Received: 17 November 2020 | Revised: 13 January 2021 | Accepted: 25 January 2021 DOI: 10.1002/ece3.7291 REVIEW Measuring temporal patterns in ecology: The case of mast seeding Marcos Fernández-­Martínez1 | Josep Peñuelas2,3 1 PLECO (Plants and Ecosystems), Department of Biology, University of Abstract Antwerp, Wilrijk, Belgium 1. Properly assessing temporal patterns is a central issue in ecology in order to un- 2 CSIC, Global Ecology Unit, CREAF-­C SIC-­ derstand ecosystem processes and their mechanisms. Mast seeding has tradition- UAB, Bellaterra, Barcelona, Spain 3 CREAF, Bellaterra, Barcelona, Spain ally been described as a reproductive behavior consisting of highly variable and synchronized reproductive events. The most common metric used to measure Correspondence Marcos Fernández-­Martínez, PLECO (Plants temporal variability and thus infer masting behavior, the coefficient of variation and Ecosystems), Department of Biology, (CV), however, has been repeatedly suggested to improperly estimate temporal University of Antwerp, 2610 Wilrijk, Belgium. variability. Biases of CV estimates are especially problematic for non-­normally dis- Email: marcos.fernandez-martinez@ tributed data and/or data sets with a high number of zeros. uantwerpen.be 2. Some recent studies have already adopted new metrics to measure temporal vari- Funding information ability, but most continue to use CV. This controversy has started a strong debate Fonds Wetenschappelijk Onderzoek about what metrics to use. 3. We here summarize the problems of CV when assessing temporal variability, par- ticularly across data sets containing a large number of zeros, and highlight the benefits of using other metrics of temporal variability, such as proportional vari- ability (PV) and consecutive disparity (D). We also suggest a new way to look at reproductive behavior, by separating temporal variability from frequency of re- production, to allow better comparison of data sets with different characteristics. 4. We suggest future studies to properly describe the temporal patterns in fully sci- entific and measurable terms that do not lead to confusion, such as variability and frequency of reproduction, using robust and fully comparable metrics. KEYWORDS disparity, frequency, reproduction, seeds, stability, synchrony, variability 1 | I NTRO D U C TI O N is crucial, is not an exception. Mast seeding, or masting, has tradi- tionally been described as a reproductive phenomenon consisting How to accurately describe temporal patterns in ecological pro- of the highly variable and synchronized production of seeds at the cesses has been a long-­standing question in ecology (McCann, 2000). population scale (Kelly, 1994; Pearse et al., 2016; Silvertown, 1980). Metrics to estimate stability, temporal variability, and resilience are, The use of the term “masting,” or describing a species or population actually, still under intense debate (Arnoldi et al., 2016). The field of as following a masting behavior, however, is sometimes confusing, masting, for which assessing temporal patterns of seed production arbitrary, or insufficiently accurate in the scientific literature to be This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd. 2990 |  www.ecolevol.org Ecology and Evolution. 2021;11:2990–2996. FERNÁNDEZ-­MARTÍNEZ and PEÑUELAS | 2991 fully accepted as a scientific term (Kelly, 1994). One study even sug- gested that perpetuating the concept of masting in the scientific lit- erature had no objective basis (Herrera et al., 1998). The concept has nonetheless recently received much attention from the scien- tific community leading to many new papers, focused on many dif- ferent aspects and especially on why highly variable reproduction occurs (Ascoli et al., 2017; Bogdziewicz, Ascoli, et al., 2020; Pearse et al., 2017; Vacchiano et al., 2018; Wion et al., 2019), because of the multiple consequences that highly variable reproduction produce in ecosystems, such as cascading effects on food webs (Bogdziewicz et al., 2016; Clotfelter et al., 2007). Clarification of what should be called masting and what should not, however, has received little attention. More important, though, is how we measure the repro- ductive behavior of organisms (plants or others) independent of ar- bitrary considerations of them being masting or nonmasting species. To fulfill that aim, we need robust metrics that allow adequate com- parisons among species, populations, and individuals. Those metrics still remain under intensive debate in the field of masting, a debate from which many other fields could benefit. Based on previous liter- ature on temporal variability metrics, we here provide some discus- sion and insights for analyzing time series of reproductive efforts that may help the field establish new and standardized protocols to study and properly measure the reproductive behavior of organisms. 