The allometry of reproduction within plant populations

Authors

  • Jacob Weiner,

    Corresponding author
    1. National Center for Ecological Analysis and Synthesis, Santa Barbara, CA 93101, USA
    2. Department of Agriculture and Ecology, University of Copenhagen, DK-1958 Frederiksberg, Denmark
      *Correspondence author. E-mail: jw@life.ku.dk
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  • Lesley G. Campbell,

    1. Department of Ecology and Evolutionary Biology, Rice University, Houston, TX 77005, USA
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  • Joan Pino,

    1. Center for Ecological Research and Forestry Applications, Autonomous University of Barcelona, E-08193 Bellaterra, Spain
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  • Laura Echarte

    1. National Research Council of Argentina (CONICET), CC 276, 7620 Balcarce, Argentina
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*Correspondence author. E-mail: jw@life.ku.dk

Summary

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 RV 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 RV 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 RV 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.

Introduction

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.

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 RV relationship. Thus, a minimum size for reproduction does not necessarily require a positive x-intercept on the RV relationship, but the latter does imply the former.

Our schematic plants also help us to define plasticity in the RV 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 RV 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 RV relationship (model c). In such cases, the classical allometric approach based on the ‘allometric equation’ (Y = axb, usually fit as log Y = log 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 RV relationship, which is strong evidence for a minimum size for reproduction, in most plant populations? (iii) Is there evidence for extensive plasticity in the RV relationship? We hope our review of RV 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

