The pace and shape of senescence in angiosperms


  • Annette Baudisch,

    Corresponding author
    • Max Planck Institute for Demographic Research, Rostock, Germany
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  • Roberto Salguero-Gómez,

    1. Max Planck Institute for Demographic Research, Rostock, Germany
    2. School of Biological Sciences, Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld, Australia
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  • Owen R. Jones,

    1. Max Planck Institute for Demographic Research, Rostock, Germany
    2. Max Planck Odense Center on the Biodemography of Aging, Odense M, Denmark
    3. Institute of Biology, University of Southern Denmark, Odense M, Denmark
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  • Tomasz Wrycza,

    1. Max Planck Institute for Demographic Research, Rostock, Germany
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  • Cyril Mbeau-Ache,

    1. School of Biomedical and Biological, Plymouth University, Plymouth, Devon, UK
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  • Miguel Franco,

    1. School of Biomedical and Biological, Plymouth University, Plymouth, Devon, UK
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  • Fernando Colchero

    1. Max Planck Institute for Demographic Research, Rostock, Germany
    2. Max Planck Odense Center on the Biodemography of Aging, Odense M, Denmark
    3. Department of Mathematics and Computer Sciences, IMADA, University of Southern Denmark, Odense M, Denmark
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Correspondence author. E-mail:


  1. Demographic senescence, the decay in fertility and increase in the risk of mortality with age, is one of the most striking phenomena in ecology and evolution. Comparative studies of senescence patterns of plants are scarce, and consequently, little is known about senescence and its determinants in the plant kingdom.
  2. Senescence patterns of mortality can be classified by distinguishing between two metrics: pace and shape. The pace of mortality captures the speed at which life proceeds and can be measured by life expectancy, while the shape of mortality captures whether mortality increases (‘senescence’), decreases (‘negative senescence’) or remains constant over age (‘negligible senescence’).
  3. We extract mortality trajectories from ComPADRe III, a data base that contains demographic information for several hundred plant species. We apply age-from-stage matrix decomposition methods to obtain age-specific trajectories from 290 angiosperm species of various growth forms distributed globally. From these trajectories, we survey pace and shape values and investigate how growth form and ecoregion influence these two aspects of mortality using a Bayesian regression analysis that accounts for phylogenetic relationships using a resolved supertree.
  4. In contrast to the animal kingdom, most angiosperms (93%) show no senescence. Senescence is observed among phanerophytes (i.e. trees), but not among any other growth form (e.g. epiphytes, chamaephytes or cryptopyhtes). Yet, most phanerophytes (81%) do not senesce. We find that growth form relates to differences in pace, that is, life span, as woody plants are typically longer lived than nonwoody plants, while differences in shape, that is, whether or not angiosperms senesce, are related to ancestral history.
  5. Synthesis: The age trajectory of mortality captures a fundamental life-history pattern for a species that is crucial to ecological understanding. We contribute to ecological knowledge by surveying these patterns across angiosperms. The novelty and strength of our study lies in the comprehensiveness of the data set, the use of a novel Bayesian analysis that accounts for phylogenetic history and in the distinction between metrics of pace and shape as two separate aspects of mortality. We believe that our approach could prove useful in future comparative studies of mortality patterns.


Demographic senescence, the decline in fertility rate and/or increase in the risk of mortality with age, remains one of the most striking phenomena in ecology and evolution, but studies of senescence in plants are scarce. Evolutionary biologists and ecologists interested in understanding how plants senesce have highlighted the need to study the influence of physiology and environmental conditions on patterns of mortality (e.g. Watkinson 1992; Roach 1993, 2003; Silvertown et al. 1993; Franco & Silvertown 1996, 2004; Thomas 2003). In this study, we explore these relationships in angiosperm species using recently developed measures of mortality: ‘pace’ and ‘shape’ (Baudisch 2011). The pace of mortality captures the speed at which life proceeds and can be measured by life expectancy, while the shape of mortality captures whether, and by how much, mortality increases (‘senescence’), decreases (‘negative senescence’) or remains constant over age (‘negligible senescence’). These metrics capture the full range of potential age patterns of senescence: positive, negligible and negative (Vaupel et al. 2004; Baudisch 2008).

At first glance, a deleterious phenomenon like senescence should stand no chance against the pressure of selection for the fittest genotype. Yet it is often observed in animals (e.g. Finch 1990; Promislow 1991; Gaillard et al. 1994; Nussey et al. 2006; Jones et al. 2008). Evolutionary theories of senescence predict that the risk of mortality should increase, and fertility decrease, over adult ages for multicellular, iteroparous species because the strength of selection diminishes with age (Medawar 1952; Williams 1957; Hamilton 1966; Kirkwood 1977). These theories propose that senescence should be universal even ‘in the farthest reaches of almost any bizarre universe’ (Hamilton 1996). Although Kirkwood and Williams propose a clear soma-germ line separation, which is commonly absent in plants, as a necessary condition for senescence, the theories remain ambiguous about whether this is also a sufficient condition for senescence to evolve.

