The evolution of rewards: seed dispersal, seed size and elaiosome size



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      Present address and correspondence: School of Tropical Biology, James Cook University, Cairns QLD 4878, Australia (tel. +61 07 40421434; fax + 61 07 40421284; e-mail
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    1. School of Biological Sciences, Macquarie University, North Ryde, NSW, 2109, Australia, and Institute for Conservation Biology, University of Wollongong, Wollongong, NSW, 2522, Australia
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    • Present address: CSIRO Sustainable Ecosystems, GPO Box 284, Canberra, ACT, 2601, Australia.


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    • Present address: School of Botany and Zoology, Building 116, Daley Road, Australian National University, Canberra, ACT, 0200, Australia.

Present address and correspondence: School of Tropical Biology, James Cook University, Cairns QLD 4878, Australia (tel. +61 07 40421434; fax + 61 07 40421284; e-mail


  • 1We examine the relationship between the reward offered to ants to disperse seeds (elaiosome size) and seed size, and the possible mechanisms that may generate this relationship in Australian plant species.
  • 2We used seed and elaiosome sizes from our own data set containing 87 Acacia species, supplemented with 22 species from a previously published data set, and 98 ‘Other species’ from 51 genera in 25 families, also from published data.
  • 3The relationship between ln(elaiosome size) and ln(seed size) was determined using standard major axis (SMA) regression for both data sets. For the Other data set we also determined the relationship among species independent of the differences between genera, among genera independent of the differences between families, among genera and among families. We used SMA to test for differences in slopes between groups.
  • 4We found a significant common slope amongst all subsets of the larger data set. The estimated common slope and the 95% confidence interval for the relationship between ln(elaiosome size) and ln(seed size) across all data sets fell above one (1.24, 95%CI = 1.17–1.32), suggesting positive allometry. Slopes were also significantly positive and strikingly similar between the Acacia species data set and the Other species data sets. Similar positive allometry was shown in the ‘other’ species data set among genera and families, and among species independent of genus means (‘species effects’).
  • 5Significant and consistent relationships between taxonomic levels, independent of relationships at other levels, along with significant relationships at the species level, and similarity of slopes, suggest independent convergence towards an underlying functional relationship that has persisted over long evolutionary periods. Our results therefore suggest that ants have been agents of selection on seed traits.
  • 6Such a functional relationship might result from a trade-off in ant foraging behaviour between the benefit of the reward (elaiosome) and the cost of the dispersal (determined by seed size). Slopes > 1 would then suggest that ants need more than proportionally larger rewards to remove larger seeds.


Many plant species entice animals to disperse their seeds by the provision of a fleshy appendage or covering (Ridley 1930; van der Pijl 1990; Willson 1992). The advantages to plants of dispersal may include a reduction in density- or distance-dependent mortality, escape from sibling competition and an increased chance of germinating in a favourable location (reviewed by Howe & Smallwood 1982; Willson 1992). Any increase in fitness resulting from dispersal is likely to result from a trade-off between many potentially conflicting factors. For example, plants that provide a reward on their seeds to attract dispersers are also potentially attracting predators (e.g. Janzen 1969; Hughes & Westoby 1992; Rodgerson 1995), and resources that are committed to rewards could alternatively be allocated to endosperm or cotyledon. Mazer & Wheelwright (1993) examined the trade-off between increasing fruit elongation and increasing fruit size in bird-dispersed plants of Costa Rica and found evidence of selection operating on fruit shape. In a similar study, Herrera (1992) concluded that developmental constraints overrode any selective advantage of increasing fruit length in bird-dispersed species of the Iberian Peninsula. Phylogeny, in addition to selective pressures and developmental constraints, may also affect the outcome of these trade-offs, as highlighted by both Herrera (1992) and Mazer & Wheelwright (1993). The solutions to the trade-offs, ecological circumstances and evolutionary histories of different species are all embodied in their dispersal attributes; hence variation in these attributes among species may shed light on the roles of different factors and mechanisms that have effected the evolution of dispersal traits.

