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- Materials and methods
1. The quantitative relationship between size and reproductive output is a central aspect of a plant’s strategy: the conversion of growth into fitness. As plant allocation is allometric in the broad sense, i.e. it changes with size, we take an allometric perspective and review existing data on the relationship between individual vegetative (V, x-axis) and reproductive (R, y-axis) biomass within plant populations, rather than analysing biomass ratios such as reproductive effort (R/(R+V)).
2. The allometric relationship between R and V among individuals within a population is most informative when cumulative at senescence (total R–V relationship), as this represents the potential reproductive output of individuals given their biomass. Earlier measurements may be misleading if plants are at different developmental stages and therefore have not achieved the full reproductive output their size permits. Much of the data that have been considered evidence for plasticity in reproductive allometry are actually evidence for plasticity in the rate of growth and development.
3. Although a positive x-intercept implies a minimum size for reproducing, a plant can have a threshold size for reproducing without having a positive x-intercept.
4. Most of the available data are for annual and monocarpic species whereas allometric data on long-lived iteroparous plants are scarce. We find three common total R–V patterns: short-lived, herbaceous plants and clonal plants usually show a simple, linear relationship, either (i) passing through the origin or (ii) with a positive x-intercept, whereas larger and longer-lived plants often exhibit (iii) classical log–log allometric relationships with slope <1. While the determinants of plant size are numerous and interact with one another, the potential reproductive output of an individual is primarily determined by its size and allometric programme, although this potential is not always achieved.
5. Synthesis. The total R–V relationship for a genotype appears to be a relatively fixed-boundary condition. Below this boundary, a plant can increase its reproductive output by: (i) moving towards the boundary: allocating more of its resources to reproduction, or (ii) growing more to increase its potential reproductive output. At the boundary, the plant cannot increase its reproductive output without growing more first. Analysing size-dependent reproduction is the first step in understanding plant reproductive allocation, but more integrative models must include time and environmental cues, i.e. development.
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- Materials and methods
Growth and reproduction are two of the most fundamental processes in plants. After a plant produces biomass, it allocates this biomass to various structures and functions, among them reproduction (Bazzaz & Reekie 1985). Offspring are the currency of natural selection, but plants must first accumulate resources and build reproductive machinery via growth. Because resources allocated to one function or organ are unavailable for other functions or organs, allocation requires investment trade-offs. Ultimately, allocation patterns reflect strategies that are the product of both selection and constraints. This relationship between the accumulation of biomass and its allocation to structures and functions is the core of plant life-history strategies.
Traditionally, allocation has been considered to be a ratio-driven process: ‘partitioning’. According to this perspective, a plant with a given amount of resources at any point in time partitions them among different structures or activities (Klinkhamer, de Jong & Meelis 1990). This has lead to the concept of ‘reproductive effort’ (RE = reproductive biomass/total biomass), which has been the measure of reproductive allocation in many studies. But the ‘partitioning’ perspective and the analysis of RE are difficult to reconcile with the observation that plant allocation is allometric in the broad sense, i.e. it changes with size. The ratio-based perspective of allocation is size independent, whereas almost all observed plant allocation patterns are size dependent (McConnaughay & Coleman 1999; Weiner 2004). There is an emerging consensus among researchers that we should be analysing and interpreting allometric patterns, not allocation ratios such as RE (Jasienski & Bazzaz 1999; Müller, Schmid & Weiner 2000; Karlsson & Méndez 2005).
While there may be no single unified concept of size for plants (Weiner & Thomas 1992), dry mass is a widely used measure for many purposes. Plants are primarily composed of carbohydrates, so the dry biomass of a plant is usually proportional to the plant’s energy content (Hickman & Pitelka 1975). A portion of this energy is mobile, e.g. sugars and starches, and can be used to produce reproductive structures. Thus, a plant’s biomass tells us something about the energy potentially available for reproduction, and it generally reflects other resources available to an individual (Reekie & Bazzaz 1987).