Due to the complex life cycles of plants, evolutionary theories of senescence have somewhat neglected the plant kingdom (Roach 2003). Among the few studies focusing on single plant species, some have provided evidence for the existence of senescence (Barot, Gignoux & Menaut 1999; Van Dijk 2009), while others have found either no evidence for senescence (Rose, Clarke & Chapman 1998; Willems & Dorland 2000; Lanner & Connor 2001), or negative senescence (Roach 2001; García, Dahlgren & Ehrlén 2011). In a study of mortality in different cohorts of the perennial herb Plantago lanceolata, Roach et al. (2009) showed that mortality was size- and weather-dependent, rather than age-dependent, except under conditions of strong competition with other plant species. In the light of this equivocal evidence, a better understanding of the conditions under which plants do, or do not, evolve senescence requires a comparative approach.

To our knowledge, Silvertown, Franco & Perez-Ishiwara (2001) have provided the only comparative study of plant senescence to date. Their analyses used a matrix algebra approach to obtain age trajectories of mortality and per-capita recruitment from population projection matrices (Cochran & Ellner 1992; Caswell 2001) for 65 perennial plant species. The authors found a great deal of variation in the age trajectories of mortality and classified them into three types: (i) increasing, (ii) hump-shaped with a long phase of decrease and (iii) U-shaped. Although this study was a leap forward in our understanding of senescence in plants, the relatively small number of species considered, the discrete classification of the mortality trajectories, and the use of a measure of senescence based on a single parametric model of mortality limited an in-depth exploration of senescence. Since then, population projection matrices have been published for hundreds of plant species from a larger range of taxonomic groups, growth forms and ecoregions (Salguero-Gómez & de Kroon 2010). In addition, the development of the pace and shape metrics of ageing (Baudisch 2011) now provide useful measures that allow a more objective classification of mortality trajectories because these metrics are not bound by any parametric model of mortality.

Baudisch (2011) argued that pace and shape metrics capture two independent aspects of change over age; pace captures the speed of life, while shape captures whether and how much species senesce (see 'Materials and methods'). Mathematically, for a given shape value, any pace value is possible and vice versa. However, not all theoretically conceivable mortality patterns will be observed in nature, because nature imposes constraints. It is believed that such constraints are determined by decisions about allocation of resources between growth, maintenance and reproduction, which in turn affect pace and shape of mortality for a population. These processes are well known to differ between growth forms (Silvertown, Franco & McConway 1992; Silvertown, Franco & Menges 1996; Boggs 2009) and to be influenced by ecological conditions (Franco & Silvertown 2004). Here, we explore the influence of growth form (Raunkiær 1934) and ecoregion (Olson et al. 2001) on the pace and shape of mortality, while accounting for phylogeny and potential confounding factors. We use Bayesian log-linear regressions and test a range of models that included either all, some or none of the aforementioned variables. This paper thus provides a contemporary survey of senescence as characterized by pace and shape values across angiosperms.

Materials and methods

Pace and shape

The concepts of pace and shape of mortality distinguish two different aspects of mortality (Baudisch 2011). The pace of mortality captures how long a species is expected to live. Pace is fast in populations that die within days or weeks (e.g. Bromus tectorum; Griffith 2010), slower in populations that can live years (e.g. Cryptantha flava; Lucas, Forseth & Casper 2008) and even slower when individual plants can live for centuries (e.g. Borderea pyrenaica; García, Dahlgren & Ehrlén 2011). Pace thus sets the time-scale of the life course of individuals in a population. In contrast, the shape of mortality is independent of time. Shape captures the direction and relative magnitude of change in mortality. Capturing direction, shape describes whether the force of mortality increases, remains constant, or decreases over an individual's life course. Capturing magnitude, shape details how much mortality changes over age, that is, whether it doubles, triples or changes by several fold relative to its average level.

