1 INTRODUCTION

As ecologists, we often ask how populations of different species respond to environmental factors (Grime, 1979; Harper, 1977). However, it is not always easy to compare environmental effects on species’ long-term population dynamics directly. Therefore, ecological studies are typically designed to collect data on the effects of environment on individuals in one life stage (e.g. seedlings; Amissah et al., 2015; Klimeš, Weiser, et al., 2021; Larson et al., 2021; Martínková et al., 2021; Švamberková & Lepš, 2020). Interpretation of such experiments is based on an assumption that the between-species differences in the response of vital rates of that single life stage are informative about the prospects of those individuals’ lifetime fitness and of dynamics of the whole population.

The population-level effects of differences in vital rates (i.e. mortality, growth, reproduction) of the single life stage strongly depend on species’ life-history strategy (Silvertown et al., 1993). For example, life-history strategy of annual plants and rodents relies more on reproduction, while trees and large mammals rely more on adult survival (Harper et al., 1996). This translates into the lesser impact of death of a young annual plant than of death of an old tree on population dynamics of their respective species. Consequently, the reliability of single life-stage ecological studies strongly decreases with increasing differences in demography of these species. Although different population-level effects of the identical changes in vital rates of different species are well known to demographers (e.g. Caswell, 1989), they are often neglected in experimental studies when single life stages are compared across species (but see e.g. Struckman et al., 2019).

The extent of the possible misinterpretation of population-level impacts of the between-species differences in response to a change in a single vital rate can be illustrated by an exceptional study of two closely related species, the common Cirsium acaule and the rare C. pannonicum (Münzbergová, 2005). The author hypothesised that predispersal seed predation is the mechanism limiting the distribution of the rare C. pannonicum. However, estimated level of seed predation was actually higher in the common species. The pattern changed directions at the population level, since the rare C. pannonicum was not able to sustain even lower levels of seed predation because it lacked the ability of clonal growth, which helped the common species mitigate losses due to seed predation, confirming thus the original hypothesis (Münzbergová, 2005).

The problem of limited applicability of extrapolation of differences in a single vital rate of a single life stage to lifetime fitness and population performance becomes more pronounced in large comparative studies, promoted by the ever increasing demand for the production of general conclusions (Enquist et al., 2009; Kattge et al., 2020). Such large studies frequently compare plants of different growth forms which are bound to differ strongly in their life-history strategies (Salguero-Gómez, 2017). This is especially tricky in studies focusing on a specific life stage such as seedlings. Unfortunately, many experiments in plant ecology compare seed banks in co-occurring grassland species (Klaus et al., 2018; Klimešová et al., 2013) or their germination and seedling recruitment among species (Kotorová & Lepš, 1999; Paulů et al., 2017). Groups known to differ in their demography such as annuals and biennials (Del Fabbro & Prati, 2014; Huhta et al., 2003), short-lived and perennial herbs or herbs and trees (Klimeš, Koubek, et al., 2021; Metcalf et al., 2006; Vesk et al., 2004; Whitman & Aarssen, 2010) or clonal and non-clonal herbs are compared as well (Klimešová et al., 2013; e.g. Albert et al., 2019; Barak et al., 2018; Martínková et al., 2020; Vítová et al., 2017). Popular are congeneric comparisons (especially in invasion ecology) where congeneric pairs (although sharing many traits) often differ in life span (annuals vs. perennials) and therefore have very different demography (Mommer et al., 2006; van Kleunen et al., 2011; Yu & He, 2021). This is also true for Arabidopsis comparative studies (Pollard et al., 2001; Shanmugam et al., 2011) as Arabidopsis thaliana is mostly annual and many of its congeners are perennial (Chytrý et al., 2021). The generality of conclusions of such broadscale comparative studies would be greatly enhanced if a correction could be found, which would take into account the main demographic differences in species life histories.

