Summary1. As they grow old, most organisms experience progressive physiological deterioration resulting in declining rates of survival and reproduction -a seemingly maladaptive phenomenon known as senescence. 2. Although senescence is usually defined with respect only to survival and reproduction, a third component of fitness, offspring quality, may also decline with age. Few studies, however, have assessed age-related changes in offspring quality using measures that truly reflect fitness. 3. In a controlled environment, we tested for age-related declines in three demographic components of fitness (survival, reproduction and offspring quality) in Lemna minor, a small aquatic plant in the subfamily Lemnoideae (the duckweeds) with a short life span and rapid rate of asexual reproduction. Our primary measure of offspring quality, the intrinsic rate of increase, more closely approximates fitness than measures used in previous studies such as size, life span and total reproductive output. 4. We observed strong age-related declines in all three components of fitness: old plants had lower rates of survival and reproduction, and produced lower-quality offspring than younger plants. 5. Theoretical and empirical research on the evolutionary biology of senescence should devote more attention to offspring quality. This often unrecognized component of fitness may change with age -as we have shown in L. minor -and may be shaped by, and feed back into, the same evolutionary forces that give rise to senescence.

Classic theories on the evolution of senescence make the simplifying assumption that all offspring are of equal quality, so that demographic senescence only manifests through declining rates of survival or fecundity. However, there is now evidence that, in addition to declining rates of survival and fecundity, many organisms are subject to age-related declines in the quality of offspring produced (i.e. parental age effects). Recent modelling approaches allow for the incorporation of parental age effects into classic demographic analyses, assuming that such effects are limited to a single generation. Does this 'single-generation' assumption hold? To find out, we conducted a laboratory study with the aquatic plant Lemna minor, a species for which parental age effects have been demonstrated previously. We compared the size and fitness of 423 laboratory-cultured plants (asexually derived ramets) representing various birth orders, and ancestral 'birth-order genealogies'. We found that offspring size and fitness both declined with increasing 'immediate' birth order (i.e. birth order with respect to the immediate parent), but only offspring size was affected by ancestral birth order. Thus, the assumption that parental age effects on offspring fitness are limited to a single generation does in fact hold for L. minor. This result will guide theorists aiming to refine and generalize modelling approaches that incorporate parental age effects into evolutionary theory on senescence.

1. Matrix population models (MPMs) are an important tool for biologists seeking to understand the causes and consequences of variation in vital rates (e.g. survival, reproduction) across life cycles. Empirical MPMs describe the age-or stagestructured demography of organisms and usually represent the life history of a population during a particular time frame at a specific geographical location. 2. The COMPADRE Plant Matrix Database and COMADRE Animal Matrix Database are the most extensive resources for MPM data, collectively containing >12,000 individual projection matrices for >1,100 species globally. Although these databases represent an unparalleled resource for researchers, land managers and educators, the current computational tools available to answer questions with MPMs impose significant barriers to potential COM(P)ADRE database users by requiring advanced knowledge to handle diverse data structures and program custom analysis functions.3. To close this knowledge gap, we present two interrelated R packages designed to (a) facilitate the use of these databases by providing functions to acquire, quality control and manage both the MPM data contained in COMPADRE and COMADRE, and a user's own MPM data (Rcompadre) and (b) present a range of functions to calculate life-history traits from MPMs in support of ecological and evolutionary analyses (Rage). We provide examples to illustrate the use of both.4. Rcompadre and Rage will facilitate demographic analyses using MPM data and contribute to the improved replicability of studies using these data. We hope that this new functionality will allow researchers, land managers and educators | 771Methods in Ecology and Evoluঞon JONES Et al.

1. Comparative studies have demonstrated extensive variation in age trajectories of mortality and fecundity, both within and among species, with many taxa exhibiting a general pattern of age-related demographic decline referred to as senescence. Whereas a considerable body of theory is devoted to explaining the origin and persistence of senescence, the evolutionary forces underlying variation in demographic trajectories more generally remain poorly understood.2. Studying variation in demographic trajectories is complicated by the fact that different species (or even different populations of a given species) may live and reproduce on different time-scales, which, for comparative purposes, can make it challenging to disentangle patterns of age-related demographic change (the shape of demographic age trajectories) from the time-scale on which those changes happen (the pace of demographic age trajectories).3. Here, we examine variation in the pace and shape of demographic trajectories among strains of the aquatic plant Lemna turionifera Landolt from 24 sites across Alberta, Canada. Our main objectives were to describe the shape of demographic trajectories in L. turionifera, and test for among-strain variation in pace and shape.We also tested whether potential variation in pace and shape is (1) constrained by trade-offs with other life-history traits, and (2) consistent with local adaptation to environmental characteristics at the sites of strain origin.4. The strains we examined were overwhelmingly subject to age-related increases in mortality and declines in fecundity, with increases in mortality tending to decelerate and plateau at advanced ages. Despite substantial among-strain variation in cumulative fecundity and plant size, measures of pace and shape did not in themselves vary significantly among strains. Both within and among strains, we observed a negative relationship between plant size and the shape of fecundity trajectories, but we found no other evidence for life-history trade-offs involving pace or shape, nor for local adaptation. Synthesis. Angiosperms display remarkable demographic variation. Our resultssuggest that the pace and shape of demographic trajectories are highly conserved within one particular angiosperm species (Lemna turionifera), despite substantial among-strain variation in other life-history traits. K E Y W O R D Sageing, biodemography, lemnoideae, life-history tradeoff, pace-shape, senescence | 2133Journal of Ecology BARKS et Al.

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