Three different kinds of allometric relationships
Before addressing allometric patterns within plant populations, it is important to distinguish among three fundamentally different kinds of allometric relationships, which address very different questions, but have been conflated throughout much of the literature:
There is no basis for assuming, as many researchers have, that relationships among individuals within a population or the allometric growth trajectories of individuals are similar to the broad interspecific relationships that have been documented. For example, larger species have a lower shoot : root ratio than smaller species (Enquist & Niklas 2002; Zens & Webb 2002), but shoot : root ratio increases as a plant grows (Müller, Schmid & Weiner 2000). Similarly, large K-selected species have lower RE than small r-selected species (Begon, Harper & Townsend 2006), but within a population, larger individuals often have greater RE than smaller individuals (Weiner 1988). Allometric relationships among individuals within a population at one point in time (or over a short interval) do not usually reflect the allometric growth patterns of these individuals. Although there have been several attempts to clear up this confusion (Weller 1989; Klingenberg & Zimmermann 1992; Weiner & Thomas 1992), it still plagues the analysis and interpretation of allometric relationships. Here we address (2) and (3) above, not (1).
Models of size-dependent reproductive output
What pattern or patterns of size-dependent reproductive output within populations would one predict from basic principles? As plants are modular and reproductive output is clearly related to module number, the null model is usually that plants allocate a simple proportion of their biomass to reproduction (Fig. 1, model a). An alternative model, based on a microeconomic analogy between a biological plant and an industrial plant (Weiner 1988), predicts a minimum size for reproduction and a linear relationship between biomass and reproductive output above that size (Fig. 1, model b). Capital investment to build the factory is necessary before any products (seeds) can be produced, and this corresponds to a threshold size for reproduction. After this initial investment, there are fixed costs for materials, maintenance, etc. resulting in a linear increase in reproductive output with size. This relationship appears to hold for many annual herbaceous species (e.g. Hartnett 1990; Thompson, Weiner & Warwick 1991; Aarssen & Taylor 1992; Schmid & Weiner 1993; Echarte & Andrade 2003).
Figure 1. The relationship between total (or vegetative) and reproductive biomass can alter ‘reproductive effort’ (reproductive biomass/total biomass). In model a, reproductive effort is size independent. In model b, there is a minimum size for reproduction and a linear relationship between biomass and reproduction above that size. In this case reproductive effort increases with size (Crawley 1983; Samson & Werk 1986; Weiner 1988). Although biologically unlikely, it is theoretically possible for an extrapolated x-intercept to be negative, which would result in decreasing reproductive effort with increasing size. In model c, there is a classical ‘allometric’ relationship between reproductive (R) and total (T) biomass (R = aTb), which is linear with slope = b on log–log scale. If b < 1, as shown, then reproductive effort decreases with size.
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A minimum size for reproduction has been erroneously considered identical to a positive x-intercept on a graph of reproductive output (y-axis) versus size (x-axis). To clarify the potential difference between a positive x-intercept and minimum size for reproduction, let us consider a schematic plant that grows several, for instance four, leaves without flowering. The fifth and all subsequent leaves have a single flower, which becomes a single fruit with a fixed number of seeds, in the axil. Such behaviour would result in the simple relationship shown in model b in Fig. 1, where the positive x-intercept and minimum size for reproduction are one and the same. Alternatively, one can imagine a modification of our schematic plant, in which five leaves are necessary for flowering to occur, but flowers are then formed in all five leaf axils. In such a case there would still be a minimum size for reproduction, but the (extrapolated) x-intercept would be the origin (Fig. 1, model a; Samson & Werk 1986): the relationship between R and V is discontinuous, with a step occurring at the minimum size for reproduction. Although they seem improbable biologically, other algorithms can result in a negative x-intercept. For example, if we further modify our schematic plant such that one or more of the leaves below the threshold number form two flowers in the axil whereas those above the threshold have only one, then there will be a positive y-intercept (and a negative x-intercept) in the extrapolated linear R–V relationship. Thus, a minimum size for reproduction does not necessarily require a positive x-intercept on the R–V relationship, but the latter does imply the former.
