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Testing the ‘island rule’ for a tenebrionid beetle (Coleoptera, Tenebrionidae)
Acta Oecologica 23 (2002) 103–107 www.elsevier.com/locate/actao
Testing the ‘island rule’ for a tenebrionid beetle (Coleoptera, Tenebrionidae) Miquel Palmer * IMEDEA (UIB-CSIC), C/ Miquel Marques, 21, 07190 Esporles (Mallorca), Spain Received 2 May 2001; received in revised form 7 February 2002; received in revised form 18 March 2002; accepted 18 March 2002
Abstract Insular populations and their closest mainland counterparts commonly display body size differences that are considered to fit the island rule, a theoretical framework to explain both dwarfism and gigantism in isolated animal populations. The island rule is used to explain the pattern of change of body size at the inter-specific level. But the model implicitly makes also a prediction for the body size of isolated populations of a single species. It suggests that, for a hypothetical species covering a wide range of island sizes, there exists a specific island size where this species reaches the largest body size. Body size would be small (in relative terms) in the smallest islets of the species range. It would increase with island size, and reach a maximum at some specific island size. However, additional increases from such a specific island size would instead promote body size reduction, and small (in relative terms) body sizes would be found again on the largest islands. The biogeographical patterns predicted by the island rule have been described and analysed for vertebrates only (mainly mammals), but remain largely untested for insects or other invertebrates. I analyse here the pattern of body size variation between seven isolated insular populations of a flightless beetle, Asida planipennis (Coleoptera, Tenebrionidae). This is an endemic species of Mallorca, Menorca and a number of islands and islets in the Balearic archipelago (western Mediterranean). The study covers seven of the 15 known populations (i.e., there are only 15 islands or islets inhabited by the species). The populations studied fit the pattern advanced above and we could, therefore, extrapolate the island rule to a very different kind of organism. However, the small sample size of some of the populations invites some caution at this early stage. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Body size; Island size; Island rule; Tenebrionidae (Coleoptera); Balearic Islands (Spain)
1. Introduction Populations of many species living on islands show conspicuous body size changes in comparison to their mainland counterparts. The island rule (Foster, 1964) initially claimed that different groups of flightless non-marine mammals inhabiting islands experience different trends in body size (i.e., carnivores tend to dwarfism and rodents to gigantism) but this has been generally reformulated as a graded trend from gigantism in small-bodied species to dwarfism in large-bodied species (Brown and Lomolino, 1998). Lomolino (1985) proposed that ecological release (e.g., decreased competition or predation) promotes an increase in body size and, conversely, resource limitation decreases it.
* Corresponding author. Fax: +34-971-61-17-61. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 1 4 6 - 6 0 9 X ( 0 2 ) 0 1 1 4 0 - 2
The island rule has also been applied to populations of the same species living on islands of different size (Heaney, 1978). The body size of populations of medium body-sized species would exhibit a bell-shaped pattern in relation to island size. A specific island size would exist where the population inhabiting it would reach a maximum body size. Departures in both directions from such an island size (i.e., either smaller or larger islands) would result in body size reduction. In small islands, this reduction is thought to be due to increased pressure in a resource-limited system. Large amounts of resources are potentially available on large islands (or on the mainland), but ecological constraints (such as competition) could limit species to using only a part of them. The outcome would also be body size reduction. The body size of the tri-coloured squirrel (Callosciurus prevosti) fits this model (Heaney, 1978). The above topic has been formulated with equivalent outcomes but stressing the factors that reduce standard energy expen
104
M. Palmer / Acta Oecologica 23 (2002) 103–107
diture (McNab, 1994). Fitness may increase with the decrease in the use of resources when such a decrease channels resources into reproduction. Consequently, body size reduction would improve population fitness on islands with severe resource limitation (McNab, 1994). This bell-shaped pattern and the theory on which it is based (Heaney, 1978) suggest that body size would show a unimodal relationship with any environmental variable associated with the amount of available resources. Island size seems to be an example of such an environmental variable in the case of the tri-coloured squirrel. Betweenspecies comparisons could broaden (or eventually limit) the extent of this pattern. However, this type of comparisons may not be suitable because the conclusion might be obscured by the existence of phylogenetic inertia. This emerges because species share characteristics from common ancestors at distinct distances in evolutionary time (Felsenstein, 1985), and it has been proved to be the source of multiple spurious patterns (Diniz-Filho et al., 1998). Moreover, between-population (intra-specific) comparisons usually focus on a small range of island sizes. Therefore, true bell-shaped patterns might result in monotonic trends when only a small range of the gradient is considered. Here I describe body size changes in seven insular populations of the flightless endemic beetle Asida planipennis Schaufuss (Coleoptera, Tenebrionidae). This is a species endemic of Mallorca, Menorca and a number of islands and islets in the Balearic archipelago (western Mediterranean). The species is known from 15 islands or islets and is absent on the Iberian Peninsula (the nearest mainland). The populations studied come from islands ranging from 0.06 to 103 km2. This allows me to analyse the relationship between island area and body size, and to check the scope of the pattern with a very different kind of organism.