Pace is measured by life expectancy at maturity, denoted by e0 (Baudisch 2011), because life expectancy is the most robust measure of life span, and senescence is a phenomenon affecting the adult life course (Williams 1957; Hamilton 1966). By definition, any shape measure needs to be independent of time and to provide a threshold level that corresponds to constant mortality, that is, negligible senescence. This threshold marks the boundary between senescence and negative senescence and clearly distinguishes shape values for increasing (senescence), constant (negligible senescence) and decreasing mortality patterns (negative senescence, sensu Vaupel et al. 2004). Shape values that are close to the threshold correspond to mortality trajectories that barely change over age. They have a ‘shallow’ shape. Shape values further away from the threshold represent mortality patterns with a ‘steep’ shape. Here, we measure shape (S) by the percentage survivors up to the expected age at death, S = l(e0). If mortality is constant over age, then l(e0) = e1, because l(x) is given by

display math

and e0 by

display math

therefore l(x) = exp(μx), e0 = 1/μ, and thus l(e0) = 1/exp(1). This inverse of e, the base of natural logarithms, is approximately equal to 0.37 and marks the threshold level of shape, that is, values above 0.37 correspond to mortality patterns that increase with age, those below 0.37 point to mortality patterns that fall with age, and values at 0.37 are indicative of mortality patterns that remain constant with age (see proof in mathematical Appendix A). Appendix A shows that, for monotonically decreasing mortality, fewer than 37% of adults survive longer than one life expectancy due to the initially high level of mortality, while in the case of monotonically increasing mortality, more than 37% of adults live up to and past the expected age at death, because death starts taking its toll only at higher ages.

ComPADRe III: the plant projection matrix data base

Our comparative analyses within angiosperms rest on a data base that integrates demographic, taxonomic, biogeographic and ecological information in vascular plants and algae: Comparative Plant & Algae Demographic Research (ComPADRe III; R. Salguero-Gómez, unpubl. data). Over 800 species in ComPADRe III have world-wide provenance, spanning all terrestrial ecoregions (Olson et al. 2001) and growth forms (Raunkiær 1934; see Raunkiaer's figure 2). The life expectancies of species in the data base range over several orders of magnitude, from annuals like Arabidopsis thaliana to the extremely long-lived Sequoia sempervirens (Namkoong & Roberds 1974).

At the demographic level, the data base contains thousands of published and personally communicated population projection matrices under different year, site and treatment conditions. Each population projection matrix contains vital rate information (e.g. survival, progression/retrogression, seed bank, vegetative dormancy, clonal and sexual reproduction) that determines the population dynamics of the species under the specified year, site and treatment (Caswell 2001; Morris & Doak 2002).

To examine the natural population dynamics of the largest sample size of angiosperm species possible, we calculated the element-by-element arithmetic mean A for all periods and sites for each species excluding experimental treatments (e.g. herbivory, fire or drought). Thus, each of the resulting matrices describes the population dynamics under conditions that are ‘normal’ to those species (but see 'Discussion' for limitations on spatial and temporal replication of the studies). The matrix A was further divided into three matrices: U details changes in classes throughout the life cycle of the species conditional on survival, F describes per-capita sexual reproductive contributions, and C represents clonal reproduction via ramets.

Age-from-stage matrix decomposition

We obtained deterministic age-specific survivorship trajectories (lx) and the probability of reaching a given age (x) using age-from-stage approaches (Cochran & Ellner 1992; Caswell 2001, 2006) applied to the U matrices for each species. The fact that we ignore F and C matrices implies that our report on ageing patterns disregards sexual and clonal reproduction of the study species. Briefly, the method relies on the fact that even though most of these projection matrices are based on size and/or developmental stage, surviving individuals inherently ‘age’, that is, grow a year older, if they survive one annual projection. In acquiring years, and by progressing or retrogressing into a different class, or by stasis (remaining in the same class) individuals are subject to a particular stage-specific survival probability that will decrease their lx values in an iterative, distinctive manner that is a property of the projection matrix of each species. An extensive explanation of the method is given by Caswell (Caswell 2001, 2006). The transformation from a survivorship (lx) schedule to the risk of mortality (μx) schedule is straightforward (Tatar, Carey & Vaupel 1993):

display math(eqn 1)

We then calculated the mean age at first reproduction (Lα), using similar methods (Cochran & Ellner 1992; Caswell 2001, 2006).

The age schedules (lx, μx and Lα) were calculated considering the first nonseed bank stage as the ‘beginning of life’. This approach avoids ambiguities about the amount of time that an individual plant might stay dormant as a propagule (Burns et al. 2010), an aspect that is difficult to quantify in plant demographic studies (Baskin & Baskin 2001).