We have chosen to investigate possible trade-offs in plant species that use ants to disperse their seeds. In this system, the dispersal reward is a lipid-rich appendage, called an elaiosome, that is attractive to many ant species (Sernander 1906; Berg 1975; Brew et al. 1989; Hughes & Westoby 1990). Removal of seeds can be very rapid, for example, in Australian sclerophyll vegetation these seeds are usually removed within 24 hours of falling to the ground (Hughes & Westoby 1990). Typically, ants carry the seed with the elaiosome to the nest where the elaiosome is eaten and the seed may be discarded (Berg 1975; Westoby et al. 1982). This dispersal mode is found in over 80 plant families, some with worldwide distribution, for example Apiaceae, Cyperaceae, Euphorbiaceae, Fabaceae and Rubiaceae; most ant-dispersed species are found in Australia (> 1500 species in 24 families) and South Africa (> 1300 species in 29 families), and relatively few in other parts of the world (c. 300 species) (Berg 1975; Rice & Westoby 1981; Bond & Slingsby 1983; Bond et al. 1991). It has evolved many times independently, with some families containing genera that have ant-dispersed species and genera that do not, and occasionally there is even divergence within a genus. Most southern hemisphere ant-dispersed species occur in sclerophyll vegetation. The remaining species are found in a diverse range of habitats in both the southern and northern hemispheres, including mesic forests, montane meadows, semi-arid and arid regions and chaparral (Beattie 1985).

In order to understand the evolution of seed dispersal by ants it is essential to identify the nature of the relationship between seed size and elaiosome size, and determine the possible mechanisms (e.g. developmental constraints, selective pressures and phylogeny) that may give rise to such a relationship. Elaiosome size appears to increase with seed size (Gunther & Lanza 1989; Oostermeijer 1989; Hughes & Westoby 1992). We know of no developmental reason why elaiosome size should be related to seed size, unlike physical constraints that may be important in the evolution of avian dispersal structures (Herrera 1992).

Several studies have shown that the ratio of elaiosome size to seed size influences seed removal by ants (Gunther & Lanza 1989; Oostermeijer 1989; Hughes & Westoby 1992), suggesting a mechanism by which natural selection could have played a role in the evolution of this relationship. Selection would be expected to optimize the trade-off between seed size and elaiosome size as this represents the compromise between the amount invested in dispersal and the amount invested in the seed (both the embryo and endosperm plus seed coat). To maximize the number of seeds produced, a parent plant should invest in dispersal structures only that amount which will ensure successful or sufficient dispersal by ants; any expenditure above this will divert resources that could otherwise be used in the production of more, or larger, seeds. The limit to the elaiosome size, for a given seed size, should therefore be set, in part, by ant behaviour. The lower limit requires that each seed be equipped with a reward whose value is commensurable with the cost of the effort expended in its removal. Below this level removal of the seed would be at a net cost, where costs could include risks of predation or desiccation as well as energetic costs. Diminishing return to the parent plant sets the upper limit of dispersal investment, as above some threshold nearly all seeds will be attractive enough to be removed by ants. Hughes & Westoby (1992) suggest that, in some ecosystems, one of the ecological factors in this dynamic is the interaction between seed and elaiosome sizes and the attraction of ants that disperse seeds and those that eat seeds. Other factors may also affect the evolution of the relationship between elaiosome and seed size, for example the relative value to a mother plant of the probability of a given seed being dispersed may vary between species.

Phylogeny has been demonstrated to be important in the evolution of variation in fruit shape in addition to developmental constraints (Herrera 1992) and selective pressures (Mazer & Wheelwright 1993). Phylogenetically, species are nested within genera and genera are nested within families. As a result of this there are a number of ways in which covariation among variables in data sets of species could arise. For example, a relationship between seed and elaiosome sizes that is apparent among species (Fig. 1a) could be due to differences between genera (Fig. 1b,d,f). Alternatively, the same relationship could result from differences between species within each genus (Fig. 1c,e,g). It is possible for a relationship among a relatively large number of species to be due to the evolution of the relationship among relatively few ancestral species with subsequent speciation (represented by Fig. 1b). In such circumstances the few genera, and not the many species, are the appropriate statistically independent units for hypotheses concerning the origin of the relationship; species are the correct units for hypotheses about the existence of relationships among species; and species may also be the correct unit for hypotheses about the persistence and/or adaptive significance of the relationship. This issue has led to much debate about the correctness or otherwise of various hypotheses (ecological, evolutionary and statistical) and methods for investigating comparative data sets (e.g. Harvey & Pagel 1991; Harvey et al. 1995a,b; Westoby et al. 1995a, 1995b; Doughty 1996; references cited in these papers).