2 | M E A S U R I N G TE M P O R A L R E PRO D U C TI V E B E H AV I O R Three main features have traditionally been used to describe mast- ing: (a) temporal variability of reproductive events (at different levels of organization, e.g., population, individual) most commonly measured using the coefficient of variation (CV = standard devia- tion · mean−1) (Kelly & Sork, 2002), (b) synchrony, often calculated among individuals within a population as the average Pearson's or Spearman's correlation coefficient among all pairwise compari- sons (Koenig & Knops, 2013), and (c) temporal autocorrelation, F I G U R E 1 Temporal variability and synchrony among measured with autocorrelation coefficients, as an indication of po- individuals within a population. Relationship between the temporal tential resource depletion (correlation of each value with the previ- variability of reproduction (100 years) at the population level as a function of the synchrony among individuals (500) for three ous, lag 1) (Fernández-­Martínez et al., 2019; Pearse et al., 2016) or levels of variability. Panels (a), (b), and (c) show results using internal cycles of reproduction or resource mobilization (lags > 1) the proportional variability (PV), consecutive disparity (D), and (Fernández-­Martínez et al., 2012; Sork et al., 1993). The intrinsic coefficient of variation (CV) indices, respectively. The shaded area link between the temporal variability of reproductive efforts of a represents the standard error of the regression line. The code for population and the average synchrony in reproduction in a popu- performing the simulation is available in Supplementary Materials lation (Buonaccorsi et al., 2003; Herrera, 1998), however, is often overlooked (Figure 1). A strong synchrony among individuals is thus required for a population to have highly variable reproduc- variable reproduction at the population level can only occur at tion, because temporal asynchrony among individuals would lead high levels of synchrony. This mathematical property has implica- to a more constant reproduction over a population. This mecha- tions for the traditional definition of masting; “highly variable and nism is actually one of the foundations of the positive relation- synchronous reproduction at the population level” is therefore a ship between diversity, productivity, and stability in ecosystems redundant definition to some degree. Analyzing temporal variabil- (Cardinale et al., 2012; Tilman & Downing, 1994). While high syn- ity and synchrony separately can nonetheless still provide relevant chrony in reproduction can be found in populations with high and information, which is not under debate. Using temporal autocor- low temporal variability, in a hypothetical stationary state, highly relation to study reproductive behavior is also not controversial. 2992 | FERNÁNDEZ-­MARTÍNEZ and PEÑUELAS How to measure temporal variability, which is the most widely where “n” is the length of a time series, and “z” the individual values to used feature for studying the causes and consequences of repro- calculate the pairwise comparisons. Further, we rediscovered the con- ductive behavior of plants, is currently strongly debated. secutive disparity (D) index (Martín-­Vide, 1986) used for decades in the field of climatology but never used in biology. D can be estimated as: 3 | TE M P O R A L VA R I A B I LIT Y: W H Y W E n−1 1 ∑ || pi+1 || D= ln N E E D A LTE R N ATI V E M E A S U R E S TO C V n − 1 i = 1 || pi || The use of CV as a measure of temporal variability has been de- where pi is the value of the time series at time i and n is length of the bated for decades in various fields of science and even in mast- time series. To summarize, PV assesses the proportional difference ing literature itself (Crone et al., 2011; Fernández-­ Martínez between all pairs of values within a time series, while D assesses the et al., 2018; Heath, 2006; Martín-­V ide, 1986; McArdle & proportional differences between consecutive values. Both PV and Gaston, 1995; Mcardle et al., 1990). Computer simulations and D overcome the mathematical problems of CV (Fernández-­Martínez heterogeneous data sets have recently been used to test the re- et al., 2018; Heath, 2006; Heath & Borowski, 2013) and provide clear sponse of CV under different conditions (Fernández-­ Martínez advantages over the traditional CV for comparing data sets with differ- et al., 2018; Heath, 2006; Heath & Borowski, 2013). The results ent statistical properties. The main benefits of PV and D over CV are supported previous concerns about the adequacy of using CVs summarized in Table 1. D is also particularly useful in masting studies, to assess differences in temporal variability across data sets, be- because it combines information about variability and temporal auto- cause estimates of CV (a) depend strongly on the mean of the time correlation with the previous year, variability by which plant resources series, (b) increase with the length of the time series, (c) are bi- and populations of seed predators and dispersers should be most af- ased when non-­n ormally distributed data sets are used, and (d) fected (Espelta et al., 2008, 2017; Sala et al., 2012). CV, however, is present a pathological behavior when rare events occur in a time easily tractable in an analytical way because it is based on the variance series. Heath developed the proportional variability (PV) index and the mean of a set of values. That has allowed it to become the basis (Heath, 2006) to try to solve these problems, defined as: of most theories describing temporal variability. Crone et al. (2011) had already warned the masting commu- ∑ 2 z nity about the potential of CV to be a poor metric for measuring PV = n(n − 1) the temporal variability of reproductive efforts and that interpret- ing CV should be considered in context. To date, only a few