2. Methods 2.1. Sampling, measuring and statistical analysis I studied 94 males of A. planipennis from seven Balearic islands (Fig. 1). There are no data available on abundance on each island studied because the main sampling purpose at that moment was to obtain presence/absence data of the species on a number of sites. The field work spanned from 1990 to 1993. Some invertebrates experience large body size differences between years. However, this seems not to be the case for A. planipennis. Two samples (nine individuals from 1991 and 21 individuals from 1993) are available for one of the islands (Cabrera). This fact allowed me to complete a preliminary one-way ANOVA. The added variability due to between-year differences is clearly nonsignificant (F = 0.036; Prob. = 0.850). Therefore, I pooled all specimens and assumed that all populations experience a similar level of between-year variability. Sample and island
Fig. 1. Location of the islands sampled.
sizes are detailed in Table 1. The specimens analysed are deposited in the Museu de la Naturalessa de les Illes Balears (Palma de Mallorca, Spain). Males and females show slight body size differences. In addition, females are apparently more scarce than males, and the few available individuals precluded performing a separate analysis. Therefore, I studied only males in order to focus only on between-population size differences. Males seem to be scarce in some of the smallest islets too. These facts limited the sample size on two scales. Firstly, only seven of the 15 known populations have been included (i.e., sites stet less than two males have been collected were excluded). Secondly, sample sizes are not very large (three for na Plana, and some other populations are represented by seven or eight specimens). There are six species of the genus Asida in the Balearics (Pons and Palmer, 1996). One of them, A. moraguesi Schaufuss, is taxonomically very close to A. planipennis. A. moraguesi is only found in the north-east of Mallorca (Artà). A. moraguesi and A. planipennis are not sympatric and not only do they show different pronotum shape and Table 1 Source, island area (km2), centroid size, standard deviation of centroid size (SD) and sample size (n) of the seven populations studied. Note that the absolute value of centroid size is meaningless, as it depends on the number of landmarks (i.e., the number of points in Fig. 2). Source (Islands)
Islandarea
Centroidsize
Serra de Tramuntana (NW Mallorca) Menorca Cabrera Sa Dragonera Illa dels Conills Na Moltona Na Plana .
1000
8.09
0.52
27
7.56 8.35 8.15 7.60 6.23 6.76
0.68 0.34 0.68 0.21 0.39 0.57
8 30 8 7 11 3
700 11.5 2.9 1.4 0.06 0.06
SD
n
M. Palmer / Acta Oecologica 23 (2002) 103–107
105
model (Huisman et al., 1993) has also been considered. It is a more complex model developed for skewed (i.e., asymmetric) unimodal patterns. 2.2. Between-sample independence Between-population body size similarity can be explained by a similar set of site-specific environmental variables. Moreover, it can arise when populations are geographically or phylogenetically close. Evidence for the existence of spatial patterns was not found for pronotum centroid size (Palmer, in press). The existence of phylogenetic inertia was indirectly tested on the assumption of no dispersal since the last ice age (i.e., assuming that the current between-island bathymetry matrix is correlated to the pair-wise phylogenetic distance matrix). Under such an assumption, evidence for the existence of phylogenetic inertia was not found for pronotum size (Palmer, in press). The biological interpretation of between-population independence (under the assumption described above) is that the time passed since isolation is enough for removing all trace of common history of the trait considered.
