitors or prey.

| Data collection
We compiled a data set containing information on mammals introduced onto islands worldwide ( Figure 1) including their insular and mainland body mass, time of introduction, the latitude, longitude and maximum elevation of the island, and the number of co-occurring species of mammalian competitors, predators and prey (noting also whether they were native or alien species). A list of the data sources is found in Appendix 1.
Our data set is the most extensive compiled thus far for body size evolution of mammals introduced to islands, comprised of information on 385 populations introduced onto 285 islands, ranging in absolute latitude from 0.13°to 63.42°, and in maximum elevation from 1 to 5,030 m. The introduced populations belong to 56 species from seven ordersmost of these being invasive species (pests), that is those that tend to spread rapidly after establishing their ranges. This is partly due to the nature of zoological collections that are often based on eradication campaigns. The five most frequently introduced species in our data set are commensal rats (Rattus exulans, Rattus norvegicus, R. rattus), house mice (Mus musculus) and rabbits (Oryctolagus cuniculus).
Based on introduction date, our data are divided into two broad temporal ranges: the Holocene for pre-modern introductions (n = 269) and the Anthropocene (n = 100) for introductions after 1610, following the definition of Lewis and Maslin (2015) (for 16 populations, no time of introduction was available) (for sources on introduction date, see Appendix S1 in Supporting Information). The year 1610 represents the onset of the European expansion, starting a new wave of species introductions.
We searched various published sources (Appendix S2) to determine the number of mammalian symbionts on each focal island. We used the conventional approach of total number of relevant species instead of a-diversity (sensu Whittaker, 1972), which is likely a better estimate of the level of competition and predation on large islands, because a-diversity is not readily available yet for our focal islands. Species richness ranged from 0 to 73 (native competitors), six (predators) and 50 (prey) (12, 6 and 12, respectively, for alien species). Geographical data (latitude, longitude and maximum elevation) for the focal islands were taken from the Islands Website of the United Nations Environment Programme (http://islands.unep.ch/). For islands not included in this database, we used alternative sources (see Appendix S1). Isolation was not included as an independent variable because it was irrelevant for species introductions, except in terms of the effects of isolation on diversity of co-occurring species, which were recorded as independent variables in our analyses. Similarly, island area was not included in our analyses because species do not respond to area per se. Rather, the relevant drivers of body size evolution (correlated with island area) include the diversity of symbionts (numbers of competitors, predators and prey) and diversity of habitats (a correlate of maximum elevation); variables explicitly included in our analyses of factors influencing body size evolution of these mammals.

| Calculations of S i
For each island, we calculated the average body size measurement of the focal, introduced population from the available museum specimens and then divided this by the average body size of the mainland population, preferably from the same geographical region (Appendix S1 and S2). The resulting ratio S i (relative insular body size) served as the dependent variable in our analyses. Body size measurements included total body length, tail and foot length, and body mass at death, and S i was expressed in mass equivalents or the ration of cubed linear dimensions when measurements were of body, tail or foot length. For rats and mice, we measured as far as available only specimens with advanced dental wear (stages V and 5, respectively, in [King, 2006]), as rats and mice grow slightly after they reach maturity (Roach, Mehta, Oreffo, Clarke, & Cooper, 2003). A number of species display sexual size dimorphism (for reference per species, see Appendix S1). We separated the sexes for these taxa (all artiodactyl species, Herpestes, Macropus, Martes, Mustela, Mus, Oryctolagus, Phalanger, Suncus) and then either used only the measurements from one sex (the one with the most available specimens) or the average for both males and females, where S i = ((S i male + S i female )/2). For species without significant sexual dimorphism (Acomys, Bandicota, Eliomys, Erinaceus, Glis, Lepus, Rattus, Sylvilagus, Trichosurus), we pooled data from males and females.
Feral domestic breeds were excluded, because either information on which specific breed was introduced was missing, or more than one breed were used to establish a local population. This is, for F I G U R E 1 Islands with introduced mammals for which we assembled data for this study, including 385 populations belonging to 56 species introduced onto 285 islands, ranging in absolute latitude from 0.13°to 63.42°[Color figure can be viewed at wileyonlinelibrary.com] VAN (King et al., 2016). For the ancestral, mainland reference for the Polynesian rat (R. exulans), we used populations from Indochina (Thomson et al., [2014] suggested that this species originates from Flores, but material from that island was not available for our measurements). See Appendix S1 for a detailed justification of mainland-island pair per introduced population.