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 RV 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 RV 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.
SpeciesnEvidence for positive x-intercept?Evidence for nonlinearity in RV relationship?Evidence for plasticity in RV relationship?r2 for linear RV (or log R–log V) relationshipPlants harvested at full maturity?Type of studyReference
Annual
Abutilon theophrasti156NNni0.46nrDThompson, Weiner & Warwick 1991
Abutilon theophrasti373YYY0.91YESugiyama & Bazzaz 1998
Amaranthus retroflexus20 or 30 per treatmentnYN0.73–0.95N & YEWang et al. 2006
Amaranthus retroflexus12YNni0.98NEMcLachlan et al. 1995
Amaranthus retroflexus20nNni0.95NEMcLachlan et al. 1995
Amsinckia tessellata10nNni0.92nrDSamson & Werk 1986
Anoda cristata14, 40NNN0.078NEPuricelli et al. 2004
Apera spica-venti213nYni0.46nEThompson, Weiner & Warwick 1991
Arabidopsis thaliana20/popNNni0.56–0.98NEAarssen & Clauss 1992
Arabidopsis thaliana108NNNnrN & YEClauss & Aarssen 1994a
Arabidopsis thaliana15/pop, 3 genotypes, 3 treatments with several levelsNNY0.51–0.97dYEClauss & Aarssen 1994b
Bromus rubens10nnni0.94nrDSamson & Werk 1986
Caulanthus lasiophyllus10nnni0.98nrDSamson & Werk 1986
Chaenactis fremontii10nnni0.90nrDSamson & Werk 1986
Chenopodium album50nNni0.95YDAarssen & Taylor 1992
Chenopodium album240NNN0.93YEGrundy, Mead & Overs 2004
Cryptantha pterocarya10nnni0.98nrDSamson & Werk 1986
Datura stramonium60NNni0.00nrEThompson, Weiner & Warwick 1991
Datura stramonium60YNni0.83nrEThompson, Weiner & Warwick 1991
Descurania pinnata8nnni1.00nrDSamson & Werk 1986
Echinochloa crus-galli15NNni0.99YDMartinková & Honek 1992
Eschscholzia minutiflora10nnni0.84nrDSamson & Werk 1986
Gilia minor10nnni0.59nrDSamson & Werk 1986
Glycine max20–72yyY0.93–0.98YENagai & Kawano 1986
Glycine max322, 77Yyn0.95, 0.98YEVega et al. 2000
Helianthus annuus37–117NyY0.82–0.90 (L-L)YEKawano & Nagai 1986
Helianthus annuus258, 60Yyy0.98, 0.97YEVega et al. 2000
Lotus humistratus10ynni0.93nrDSamson & Werk 1986
Malacothrix coulteri10nnni0.85nrDSamson & Werk 1986
Mentzelia congesta10nnni0.95nrDSamson & Werk 1986
Panicum miliaceum243NyN0.94–0.98nrEThompson, Weiner & Warwick 1991
Phacelia fremontii10nnni0.85nrDSamson & Werk 1986
P. tanacetifolia10nnni0.94nrDSamson & Werk 1986
Raphanus raphanistrum200NYy0.61 (L-L)dYECampbell & Snow 2007
R.raphanistrum x R. sativus155NYy0.55 (L-L)dY (with some exceptions)ECampbell & Snow 2007
Schismus barbatus10nnni0.95nrDSamson & Werk 1986
Senecio vulgaris117NNy0.97 (L-L)YEWeiner et al. 2009
Setaria glauca50nNni0.93YDAarssen & Taylor 1992
Sinapis arvensis256ninYnr, analysis L-LNEBrophy et al. 2008
Thlaspi arvense50nyni0.98YDAarssen & Taylor 1992
Triticum aestivum50 per pop.YNN0.89–0.96dYEPan et al. 2003a
Triticum aestivum50 or 60YnNnrYEPan et al. 2003b
Triticum aestivum552yNY0.97dNELiu et al. 2008
Xanthium canadense26YNni0.96cYEMatsumoto et al. 2008
Zea mays298, 287Yny0.94, 0.97YEVega et al. 2000
Zea mays200 per varietyYNni0.93–0.95dYEEcharte & Andrade 2003
Clonal perennial
Artemisia halodendron118, 118nnni0.32, 0.35YDLi et al. 2005
Aster lanceolatus42, 39Ynni0.85, 0.88YESchmid, Bazzaz & Weiner 1995
Erythronium americanum50nnni0.19YDAarssen & Taylor 1992
E. americanum25NNni0.77NDWolfe 1983
Maianthemum canadensis50Nnni0.02YDAarssen & Taylor 1992
Pistia stratiotes195YNni0.81nrDCoelho, Deboni & Lopes 2005
Pityopsis graminifolia31YNni0.76nrDHartnett 1990
Ranunculus muelleri50Nnni0.42NDPickering 1994
R. dissectifolius83Nnni0.34NDPickering 1994
R. graniticola92Nnni0.34NDPickering 1994
R. niphophilus46Nnni0.11NDPickering 1994
Saxifraga hirculus23–45NnninrniDOhlson 1988
Silphium speciosum56YNni0.85YDHartnett 1990
Solidago altissima24 familiesYNY0.71–0.91NDSchmid & Weiner 1993
S. canadensis35YNni0.71YDHartnett 1990
S. canadensis48, 48Ynni0.80, 0.78YESchmid, Bazzaz & Weiner 1995
Sorghum halepense48NNninanrDThompson, Weiner & Warwick 1991
Sorghum halepense136YNninanrEThompson, Weiner & Warwick 1991
Trillium grandiflorum50YNni0.95YDAarssen & Taylor 1992
Veronia baldwinii33YNni0.90YDHartnett 1990
Viola pubescens50nnni0.73YDAarssen & Taylor 1992
Monocarpic biennial or perennial
Alliaria officinalis50nyni0.86YDAarssen & Taylor 1992
Barbarea vulgaris50ynni0.72YDAarssen & Taylor 1992
Cynoglossum officinale21–54NNn0.58–0.94YDKlinkhamer & de Jong 1987
Cynoglossum officinale20Nyni0.89–0.95 (L-L)NEde Jong & Klinkhamer 1989
Diplotaxis erucoides88yyninrNDSans & Masalles 1994
Erodium cicutarium10nnni0.83nrDSamson & Werk 1986
Gossypium hirsutum104nYY0.81N & YESadras, Bange & Milroy 1997
Lepidium campestre50NYni0.97YDAarssen & Taylor 1992
Lesquerella fendleri33NNN0.58, 0.75 (provided by author)YEPloschuk, Slafer & Ravetta 2005
Melilotus alba50nNni0.89YDAarssen & Taylor 1992
Polycarpic, non-clonal perennial
Arum italicum151YNni0.90dNDMéndez & Obeso (1993)
Chrysanthemum leucanthemum50nYni0.76YDAarssen & Taylor (1992)
Cichorium intybus50nNni0.88YDAarssen & Taylor (1992)
Hesperis matronalis50nNni0.60YDAarssen & Taylor (1992)
Hordeum jubatum50nYni0.96YDAarssen & Taylor (1992)
Lesquerella mendocina40NNN0.67, 0.73 (provided by author)YEPloschuk, Slafer & Ravetta (2005)
Mitella diphyla50nnni0.47YDAarssen & Taylor (1992)
Pinguicula vulgaris49–51 per pop.Nnini0.27–0.75NDMéndez & Karlsson (2004)
Plantago major130YNY0.72YEWeiner (1988)
Plantago major252 totalnnni0.02, 0.03 (ns)dYEReekie (1998)
Potentilla recta50yNni0.94YDAarssen & Taylor (1992)
Potentilla recta6ynni0.86nrDSoule & Werner (1981)
Quercus serrata29YYninrNDNakashizuka, Takahashi & Kawaguchi (1997)
Rumex crispus50nNni0.59YDAarssen & Taylor (1992)
R. obtusifolius181NYni0.81 (L-L)dYEPino, Sans & Masalles (2002)
Taraxacum officinale50nnni0.58YDAarssen & Taylor (1992)
Taraxacum officinale32ynni0.92niDWelham & Setter (1998)
Taraxacum officinale39nnni0.66niDWelham & Setter (1998)
Thalictrum dioicum50Yyni0.82YDAarssen & Taylor (1992)
Tragopogon pratensis50Nyni0.35YDAarssen & 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 RV 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 RV relationship, we tested for effects of different treatments on the RV 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.