Our schematic plants also help us to define plasticity in the R–V relationship. A change in RE with density has been interpreted as an example of plasticity, but it is usually an effect of size and allometric growth: ‘apparent plasticity’ (McConnaughay & Coleman 1999). At higher densities plants are smaller, and if there is a positive x-intercept on the R–V relationship, plants will be closer to, or even below, this intercept, which means lower or even zero RE. ‘True’ plasticity in allocation can be defined as a change in the allometric relationship itself, rather than a change in the rate of growth (Weiner 2004). For example, if our schematic plant were to produce a flower and then fruit in every leaf axil starting with the fifth under some conditions, but only one flower in every second leaf axil under other conditions, this would represent true plasticity in reproductive allocation.
The simple models a and b illustrated in Fig. 1 and by our first two schematic plants may be reasonable hypotheses for herbaceous plants, such as annual crops and weeds, but as size increases further we would not expect reproductive output to remain a simple linear function of size. Increased per-unit-size costs of biomechanical support and internal transport, and, in woody plants, an increase in the proportion of non-living structural tissues, may result in a decrease in the slope of the R–V relationship (model c). In such cases, the classical allometric approach based on the ‘allometric equation’ (Y = axb, usually fit as log Y = log a + b log X) is often useful. It is also possible to model both a positive x-intercept and an allometric relationship above this intercept (Klinkhamer et al. 1992).
Here, we explore allocation trends in published data on herbaceous plants and ask the following questions: (i) Are there one or a few general patterns of size-dependent reproductive output within plant populations? (ii) Is there evidence for a non-trivial positive x-intercept in the R–V relationship, which is strong evidence for a minimum size for reproduction, in most plant populations? (iii) Is there evidence for extensive plasticity in the R–V relationship? We hope our review of R–V relationships within herbaceous plant populations will serve as an alternative to the analysis of biomass ratios such as RE, and thus contribute to an allometric approach to reproductive allocation.
Materials and methods
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- Materials and methods
We limited our review to herbaceous plants, both because of the problem of defining size for long-lived organisms that build up dead tissues and because of the lack of data on lifetime R and V for woody plants. We reviewed all published relevant data we could find, with special emphasis on figures showing individual data or data made available to us by researchers. Our requirements for inclusion of studies included (i) accurate measurement of above-ground (or above- and below-ground) vegetative biomass and (ii) biomass of reproductive structures or seed production that reflect cumulative R–V relationships for genets or at least whole ramets. In addition to searching the literature, we also requested relevant data from all members of the Plant Population Biology Section of the Ecological Society of America and the Ecological Section of the Botanical Society of America via E-mail. All data we found that fit our criteria were included. Although we may have missed some published results, we are confident that we have compiled the majority of the peer-reviewed scientific literature available on this topic.
There has been much discussion about how to distinguish between vegetative and reproductive structures, as many supporting structures, such as leafy bracts, pedicels and calices, have both vegetative and reproductive functions (Bazzaz & Reekie 1985; Reekie & Bazzaz 2005). Previous studies have shown that all measures of reproductive biomass are highly correlated within a population (e.g. Bazzaz, Ackerly & Reekie 2000), so we included studies that used different definitions of reproductive structures, as long as these were consistently applied within a study. We included studies that presented estimates of reproductive output only when these estimates were based on extensive measurements and were calibrated with harvest data. As mean size of seeds produced by an individual is known to be among the least plastic of plant traits, we also include studies in which the number of seed produced was estimated with a high degree of accuracy.
In our search, we found 44 publications, involving 97 experimental or descriptive studies on 76 species (Table 1)*. From each publication, we collected information on plant life history, experimental sample size, the timing of experimental harvest and the proportion of variation (r2) explained by a simple R–V relationship. We report relevant published results, and we reanalysed the data when doing so was desirable and possible. Because our goal here is to look for general patterns, we employ simple least-square linear models (log-transformed when this improved the residual structure), rather than more sophisticated methods (e.g. Klinkhamer et al. 1992; Brophy et al. 2007). This allows us to use and compare all previous studies, including those in which data is not available for reanalysis, as simple regression results are always presented, even in the oldest studies. We take a ‘common sense’ approach to reviewing published studies: reporting all published results, evaluating data visually when possible while giving more weight to statistical tests when presented or when we could perform them ourselves, and keeping our own analyses relatively simple so that older and more recent studies can be compared.