| Statistical analyses
We conducted all statistical analyses using XLSTAT (version 2012; Addinsoft, New York, USA), which is a program that runs in the EXCEL environment. First, we expressed body size variables as the mean values of measurements for individuals of each insular population, and we then conducted statistical analyses at this (i.e. the population) level. Because each insular population was the product of a distinct introduction, often at periods quite disparate in time, and with genetic and geographical isolation to assure their independence, we consider each insular population to be an evolutionary independent unit. Our dependent variable (S i ) is a comparison of the means for a particular insular population and its mainland source/reference population and, thus, reflects the evolutionary independence of each species population. Although we included taxonomic order as a covariate in the analyses described below, we chose not to include species identity of each insular population as a variable in the analyses because it would have likely confounded any inferences and possibly introduce a narcissus effect (as described above, the variable for body size [M] was fixed for each species population, and thus, species identity is a surrogate for M). We did, however, conduct an initial analysis of the island rule pattern (i.e. the relationship between S i and M) after pooling the data for insular populations to the species level; this yielding results qualitatively identical to those for the entire data set. All other analyses were conducted with the expanded data set (i.e. at the level of insular populations), which enabled us to assess the influence the full set of relevant independent variables, including M, taxonomic order, latitude and maximum elevation of the islands, and diversity of co-occurring mammalian competitors, predators and prey.
We used analysis of covariance (ANCOVA; significance level 5%) to assess the relationship between relative insular body size (S i ) and two independent variablesbody size of the species on the mainland (M) and taxonomic order (using log 10 transformation of body size variables S i and Ms; regression model LogS i = b 1 (order) + b 2 (LogM) + b 3 (order)*(LogM)). We first conducted these analyses with both variables (S i , M ) and an interaction term ((order)*(LogM)) to test whether the slopes of the relationship between S i and M differed among mammalian orders. When this was found not to be the case, we conducted a second ANCOVA, this time without the interaction term (assuming the same generalized slope across orders) to assess differences in S i -M relationships (i.e. island rule patterns) among orders (as indicated by differences in the intercepts of these relationships). This latter analysis also generated residuals, which are essentially deviations above or below the island rule pattern after adjusting for the influences of both body size and of taxonomic order.

Residuals from ANCOVAs for both Holocene and Anthropocene
introductions, taken separately, were then used as the dependent variable in regression tree analyses (RTA) to assess the effects of the remaining independent variables: latitude and maximum elevation of the islands, and diversity of co-occurring mammalian competitors, predators and prey. RTA parameters included the following: method = CHAID, maximum tree depth = 5, significance level = 5%, split threshold = 5%, authorize redivision, Bonferroni correction/merge threshold = 5%, minimum parent size = 4, minimum son size = 2 and number of intervals = 10. RTA is a recursive, binary machine-learning nonparametric and distribution-free method that does not require transformations. RTA is able to deal efficiently with missing variables, which is not affected by outliers, non-normality or monotonic transformation of data (Bell, 1999;Breiman, Friedman, Olshen, & Stone, 1984;Loh, 2011Loh, , 2014Olden, Lawler, & Poff, 2008;Steinberg & Colla, 1997;Steinberg & Golovnya, 2006). One especially important advantage of machine-learning methods in ecological and evolutionary applications is that they do not assume data independence, thus alleviating the need for phylogenetic controls of such data (Davidson, Hamilton, Boyer, Brown, & Ceballos, 2009; see also Westoby, Leishman, & Lord, 1995;Melo, Rangel, & Diniz-Filho, 2009). Its principal product is a recursively branching tree that describes the direct, interactive and contextual relationships between the response variable (here S i ) and a subset of the predictor variables. The first branch is determined by first sorting the entire data set by the values of each predictor variable and then determining which of those variables is best at splitting the data into two subgroups that are most homogeneous with respect to values of the response variable. This process is then repeated for each of the subsequent branches. The resulting 'maximal trees' are then pruned until an optimal tree is selected, in our case the tree with the smallest relative error rate for predicting test data based on models (trees) developed from independent training data.