Results

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 RV relationship, corresponding to the three models described in the Introduction:

  • (a) a linear relationship passing through the origin (e.g. Senecio vulgaris, Fig. 2);
  • (b) a linear relationship with a positive x-intercept (e.g. Zea mays, Fig. 3);
  • (c) 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.

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 RV 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).

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 (inline image), 2 (inline image), 3 (inline image), 4 (inline image) and 8 (inline image) 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 RV (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).

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).

We found 48 data sets conforming to RV 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 RV 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 RV 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 RV 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 RV 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 RV 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 RV 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 RV relationship within and among populations, i.e. different genotypes have significantly different RV 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 RV relationships than plants grown from vegetative organs (Schmid & Weiner 1993).

Discussion

Our review of the available data yielded (i) evidence for three general patterns of size-dependent reproduction in plant populations, corresponding to models a, b and c described in the Introduction. There was also (ii) evidence for a positive x-intercept in 29% of the cases, which is strong support for a minimum size for reproduction in these cases, but this pattern is by no means universal. Finally, we document (iii) plasticity in the RV relationship in 37% of the species for which relevant data were collected, but the effects of plasticity were always very small compared to the effects of size alone. Below we address the implications of our findings for our understanding of reproductive allocation within plant populations.

An allometric approach to reproductive strategies

Allometric effects on allocation are still analysed and interpreted in terms of ratios such as RE (e.g. Cheplick 2005), but our results and recent studies (Jasienski & Bazzaz 1999; Müller, Schmid & Weiner 2000; Weiner 2004; Karlsson & Méndez 2005) argue convincingly that the converse is more useful. It is the RV relationship that is selected, and RE results from this. We urge researchers to interpret RV allometric relationships themselves, rather than interpreting allometric phenomena in terms of the resultant ratios. Fitness is closely related to reproductive output, not to reproductive effort, so interpreting such ratios can be misleading biologically (Jasienski & Bazzaz 1999).

We have implicitly defined the RV relationship as cumulative over the life of the plant. This idea is intuitive for monocarpic plants, which are much easier to study in this context, so it is not surprising that most of the currently available data are for annual and monocarpic species. To apply this approach to iteroparous species, such as woody perennials, the minimal allometric model would be that allocation is a function of production, and we propose this as a null hypothesis for future investigations. According to this model, a plant produces biomass and allocates it to different organs and structures according to a relatively fixed allometric programme. Some of this biomass (a) remains in living tissue, (b) becomes dead but structural tissue or (c) is shed (including leaves, bark, dead branches, etc.). (It is important to remember that production allocated to (d) reproductive structures (fruits and seeds), is also shed.) Thus, using biomass production, which in practice means including dead and shed structures in V, is one solution to defining size in RV relationships for iteroparous plants. The best way to investigate the total RV relationship is to collect all the seeds produced by an individual throughout its life (Fig. 2; Weiner et al. 2009). Information from any single harvest or bout of reproduction will not reflect the total RV relationship.