Table 1. Summary of reproductive output (R, reproductive biomass or fecundity, y-axis) versus size (V, vegetative or total biomass, x-axis) relationships within plant populations collected for 71 species from 44 sources from both experimental (E) and descriptive (D) studies. The r2 reported is for a simple, linear regression or linear on a log–log scale (noted as L–L), determined by the residual structure (when the data were available for analysis) or as reported. ni, not investigated; nr, not reported; y, weak (ns) evidence for pattern; Y, strong (significant) evidence for pattern; n, weak evidence against a pattern (no evidence, but low statistical power); N, strong evidence against a pattern (no evidence, high statistical power); c, calculated from published data; d, calculated from original data provided by researchers; all other results as reported in publications.
|Species||n||Evidence for positive x-intercept?||Evidence for nonlinearity in R–V relationship?||Evidence for plasticity in R–V relationship?||r2 for linear R–V (or log R–log V) relationship||Plants harvested at full maturity?||Type of study||Reference|
|Abutilon theophrasti||156||N||N||ni||0.46||nr||D||Thompson, Weiner & Warwick 1991|
|Abutilon theophrasti||373||Y||Y||Y||0.91||Y||E||Sugiyama & Bazzaz 1998|
|Amaranthus retroflexus||20 or 30 per treatment||n||Y||N||0.73–0.95||N & Y||E||Wang et al. 2006|
|Amaranthus retroflexus||12||Y||N||ni||0.98||N||E||McLachlan et al. 1995|
|Amaranthus retroflexus||20||n||N||ni||0.95||N||E||McLachlan et al. 1995|
|Amsinckia tessellata||10||n||N||ni||0.92||nr||D||Samson & Werk 1986|
|Anoda cristata||14, 40||N||N||N||0.078||N||E||Puricelli et al. 2004|
|Apera spica-venti||213||n||Y||ni||0.46||n||E||Thompson, Weiner & Warwick 1991|
|Arabidopsis thaliana||20/pop||N||N||ni||0.56–0.98||N||E||Aarssen & Clauss 1992|
|Arabidopsis thaliana||108||N||N||N||nr||N & Y||E||Clauss & Aarssen 1994a|
|Arabidopsis thaliana||15/pop, 3 genotypes, 3 treatments with several levels||N||N||Y||0.51–0.97d||Y||E||Clauss & Aarssen 1994b|
|Bromus rubens||10||n||n||ni||0.94||nr||D||Samson & Werk 1986|
|Caulanthus lasiophyllus||10||n||n||ni||0.98||nr||D||Samson & Werk 1986|
|Chaenactis fremontii||10||n||n||ni||0.90||nr||D||Samson & Werk 1986|
|Chenopodium album||50||n||N||ni||0.95||Y||D||Aarssen & Taylor 1992|
|Chenopodium album||240||N||N||N||0.93||Y||E||Grundy, Mead & Overs 2004|
|Cryptantha pterocarya||10||n||n||ni||0.98||nr||D||Samson & Werk 1986|
|Datura stramonium||60||N||N||ni||0.00||nr||E||Thompson, Weiner & Warwick 1991|
|Datura stramonium||60||Y||N||ni||0.83||nr||E||Thompson, Weiner & Warwick 1991|
|Descurania pinnata||8||n||n||ni||1.00||nr||D||Samson & Werk 1986|
|Echinochloa crus-galli||15||N||N||ni||0.99||Y||D||Martinková & Honek 1992|
|Eschscholzia minutiflora||10||n||n||ni||0.84||nr||D||Samson & Werk 1986|
|Gilia minor||10||n||n||ni||0.59||nr||D||Samson & Werk 1986|
|Glycine max||20–72||y||y||Y||0.93–0.98||Y||E||Nagai & Kawano 1986|
|Glycine max||322, 77||Y||y||n||0.95, 0.98||Y||E||Vega et al. 2000|