3. Results Fig. 2. Pronotum of A. planipennis. Arrows point to the recorded landmarks.
size, but also divergent allometric trajectories (Palmer, in press). The taxonomy follows Español (1954). The geometry (shape and size) of the pronotum was captured by recording two-dimensional coordinates of landmark points (Rohlf and Marcus, 1993). Eight landmarks were chosen as reliably comparable biological structures (Fig. 2). Two-dimensional coordinates of these landmarks were collected from every specimen using an imageanalyser composed of a Wild dissecting microscope, a video camera, and VIDAS21 software (Kontron Elektronic, Munich). Specimen size was estimated by its centroid size (i.e., the squared root of the sum of the squared distances from each landmark to the centre of gravity (Rohlf and Marcus, 1993) of the pronotum. Centroid size was determined using the TPSReg program (Rohlf, 1998). Every specimen was measured in triplicate and the values averaged. The centroid size of a population was determined by averaging the centroid size for every specimen. The relationship between island area (ln-tranformed) and centroid size was analysed by fitting the data to some alternative models. A simple linear model was tested by conventional regression analysis. A two-order polynomial was also considered because it was the original choice of Heaney (1978). A Gaussian response curve was also fitted to the data because this is a simple and theoretically wellsupported model for unimodal (i.e., bell-shaped) relationships (ter Braak and Verdonachot, 1995). The full HOF
Centroid size of the pronotum (as a general estimate of body size) and island size for the seven populations of A. planipennis are shown in Table 1. The scatter plot (Fig. 3) of centroid size against island size (ln-tranformed) shows the same pattern described by Heaney (1978) for the tri-coloured squirrel (Callosciurus prevosti): body size increases from tiny islands (na Moltona, and na Plana, 0.06 km2) to medium-sized islands. However, after reaching a maximum on Cabrera (11.5 km2), body size decreases on the largest islands (Menorca, 700 km2, and in the Serra de Tramuntana population in Mallorca, 1000 km2). The data did not fit a linear regression model (Pearson r2 = 0.457; P = 0.096), but clearly matched the two symmetric unimodal models (i.e., two-order polynomial and Gaussian). The parameters estimated and the r2 values reached are detailed in Table 2. The other model considered (the full HOF model) is potentially asymmetric. Note, however, that the fitting of the data to the full HOF model is made with a descriptive purpose only because the number of parameters (five) is too close to the number of degrees of freedom (seven samples). Under these circumstances it is unreasonable to test the goodness of fit of this last model. The relevant point is that the fitted values for all of these three models are virtually the same along the range of island sizes considered (Fig. 3). Two additional points should be considered here. First, the inclusion of A. moraguesi does not break the pattern (Fig. 3). It was removed from the analysis because it belongs to a different taxon. Secondly, it is difficult to estimate the effective island area for the largest islands (i.e.,
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4. Discussion
Fig. 3. Scatter-plot of centroid size against island area (km2, lntransformed). Points indicate the populations studied. Note that the dimensionality of centroid size is M instead of M2 (i.e., it is comparable to a length). Moreover, the absolute value of centroid size is meaningless because it depends on the number of landmarks (i.e., the number of points in Fig. 2). A. moraguesi (denoted by a triangle) is not included in the analysis but its inclusion does not break the pattern. A. moraguesi is phylogenetically close to A. planipennis and it is also found on Mallorca. The lines correspond to the two-order polynomial model, the Gaussian model and the Hole model, and all are practically identical.
the area of the currently suitable habitat). Certainly, A. planipennis does not inhabit the whole of Mallorca (3639 km2), nor the whole of its Serra de Tramuntana mountain range (approx. 1000 km2) and the same holds for the population on Menorca. Instead, A. planipennis seems to be more abundant in open habitats. Therefore, the effective island size is probably overestimated in the cases of Mallorca and Menorca. However, it must be emphasised that reasonable reductions of the island area in these two cases would not change, but rather exaggerate the bell-shaped pattern shown in Fig 3. In relation to this, there is no direct evidence that the specimens from the larger islands form a continuous population. However, the presence/absence data available for the central sector of the Serra de Tramuntana show that the species is present in more than 75% of the 1 km2 cells of a quasi-regular grid (150 cells surveyed), showing a quite continuous distribution (unpublished data). Table 2 Parameters (a to c) and fit (r2) of the two-order polynomial model [Y = a + bX + cX2] and the Gaussian model [Y = a + EXP(–((X – b)2)/(2c2))]. Centroid size is denoted by Y, and X is (ln-transformed) island size. Probabilities (Prob.) under the ordinary assumptions of the general linear model are also added (H0: the residual mean squares are larger than the explained mean squares). Parameters
Polynomial
Gaussian
a b c r2 Prob. .