As the allometric exponent of dead structural tissue (b) versus ((a) + (c) + (d)) will be greater than unity for large upright plants due to biomechanical constraints, and for iteroparous herbaceous perennials if storage organs are included in V, we would expect the allometric exponent of reproductive structures (d) versus ((a) +(b) + (c)) to be <1, assuming the proportion of structures that are shed as dead (c) is relatively constant. This argument may not be relevant for short-lived herbaceous plants but valid for long-lived woody plants. This may explain why short-lived herbaceous plants tend to show linear RV relationships, whereas longer-lived organisms with more structural tissue or storage organs (such as Raphanus raphanistrum (Fig. 4) and Rumex obtusifolius (Fig. 5)) show log R–log V slopes <1.

Plant life-history theory would benefit from an allometric perspective. For example, according to optimal allocation theory, to maximize seed production, plants should reinvest all resources into further growth (stems, leaves and roots), 100% vegetative investment and 0% reproductive allocation, for most of their lives, and then switch at a certain time to investing all resources into reproduction, 0% further vegetative investment, 100% reproductive investment: a monocarpic strategy (Cohen 1968; Ellner 1987). In the allometric view, this means that the plant should grow along the x-axis and then switch to growth in the y-variable (Fig. 6). If plants do not succeed in completing their potential reproduction, the RV graph will lie below the line. In such a case, the allometric growth trajectory is distinct from the static, inter-individual allometric relationship (Clauss & Aarssen 1994a). For example, the static inter-individual allometric slope of estimated R versus estimated V for tropical trees was much >1 (Thomas 1996). This would occur if the individuals were distributed along the optimal strategy line in Fig. 6. An extreme example would be a monocarpic species, in which an individual does not produce fruits and seeds until the end of its life. The RV relationship among individuals in a population cannot reflect the developmental trajectory for a plant that only flowers at the end of its life. The other extreme is a plant such as Senecio vulgaris, an ‘iteroparous annual’ that starts flowering at a very small size and continues growing and reproducing until it dies (Weiner et al. 2009). In this case, the total RV relationship among individuals does reflect the developmental trajectory.

Figure 6.

 Illustration of the relationship between a total RV relationship (dark line), and two potential developmental trajectories (lines with arrows). The simple linear RV relationship with positive x-intercept (model b) was chosen for convenience, the point applies to any RV relationship. In the low-risk, bet-hedging strategy, the developmental trajectory follows the total RV relationship, and the plant starts reproducing as soon as it has reached the minimum size for reproduction. This strategy assures that the plant will produce seeds as long as it is above the threshold size, but there is a cost in growth and therefore size achieved, because resources allocated to reproductive structures do not contribute to further growth. In the high-risk ‘optimal’ strategy, the plant invests all resources into growth until it has reached a specific size or age or receives necessary environmental cues (Thomas 1996). After a given period of growth, the optimal strategist will be larger than the bet-hedging strategist, and it will also produce more seeds if it has the time necessary to complete its reproduction, but its risk of very low or zero seed production is much greater if it stops growing or dies before completing reproduction.

Of course plant behaviour is not solely a function of size, but we argue the role of size relative to the other factors has been under-appreciated and many effects attributed to time are actually due to size (e.g. Weiner & Thomas 2001). This may be because time is more central to our daily and scientific thinking: ontological processes are usually described in terms of time, experiments are completed and plants harvested at one point in time (Coleman, McConnaughay & Ackerly 1994), and classic demographic models are based on age rather than size. A complete understanding of plant behaviour must encompass time, size, environmental signals and genotype.