|Helianthus annuus||37–117||N||y||Y||0.82–0.90 (L-L)||Y||E||Kawano & Nagai 1986|
|Helianthus annuus||258, 60||Y||y||y||0.98, 0.97||Y||E||Vega et al. 2000|
|Lotus humistratus||10||y||n||ni||0.93||nr||D||Samson & Werk 1986|
|Malacothrix coulteri||10||n||n||ni||0.85||nr||D||Samson & Werk 1986|
|Mentzelia congesta||10||n||n||ni||0.95||nr||D||Samson & Werk 1986|
|Panicum miliaceum||243||N||y||N||0.94–0.98||nr||E||Thompson, Weiner & Warwick 1991|
|Phacelia fremontii||10||n||n||ni||0.85||nr||D||Samson & Werk 1986|
|P. tanacetifolia||10||n||n||ni||0.94||nr||D||Samson & Werk 1986|
|Raphanus raphanistrum||200||N||Y||y||0.61 (L-L)d||Y||E||Campbell & Snow 2007|
|R.raphanistrum x R. sativus||155||N||Y||y||0.55 (L-L)d||Y (with some exceptions)||E||Campbell & Snow 2007|
|Schismus barbatus||10||n||n||ni||0.95||nr||D||Samson & Werk 1986|
|Senecio vulgaris||117||N||N||y||0.97 (L-L)||Y||E||Weiner et al. 2009|
|Setaria glauca||50||n||N||ni||0.93||Y||D||Aarssen & Taylor 1992|
|Sinapis arvensis||256||ni||n||Y||nr, analysis L-L||N||E||Brophy et al. 2008|
|Thlaspi arvense||50||n||y||ni||0.98||Y||D||Aarssen & Taylor 1992|
|Triticum aestivum||50 per pop.||Y||N||N||0.89–0.96d||Y||E||Pan et al. 2003a|
|Triticum aestivum||50 or 60||Y||n||N||nr||Y||E||Pan et al. 2003b|
|Triticum aestivum||552||y||N||Y||0.97d||N||E||Liu et al. 2008|
|Xanthium canadense||26||Y||N||ni||0.96c||Y||E||Matsumoto et al. 2008|
|Zea mays||298, 287||Y||n||y||0.94, 0.97||Y||E||Vega et al. 2000|
|Zea mays||200 per variety||Y||N||ni||0.93–0.95d||Y||E||Echarte & Andrade 2003|
|Artemisia halodendron||118, 118||n||n||ni||0.32, 0.35||Y||D||Li et al. 2005|
|Aster lanceolatus||42, 39||Y||n||ni||0.85, 0.88||Y||E||Schmid, Bazzaz & Weiner 1995|
|Erythronium americanum||50||n||n||ni||0.19||Y||D||Aarssen & Taylor 1992|
|E. americanum||25||N||N||ni||0.77||N||D||Wolfe 1983|
|Maianthemum canadensis||50||N||n||ni||0.02||Y||D||Aarssen & Taylor 1992|
|Pistia stratiotes||195||Y||N||ni||0.81||nr||D||Coelho, Deboni & Lopes 2005|
|Pityopsis graminifolia||31||Y||N||ni||0.76||nr||D||Hartnett 1990|
|Ranunculus muelleri||50||N||n||ni||0.42||N||D||Pickering 1994|
|R. dissectifolius||83||N||n||ni||0.34||N||D||Pickering 1994|
|R. graniticola||92||N||n||ni||0.34||N||D||Pickering 1994|
|R. niphophilus||46||N||n||ni||0.11||N||D||Pickering 1994|
|Saxifraga hirculus||23–45||N||n||ni||nr||ni||D||Ohlson 1988|
|Silphium speciosum||56||Y||N||ni||0.85||Y||D||Hartnett 1990|
|Solidago altissima||24 families||Y||N||Y||0.71–0.91||N||D||Schmid & Weiner 1993|
|S. canadensis||35||Y||N||ni||0.71||Y||D||Hartnett 1990|
|S. canadensis||48, 48||Y||n||ni||0.80, 0.78||Y||E||Schmid, Bazzaz & Weiner 1995|
|Sorghum halepense||48||N||N||ni||na||nr||D||Thompson, Weiner & Warwick 1991|
|Sorghum halepense||136||Y||N||ni||na||nr||E||Thompson, Weiner & Warwick 1991|
|Trillium grandiflorum||50||Y||N||ni||0.95||Y||D||Aarssen & Taylor 1992|
|Veronia baldwinii||33||Y||N||ni||0.90||Y||D||Hartnett 1990|
|Viola pubescens||50||n||n||ni||0.73||Y||D||Aarssen & Taylor 1992|
|Monocarpic biennial or perennial|