7.72 0.31 –0.04 0.876 0.015
8.32 3.63 9.17 0.879 0.014
The analysis of body size variation performed for A. planipennis seems to broaden the taxonomic scope of the island rule. The biogeographical scenario and the size pattern described here make unlikely the null hypothesis that size was determined by chance (e.g., by random sampling of subpopulations at the isolation event). In contrast, it seems likely that size has evolved by selection related to sitespecific environmental factors linked with island area. A monotonic relationship between island and body sizes seems improbable. Instead, the scatterplot of centroid size versus island area displays a bell-shaped pattern. A biological interpretation of the parameters obtained is difficult. However, the parameters of the Gaussian model are potentially interpretable by comparison with applications of the model to species abundance variation along environmental gradients (ter Braak and Smilauer, 1998). The a-value (8.326) would correspond to the maximum body size, and the b-value to the island size where this maximum is reached (37.7 km2). An alternative to the symmetric unimodal model should also be considered because it can be expected that insular body size experiences some sigmoidal relationship as island size increases, with an asymptote at the body size of the mainland population. Body shape would increase with island area up to a maximum, but it would continue stable along further increases of island area. The full HOF model has been developed for covering the full range of skewness (Huisman et al., 1993). Therefore, it is noticeable that the line predicted by this model is virtually identical to the lines corresponding to the other two models (which are in essence symmetric). This supports the existence of an optimallysized island. However, the sense of optimality is here limited to a specific island where the balance between resources available and ecological constraints (such as inter-specific competition) allows body size to reach a maximum. In any case, a predictive extrapolation outside the range of the observed island sizes (for example, applied to mainland populations) is out of the aims of the present study. In the foregoing paragraphs inter-specific competition is claimed to affect body size. However, experimental evidence is lacking and this contention is only founded on a theoretical scenario extracted from the observed patterns rather than from the processes involved (e.g., Heaney, 1978; McNab, 1994; Lomolino, 1985). Following the generally accepted explanations suggested by the latter authors, the small size on tiny islands would be related to severely limited resources. On these tiny islands, selection could favour small-bodied individuals that maximise the probability of population persistence. Extinction probability would be minimised when population size is above a critical value, and one way for assuring such a value is by reducing body size (Brown and Lomolino, 1998). Body size increases from these tiny islands to medium-sized ones, reaching for
M. Palmer / Acta Oecologica 23 (2002) 103–107
A. planipennis a theoretical maximum between 8.7 and 162.8 km2 (95% confidence limits determined from the Gaussian model). The mechanism explaining this increase would be the advantage it confers to intra-specific interactions, or the greater capability it permits for storing energy and water reserves (Brown and Lomolino, 1998). Additional increases of island area from the optimum promote body size decreases. One plausible causal mechanism could be a significant increase in inter-specific competition, although predation has also been proposed for other species (Brown and Lomolino, 1998).
Acknowledgements I thank Tonyo Alcover, Enric Descals, Txus GómezZurita, Carlos Juan, and José Alexandre Felizola DinizFilho for their help and suggestions. I thank James Rohlf, Mauro Cavalcanti and others that have made their software available on the web. This research has been supported by the scientific project DGES PB96-0090 (Ministry of Education and Sciences, Spain).
References Brown, J.H., Lomolino, M.V., 1998. Biogeography, Sinauer Assoc., Sunderland. .