New statistical methods allow us to include values of R = 0 when fitting a line to an RV relationship (Schmid et al. 1994; Brophy et al. 2007), thus improving our ability to estimate the x-intercept and slope of an RV relationship when a population contains plants that have not reproduced at all, but we also need methods that allow us to estimate the total RV relationship when there are individuals far below the line but with R greater than zero (e.g. Figs 4 and 7). We need methods that can exclude points that lie below a presumed limiting relationship, using reasonable assumptions and criteria. In some cases (e.g. Fig. 7, t = 1), there may not be enough information in the data to estimate the total RV relationship, but in other cases (e.g. Fig. 7, t = 2) it should be possible. Potential methods include frontier production function models (Aigner, Lovell & Schmidt 1977) and quantile regression (Cade & Noon 2003; Koenker 2005). We encourage statistically oriented ecologists to address this issue and suggest the best tools for this purpose.

Figure 7.

 Some commonly observed variation in RV patterns can be understood in the context of developmental time (t) and a total RV relationship (line). These patterns can also occur at the same time from different treatments that affect the rate of development. A linear relationship with a positive x-intercept (model b) is chosen for convenience, the point applies to any total RV relationship.

How plastic is the total RV relationship?

In the allometric view, plasticity in allocation is defined as a change in an allometric trajectory, not a change in the speed with which a trajectory is followed (Weiner 2004). Although there was clear evidence for plasticity in the total RV relationship (statistically significant in 9 of 25 cases and 7 of 19 species; Table 1), in every case the effects were very small in comparison to the effects of size and developmental stage (see below). Meristems can have alternative fates and this suggests that plasticity in the RV relationship is possible, yet attempts to find evidence for plasticity in allocation of meristems to reproductive versus other functions have been unsuccessful to date (Lehtilä & Larsson 2005; Zhang et al. 2008). This leads to the hypothesis that the total RV relationship is, along with mean size of seeds produced by an individual, one of the least plastic plant attributes. According to this hypothesis, plant size is influenced by a myriad of factors and interactions, but at a given size, a plant’s potential reproductive output is relatively fixed. A weaker version of this hypothesis is that this generalization holds for annual and monocarpic plants, which should allocate all available (i.e. mobile) resources to reproduction at maturity, but that iteroparous perennial species will show much more plasticity in their total RV relationship. The available data are strongly biased toward annuals and monocarpic perennials, so it would be premature to generalize at this point. Tests of these hypotheses are needed. Simple allometric growth should be the null or minimal hypothesis, while support for true plasticity requires that we can reject the simple allometric model (Weiner 2004).

The available data suggest that the total RV relationship of a genotype is not very plastic, but there can be much genetic variation in the total RV relationship within a population, especially among local populations of a species (Aarssen & Clauss 1992; Schmid & Weiner 1993; Reekie 1998). The results of Echarte & Andrade (2003; Fig. 3) on Zea mays are especially relevant here, because cultivars are genetically homogeneous. Echarte & Andrade grew one variety for 2 years at five densities. Ninety-four percent of the variation in R could be explained by variation in V. Inclusion of year, density and all interactions increased this by 2.5%. Other varieties, which were only tested in 1 year, showed slightly different x-intercepts and slopes, but the general RV pattern was the same for all varieties. If a population’s RV relationship is primarily due to genetic rather than environmental variation, there is no reason to expect any of the three general RV patterns described here. Indeed, there may be no clear relationship between R and V, as observed among genotypes of Plantago major (Reekie 1998).

Size, time, development and reproductive output –reconciling phenology and allometry

According to our allometric model, the total RV relationship can be seen as a boundary condition below which reproductive behaviour takes place. The total RV relationship for a genotype does not explain all of its reproductive behaviour, but it reframes plant reproductive behaviour in terms of allometry + development. Like a self-thinning trajectory, the total RV relationship sets a limit, and although there is much room for variation in behaviour below this limit, it often dominates behaviour. In this view, a plant can increase its reproductive output in one of two ways: (i) by converting more of its current biomass into reproductive biomass and/or (ii) by increasing its size and therefore its potential reproductive output. The former is constrained by the total RV relationship, whereas the latter is only limited by the maximum size a genotype can achieve. If a plant is at or near the total RV boundary, it can only increase its reproductive output by growing more first.