In demography, there are several methods which can solve related problems. Using sensitivity analysis (Caswell, 1978) and loop analysis (van Groenendael et al., 1994), we can disentangle the contributions of different vital rates on population growth rate. Therefore, these methods can be used to infer which individual-level responses are important (and to what degree) for population-level dynamic. In the comparative setting, analysis of life table response experiments can be used for intra- as well as interspecific studies. However, to do so, it requires a population model for all compared species in all studied conditions which is hardly ever available and laborious to obtain.

In this paper, we illustrate the consequences of ignoring species’ demography when extrapolating from individuals to population performance using a fictitious example of two species and results of a single life-stage experiment, and an example based on the data from the COMPADRE database (Salguero-Gómez et al., 2015). As a solution, we propose to translate the effects of experimental treatments on different vital rates into a ‘common currency’, that is, differences in population growth rates (commonly used fitness measure; Caswell, 2006; Metz et al., 1992), by inserting the effects of experimental treatments into transition matrix model of species’ population. We call this procedure a ‘demographic correction’ (Figure 1) and it belongs into sensitivity analyses in a broad sense (since it aims to solve the sensitivity problem: How outcomes change due to change in parameters; Caswell, 2019); specifically it is what Caswell calls analysis of scenarios (Caswell, 2019). We discuss its utility and limitations. Thanks to the recent synthesis of plant demographic information (Salguero-Gómez et al., 2015), information on the whole species’ life cycle is now available for large sets of species, which makes the proposed ‘demographic correction’ largely applicable.

2 EFFECT OF DEMOGRAPHY—A FICTITIOUS EXAMPLE

Demography of a plant species is typically recorded as a set of transition probabilities of individuals from one life stage into another coupled with data on seed/seedling production (e.g. Valverde & Silvertown, 1998). These together can be used to parameterise a matrix projection model (Caswell, 2006). The proximate population characteristic extractable from matrix projection model is the asymptotic population growth rate (dominant eigenvalue of the projection matrix, further as population growth rate) which tells us how much the population would grow or decline provided it remained under constant conditions (Caswell, 1989). We use population growth rate as a measure of population long-term fitness throughout the examples (although this measure might be insufficient to assess the fates of populations in more complex settings; Tuljapurkar & Orzack, 1980).

Let us consider that we are interested in the response of two species to grazing (e.g. as management considered to be carried out periodically in their habitat) and we have conducted a comparative (sensu Sanford et al., 2002) greenhouse experiment to investigate that. We obtained seedlings of both species, planted each seedling into a pot and let it grow into maturity. We divided adult plants randomly between treatment and control groups and simulated grazing on plants assigned to the treatment group (with timing corresponding to the proposed management). We recorded the reproduction of adult plants in both groups and analysed the differences between control and treatment groups. The treatment led (on average) to a 30% decrease in adult reproduction of species A and to a 50% decrease in adult reproduction of species B (and this difference was statistically significant; Figure 2). Based on such results, we would typically conclude that species B would be much more impacted by grazing than species A.

Let us further assume that demography of both species is known—they have a very simple and similar life history—there is no stasis and no retrogression, only growth and reproduction of young and adult plants. Populations of both species are stable—population growth rate equals one. Species A and B differ only in fecundity and in survival of young plants (Figure 3).

Our grazing treatment impacted the reproduction of adult plants. We can take demography into account by adjusting corresponding transitions in the projection matrices (highlighted in Figure 3) and inspect predicted population growth rate. Treatment affected only adult plants; therefore, the only impacted transition is their reproduction. In species A, transition was 4 and expected decrease due to treatment is according to the experiment 30% resulting in new transition of 2.8. For species B, decrease in adult reproduction was 50% which changes the transition from 2 into 1. New population growth rate is 0.9293 for species A and 0.9584 for species B. Thus, when we took the demography of our species into account, in contrast to the first conclusion, the population of species A suffers from grazing little bit more than that of species B.