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Diniz-Filho, J.A.F., de Sant’Ana, C.E.R., Bini, L.M., 1998. An eigenvector method for estimating phylogenetic inertia. Evolution 52, 1247–1262. Español, F., 1954. Los Tenebriónidos (Col.) de Baleares. Trab. Mus. Cienc. Nat. Barcelona (N. S. Zool.) 1, 1–93. Felsenstein, J., 1985. Phylogenies and the comparative method. Am. Nat. 125, 1–15. Foster, J., 1964. The evolution of mammals on islands. Nature 202, 234–235. Heaney, L.R., 1978. Insular area and body size of insular mammals: Evidence from the tri-coloured squirrel (Callosciurus prevosti) of Southeast Asia. Evolution 32, 29–44. Huisman, J., Olff, H., Fresco, L.F.M., 1993. A hierarchical set of models for species response analysis. J. Veg. Sci. 4, 37–46. Lomolino, M.V., 1985. Body size of mammals on islands: The island rule reexamined. Am. Nat. 125, 310–316. McNab, B.K., 1994. Resource use and the survival of land and freshwater vertebrates on oceanic islands. Am. Nat. 144, 643–660. Pons, G.X., Palmer, M., 1996. Fauna endèmica de les Illes Balears, Inst. Est. Balearics, Conselleria d’Obres Públiques, Ordenació del Teritori i Medi Ambient. Soc. Hist. Nat. Balears, Palma de Mallorca. Rohlf, F.J., 1998. TPSRegr: a program for regression of partial warps scores, Dept. Evolutionary Biology. Univ. New York, Stony Brook, New York. . Rohlf, F.J., Marcus, L.F., 1993. A revolution in morphometrics. TREE 8, 129–133. ter Braak, C.J.F., Smilauer, P., 1998. CANOCO reference manual and user’s guide to Canoco for Windows: Software for Canonical Community ordination (version 4), Microcomputer Power, Ithaca, NY, USA. . ter Braak, C.J.F., Verdonachot, P.F.M., 1995. Canonical correspondence analysis and related multivariate methods in aquatic ecology. Aquat. Sci. 57, 255–289.
Testing the ‘island rule’ for a tenebrionid beetle (Coleoptera, Tenebrionidae) Miquel Palmer * IMEDEA (UIB-CSIC), C/ Miquel Marques, 21, 07190 Esporles (Mallorca), Spain Received 2 May 2001; received in revised form 7 February 2002; received in revised form 18 March 2002; accepted 18 March 2002
Abstract Insular populations and their closest mainland counterparts commonly display body size differences that are considered to fit the island rule, a theoretical framework to explain both dwarfism and gigantism in isolated animal populations. The island rule is used to explain the pattern of change of body size at the inter-specific level. But the model implicitly makes also a prediction for the body size of isolated populations of a single species. It suggests that, for a hypothetical species covering a wide range of island sizes, there exists a specific island size where this species reaches the largest body size. Body size would be small (in relative terms) in the smallest islets of the species range. It would increase with island size, and reach a maximum at some specific island size. However, additional increases from such a specific island size would instead promote body size reduction, and small (in relative terms) body sizes would be found again on the largest islands. The biogeographical patterns predicted by the island rule have been described and analysed for vertebrates only (mainly mammals), but remain largely untested for insects or other invertebrates. I analyse here the pattern of body size variation between seven isolated insular populations of a flightless beetle, Asida planipennis (Coleoptera, Tenebrionidae). This is an endemic species of Mallorca, Menorca and a number of islands and islets in the Balearic archipelago (western Mediterranean). The study covers seven of the 15 known populations (i.e., there are only 15 islands or islets inhabited by the species). The populations studied fit the pattern advanced above and we could, therefore, extrapolate the island rule to a very different kind of organism. However, the small sample size of some of the populations invites some caution at this early stage. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Body size; Island size; Island rule; Tenebrionidae (Coleoptera); Balearic Islands (Spain)
1. Introduction Populations of many species living on islands show conspicuous body size changes in comparison to their mainland counterparts. The island rule (Foster, 1964) initially claimed that different groups of flightless non-marine mammals inhabiting islands experience different trends in body size (i.e., carnivores tend to dwarfism and rodents to gigantism) but this has been generally reformulated as a graded trend from gigantism in small-bodied species to dwarfism in large-bodied species (Brown and Lomolino, 1998). Lomolino (1985) proposed that ecological release (e.g., decreased competition or predation) promotes an increase in body size and, conversely, resource limitation decreases it.