Figure 1.

A representation showing two possible patterns of covariation between two traits among species that give the same observed correlation (a). Covariation resulting from correlation among the genus means (b). Covariation resulting from correlation among species independent of their genus means (c). Standard deviations of species within genera are shown on the genus means (d, e). The former pattern (b) could result just from the evolution of the correlation among three ancestor species, with uncorrelated changes in the relationship across subsequent speciation events. In which case species values will be randomly distributed around genus means and there will be no correlation among species independent of their genus means (f). The later pattern (c) could result just from the evolution of the correlation among the 15 extant species, in which case covariation will produce a correlation among species independent of their genus means (g).

In this paper we examine the relationship between elaiosome size and seed size among Australian ant-dispersed plant species. We determine the form of this relationship at different taxonomic levels as an exploration of its consistency across evolutionary time-scales. We do this by examining the relationships among species independent of the differences between genera (species effect as represented in Fig. 1f,g), and similarly among genera independent of the differences between families and among families.

Materials and methods

data sets

In order to investigate the relationship between elaiosome size and seed size among ant-dispersed species we examined a total of 207 species in two groups. The first group contained 109 Acacia (Mimosaceae) species. The data came from our own estimates of seed and elaiosome mass for 87 species from a single genus, Acacia, supplemented with information on 22 species from a previously published study (O'Dowd & Gill 1986). O'Dowd & Gill (1986) provide estimates for elaiosome (aril) and seed masses for 70 ant-dispersed Acacia species. There were 39 species in common between our Acacia data set and O'Dowd & Gill's (1986) data set. In these cases we used the mean values for elaiosome and seed masses generated from both data sets (Appendix S1). The second data set comprised estimates for 98 species from 49 different genera (excluding Acacia) in 25 families from a data base of Hawkesbury sandstone vegetation around Sydney NSW(Westoby et al. 1990), hereafter referred to as ‘Other species’ (Appendix S1 in Supplementary Material).

data analysis

It is not clear which of seed and elaiosome size is the dependent and which the independent variable. Seed size, whilst likely to be influencing the evolution of elaiosome size, may itself be influenced by elaiosome size. Because the emphasis in this study was on comparing proportional changes in elaiosome and seed masses in log-log analyses, we used slopes generated from standard major axis (SMA) regressions. SMA routines and tests were all calculated using the program (S)MATR (Falster et al. 2003). The SMA slope, calculated on log-transformed variables, gives the proportional relationship between them.

Our analysis investigated the linear relationship between the natural logarithms of elaiosome size and seed size for each species in both data sets (Acacia and Other). For the Other data set, variation in ln(elaiosome size(mg)) and variation in ln(seed size(mg)) was also partitioned into a number of components. For each genus, a ‘genus mean’ was calculated by taking the average of ln(elaiosome size) for all the species in each genus and a ‘species effect’ was calculated for each species by subtracting the species ln(elaiosome size) from its corresponding genus mean. For each family a ‘family mean’ was calculated by taking the average of the genus means of all genera in the family and ‘Genus effects’ were calculated by subtracting the particular genus mean from the family mean. Genus means, species effects, family means and genus effects were similarly calculated for ln(seed size). The original ‘species data’ for a given species is its family mean plus its genus effect plus its species effect. Some of the genus means and family means were ‘averages’ of only one value (28 out of 51 genera were represented by only one species and 15 out of 25 families by only one genus). Such means clearly lack precision, hence analysis of them may be somewhat less rigorous than if the means were of more data, but their exclusion considerably reduces statistical power. To address this possible trade-off between power and rigour we calculated genus means and family means for the complete Other data set and for two additional data sets (genus means following the exclusion of genera with only one species, and family means for an additional data set in which families with only one genus were excluded). The statistical analyses were conducted on both sets of genus and family means. Our use of taxonomic groupings obviously prevents consideration of relationships that may exist between species within them. While techniques such as phylogenetic regression can address these relationships, more detailed phylogenetic hypotheses for all relationships between species in our sample are not available at this time.