Statistical analyses

We constructed Bayesian log-linear regression models to investigate how ecoregion, plant growth form and phylogenetic relationships influenced our measures of the pace and shape of mortality across angiosperms. The aim of the analysis was to determine the extent to which the expected values of pace or shape overlapped between different combinations of growth form and ecoregion and the extent to which phylogeny influenced these expected values. The basic model follows Freckleton, Harvey & Pagel (2002), whereby the probability density for the dependent variable, either pace or shape, is given by

display math(eqn 2)

where y is a vector of logged values of pace or shape for each species in the data set, β is a vector of parameters linking the covariates to y, X is the design matrix containing covariate values for each species in y, σ2 is the process model error, and V(λ) is the variance-covariance (VCV) matrix obtained from the phylogenetic tree with off-diagonal elements scaled by λ, also known as Pagel's lambda (Pagel 1999).1 This parameter is a scaling factor that is informative about the role of evolution in influencing trait values of terminal taxa; if ancestral trait values have no influence on the trait values of terminal taxa, the best model will be one where the VCV matrix has had the phylogenetic structure removed by the scaling factor (i.e. it is scaled with λ = 0, and is thus equivalent to a simpler nonphylogenetic model). On the other hand, if the ancestral trait values have a strong influence and have evolved via a Brownian motion process, the best model will be one where the phylogenetic structure is maintained in the VCV matrix (i.e. the VCV matrix is scaled by multiplying by 1, perfectly recovering the tree structure). An intermediate influence of phylogeny would result in the best model having a λ value somewhere between 0 and 1.

The covariates we tested were Raunkiær growth form (Raunkiær 1934) and ecoregion (Olson et al. 2001); Table S1, Supporting information). Raunkiær's classification is based on the location of the dormant shoot meristems of the species in relation to the ground during season of adverse conditions. In this categorization, species for which meristems are located close to the ground regenerate most or all of their aerial parts every year, thus having the potential to lose senescent aerial tissues (Salguero-Gómez & Casper 2010). The categories for this variable are the following: cryptophytes (shoot meristems are below-ground; rhizome, bulb and corm-producing plants), hemicryptophytes (shoot meristems at or near the surface; many rosette-forming plants), chamaephytes (shoot meristems < 25 cm above-ground; typically succulents and shrubs), phanerophytes (shoot meristems > 25 cm above-ground; typically shrubs and trees) and epiphytes (the height of the shoot meristems is measured with respect to their position on the host plant). To classify plants with respect to their habitat, we used a simplified version of Olson's classification of ecoregions based on information extracted from each publication containing the projection matrices in ComPADRe III. The ecoregions we used were temperate (‘Temperate Broadleaf and Mixed Forest’, ‘Temperate Coniferous Forest’ and ‘Temperate Grassland, Savanna and Shrubland’), tropical (‘Tropical and Subtropical Moist Broadleaf Forest’, ‘Tropical and Subtropical Dry Broadleaf Forest’, ‘Tropical and Subtropical Coniferous Forest’, and ‘Tropical and Subtropical Grassland, Savanna and Shrubland’), desert (‘Desert and Xeric Shrubland’), mediterranean (‘Mediterranean Forest, Woodland and Scrub’), montane (‘Montane Grassland and Shrubland’) and boreal (‘Boreal Forest/Taiga’).

Because the matrices used for this analysis were based on a range of modelling approaches, the population dynamics resulting from them could vary widely from species to species. These differences could affect comparative analysis of mortality patterns between species. To account for these potential confounding effects, we added life cycle criteria, matrix dimension and clonality as covariates in our analyses. The life cycle criteria used to classify individuals in a population were size, developmental stage, age or a combination of these state variables (Caswell 2001). We categorized each species’ mean control matrix, the matrix resulting from the element-by-element arithmetic mean of the matrices that report control conditions, into one of the seven possible combinations (i.e. size, stage, age, size and stage, size and age, stage and age, as well as size, stage and age). The number of dimensions of a population projection matrix (i.e. the number of life cycle stages) is positively correlated with the rates of progression and retrogression and negatively correlated with class-specific survival (Enright, Franco & Silvertown 1995; Salguero-Gómez & Plotkin 2010) and could thus also influence age-based trajectories obtained from them (R. Salguero-Gómez, unpubl. data). Finally, we classified the matrix of each species as genet-based or ramet-based. The latter was defined as species whose C matrix had at least one element > 0. This information is critical because in our analyses the mortality trajectory only refers to the U matrix (see section 'Age-from-stage matrix decomposition' above). Matrix dimension, the criteria used to specify the life cycle of the species, and the presence of clonality were included to control for potential confounding effects in our analyses.

Finally, to incorporate the phylogenetic structure in the aforementioned VCV matrix, we constructed a fully resolved tree by first obtaining a family-level tree with PHYLOMATIC (, then manually resolving it using MESQUITE (Maddison & Maddison 2009) by employing information from the Angiosperm Phylogeny Website (Stevens 2001) and specific detailed studies of phylogenetic relationships within families (see C. Mbeau-Ache & M. Franco, unpubl. data). Phylogenetic distances were interpolated by employing the bladj function of PHYLOCOM (Webb, Ackerly & Kembel 2008), using the estimated node ages from Wikström, Savolainen & Chase (2001).

