On the seed mass–regional abundance relationship: the Eriksson & Jakobsson (1998) model does not apply to Danish grasslands

The seed mass–regional abundance relationship

Eriksson & Jakobsson (1998) developed a heuristic model predicting species regional abundance from their seed mass. The model took as a starting point the diversity of seed masses found in single communities (Westoby et al. 1996). This phenomenon does not, however, fit the theoretical predictions that seeds of a given mass will be fittest in a given environment (Smith & Fretwell 1974). Rees & Westoby (1996) showed that a game-theory approach would allow for variation in seed mass within communities. The Eriksson–Jakobsson model had two basic assumptions: (i) in a given microsite, a seedling emerging from a large seed will out-compete one from a small seed (a game rule supported empirically by Eriksson (1997) and Turnbull et al. (1999)), and (ii) that there is a trade-off between seed mass and seed number (Harper 1977) (empirically supported by Shipley & Dion (1992), Turnbull et al. (1999) and Jakobsson & Eriksson (2000)). In other words, it assumes there to be an inverse relationship between colonization ability (large, but few seeds) and dispersability (many, but small seeds). The model predicts that species with intermediate-sized seeds will gain larger regional abundance than either larger- or smaller-seeded species. Eriksson & Jakobsson (1998) identified the species with intermediate-sized seeds by use of the absolute deviance in log seed mass from the community median log seed mass. Data from Danish grasslands were used in an empirical test of the model’s validity, both by phylogenetically corrected and traditional cross-species analysis.

The Danish data

Study Region 1 is situated on the island of Sjælland, Denmark (12 E, 56 N), and Region 2 on the peninsula of Jutland, Denmark (10 E, 57 N). Within each region all sites of old, unimproved semi-natural grasslands on well-drained soils were included. Species lists from each site were compiled during several exhaustive searches made on foot. Sampling effort was adjusted to site area (for detailed information on sampling see Bruun (2000)). Seed-mass data for 105 species were obtained from Grime et al. (1988), and for the remainder seeds were collected in the field and weighed individually. In practice, ‘seed’ refers to germinule, which for some species is an achene. Only herbaceous species and chamaephytic seed plants were considered. The three orchid species (all infrequent) with minute seeds, as well as Pulmonaria angustifolia and Asparagus officinalis (each found once in Region 1), were omitted due to lack of information on seed mass. Corynephorus canescens was omitted because its phylogenetic relationship within Poaceae was unknown and its inclusion would lead to a collapse of the tree for the whole family (see below). A total of 172 species were found in Region 1, and 155 species in Region 2, of which 133 species were found in both regions. Most species were perennial herbs, but 33 annuals and four chamaephytes were included. The regional abundance was ln(y + 1) transformed. The absolute deviation from the median log seed mass for each species was estimated by summing the absolute deviation from the median log seed mass at a particular site over all sites occupied by that species. Henceforth, this is called deviation from community median.

As no published phylogeny contained all the studied taxa right down to the species level, a phylogenetic supertree (Sanderson et al. 1998) was constructed. The angiosperm phylogeny of Nandi et al. (1998; fig. 4) was used as a backbone. Phylogenies (strict consensus trees based on morphological or molecular data wherever possible) for higher-order groups were grafted onto this phylogenetic tree in all the cases where the clade in question contained more than two study species. Where no phylogenetic information was found, species allocated to the same taxonomic unit (e.g. genus) by Tutin et al. (1964–1980) were assumed to be more closely related than species belonging to different units. For the phylogenetic supertree and the sources used to construct it, see Appendix 1 (in the Journal of Ecology archive on the World Wide Web; see the cover of a recent issue of the journal for the WWW address). Unit branch lengths were assumed. The tree contained 11 soft polytomies. Because the program Phylogenetic Independence (see below) does not deal with polytomies, a fully resolved tree was made using the most parsimonious trees from the same sources as above.

Seed size is far from phylogenetically independent. For example Peat & Fitter (1994) found that most of the variation in seed mass of species in the British flora was at the taxonomic levels of genus and family. Gittleman et al. (1996) proposed to treat the null assumption of phylogenetic independence as an empirical issue, and Abouheif (1999) devised an operational test. The log transformation of seed mass was tested for phylogenetic independence over the entire set of species from both regions. This was done by a test for serial independence (TFSI) using the program Phylogenetic Independence version 1.1 (Reeve & Abouheif 1999). The test used log seed-mass values for species arranged along the tips of the phylogenetic tree as observations. The test is based on the sum of successive squared differences between observations ∑d² = ∑(Y_i+1 − Y_i)². If the observations are independent from each other, then the sum of successive squared differences will be twice the sum of squares ∑y² = ∑(Y_i − Y¯)² (Sokal & Rohlf 1995). The test is evaluated with the C-statistic which equals (1 − (∑d²/∑y²)/2). Because the topology of a phylogenetic tree is arbitrary, Abouheif (1999) proposed to estimate the value of C as a mean of a number of randomizations in which nodes are rotated, and to estimate the distribution of C by shuffling the observed species traits over the tips of the phylogenetic tree. For each trait, the 192 nodes in the phylogenetic tree were randomly rotated in 4999 randomizations. The original topology was randomly shuffled 999 times to obtain a null distribution of C. In the test for serial independence, log seed mass did not show significant phylo-genetic independence (C = 0.4871). The C-value for observed phylogenetic topology was larger than any of the shuffled topologies, yielding a P-value of 0.001.

Phylogenetic correction should therefore be considered when analysing the data. The independent contrasts method (Felsenstein 1985; Harvey & Pagel 1991; Garland et al. 1992) was applied to the relationship between log regional abundance on the one hand and log seed mass and log deviation from the community median on the other. This was done using the program pdtree in the package pdap version 5.0 (Garland et al. 1999). Soft polytomies were dealt with as proposed by Pagel (1992). The differences were evaluated using the sign test (Sokal & Rohlf 1995, p. 445; Rohlf & Sokal 1995, table B). The independent contrasts method is only suitable for the detection of correlated evolution of two traits (Westoby et al. 1996; Ackerley 1999), and it correctly estimates the degrees of freedom in that situation. Regional abundance is, however, not a trait subjected to evolutionary processes, but an outcome of ecological processes, and the independent contrasts method may thus underestimate the degrees of freedom. Cross-species analyses were therefore also performed using correlations between variables estimated with Pearson’s product moment.

No statistically significant relationships of log regional abundance with either log seed mass or deviation from community median were found with any method. In fact, the tendency in both regions was that smaller deviations from community medians coincided with larger regional abundances in fewer comparisons than expected by chance (Table 1). The same tendency was seen in the cross-species analysis (Table 2).

What may be wrong with the model?

Seed mass is often claimed to be a key functional trait because its close correlation with potential relative growth rate (Shipley & Peters 1992; Swanborough & Westoby 1996) provides a link between the regeneration and the vegetation niches. Linking seed mass to regional abundance through a game theory model (Eriksson & Jakobsson 1998) is as attractive as it is simple, but it does not apply to the investigated Danish grasslands.

Four independent explanations seem plausible.

In conclusion, the model needs to at least adjust for unequal reproductive effort between species, if it is to gain general validity.

Acknowledgements

Ove Eriksson, Martin Zobel and Merit Otsus are thanked for providing seed mass data for a few selected species. Martin Zobel, Ove Eriksson, and one anonymous referee, are thanked for valuable comments on the manuscript.