Slopes were first fitted to each data set using SMA, with confidence intervals (95%) calculated following Falster et al. (2003). To compare observed relationships between data sets, we tested for statistical differences in the slope and intercept of group relationships (Falster et al. 2003). An SMA slope common to all groups was estimated following Warton & Weber (2002), using a likelihood ratio method. The significance of this estimate was determined by testing for significant heterogeneity among group slope estimates by permutation (Manly 1997). When a common slope can be estimated there is no reason to assume heterogeneity of slopes between groups and the common slope can be used. Although a common slope could be determined across our data sets, we examined all post-hoc multiple comparisons of slopes among groups to investigate potential pairwise differences between data sets. In addition (S)MATR allows for tests of slopes against a specified a priori hypothesized value (Falster et al. 2003). Therefore, we also tested each within-group slope estimate against the null expectation of isometry.


Across all data sets the results of the SMA analyses were highly significant (Table 1). More importantly, we found evidence for a common slope between groups ((S)MATR test statistic = 5.64, P = 0.61). The estimate for the common slope across groups had confidence intervals that did not include unity, indicating a significant positive allometry (common slope estimate = 1.24, 95% CI of slope 1.17–1.32). Post-hoc tests performed on all possible pairwise comparisons of slopes revealed no instance of significant differences in the scaling relationship between any two groups. Thus, across all data sets, ln(elaiosome size) scaled proportionally faster than ln(seed size).

Table 1.  Summary of analysis of covariation between ln(elaiosome size) and ln(seed size) for Australian ant-dispersed Acacia and Other species. For the Other species, variation in ln(elaiosome size) and ln(seed size) has been decomposed into various phylogenetically determined components (see text for details). Slopes and tests of significance were determined using SMA (Falster et al. 2003). Also shown are the results of the test of each within-group slope estimate against the null expectation of isometry
Group n r 2 P SlopeLower 95% CIUpper 95% CITest for isometry
Acacia species1080.42< 0.0011.231.061.42 7.72    0.006
Other species
 Species 970.72< 0.0011.221.091.3513.01    0.0005
 Genus means 520.72< 0.0011.211.041.41 6.75    0.012
 Genus means > 1 sp. 240.80< 0.0011.130.931.38 1.71    0.204
 Species effect 700.69< 0.0011.411.241.6227.37< 0.0001
Family means 240.81< 0.0011.261.041.52 6.266    0.022
Family means > 1 genera  90.79    0.00141.260.71.57 0.08    0.78
Genus effect 360.22    0.0041.280.951.74 2.75    0.106

The slopes of the individual relationships between ln(elaiosome size) and ln(seed size) were (in most cases) significantly positive. In five of the eight tests the slopes and estimated 95% confidence interval were greater than one (Table 1). We found a significantly positive relationship between ln(elaiosome size) and ln(seed size) among Acacia species, among Other species, among species independent of genera (species effect), among genera (genus means), and among families (family means) (Fig. 2a,b,c,d,e, Table 1). Furthermore, the relationships among the Acacia species and Other species data were surprisingly similar (Acacia slope = 1.23, 95% CI = 1.06–1.42, r2 = 0.49, P < 0.001; Other species slope = 1.22, 95% CI = 1.09–1.35, r2 = 0.79, P < 0.001) (post-hoc pairwise comparison Acacia vs. Other species; common slope estimate = 1.22 (S)MATR statistic = 0.01, P = 0.93). This might have been due to the inclusion of Acacia juncifolia (a potential outlier in the Acacia data set). A. juncifolia is described as having a vestigial aril or exarilate (Orchard & Wilson 2001). In the O'Dowd & Gill (1986) data set, A. juncifolia is recorded as ant dispersed, with seed mass 13.8 mg but no elaiosome (aril) mass, whereas in our data set it had seed mass 12.5 mg and elaiosome mass 0.04 mg. The inclusion of A. juncifolia may conceivably increase the estimated slope in this group because its aril mass is much less than other species with similar seed sizes (A. juncifolia appears at the bottom of Fig. 2a). We therefore re-ran the analysis after exclusion of this species but this did not alter the finding of a common slope among groups that was greater than one ((S)MATR stat = 7.16, P = 0.42, common slope estimate = 1.23, 95% CI of slope 1.15–1.30), nor did it result in significant differences in post-hoc pairwise comparison between the Acacia and Other species data sets ((S)MATR stat = 0.63, P = 0.43, common slope estimate = 1.18). Removing A. juncifolia did, however, alter the estimated slope of the Acacia data set, such that the lower 95% CI of the estimated slope fell just below one (Acacia slope = 1.13, 95% CI = 0.99–1.30, r2 = 0.48, P < 0.001).