|Alliaria officinalis||50||n||y||ni||0.86||Y||D||Aarssen & Taylor 1992|
|Barbarea vulgaris||50||y||n||ni||0.72||Y||D||Aarssen & Taylor 1992|
|Cynoglossum officinale||21–54||N||N||n||0.58–0.94||Y||D||Klinkhamer & de Jong 1987|
|Cynoglossum officinale||20||N||y||ni||0.89–0.95 (L-L)||N||E||de Jong & Klinkhamer 1989|
|Diplotaxis erucoides||88||y||y||ni||nr||N||D||Sans & Masalles 1994|
|Erodium cicutarium||10||n||n||ni||0.83||nr||D||Samson & Werk 1986|
|Gossypium hirsutum||104||n||Y||Y||0.81||N & Y||E||Sadras, Bange & Milroy 1997|
|Lepidium campestre||50||N||Y||ni||0.97||Y||D||Aarssen & Taylor 1992|
|Lesquerella fendleri||33||N||N||N||0.58, 0.75 (provided by author)||Y||E||Ploschuk, Slafer & Ravetta 2005|
|Melilotus alba||50||n||N||ni||0.89||Y||D||Aarssen & Taylor 1992|
|Polycarpic, non-clonal perennial|
|Arum italicum||151||Y||N||ni||0.90d||N||D||Méndez & Obeso (1993)|
|Chrysanthemum leucanthemum||50||n||Y||ni||0.76||Y||D||Aarssen & Taylor (1992)|
|Cichorium intybus||50||n||N||ni||0.88||Y||D||Aarssen & Taylor (1992)|
|Hesperis matronalis||50||n||N||ni||0.60||Y||D||Aarssen & Taylor (1992)|
|Hordeum jubatum||50||n||Y||ni||0.96||Y||D||Aarssen & Taylor (1992)|
|Lesquerella mendocina||40||N||N||N||0.67, 0.73 (provided by author)||Y||E||Ploschuk, Slafer & Ravetta (2005)|
|Mitella diphyla||50||n||n||ni||0.47||Y||D||Aarssen & Taylor (1992)|
|Pinguicula vulgaris||49–51 per pop.||N||ni||ni||0.27–0.75||N||D||Méndez & Karlsson (2004)|
|Plantago major||130||Y||N||Y||0.72||Y||E||Weiner (1988)|
|Plantago major||252 total||n||n||ni||0.02, 0.03 (ns)d||Y||E||Reekie (1998)|
|Potentilla recta||50||y||N||ni||0.94||Y||D||Aarssen & Taylor (1992)|
|Potentilla recta||6||y||n||ni||0.86||nr||D||Soule & Werner (1981)|
|Quercus serrata||29||Y||Y||ni||nr||N||D||Nakashizuka, Takahashi & Kawaguchi (1997)|
|Rumex crispus||50||n||N||ni||0.59||Y||D||Aarssen & Taylor (1992)|
|R. obtusifolius||181||N||Y||ni||0.81 (L-L)d||Y||E||Pino, Sans & Masalles (2002)|
|Taraxacum officinale||50||n||n||ni||0.58||Y||D||Aarssen & Taylor (1992)|
|Taraxacum officinale||32||y||n||ni||0.92||ni||D||Welham & Setter (1998)|
|Taraxacum officinale||39||n||n||ni||0.66||ni||D||Welham & Setter (1998)|
|Thalictrum dioicum||50||Y||y||ni||0.82||Y||D||Aarssen & Taylor (1992)|
|Tragopogon pratensis||50||N||y||ni||0.35||Y||D||Aarssen & Taylor (1992)|
To determine how many general patterns of size-dependent reproductive output within plant populations exist, we assessed whether a study presented evidence for nonlinearity in the R–V relationship, i.e. log–log slope significantly different from 1. To determine whether there is evidence for a non-trivial minimum size for reproduction in most plant populations, we recorded the sign of the x-intercept in each publication or our own analyses. Finally, to search for evidence of extensive plasticity in the reproductive R–V relationship, we tested for effects of different treatments on the R–V relationship. Patterns within each publication were classified as significant or non-significant.