* Corresponding author. Fax: +34-971-61-17-61. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 1 4 6 - 6 0 9 X ( 0 2 ) 0 1 1 4 0 - 2
The island rule has also been applied to populations of the same species living on islands of different size (Heaney, 1978). The body size of populations of medium body-sized species would exhibit a bell-shaped pattern in relation to island size. A specific island size would exist where the population inhabiting it would reach a maximum body size. Departures in both directions from such an island size (i.e., either smaller or larger islands) would result in body size reduction. In small islands, this reduction is thought to be due to increased pressure in a resource-limited system. Large amounts of resources are potentially available on large islands (or on the mainland), but ecological constraints (such as competition) could limit species to using only a part of them. The outcome would also be body size reduction. The body size of the tri-coloured squirrel (Callosciurus prevosti) fits this model (Heaney, 1978). The above topic has been formulated with equivalent outcomes but stressing the factors that reduce standard energy expen
104
M. Palmer / Acta Oecologica 23 (2002) 103–107
diture (McNab, 1994). Fitness may increase with the decrease in the use of resources when such a decrease channels resources into reproduction. Consequently, body size reduction would improve population fitness on islands with severe resource limitation (McNab, 1994). This bell-shaped pattern and the theory on which it is based (Heaney, 1978) suggest that body size would show a unimodal relationship with any environmental variable associated with the amount of available resources. Island size seems to be an example of such an environmental variable in the case of the tri-coloured squirrel. Betweenspecies comparisons could broaden (or eventually limit) the extent of this pattern. However, this type of comparisons may not be suitable because the conclusion might be obscured by the existence of phylogenetic inertia. This emerges because species share characteristics from common ancestors at distinct distances in evolutionary time (Felsenstein, 1985), and it has been proved to be the source of multiple spurious patterns (Diniz-Filho et al., 1998). Moreover, between-population (intra-specific) comparisons usually focus on a small range of island sizes. Therefore, true bell-shaped patterns might result in monotonic trends when only a small range of the gradient is considered. Here I describe body size changes in seven insular populations of the flightless endemic beetle Asida planipennis Schaufuss (Coleoptera, Tenebrionidae). This is a species endemic of Mallorca, Menorca and a number of islands and islets in the Balearic archipelago (western Mediterranean). The species is known from 15 islands or islets and is absent on the Iberian Peninsula (the nearest mainland). The populations studied come from islands ranging from 0.06 to 103 km2. This allows me to analyse the relationship between island area and body size, and to check the scope of the pattern with a very different kind of organism.
2. Methods 2.1. Sampling, measuring and statistical analysis I studied 94 males of A. planipennis from seven Balearic islands (Fig. 1). There are no data available on abundance on each island studied because the main sampling purpose at that moment was to obtain presence/absence data of the species on a number of sites. The field work spanned from 1990 to 1993. Some invertebrates experience large body size differences between years. However, this seems not to be the case for A. planipennis. Two samples (nine individuals from 1991 and 21 individuals from 1993) are available for one of the islands (Cabrera). This fact allowed me to complete a preliminary one-way ANOVA. The added variability due to between-year differences is clearly nonsignificant (F = 0.036; Prob. = 0.850). Therefore, I pooled all specimens and assumed that all populations experience a similar level of between-year variability. Sample and island
Fig. 1. Location of the islands sampled.
sizes are detailed in Table 1. The specimens analysed are deposited in the Museu de la Naturalessa de les Illes Balears (Palma de Mallorca, Spain). Males and females show slight body size differences. In addition, females are apparently more scarce than males, and the few available individuals precluded performing a separate analysis. Therefore, I studied only males in order to focus only on between-population size differences. Males seem to be scarce in some of the smallest islets too. These facts limited the sample size on two scales. Firstly, only seven of the 15 known populations have been included (i.e., sites stet less than two males have been collected were excluded). Secondly, sample sizes are not very large (three for na Plana, and some other populations are represented by seven or eight specimens). There are six species of the genus Asida in the Balearics (Pons and Palmer, 1996). One of them, A. moraguesi Schaufuss, is taxonomically very close to A. planipennis. A. moraguesi is only found in the north-east of Mallorca (Artà). A. moraguesi and A. planipennis are not sympatric and not only do they show different pronotum shape and Table 1 Source, island area (km2), centroid size, standard deviation of centroid size (SD) and sample size (n) of the seven populations studied. Note that the absolute value of centroid size is meaningless, as it depends on the number of landmarks (i.e., the number of points in Fig. 2). Source (Islands)
Islandarea
Centroidsize
Serra de Tramuntana (NW Mallorca) Menorca Cabrera Sa Dragonera Illa dels Conills Na Moltona Na Plana .