This example illustrates the need to examine the effect of single vital rates on the whole life cycle. The contrasting effects of demographic correction versus experimental result are a consequence of the differing importance of reproduction from the young and adult stages. Thus, when only the reproduction of adult life stage is impacted by the treatment—population of species B suffers much less than would correspond to the observed data (from the experiment). Species A has mainly reproducing adult life stage; therefore, treatment impacts most of its reproduction. This can be nicely described using the loop analysis (van Groenendael et al., 1994): Both species have two loops—one goes through the reproduction of the young life stage the other through the adult one. Species A and B differ in the relative importance of loops in their lifecycle. The main loop of species A was impacted by the treatment; for species B only, the loop with lower importance for population growth rate was impacted by the treatment (Figure 4). Importance of loops is determined by the sum of elasticities of their transitions, where elasticities are measures which describe how proportional change (proportional perturbation) of transitions in matrix population model changes population growth rate (or other population characteristic). Elasticities sum to 1—species A has elasticity of the young loop 0.16 and of the adult loop 0.84, and for species B, these are 0.69 and 0.31 respectively.

3 EFFECT OF DEMOGRAPHY—SIMULATED SEED PREDATION IN NON-CLONAL AND CLONAL CLOSELY RELATED HERBS

We now use real matrix projection models to illustrate how the effect of demographic correction can be strong if the loop structure of the life cycle due to the presence of clonal reproduction differs between species and how it modifies the effect of seed reproduction. To illustrate the generality of the problem, we selected several congeneric pairs (as congeneric pairs are often used in experimental ecology) as replicates. We selected all congeneric pairs of clonal and non-clonal species with available projection matrices in COMPADRE database (Salguero-Gómez et al., 2015; with amendments done by Janovský & Herben, 2020). The congeners Saxifraga aizoides and S. cotyledon were excluded since clonal reproduction has been observed in allegedly non-clonal S. aizoides (Botanical Society of Britain & Ireland, and Biological Records Centre, 2021). For each projection matrix, we computed original population growth rate and population growth rate after 50% reduction of seed production transitions to simulate loss of seeds, for example, by a specialist seed predator. While the reduction of transitions was identical in all species, the population growth rates of all non-clonal plants decrease much more due to the reduction of seed reproduction than population growth rates of clonal plants (Figure 5; however, the decrease in population growth rate was correlated with the original population growth rate which prevents its full separation from the effect of clonality).

In this example, we may observe that the same effect on the individual level (50% reduced seed reproduction) leads to very different effects on population level if the compared species differ in some important life-history traits (clonality in this case). The differences in species’ life history translates into differences in the loop structures of their life cycle and consequently changes in population growth rates.

4 DISCUSSION

Demographic correction is the translation of individual level effects on vital rates into population characteristics (such as population growth rate) using information on species demography (such as matrix projection models). It consists of identification of life stages used to assess individual level effects and transitions in demographic model(s), adjustment of the transitions according to estimated relative individual level effects and finally the calculation of changes of population characteristics caused by the adjustment (Box 1).

The considerable effect of demographic correction in our fictitious example might seem unlikely since the difference between the species in early (young) reproduction is unnaturally large but is inevitable when vital rates differ across species (Figure S1). Comparison of reduced sexual reproduction in clonal and non-clonal plants using published demographic models is one such example (Figure 5). We can expect an analogous effect to these examples virtually in all cases when studied species differ in the importance of impacted transitions for the population growth rate (i.e. when they differ in elasticity of population growth rate of these transitions; Caswell, 2006; but see Carslake et al., 2008). Consequently, interpretation of any individual-derived data requires demographic correction which uses population projection matrix to translate the observed effects into changes in meaningful population characteristics (such as population growth rate) in order to make a valid conclusion about the population response to the studied treatment (Figure 1). This applies to species comparisons as well as studies on one species.