There has been much debate about whether one should analyse the relationship between reproductive biomass (R) and vegetative (i.e. non-reproductive, V) biomass, or whether it is more appropriate to analyse the relationship between reproductive biomass and total (T = V + R) biomass. As total biomass includes reproductive biomass, it has been argued that this can result in a ‘spurious correlation’ (Brett 2004). Other researchers have argued that the problem is insoluble or non-existent, as none of the three variables is independent from the other two (Prairie & Bird 1989). Although this debate has not been resolved to the satisfaction of all researchers and is beyond the scope of this paper, we think it is most appropriate to analyse reproductive biomass (R) versus vegetative biomass (V) when possible. When R is measured or estimated as fecundity (number of seeds produced) then we see no clear advantage of V over T as a measure of size.
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- Materials and methods
Reproductive allocation studies within populations have been performed on a wide range of plant species (Table 1), with experimental (n = 37) and descriptive (n = 60) data sets over a wide range of conditions. Of these, there were 33 annual, nine monocarpic, 16 polycarpic and 18 clonal perennial species (two species, Arum italicum and Pinguicula vulgaris, which can reproduce by gemmae but clonal ramets do not remain physically attached to the parent plant, are considered non-clonal here). There were three common forms of the R–V relationship, corresponding to the three models described in the Introduction:
a linear relationship passing through the origin (e.g. Senecio vulgaris
, Fig. 2
a linear relationship with a positive x-intercept (e.g. Zea mays
, Fig. 3
a classical ‘simple allometric’ relationship (Seim & Sæther 1983
), i.e. linear on a log–log scale, with a slope <1 (e.g. Raphanus raphanistrum
, Rumex obtusifolius
; Figs 4 and 5
Figure 2. Relationship between mass of seeds (actually fruits) produced by Senecio vulgaris individuals and their vegetative biomass in two glasshouse experiments. Circles are from experiment 2 (shading represents different fertility levels), all other data from experiment 1 (symbols represent different treatment combinations of water, nutrients and competition). Single regression line (shown): log R = −0.57 + 1.026 log V; r2 = 0.971 (Weiner et al. 2009). Data are shown and analysed here on log–log scale because the residual structure is not consistent with regression on a linear scale, but a log R–log V slope = 1 is equivalent to model a: R ∝ V. There were small but significant effects of the treatments on the intercept, but not the slope, of the log R–log V relationship.
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Figure 3. Individual plant grain yield versus shoot biomass for maize (Zea mays cv. DK752) in two experiments (circles, squares) at five densities (2 plants m−2: black, 4 plants m−2: dark grey, 8 plants m−2: middle grey, 16 plants m−2: light grey and 30 plants m−2: empty symbol). Two features of these data illustrate the importance of reproductive morphology for the R–V relationship: (i) because there is a minimum size for an ear, there is clear evidence of a minimum size for reproduction; (ii) plants above the dotted line have more than one ear. Relatively large individuals that only make one ear cannot fully utilize their size to produce more yield. Overall r2 = 0.941. When experiment and density are added as variables r2 = 0.952; with all interactions r2 = 0.966. Thus, although plasticity can be detected, its effects are very small (after Echarte & Andrade 2003).
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Figure 4. Log seed production versus log biomass for wild Raphanus raphanistrum and hybrid (R. raphanistrum × R. sativus) grown in pots at densities of 1 (), 2 (), 3 (), 4 () and 8 () plants per pot. General linear model: log biomass, SS = 30.6, d.f. = 1, P < 0.0001; density level, SS = 1.8, d.f. = 4 P = 0.006, r2 = 0.55. These data show several of the common patterns in R–V (or, as here, fecundity–size) relationships: (i) a classical allometric relationship with slope <1 (here 0.85), (ii) a cloud of points below the line, representing plants that have not completed reproduction (in this case hybrids that have obtained genes that delay maturation from the crop), (iii) weak or no evidence of plasticity in the allometric relationship, but (iv) clear effects of treatments on size and the rate of development, and therefore reproductive output (after Campbell & Snow 2007).