studies where z is analyzed their data sets using D or PV (Bogdziewicz, Fernández-­ Martínez, et al., 2020; Fernández-­Martínez et al., 2017, 2019; Koenig ( ) min zi , zj et al., 2020; Pesendorfer et al., 2020; Vergotti et al., 2019) after our z=1− ( ) max zi , zj first warning about the problems linked to using CV for masting was TA B L E 1 Summary of the PV D CV mathematical and statistical benefits of Equal range for Yes No No the indices of proportional variability (PV) comparison across data and consecutive disparity (D) over the sets coefficient of variation (CV) Chronology of the time No Yes No series matters Robust estimates when Yes Yes No comparing data sets Negatively correlated with the mean with very different means Robust estimates when Yes Yes No comparing data sets of Positively correlated with the size different sizes Robust estimates across Yes Yes No non-­normally distributed Pathological increase with rare events data sets Detects high number of Yes Yes No zeros as low variability Highest values at highest percentage of (Figure 2) zeros Note: Properties of the indices are based on (Fernández-­Martínez et al., 2018; Heath, 2006; Heath & Borowski, 2013) and our results. FERNÁNDEZ-­MARTÍNEZ and PEÑUELAS | 2993 F I G U R E 2 Behavior of (a) proportional variability (PV), (b) consecutive disparity (D), and (c) the coefficient of variation (CV) to increasing variability and the percentage of zeros in a time series. Estimates of variability using PV and D increase with increasing the originally simulated CV (y-­axis) and peak at around 50% of zeros in a time series. Instead, estimates of CV are mainly driven by the percentage of zeros, reaching the highest estimates at >90% of zeros. Notice that the color scale in panel c has been log-­transformed to try to maximize the different response of CV across the proportion of zeros and simulated variability. The code for performing the simulation is available in Supplementary Materials published (Fernández-­Martínez et al., 2018). Ascari et al. (2020) still low, and, thus, it could still be used in order to provide compari- used CV but suggested that new indices should also be used. Most sons with previous studies. Most of the time series of highly vari- authors, however, have not yet been persuaded to use new metrics able reproduction in plants, though, are not normally distributed and have used CV without mentioning problems of comparability (Fernández-­Martínez et al., 2017; Kelly, 1994; Silvertown, 1980). among different data sets. Results based on CV may still be correct, This observation is particularly exacerbated when assessing time but biased results are also possible depending on the characteristics series of individuals instead of populations, for which the percent- of the data sets. age of zeros can dramatically exceed 50% because of an intrinsic Recurrent arguments for maintaining the use of CV are that CV is higher temporal variability at the individual scale (Bogdziewicz, strongly correlated with the proportion of zeros in a time series and Szymkowiak, Calama, et al., 2020). CVs would then be measuring that masting is about skipping reproductive attempts (see the hypoth- temporal variability for individuals with a low proportion of zeros, esis of predator satiation (Espelta et al., 2008; Kelly & Sork, 2002)), but for individuals with a large percentage of zero values CVs would for which the correlation between CV and zeros could be desirable only be measuring zeros (i.e., frequency of reproduction, and not its (but implies that variability and frequency of reproduction is con- temporal variability). These comparisons using CVs are therefore founded). The statement that CV is strongly correlated with the per- unreliable and conceptually misleading, because two different, and centage of zeros is essentially correct (Figure 2), but a time series to some degree opposed, processes are involved. We suggest that with most of its values (e.g., 95%) being equal (in this case to zero) we should separate the measurement of temporal variability, using cannot be considered highly variable, which is one of the foundations either PV or D (if the chronological order of the values is important), of masting behavior so far. PV and D thus increase with the variabil- from the frequency of reproduction, easily measured as the percent- ity of a time series, but when time series present approximately more age of reproductive events over a total of observations. Both repro- than 50% of zeros, they relate increasing the percentage of zeros ductive behaviors could thus be estimated for any potential data set with decreasing variability, as one would intuitively think. Most im- without risking biased results nor providing misleading conclusions portantly, the variability of CV across data sets is dangerously driven regarding the variability of the data sets. by the percentage of zeros (i.e., frequency of reproduction) rather than by differences in variability across the data sets. That should preclude the use of an index that is supposed to measure variability, 4 | S H O U LD W E TH U S R E D E FI N E at least when the percentage of zeros is large. Hence, CV may not M A S TI N G ? only not have any mathematical advantage over PV or D but it also has the drawback of misleadingly interpreting a large number of equal We probably should. Our suggestion would lead to a