Figure 2.

Covariation between ln(elaiosome size/mg) and ln(seed size/mg) for two samples of Australian ant-dispersed species, (a) 109 Acacia species and (b) 98 Other species from 51 genera (excluding Acacia), and between various phylogenetically determined components of ln(elaiosome size/mg) and ln(seed size/mg) for the Other species. (c) Species effect: variation among species independent of their genus means, n = 71. (d) Genus means: variation among the means of each genus, n = 24, ‘○’ genera represented by 1 species only, ‘◆’ genera represented by more than one species. (e) Genus effect: variation among genus means independent of their family means, n = 37. (f) Family means: variation among the means of each family, n = 24, ‘○’ families represented by 1 genus only, ‘◆’ families represented by more than one genus. See text for details.


We found that, for a diverse group of Australian ant-dispersed species, the size of the dispersal reward (in mg) is approximately proportional to the size of the seed (in mg) raised to the power of 1.25. More importantly, the confidence interval for the common exponent did not include unity, indicating significantly positive allometry. This relationship was consistent across groups. Each of the individual relationships was highly statistically significant. The relationship between elaiosome size and seed size was highly significant at the species, genus and family levels, with the exponent ranging from 1.21 to 1.26. The relationship was also highly significant for species independent of genera and genera independent of families, and these exponents were greater (1.28 and 1.41, respectively). In only three of eight instances did confidence intervals for individual exponents include one. These three cases were analyses of genus means where genera with single species were excluded, family means where families with single genera were excluded and the genus effect. In one of these cases (families with greater than one genera) there were only 10 data points, and consequently the confidence interval was large, while in the other two cases the confidence limit was only just less than one.

the role of phylogeny

A strong relationship among many species can result from the evolution of the relationship among a few ancestors followed by its persistence via phylogenetic constraint or conservatism and ‘strengthening’ due to speciation (e.g. Fig. 1b,d,f; Gould & Lewontin 1979; Harvey & Pagel 1991). For example, if the relationship evolved at the family level or earlier (using taxonomy as a surrogate for phylogeny), then there should not be a significant relationship among genera independent of families (i.e. among genus effects) nor species independent of genera (i.e. among species effects). Similarly, if the relationship evolved at the genus level then no relationship should be observed among the family means or among the species effects. Alternatively, if it arose at the species level (i.e. due to relatively recent evolution only) then no relationship should be observed among family means or genus effects. We observed significant relationships at the family, genus and species levels independently of each other, as well as independently among species in the Acacia and Other species data sets (with a common slope across all groups). This suggests that the strong relationship between seed and elaiosome sizes in Australian ant-dispersed plants is due to it being continually selected for across long evolutionary time periods.

the role of developmental constraint

In some systems covariation between two variables could be the result of some form of developmental constraint. Herrera (1992) proposes such an explanation for the relationship between fruit length and width (i.e. fruit shape) in bird-dispersed species of the Iberian Peninsula. The seeds of fleshy fruited, bird-dispersed species are usually enclosed within a casing of pulp (van der Pijl 1990), and the development of the fruit is dependent on the expansion of the maternal tissue that covers the seed. The resultant shape arises due to the roughly symmetrical expansion of the developing fruit, and an allometric relationship among fruit dimensions. In contrast, elaiosomes are produced via the expansion of a seed appendage, the aril, while the seed is a combination of seed coat, embryo and endospermic tissue. Indeed, because of these differences in origin and development, elaiosome size and seed size may be able to undergo independent change more easily than fruit length and width.

the role of natural selection

The strong correlations between elaiosome size and seed size, the lack of evidence for phylogenetic constraint and the apparent absence of developmental constraints suggest that natural selection is likely to have played a significant role in the evolution of the observed relationship. Indeed it would be surprising if this were not the case, especially given evidence that the relationship between seed size and elaiosome size can affect seed dispersal (Gunther & Lanza 1989; Oostermeijer 1989; Hughes & Westoby 1992; Mark & Olesen 1996) and therefore almost certainly fitness, and the ubiquity of natural selection. The existence of a significant common slope across these data sets suggests evolution convergent on some underlying functional relationship. This is further supported by the strength of the correlations among large numbers of species from different environments, i.e. experiencing a range of ecological conditions including different ant assemblages. The question is what ecological factor or factors determine the nature of the functional relationship? We suggest that a trade-off between the costs and benefits to seed-dispersing ants, reflected in their foraging behaviour, is likely to be critical. There are, of course, many other factors that might influence how natural selection shapes the relationship between seed and elaiosome size, including the impact of seed size on the size of ants that are physically capable of removing a seed (Hughes & Westoby 1992), conflict between genetically distinct tissues in the seed, and the interplay between evolutionary strategies for a mother plant of risk spreading (greater number of seeds) and risk avoidance (greater certainty in dispersal).