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Figure 5. Log R–log V relationship for Rumex obtusifolius growing in a Medicago sativa crop and harvested on four dates over 2 years (represented by different colours). Least-squares regression line is log R = −0.0026 + 0.795 log V, r2 = 0.81. The slope is significantly <1. There was no effect of harvest date on the relationship, although data from a later harvest, when taproots were being depleted and there was large variation among individuals in developmental stage, did not fit this pattern. All points, however, were near or below the line shown (after Pino, Sans & Masalles 2002).
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We found 48 data sets conforming to R–V relationship of type (a) (no evidence of a positive x-intercept and no evidence of nonlinearity), 25 data sets conforming to type (b) (evidence for a positive x-intercept but no evidence for nonlinearity), and five conforming to the third type (c) (evidence for nonlinearity and residual structure consistent with log–log transformation). The remaining 19 data sets did not conform to any type of R–V relationship. Although variation in V accounted for most of the variation in R in most studies, there were also several studies in which the r2 for the R–V relationship was very low (e.g. four studies had r2 < 0.1) and therefore did not fit any of the above models.
In many cases in which data were available, there was a cloud of points below the R–V line, likely representing plants that had not yet completed their reproduction at the time of harvest (e.g. Fig. 4). In 21% of the species (18% of cases), we found evidence that the plants had been harvested prior to maturity.
Overall 27.6% (21 of 76 species; 24.7%– 24 of 97 cases) of the species showed strong evidence for, and 32.9% of species had strong evidence against (25 of 76 species, 30.0%– 29 of 97 cases) a positive x-intercept (Table 1). Evidence for a positive x-intercept size was less common in clonal perennials than annuals (χ2 = 3.477, d.f. = 1, P = 0.062 (species-level analysis); χ2 = 4.61, d.f. = 1, P = 0.032 (case-level analysis)).
For most studies (86 of 97 of cases and 68 of 76 species), the R–V relationship was linear (i.e. the residual structure of the linear regression on untransformed data was good and/or the log R–log V slope was not significantly different from 1). In the remaining studies, the R–V relationship was nonlinear (i.e. the log R–log V slope was significantly different from 1). In all the cases of nonlinearity, the log R–log V slope was <1 (i.e. RE decreased with size). There was no difference among life histories in the frequency of species exhibiting nonlinear relationships (χ2 = 5.37, d.f. = 3, P = 0.147 (species-level analysis); χ2 = 4.90, d.f. = 3, P = 0.177 (case-level analysis)).
Twenty-five studies (across 19 species) investigated potential plasticity in the R–V relationship, nine cases of which (nine species) provided statistically significant support for the existence of plasticity. In those cases that demonstrated plasticity, the effects were very small compared to the effects of size alone. For example, in experiments on Arabidopsis thaliana (Clauss & Aarssen 1994b), in which siliques were counted as the measure of R, variation in log V alone accounted for 94.4% of the variation in log R, and inclusion of treatment effects increased this to 96.6%. In Triticum aestivum (wheat) populations grown at five densities (Liu et al. 2008), log V, density and the log V × density interactions all had significant effects on log (spike mass). Log V alone accounted for 97.4% of the variation in log (spike mass), and inclusion of density and the interaction term increased this to 98.4%.
There is much evidence for genetic variation in the R–V relationship within and among populations, i.e. different genotypes have significantly different R–V relationships (Aarssen & Clauss 1992; Schmid & Weiner 1993; Reekie 1998). There is also evidence for developmental effects in clonal perennials; Solidago altissima plants grown from seeds had different R–V relationships than plants grown from vegetative organs (Schmid & Weiner 1993).
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This work was supported by a Sabbatical Fellowship from the National Center for Ecological Analysis and Synthesis, a Center funded by NSF (Grant #DEB-0553768), the University of California, Santa Barbara, and the State of California, and by the Danish Natural Science Research Council (Grant nr. 21-04-0421). We thank Maria Clauss, Jing Liu, Marcos Méndez, Edmundo Ploschuk and Gen-Xuan Wang for providing us with data, and Stephen Bonser, Marcos Méndez, and an anonymous referee for comments. Special thanks to Ed Reekie for critical comments and discussion.