| RESULTS
The range in relative insular body size was greatest for the Holocene introductions (n = 269; S i ranging from 0. F I G U R E 2 The effects of time on body size evolution of insular mammals are evident in comparisons of patterns among populations differing in residence times on islands. Mammal populations introduced onto islands during the Anthropocene (within the last 400 years) failed to exhibit the island rule (a graded trend from gigantism in small species to dwarfism in large species), those with longer residence times (i.e. introduced during the Holocene) exhibited the predicted pattern, albeit not as pronounced as that exhibited by palaeo-insular mammals (residence times >10,000 years). Anthropocene: R 2 < .001; Holocene: R 2 = .293; Uncertain period: R 2 = .076; Palaeo-insulars: Lomolino et al. (2012)

| The role of time
Although body size evolution of Holocene introductions (those prior to 1610) was comparable to that for Holocene native species, it was much less pronounced than that of palaeo-insular mammals (i.e. residence times > 10,000 years; Figure 2; see also Lomolino et al., 2013;fig. 5). This of course is entirely consistent with the predicted effects of time in isolation, but it also provides a measure of the rate of body size shift in these mammals. The commensal rats illustrate the effect of time perhaps best: all insular populations of the Polynesian rat, R. exulans, (n = 94) and the Asian house rat, R. tanezumi (n = 12), both Holocene introductions, evolve larger body sizes (except R. exulans on Fergusson Island where S i~1 ). Almost all Anthropocene populations of the brown rat, R. norvegicus (n = 21), on the other hand evolved smaller body sizes. Likely, it is not the relatively short time in isolation that causes this aberrant pattern, but rather a combination of factors including the unnatural, modified ecosystems in which these rats have to survive. We refrain here from further speculation, as too many factors can be thought of (e.g. drought, population size, stress, biased database).
Individual taxa, however, varied substantially in their rate of body size evolution, with numerous populations of some species exhibiting significant change in body size during the Anthropocene (i.e. within < 400 years), for example house mice on several islands (see also below). The rate as well as the magnitude of body size evolution was especially rapid for populations of small mammals introduced to isolated islands lacking other mammals, but dominated by alternative prey in the form of dense colonies of seabirds.
Our results are consistent with observations of a fast change in other introduced populations, for example the Orkney vole (Cucchi et al., 2014) and tiger snakes on southern Australian islands (Aubret, 2015). For rodents, which form the greater part of our database, Alhajeri and Steppan (2016) reported a positive association between body mass and precipitation variables, especially those that are associated with primary productivity, whereas they found no association between body size and temperature. While still speculative, we may infer that the set of species we studied, dominated by commensals, is far from representative of the character of native mammalsboth in their responses to environmental characteristics and their close association with anthropogenic environments. We admit, however, that more rigorous studies are required to investigate why introduced species are larger on tropical islands; or, alternatively, why body size of these commensals is lower on islands in the higher latitudes.