A major difficulty of application of demographic correction is the limited number of plant species with studied demography, but the number is steadily rising (Salguero-Gómez et al., 2015). The low number of species studied for demography is mainly due to laborious and time-demanding data collection. We would like to point out that phylogenetic information was quite as rare at the time as when Felsenstein pointed out its importance in analyses (Felsenstein, 1985). As with phylogenetic information, a solution is to gather demography for species selected for the study. If there is no available demographic data and we cannot obtain it ourselves, it could still be in principle (as reliable methods have not been developed yet) estimated based on functionally similar species (if we have independent information for the estimation; Salguero-Gómez, 2017; but see: Che-Castaldo et al., 2018). Thus, we can end up with more or less accurate estimation of demography of populations about which we want to make inference.

Even if demographic information is available, it might not be usable for demographic correction. Proposed demographic correction assumes that used population model is an appropriate model for control plants in the experiment. Since life histories of species are known to depend on conditions in which the species live (Ballinger, 1979; Ehrlén et al., 2005), collection of demographic information directly for plants used in the experiment is advisable (when collected for all studied conditions life table response experiment analyses can be used; Caswell, 1989, 2019). When this is not possible and published demographic information is used instead, control for conditions in which it had been collected and quality should be done (preferably using primary sources since database information might lack in detail or contain transcription mistakes; Janovský & Herben, 2020; Kendall et al., 2019). Furthermore, demographic correction includes identification of transitions in the demographic model with life stages (and their responses) of individuals in the experiment. We recommend measuring in the experiment those variables which were used for classification of stages in demographic model(s) used for the correction. Still identification of those transitions will often be non-trivial. Studied treatment would often influence more than one transition in the demographic model and responses of vital rates to the conditions can differ compensating one for the other (Villellas et al., 2015). Finally, importance of life stages also differ in growing and declining populations where reproduction was shown to be important for population growth in growing populations while it was survival in the declining ones (Oostermeijer et al., 1996). As in our example where non-clonal plants had generally larger population growth rate and larger effect of reduction of reproduction than clonal plants (Figure 5), this might lead to correlation between studied effect and population growth rate—complicating separation of both. Therefore, available demographic information will in many cases be only approximate leading to only approximate correction or only to the assessment of how sensitive are the results to the choice of fitness measure. Still we strongly believe that demographic correction with such information is better than none as it is the case with incomplete phylogenetic information in phylogenetic comparative analysis (Freckleton et al., 2002). Especially since groups with very different demography are often compared.

Results of proposed demographic correction can be further enhanced by existing demographic tools. First, when primary data used for the construction of demographic models are available, bootstrap methods have been described for the estimation of confidence intervals of population growth rate (Caswell, 1989) by resampling individuals and repeated calculation of population growth rate. In such case, fate of these individuals can be altered by the same change as done in the demographic correction to compute the confidence intervals of the population growth rate under studied conditions. Second, sensitivity analysis can be used to get better insight into which changes of demographic model influence population growth rate and how much. When the changes of demographic model are substantial, sensitivity and elasticity measures (of population growth rate to changes in matrix projection model) might not be sufficient and nonlinear analyses would be necessary (Carslake et al., 2008).

5 CONCLUSION

We have illustrated the potentially large effect of omitting demography in comparative experimental studies and showed that it can lead to erroneous conclusions about relative effect of environmental factors on populations of these species. We propose ‘demographic correction’ as a concept and as a tool to deal with this problem. Adjustment of transition(s) of population projection matrices according to the changes induced by the experimental treatments is a way to make justifiable inference from single-life stage experiments to whole populations. We see this approach as a way how to synthesise the field data on species’ demography and life cycle with the results of manipulative experiments in controlled conditions to gain more insight into the ecology of plants.

CONFLICT OF INTEREST

The authors declare they have no conflicts of interest.

AUTHORS' CONTRIBUTIONS

A.K., J.K. and Z.J. conceived the research; A.K. designed the analysis and wrote the manuscript with contributions of all other authors.