ant dispersal behaviour

What can the form of the relationship between elaiosome size and seed size tell us about the behaviour of ants towards elaiosome-bearing seeds, and about the costs and benefits to plants of different sized elaiosomes? It is logical to hypothesize that ants will need a larger inducement to remove larger seeds and hence that elaiosome size should increase with seed size. Hughes & Westoby (1992) and Mark & Olesen (1996) found evidence supporting the hypothesis that seeds with the same elaiosome size to seed size ratio are equally attractive to ants. A constant ratio of elaiosome size to seed size is equivalent to a slope of 1 on a plot of ln(elaiosome size) and ln(seed size). We found a common slope 1.24, with 95% confidence interval 1.17–1.32. We also found no significant difference between Acacia and Other species data sets. If these relationships were due to the interaction between ant behaviour and elaiosome and seed size, then our results suggest that, as seed size increases, elaiosome size must increase more than proportionally for seeds to remain equally attractive to ants; in other words it is relatively more expensive for ants to remove larger seeds. Although Hughes & Westoby (1992) did not explicitly consider the hypothesis of a slope greater than 1, there is some evidence consistent with this hypothesis from their experiment using seeds with experimentally manipulated elaiosome size to seed size ratios: for a given ratio, the heavier seeds (Hibbertia ovata) tended to be removed less than the lighter seeds (Dillwynia juniperina) (Fig. 8 in Hughes & Westoby 1992). Hughes & Westoby (1992) suggest that this relationship is more likely to be related to an increased risk of predation than to increased energetic costs for ants removing larger seeds. Unfortunately, there are no published data on the interaction between load (elaiosome and seed) size, ant foraging time and predation risk.

There are likely to be many other factors that influence the relationship between seed mass and elaiosome mass that are not captured in our data set. First, our interpretation of these results assumes that selection of seed traits by ants results from one-to-one encounters, that is, by single ants moving single seeds. Alternatively, many species of tiny ants, such as in the genus Monomorium, recruit multiple workers to single seeds, who dismember the elaiosome often without actually dispersing seeds (Berg 1975). We suggest that the influence of this type of asymmetric interaction on the functional relationship between elaiosome and seed masses will be weak. Seeds that have elaiosomes removed remain undispersed. Under these conditions they are at a much greater risk of mortality than those that are moved. Seeds that die as a result of having elaiosomes removed have an effective fitness of zero, and thus selection due to asymmetries such as elaiosome robbing will not be expressed in subsequent generations. Secondly, ants might not select seeds based on elaiosome mass per se, but rather on some measure of the quality of the elaiosomes, such as lipid content. Although O'Dowd & Gill (1986) provide estimates for the lipid content of the elaiosome, none of our other data included similar estimates and we were unable to assess the relationship between quality and seed mass. Nevertheless, in spite of the numerous other factors likely to influence the trade-off between elaiosome and seed size in ant-dispersed species, the apparent ubiquity of the functional relationship we report becomes both more convincing and more impressive.

One possible way to examine the interaction between ant behaviour and the relationship between elaiosome size and seed size might be to consider a three-dimensional surface, with a measure of successful dispersal on the vertical axis and the logarithms of seed mass and elaiosome mass on the two horizontal axes. Contours on the surface would then represent elaiosome size–seed size curves of ‘equal attractiveness’ to ants. Such curves could be derived using experiments on seed dispersal then compared with the slopes derived from the observed relationship between elaiosome size and seed size among species.


We would like to thank Gerry Quinn, Warren Muller and Dan Falster for useful discussions about the statistical analyses and data handling. Lesley Hughes and Mark Westoby provided comments on the manuscript and their ideas were appreciated. Two anonymous reviewers provided very helpful advice that greatly improved the manuscript. We especially thank Peter Green for sharing the O'Dowd and Gill data with us and for many constructive suggestions and comments.