Reproductive behaviour can be extremely plastic even if there is little plasticity in the total RV relationship. As many gardeners know, if one over-fertilizes tomato plants with nitrogen, growth and therefore size will increase greatly, as does potential fruit production, but this fruit production may be postponed. Many inexperienced gardeners, who are overenthusiastic with nitrogen fertilizer, observe huge but non-flowering tomato plants as the end of the growing season approaches. Such a postponement in reproduction can be interpreted as developmental plasticity in the direction predicted by optimal allocation theory, which predicts that plants should devote 100% of their resources towards growth, and then switch to 100% allocation to reproduction (Cohen 1968; Ellner 1987). A high level of nitrogen may be a signal that much more growth is possible, and therefore the switch should be postponed to take advantage of the increased potential reproductive output. Thus, increased nutrient levels can give the impression of reduced reproductive output if plants do not have time to complete their life cycles. What appears to be plasticity in the RV relationship is often plasticity in the rate of growth and development (Fig. 7; Bonser & Aarssen 2009).

Plant size affects the probability of a plant flowering as well as the magnitude of reproductive success once it occurs. However, our review and previous work (e.g. Schmitt 1983) suggest that size determines the potential amount of reproduction more tightly than it determines the probability of reproduction. Although the probability of reproducing increases with size, specific triggering mechanisms, such as photoperiod or vernalization, are sometimes required to induce flowering. In the original research by Garner & Allard (1920) on photoperiodism in Nicotiana tabacum (tobacco), it was noted that only plants above a certain size threshold could respond to night length cues by flowering.

Reproductive morphology and reproductive allometry

A clear relationship between reproductive morphology and allometry is shown in the results from Zea mays (Fig. 3; Echarte & Andrade 2003). A maize plant must reach a certain biomass before it can produce an ear, presumably because an ear itself cannot be below a certain size. Above this threshold, grain yield per plant is a linear function of V. There is a maximum, as well as a minimum, yield per ear, so there is an upper limit on R for plants that do not produce a second ear (‘non-prolific’ individuals), whereas the RV relationship continues its linear increase for plants that do produce a second ear (‘prolific’ individuals; Fig. 3). The same pattern is found in every variety and experiment in the study. The microeconomic analogy suggests the hypothesis of a positive correlation between the x-intercept and RV slope: greater capital investment (larger minimum size for reproduction) could lead to decreased per-unit cost above the minimum size (increased slope), but there was no evidence for this among the varieties of Z. mays or genotypes of Solidago altissima (Schmid & Weiner 1993).

Implications of the most common RV patterns

When reproductive output is proportional to vegetative biomass (model a), an individual’s fitness is more closely related to the total biomass produced by its offspring than to the number of surviving offspring. When the total RV relationship has a positive x-intercept (model b), then the effect of size on reproductive output is more than proportional. In this case, achieving a large size is even more important for fitness than if there is no positive intercept. A plant with such reproductive allometry may have higher fitness if it produces a few large offspring than many small ones with the same total offspring biomass, so this strategy could lead to the evolution of larger seed size (Venable & Rees 2009). This is also the type of relationship that can produce oscillations in population dynamics models with density dependence (Rees & Crawley 1989), because the population’s total seed production will decrease at high density, even if total population biomass does not.

In the third type of RV relationship, a classical log–log allometric relationship with slope <1 (model c), the efficiency of the conversion of biomass production to reproductive output decreases with size. Although this pattern was not as common as the other two within the data sets we surveyed, we predict that it will prove to be much more common as more larger and long-lived species are investigated. This pattern is consistent with the hypothesis that smaller species are more ‘reproductively economical’ than larger species (Aarssen 2008). An individual’s fitness will be higher if it produces many small rather than few large offspring, and inequality in fitness will be lower than inequality in size within the population.

Conclusions

The study of reproductive allocation in plants will benefit from an allometric approach, rather than an emphasis on ratios such as reproductive effort, which still dominate research in this area. It is important not to conflate the three kinds of allometric relationships. The hypothesis that a genotype has a genetically determined and relatively fixed total RV relationship, below which allometric growth and variation occur, is a useful starting point for interpreting reproductive behaviour. The effects of size are a good place to begin, but a deeper understanding of plant reproductive behaviour and reproductive strategies must also include time and triggering mechanisms, in short, development.

Footnotes

  • *

    [Correction added on 15 September 2009, after first online publication: 90 changed to 97 and 71 changed to 76 for experiments and species, respectively].

Acknowledgements

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.

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