After obtaining all the covariates and the VCV matrix mentioned previously, we constructed a Bayesian log-linear regression model for both pace and shape. The full Bayesian model was

display math(eqn 3)

where the first element of the input (p(y|β…) is the likelihood function described in (eqn 2), and the second element of this input (p(β|β0…) corresponds to the prior densities for the parameters. We used a conjugate multivariate-normal prior density for β, with mean β0 and VCV matrix βs I, and inverse gamma for σ2, with parameters s1 and s2. For parameter λ, we used a truncated normal distribution, with lower truncation at 0 and upper truncation at 1. We used a Markov Chain Monte Carlo algorithm to find posterior parameter distributions. We ran five parallel simulations for 10 000 iterations with a burn in of 2000 iterations, and each simulation was started from different parameter values to assess convergence. We used direct sampling for parameters β and σ2, and a Metropolis algorithm for Pagel's λ (Clark 2007).

To test the influence of the covariates described earlier, we ran 16 nested models for both pace and shape as dependent variables. These models had different combinations of explanatory variables (i.e. ecoregion and growth form), phylogeny (i.e. Pagel's λ > 0 or fixed to be equal to 0) and the presence of confounding variables (i.e. life cycle criteria, matrix dimension and clonality). We evaluated model fit by calculating deviance information criterion (DIC; Spiegelhalter et al. 2002).

When the selected model(s) included any of our explanatory covariates (ecoregion or growth form), both of which are categorical, we used Kullback–Leibler discrepancies (Burnham & Anderson 2001) to determine the level of overlap between the posterior distributions of their parameters. For instance, let Pi and Pj be the posterior densities for parameters βi and βj, where i and j are specific combinations of growth form or ecoregion. The K–L value that measures the amount of overlap of Pi over Pj, namely K(Pi, Pj), is calculated as

display math(eqn 4)

If both distributions are identical, then K(Pi, Pj) = 0, suggesting that there is no distinction between the expected values from i and j; as the K–L values increase, the discrepancy between the two distributions becomes higher. As can be inferred from (eqn 4), the relationship is asymmetric, namely K(Pi, Pj) ≠ K(Pj, Pi). Thus, for each combination of i’s and j's, we calculated two K–L values. We used McCulloch's calibration (McCulloch 1989) to make the K–L values easier to interpret. This calibration modifies the K–L values to range between 0.5 and 1, where values close to 0.5 imply high overlap and values close to 1 correspond to minimal overlap.


In theory, a species living at fast or slow pace could exhibit any shape of mortality (Baudisch 2011). In fact, the 290 angiosperms in our analysis included species living at fast, moderate and slow pace with increasing, constant or decreasing mortality patterns (left panel, Fig. 1). Yet, angiosperms do not cover the full pace-shape landscape (right panel, Fig. 1). While pace measures range from fast to slow and thus cover short, moderate and long-lived plants, shape values fall within a relatively narrow range of between 0.1 and 0.5. Within this range, the majority of species (93%) exhibit shape values at or below the senescence threshold, that is, exp(−1); they show negligible or negative senescence (Fig. 2). Senescence is found exclusively among phanerophytes. But strikingly, not all phanerophytes senesce: 81% show negligible or negative senescence. In addition, 44% of species that show negligible senescence are nonphanerophytes.

Figure 1.

Left panel: mortality patterns for an array of different pace and shape values. The dashed, vertical line indicates life expectancy, our measure of pace. Trajectories end when 95% of plants potentially of reproductive age or stage are dead. Across angiosperms, alternative shapes of mortality can be found at different levels of mortality, which correspond to species with fast pace (short-lived), moderate pace, or slow pace (long-lived). Similarly, for alternative levels of pace, mortality can increase, decrease or remain constant with age. The species and their pace (P) and shape (S) values (the latter expressed as the difference from the threshold of 0.37) are: (a) Agave marmorata:= 7.50, = 0.015; (b) Cimicifuga elata:= 8.75, = −0.008; (c) Arisaema triphyllum:= 4.95, = −0.081; (d) Thrinax radiata:= 28.85, = 0.031; (e) Sabal yapa:= 24.94, = −0.001; (f) Rourea induta:= 21.31, = −0.041; (g) Prioria copaifera:= 106.27, = 0.027; (h) Scaphium borneense:= 92.36, = −0.006; (i) Lepanthes eltoroensis:= 90.98, = −0.024. Pace units are in years and their values are plotted in log-scale. Right panel: pace and shape values for the mortality trajectories of 290 angiosperm species. Each point represents a single species and the colour of each point distinguishes: 1) alternative growth forms (which were found to mainly drive pace); and 2) different ecoregions. The horizontal dashed line represents the senescence threshold (0.37).

Figure 2.