scenario in values as high variability. Any conclusion drawn regarding variability which we would be able to describe the temporal behavior of re- based on the use of CV on a data set with a large number of zeros productive efforts based on Figure 3: (a) from temporally variable to should, therefore, be very carefully addressed. stable reproduction and (b) from frequent to occasional reproduc- CV, however, correlates well with PV and D when time series tion in iteroparous species to single reproductive event in a lifetime are normally distributed, and the proportion of zeros is accordingly (in semelparous species). Full comparability could be achieved across 2994 | FERNÁNDEZ-­MARTÍNEZ and PEÑUELAS F I G U R E 3 Scheme showing different types of reproductive behavior. Reproductive behavior is described as a function of the frequency of no reproduction (or percentage of zeros as in Figure 2, x-­axis) and the temporal variability of reproductive efforts (y-­axis, relative to maximum temporal variability). Traditionally defined masting behavior would be placed at high levels of temporal variability and between frequent and irregular reproduction. Notice that highly variable data sets are not possible when the frequency of no reproduction is high, because most of the values of the time series are equal (0) any type of organism using PV and the frequency of reproduction to describe reproductive behaviors using purely mathematical because both metrics are restricted to values between 0 and 1 and universally comparable terms such as temporal variability and (Table 1). We could then even establish working thresholds to de- frequency. termine whether a species is likely to have masting behavior, if even deemed necessary. Some authors consider that occasional or ex- AC K N OW L E D G M E N T S tremely infrequent reproduction and low temporal variability equals This research was supported by the Spanish Government project masting (e.g., bamboo flowering once after >60 years (Kitzberger CGL2016-­79835-­P (FERTWARM), the European Research Council et al., 2007), individuals skipping reproduction largely more than Synergy grant ERC-­2013-­726 SyG-­610028 IMBALANCE-­P, and the 50% of the years (Bogdziewicz, Szymkowiak, Calama, et al., 2020; Catalan Government project SGR 2017-­1005. M.F-­M. is a postdoc- Bogdziewicz, Szymkowiak, Tanentzap, et al., 2020)), but that repro- toral fellow of the Research Foundation–­Flanders (FWO). ductive behavior does not match with the current definition of mast- ing because of the mathematical concept of temporal variability. The C O N FL I C T O F I N T E R E S T “masting” community of researchers should definitely try to reach a The authors declare no conflict of interests. consensus and redefine the traditional concept of masting, which is so far based on high temporal variability and synchrony. AU T H O R C O N T R I B U T I O N S From our point of view, and given the current diverse use of the Marcos Fernández-­Martínez: Conceptualization (lead); Formal term, masting is mainly a cultural and arbitrary term, referring to analysis (lead); Funding acquisition (equal); Investigation (equal); some species producing many seeds in some years and very few, or Methodology (lead); Writing-­original draft (lead); Writing-­review none, in others. Temporal variability and frequency of reproduction & editing (equal). Josep Peñuelas: Conceptualization (supporting); follow a continuous gradient across species (Fernández-­Martínez Funding acquisition (equal); Investigation (equal); Methodology et al., 2019; Herrera et al., 1998; Kelly, 1994), so dichotomous clas- (equal); Writing-­original draft (supporting); Writing-­review & editing sifications (i.e., masting species, nonmasting species) do not really (equal). make much sense. We think we should not try to classify species as masting or nonmasting but instead systematically describe their DATA AVA I L A B I L I T Y S TAT E M E N T behavior by (i) the degree of temporal variability and frequency of Data sharing is not applicable to this article as no new data were reproduction, (ii) the synchronicity of reproduction among individ- created or analyzed in this study. The code for performing all simula- uals, and (iii) the degree of dependence between reproduction in tions is available in Supplementary Materials. consecutive years. We, therefore, recommend avoiding the use of the term “masting” in the scientific literature due to the confusion ORCID that it causes and use instead terms defining what we are actually Marcos Fernández-­Martínez https://orcid. studying: variable plant reproduction. Avoiding the use of an am- org/0000-0002-5661-3610 biguous term such as masting will help the scientific community Josep Peñuelas https://orcid.org/0000-0002-7215-0150 FERNÁNDEZ-­MARTÍNEZ and PEÑUELAS | 2995 REFERENCES acorn predation in Mediterranean oak forests. Ecology, 89, 805–­817. https://doi.org/10.1890/07-­0217.1 Arnoldi, J.-­F., Loreau, M., & Haegeman, B. (2016). Resilience, reactivity Fernández-­Martínez, M., Belmonte, J., Maria Espelta, J., & Espelta, J. M. and variability: A mathematical comparison of ecological stabil- (2012). Masting in oaks: Disentangling the effect of flowering phe- ity measures. Journal of Theoretical Biology, 389, 47–­59. https://doi. nology, airborne pollen load and drought. 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