1000
8.09
0.52
27
7.56 8.35 8.15 7.60 6.23 6.76
0.68 0.34 0.68 0.21 0.39 0.57
8 30 8 7 11 3
700 11.5 2.9 1.4 0.06 0.06
SD
n
M. Palmer / Acta Oecologica 23 (2002) 103–107
105
model (Huisman et al., 1993) has also been considered. It is a more complex model developed for skewed (i.e., asymmetric) unimodal patterns. 2.2. Between-sample independence Between-population body size similarity can be explained by a similar set of site-specific environmental variables. Moreover, it can arise when populations are geographically or phylogenetically close. Evidence for the existence of spatial patterns was not found for pronotum centroid size (Palmer, in press). The existence of phylogenetic inertia was indirectly tested on the assumption of no dispersal since the last ice age (i.e., assuming that the current between-island bathymetry matrix is correlated to the pair-wise phylogenetic distance matrix). Under such an assumption, evidence for the existence of phylogenetic inertia was not found for pronotum size (Palmer, in press). The biological interpretation of between-population independence (under the assumption described above) is that the time passed since isolation is enough for removing all trace of common history of the trait considered.
3. Results Fig. 2. Pronotum of A. planipennis. Arrows point to the recorded landmarks.
size, but also divergent allometric trajectories (Palmer, in press). The taxonomy follows Español (1954). The geometry (shape and size) of the pronotum was captured by recording two-dimensional coordinates of landmark points (Rohlf and Marcus, 1993). Eight landmarks were chosen as reliably comparable biological structures (Fig. 2). Two-dimensional coordinates of these landmarks were collected from every specimen using an imageanalyser composed of a Wild dissecting microscope, a video camera, and VIDAS21 software (Kontron Elektronic, Munich). Specimen size was estimated by its centroid size (i.e., the squared root of the sum of the squared distances from each landmark to the centre of gravity (Rohlf and Marcus, 1993) of the pronotum. Centroid size was determined using the TPSReg program (Rohlf, 1998). Every specimen was measured in triplicate and the values averaged. The centroid size of a population was determined by averaging the centroid size for every specimen. The relationship between island area (ln-tranformed) and centroid size was analysed by fitting the data to some alternative models. A simple linear model was tested by conventional regression analysis. A two-order polynomial was also considered because it was the original choice of Heaney (1978). A Gaussian response curve was also fitted to the data because this is a simple and theoretically wellsupported model for unimodal (i.e., bell-shaped) relationships (ter Braak and Verdonachot, 1995). The full HOF
Centroid size of the pronotum (as a general estimate of body size) and island size for the seven populations of A. planipennis are shown in Table 1. The scatter plot (Fig. 3) of centroid size against island size (ln-tranformed) shows the same pattern described by Heaney (1978) for the tri-coloured squirrel (Callosciurus prevosti): body size increases from tiny islands (na Moltona, and na Plana, 0.06 km2) to medium-sized islands. However, after reaching a maximum on Cabrera (11.5 km2), body size decreases on the largest islands (Menorca, 700 km2, and in the Serra de Tramuntana population in Mallorca, 1000 km2). The data did not fit a linear regression model (Pearson r2 = 0.457; P = 0.096), but clearly matched the two symmetric unimodal models (i.e., two-order polynomial and Gaussian). The parameters estimated and the r2 values reached are detailed in Table 2. The other model considered (the full HOF model) is potentially asymmetric. Note, however, that the fitting of the data to the full HOF model is made with a descriptive purpose only because the number of parameters (five) is too close to the number of degrees of freedom (seven samples). Under these circumstances it is unreasonable to test the goodness of fit of this last model. The relevant point is that the fitted values for all of these three models are virtually the same along the range of island sizes considered (Fig. 3). Two additional points should be considered here. First, the inclusion of A. moraguesi does not break the pattern (Fig. 3). It was removed from the analysis because it belongs to a different taxon. Secondly, it is difficult to estimate the effective island area for the largest islands (i.e.,
106
M. Palmer / Acta Oecologica 23 (2002) 103–107
4. Discussion
Fig. 3. Scatter-plot of centroid size against island area (km2, lntransformed). Points indicate the populations studied. Note that the dimensionality of centroid size is M instead of M2 (i.e., it is comparable to a length). Moreover, the absolute value of centroid size is meaningless because it depends on the number of landmarks (i.e., the number of points in Fig. 2). A. moraguesi (denoted by a triangle) is not included in the analysis but its inclusion does not break the pattern. A. moraguesi is phylogenetically close to A. planipennis and it is also found on Mallorca. The lines correspond to the two-order polynomial model, the Gaussian model and the Hole model, and all are practically identical.