Frequency distribution of shape values for the different growth forms. The dashed grey vertical line marks the boundary of senescence. Below this point, species show negative senescence, at that point species show negligible senescence and above that point species show senescence.

Our exploration of pace and shape values revealed a nonlinear, positive relationship between the two metrics of mortality (right panel, Fig. 1). We found that each metric was constrained by different factors that keep them from reaching extreme areas in the pace-shape landscape. Of the 16 models tested for shape, the model with the lowest DIC value showed an influence of phylogeny (i.e. Pagel's λ > 0; Table 1). The difference in DIC values between this model and the next best one was large (ΔDIC = 26.6). The phylogenetic signal for shape, estimated by Pagel's λ, was moderately high (λ = 0.55 ± 0.087), which suggests that shape values are associated with phylogenetic relatedness but not with growth form or ecoregion. On the other hand, for pace the model with lowest DIC included both phylogeny and growth form as explanatory variables, while the second best model had only growth form (Table 2). In this case, the difference in DIC values was lower than 3 (ΔDIC = 2.8), which means that both models had similar support from the data. However, this small difference in DICs between the two best models for pace can be easily explained because the value of Pagel's λ for the second model was low (λ = 0.21 ± 0.072). Thus, the phylogenetic signal for pace appears to be much weaker than that for shape (Fig. 3; Fig. S1, Supporting information). It is important to stress that none of the covariates included as potentially confounding variables – life cycle criteria, matrix dimension, and the absence/presence of clonality – had a significant effect on either pace or shape. In both cases, models with confounding variables had DIC values far from the best model (Pace: ΔDIC = 15; Shape: ΔDIC = 40).

Table 1. Model selection for the log-linear regression on shape as a function of growth form (grow), ecoregion (ecoreg), phylogeny and additional confounding variables
Explanatory variablesPhylogeny (λ > 0)Confound. variablesModel fit
  1. D.ave = average posterior value; D.mode = posterior value at the model; pD = effective number of parameters; k = real number of parameters; DIC = deviance information criterion (Spiegelhalter et al. 2002).

Table 2. Model selection for the log-linear regression on pace as a function of growth form (grow), ecoregion (ecoreg), phylogeny and additional confounding variables
Explanatory variablesPhylogeny (λ > 0)Confound. variablesModel fit
  1. DIC, deviance information criterion. See Table 1 for description of variables.

Figure 3.

Pace and shape values for mortality trajectories across the time-calibrated angiosperm phylogeny. The bars in each plot are proportional to the natural logarithm of the pace and shape values for each of the corresponding species in the phylogeny. The bars are colour coded according to growth form (see legend for Fig. 2).

The overlap in posterior distributions of the growth form parameters for the pace of mortality showed that the only growth form consistently different from the others was phanerophytes (K–L calibration close to 1 in all cases; Fig. 4). This result is in line with the observation that woody plants are commonly longer lived than herbaceous plants. All the other growth forms had K–L calibration values below 0.75, which suggests a large degree of overlap between them (Table S2, Supporting information).

Figure 4.

Posterior distributions of the parameters that describe the relationship between growth form and the pace of mortality. *Phanerophytes (trees and shrubs) were the only growth form with negligible overlap with the other growth forms.


The pace and shape landscape of angiosperms

We calculated pace and shape metrics of mortality trajectories to distinguish the speed of life from the shape of senescence as two separate aspects. Contrary to the common association of long-lived species with the capacity to escape senescence, our results suggest that, instead, shorter life span in plants is associated with lower shape values and thus less senescence. Although pace and shape are obviously related (Fig. 2), our study shows that these metrics are statistically associated with different factors. We find that for senescence in angiosperms, pace is best explained by growth form, while shape is best explained by phylogenetic relatedness. Ecoregion did not have any effect on pace and shape and therefore, surprisingly, does not seem to be a dominant constraint to the way plants senesce (or not). Gradients in temperature and precipitation exist across ecoregions (Wright et al. 2004), yet they do not seem to lead to different pace and shape values in angiosperms.

The void areas in the landscape of pace and shape of senescence (Fig. 1) correspond to combinations of slow pace with steeply decreasing mortality over age (low shape value; bottom right corner) and fast pace with steeply increasing mortality (high shape value; top left corner). These regions represent rather extreme life histories. On the one hand, low shape values and thus strong negative senescence coupled with long life span occurs if virtually all plants die immediately after (but not before) maturity, that is, after reaching the stage of being established enough to produce seeds, and if the few survivors would remain alive for a long time (slow pace, low shape and thus strong negative senescence). This could be the case for long-lived plants that drastically improved their ability to withstand destruction with age, which might conceivably occur in some tree species (Lanner & Connor 2001). On the other hand, high shape values and thus strong positive senescence coupled with short life span occurs if virtually all plants remain alive after reaching maturity and die almost simultaneously close to the expected age at death. Such a pattern can be found among semelparous species (Metcalf & Koons 2007; Jaremo & Bengtsson 2011). Annual species may or may not exhibit such a pattern, depending on whether they start adult life with low mortality and have synchronized deaths after their short life span (Kalisz & McPeek 1993; Griffith & Forseth 2005). In our analysis, we omitted annuals due to the different time-scale on which their matrix models are based (e.g. periodic matrices, Caswell & Trevisan 1994).