| The ecology of evolution
Although body size of introduced species evidenced the influence of co-occurring species of mammals, consistent with our previous findings and our hypothesis on the ecology of evolution, evidence for the effects of competitors was not pervasivelimited to the effects of alien competitors on body size of rodents introduced during the Anthropocene. Again, we can only speculate at this point, but submit that the differences in the influence of competition on natives versus introduced species may be a function of the atypical nature of commensal species. A review of the list of the most commonly introduced species, above, reveals that they are not only commensal, but also highly invasivespreading rapidly, especially across anthropogenic habitats, once introduced onto islands. In the Philippines, for example, the three commensals -R. tanezumi, R. exulans and S. murinusonly become established in disturbed forests where there are few native competitors (Rickart, Balete, & Heaney, 2007; see also de Guia & Quibod, 2014). This may also help explain the larger body size of introduced mammals on low elevations islands, where human populations often dominate and transform most insular habitats, thus favouring the invasive commensals.
Our results for the differential responses of two commonly introduced species (M. musculus and R. rattus) in sympatry versus in allopatry are consistent with those reported for black rats in New Zealand, which are larger in the absence of mice (Yom-Tov et al., 1999), and for those reported for a variety of small mammals of the Mediterranean palaeo-islands, where body size evolution trends reversed after introductions of competitors . It likely is no coincidence that the world's largest wild house mice live on Gough Island, South Atlantic Ocean (Rowe-Rowe & Crafford, 1992), where they are the only mammalian inhabitants and feast heavily on chicks of two dozen species of seabirds that breed F I G U R E 4 Regression tree analyses indicated that residual variation about the island rule trend for mammals introduced onto islands during the Holocene (after controlling for the effects of taxonomic order and body size of the ancestral, mainland species; Figure 3a) was higher (larger than expected body size) for populations on tropical islands and those with lower maximum elevation and fewer co-occurring species of native predators and prey. Numbers in parentheses indicate range for each split (branch) of the regression tree for this independent variable [Color figure can be viewed at wileyonlinelibrary.com] VAN DER GEER ET AL.
| 521 in dense populations on these islands (Cuthbert et al., 2016;Gray et al., 2014). This super-normal abundance of food and lack of predators and competitors allowed the mice to grow almost twice as large as their ancestors (S i = 1.89). A similar condition may be present on many other, low elevation islands where mice grow to relatively large size: many of these low elevation islands are covered by colonies of breeding birds that are released from predation by terrestrial mammals, in turn providing a bumper crop of atypical prey for rodents and other mammals introduced onto these islands (see also Jones & Ryan, 2010;Jones et al., 2008;Lomolino, 1984). A diet of almost exclusively sea birds until the latter's extinction has also been attested for the Polynesian rat in French Polynesia (Swift, Miller, & Kirch, 2016), indicating that this is an unfortunate result of rat introductions. Interestingly to note in this light is that the skulls of house mice of the Island of Heligoland suggest specific adaptations to a more carnivorous diet (Babiker & Tautz, 2015).
The super-normal abundance of seabird chicks and eggs on many relatively small and isolated islands may also account for the tendency for alien carnivores to be larger on islands lacking alien prey (i.e. introduced rats and mice), which might otherwise depress the prey base for carnivores by limiting productivity of seabird colonies on these islands. This is indeed the case for the two islands with the relatively largest carnivores (Bering and Mednyi, with S i = 1.306 and S i = 1.397, respectively), where these foxes exclusively feed on sea birds and seals (Mednyi) or on these atypical prey plus small voles (Bering) (Zagrebel'nyi, 2000). F I G U R E 6 Regression tree analyses indicated that residual variation about the island rule trend for (a) mammals (all orders), (b) rodents and (c) carnivores introduced onto islands during the Anthropocene (after controlling for the effects of taxonomic order and body size of the ancestral, mainland species; Figure 3b) was higher (larger than expected body size) for populations on tropical islands and those with lower maximum elevation and fewer co-occurring species of competitors, predators and prey. Numbers in parentheses indicate range for each split (branch) of the regression tree for this independent variable [Color figure can be viewed at wileyonlinelibrary.com] VAN DER GEER ET AL.

| CONCLUSION
| 523 typically mammal-free islands. Finally, given the antiquity of many of these species introductions, which often predate the onset of the Anthropocene by many centuries if not millennia, it appears that much of what we now view as the natural character, composition and ecological dynamics of recent insular communities may have been rendered artefacts of ancient colonizations by humans and our commensals (see van der Geer, Lomolino et al., 2017:592-594).

ACKNOWLEDGEMENTS
We are much indebted to colleagues from numerous museums and institutes for providing data and other information. We especially thank John Parkes and Dov Sax for insightful discussions. We thank