the area of the currently suitable habitat). Certainly, A. planipennis does not inhabit the whole of Mallorca (3639 km2), nor the whole of its Serra de Tramuntana mountain range (approx. 1000 km2) and the same holds for the population on Menorca. Instead, A. planipennis seems to be more abundant in open habitats. Therefore, the effective island size is probably overestimated in the cases of Mallorca and Menorca. However, it must be emphasised that reasonable reductions of the island area in these two cases would not change, but rather exaggerate the bell-shaped pattern shown in Fig 3. In relation to this, there is no direct evidence that the specimens from the larger islands form a continuous population. However, the presence/absence data available for the central sector of the Serra de Tramuntana show that the species is present in more than 75% of the 1 km2 cells of a quasi-regular grid (150 cells surveyed), showing a quite continuous distribution (unpublished data). Table 2 Parameters (a to c) and fit (r2) of the two-order polynomial model [Y = a + bX + cX2] and the Gaussian model [Y = a + EXP(–((X – b)2)/(2c2))]. Centroid size is denoted by Y, and X is (ln-transformed) island size. Probabilities (Prob.) under the ordinary assumptions of the general linear model are also added (H0: the residual mean squares are larger than the explained mean squares). Parameters
Polynomial
Gaussian
a b c r2 Prob. .
7.72 0.31 –0.04 0.876 0.015
8.32 3.63 9.17 0.879 0.014
The analysis of body size variation performed for A. planipennis seems to broaden the taxonomic scope of the island rule. The biogeographical scenario and the size pattern described here make unlikely the null hypothesis that size was determined by chance (e.g., by random sampling of subpopulations at the isolation event). In contrast, it seems likely that size has evolved by selection related to sitespecific environmental factors linked with island area. A monotonic relationship between island and body sizes seems improbable. Instead, the scatterplot of centroid size versus island area displays a bell-shaped pattern. A biological interpretation of the parameters obtained is difficult. However, the parameters of the Gaussian model are potentially interpretable by comparison with applications of the model to species abundance variation along environmental gradients (ter Braak and Smilauer, 1998). The a-value (8.326) would correspond to the maximum body size, and the b-value to the island size where this maximum is reached (37.7 km2). An alternative to the symmetric unimodal model should also be considered because it can be expected that insular body size experiences some sigmoidal relationship as island size increases, with an asymptote at the body size of the mainland population. Body shape would increase with island area up to a maximum, but it would continue stable along further increases of island area. The full HOF model has been developed for covering the full range of skewness (Huisman et al., 1993). Therefore, it is noticeable that the line predicted by this model is virtually identical to the lines corresponding to the other two models (which are in essence symmetric). This supports the existence of an optimallysized island. However, the sense of optimality is here limited to a specific island where the balance between resources available and ecological constraints (such as inter-specific competition) allows body size to reach a maximum. In any case, a predictive extrapolation outside the range of the observed island sizes (for example, applied to mainland populations) is out of the aims of the present study. In the foregoing paragraphs inter-specific competition is claimed to affect body size. However, experimental evidence is lacking and this contention is only founded on a theoretical scenario extracted from the observed patterns rather than from the processes involved (e.g., Heaney, 1978; McNab, 1994; Lomolino, 1985). Following the generally accepted explanations suggested by the latter authors, the small size on tiny islands would be related to severely limited resources. On these tiny islands, selection could favour small-bodied individuals that maximise the probability of population persistence. Extinction probability would be minimised when population size is above a critical value, and one way for assuring such a value is by reducing body size (Brown and Lomolino, 1998). Body size increases from these tiny islands to medium-sized ones, reaching for
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A. planipennis a theoretical maximum between 8.7 and 162.8 km2 (95% confidence limits determined from the Gaussian model). The mechanism explaining this increase would be the advantage it confers to intra-specific interactions, or the greater capability it permits for storing energy and water reserves (Brown and Lomolino, 1998). Additional increases of island area from the optimum promote body size decreases. One plausible causal mechanism could be a significant increase in inter-specific competition, although predation has also been proposed for other species (Brown and Lomolino, 1998).
Acknowledgements I thank Tonyo Alcover, Enric Descals, Txus GómezZurita, Carlos Juan, and José Alexandre Felizola DinizFilho for their help and suggestions. I thank James Rohlf, Mauro Cavalcanti and others that have made their software available on the web. This research has been supported by the scientific project DGES PB96-0090 (Ministry of Education and Sciences, Spain).
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