Evolutionary theories of senescence

In our angiosperm data set, senescence is found exclusively among the phanerophytes, although the majority of phanerophytes do not senesce. Most of the species in our study fall at or below the senescence threshold; they appear to show negligible or negative senescence (Fig. 2). No clear explanation for this striking observation is yet available, but the answer could provide valuable insights into the evolution of senescence in plants. Hamilton (1966) predicted universal senescence for iteroparous, multicellular creatures. So, why do many angiosperms not fulfil his prediction? Silvertown and colleagues (2001) suggested that under natural conditions, extrinsic forces of mortality (e.g. fires and herbivores) prevent senescence being observed in plants, except under greenhouse conditions (M. Franco, pers. comm., 2012). If we put aside potential data limitations and detection problems (which we return to later) and focus on potential biological explanations, it is probably significant that angiosperms lack a rigid separation between germ line and soma. Meristem cells are not predestined for a particular fate, but differentiate as required. At first sight, this could be the answer, since Williams and Kirkwood, proposed that a necessary condition for the evolution of senescence was the existence of a clear distinction between the germ line and somatic cell lines (Williams 1957; Kirkwood 1977). In contrast, Medawar and Hamilton neglected the soma-germ line distinction and instead identified the declining strength of selection as a sufficient explanation for senescence (Medawar 1952; Hamilton 1966). As any organism under evolutionarily equilibrial conditions experiences a declining strength of selection with age, the ‘classic’ logic of Hamilton (1966) should also apply to species that lack a rigid germ line-soma distinction. Therefore, even iteroparous angiosperms should show increasing mortality with age unless the weakening strength of selection with age is not sufficient for the evolution of senescence (Baudisch & Vaupel 2012).

Baudisch & Vaupel (2012) argue that although the weakening selective force plays a role, whether senescence evolves or not depends on the nature of the species’ life-history constraints. These constraints determine the costs and benefits of allocating more or less energy and time to survival versus reproduction, and thus, whether or not sufficient growth, regeneration and repair is affordable given the associated sacrifice in reproduction. Therefore, we propose that understanding life-history constraints in plants will be the key to understanding why some plants have shape values above, at, or below the senescence threshold.

The vital rates of plant species correlate with developmental stage and/or size rather than with age. A larger size/stage is often associated with improved survival and reproduction, but it takes time to grow. Larger (and thus usually older) individuals contribute significantly to reproductive output, as demonstrated by models that account for stage-specific selection pressure (Caswell 1985; and see Caswell & Salguero-Gómez, in this special feature). The ‘simple’ age-structured approach underlying classic evolutionary theories of senescence is not sufficient to capture the complex life cycle of plants. The typically highly modular architecture of plants, their great plasticity in terms of both positive and negative changes in size, and their potential for clonal propagation, require more complex models such as those developed by Orive (1995) and Pedersen (1995) to shed light on the nature of the life-history constraints faced by plants.

Utility of pace and shape metrics in comparative studies

As is common in comparative studies of senescence (e.g. Finch 1990; Promislow 1991; Jones et al. 2008), Silvertown, Franco & Perez-Ishiwara (2001) classified ageing in plants by the ‘rate of ageing’ given by a parameter fitted from a specific mortality model. Given the wide range of mortality patterns observed, it is unlikely that one can find a single model that fits all data equally well, and utilizing different mortality models would require standardization techniques to make comparison between parameters reasonable. Pace and shape measures circumvent all these limiting factors because they can be calculated directly from the data.

The distinction between measures of pace versus shape clearly separates life span from senescence. One is easily led to treat the longest lived creatures as those that conquer senescence most successfully, but this view is misleading. A constant risk of death over age can imply a very long life, if the level of mortality is low enough, but life would be very short, even if mortality risk was constant, if mortality was high. Our analysis shows that, contrary to the seemingly intuitive association between long life and negligible senescence, the opposite tends to be the case. Short-lived angiosperms tend to show more negative senescence, while long-lived plants tend to show stronger senescence.

Ageing rates depend on units of time and cannot distinguish between pace and shape. This limits previous hypotheses about senescence. For example, Finch (1990) predicts that lower ageing rates will be associated with greater modularity. But it remains unclear whether lower ageing rates mean longer lived species (slow pace), or whether species that, although potentially short-lived, have negligible or negative senescence and therefore exhibit low shape values. Given this uncertainty, Finch's classification of species with greater modularity, and thus, lower ageing rates under ‘negligible senescence’ needs to be revisited. Another classic hypothesis, the so-called Williams hypothesis (1957), states that a greater ‘extrinsic’ hazard should promote higher rates of senescence. This prediction is ambiguous because it remains vague about what hazards are ‘extrinsic’. Predictions regarding pace and shape can differ depending on exactly how the extrinsic hazard affects mortality in different age groups (Baudisch 2011).

Pace and shape measures provide a broad perspective on the complex landscape of life histories. They offer a means of comparing mortality patterns employing scalar values not as a replacement but in addition to parametric analyses of mortality trajectories. When comparing complete trajectories, the pace and shape framework allows us to pace-standardize age and mortality, thereby offering a typological framework for comparing species (see panel 3 of figs 1 and 2 in Baudisch 2011). This framework is still under development and its value for comparative studies awaits further assessment.

Data limitations

The availability of vast amounts of information – here in the form of projection matrices – is fundamental for the exploration of generalities in phenomena like senescence across the tree of life. However, using projection matrices has its own limitations. For example, using our methods, it is a mathematical certainty that the age trajectories of mortality will reach an asymptote as the cohorts in the model converge to a quasi-stationary distribution (Horvitz & Tuljapurkar 2008). Other things being equal, this will happen faster for matrices with no retrogression (i.e. in most phanerophytes, especially trees). Nevertheless, we are confident that the observed patterns are informative about the direction of senescence, especially because this is the group where we tended to observe increasing mortality. In addition, in most cases, our measure of pace (life expectancy) falls at an age considerably earlier than ages potentially confounded by mortality plateaus. Therefore, we argue that the availability of larger matrices would not significantly change our overall insights. Another potential issue is the limited temporal and spatial replication of studies that contribute matrices we use which may reduce our power to accurately quantify senescence. This aspect is particularly troubling in studies of senescence because of the potential for some species to live for hundreds of years (e.g. García, Dahlgren & Ehrlén 2011), and the fact that populations of the same species can display significant difference in demography even if only separated by a few kilometres (Jongejans & de Kroon 2005). Although we must acknowledge these issues, our analysis uses the most comprehensive source of demographic information in plants and is thus as statistically powerful as is currently possible.


Mortality is a major component of population dynamics and fitness and thus lies at the heart of every ecological and evolutionary question. Changes in mortality rates with age reflect whether and how organisms senesce. Our study of senescence in angiosperms highlights the importance of addressing changes in mortality risk across the life span of an individual using two distinct metrics: how fast (pace), and in what direction and by what magnitude (shape) senescence occurs. Our study has revealed factors (growth form and phylogenetic relatedness) that are associated with these two metrics. We foresee a promising avenue of research in the exploration of plant anatomical and physiological traits in relation to these metrics. Certainly, an immense amount of plant functional trait data already exists that would allow this type of analysis (Kattge et al. 2011). Finally, to obtain a more comprehensive picture of demographic senescence across the tree of life, we call for demographic studies that focus on hitherto under-explored and perhaps less charismatic clades.


This research was funded by the Max Planck Research Group on Modelling the Evolution of Ageing and the Max Planck Institute for Demographic Research. R.S.G. acknowledges support from the Reece Family foundation and the Evolutionary Biodemography laboratory student worker support (S. Zeh, E. Brinks, C. Farack, G. Roemer, A. Henning and G. Hoppe) in the digitalization of ComPADRe III, as well as the countless authors who clarified the life cycles of the studied plant species.


  1. 1

    Not to be confused with the asymptotic population growth rate (also λ), the dominant eigenvalue of the projection matrix A in matrix population models (Caswell 2001).

Appendix A

If mortality, that is, the hazard of death μ(t), is monotonically increasing over age, then the cumulative hazard of death at age x, given by

display math

is a convex function, that is, there exist constants a, b with H(x) ≥ a x + b for all x and H(e0) = a e0 + b. Noting that for the probability density function, f(x), it holds that

display math

the cumulative hazard at the expected age of death e0 can be expressed as follows:

display math

Integration by parts reveals that

display math

since μ(x) = f(x)/l(x), so that H(e0) ≤ 1, which implies l(e0) ≥ 1/e, because H(x) = log(l(x)). Analogously, for a monotonically decreasing μ(x), H(x) is concave, and the proof above with the inequality sign in reverse direction shows that l(e0) ≤ 1/e. This is an application of Jensen's inequality.