LINEA BASE

In reviewing population projection matrices from published studies, we realized that shrinkage is likely to be even more common than it is currently reported due to limitations in methodological procedures used in the collection of field data, construction of matrix models and interpretation of their outputs. Here we identify such limitations and suggest ways to circumvent them (Table VI.1).

Collection of field data

The low temporal and spatial replication typical of field studies may not accurately capture demographic traits, especially considering the great potential for

phenotypic plasticity among sites (Morris & Doak 2005). The studies collected in COMPADRE II show low spatial (2.74 ± 0.27 [S.E.] sites) and temporal replications (4.48 ± 0.27 years). The issue is that poor replication may not satisfactorily describe shrinkage –or any other demographic process– if that process results from temporal and spatial environmental fluctuations or if the process is naturally rare, e.g. masting. The implications are far reaching since comparative demographic research assumes that the characteristics of a species observed in a few populations or in a few census periods are representative of that species as a distinct unit (Silvertown, Franco & McConway 1992; Franco & Silvertown 2004). Shrinkage may occur frequently in some populations, but not in others (Jongejans et al. 2010) and vary spatially even within the same population. For instance, in arid land patches of vegetation, the dynamics of Hilaria mutica are

dominated by stasis and shrinkage both in the center and periphery of the patch, but in years of high precipitation, growth and reproduction become more important in the periphery while the center’s dynamics do not change (Vega & Montana 2004).

We cannot emphasize enough the importance of following multiple sites for the same species simultaneously for as long as possibly sustained by available funding. Importantly, many herbaceous perennial species have life spans as long as or longer than the researcher investigating them (e.g., Borderea pyrenaica = 100-300 years, fig. VI.1.a, García & Antor 1995; Silene acaulis >300 years, fig. VI.1.b, Morris & Doak 2005), and so studying their populations for 4-5 years may not be tremendously informative. We know of only a handful of on-going, long-term studies with herbaceous perennials (e.g. Carduus nutans, de Kroon; Dicerandra frutescens and Eryngium cuneifolium, E. Menges; Frasera speciosa, D. Inouye; Plantago lanceolata, D. Roach; Trillium

that the low number of species with long-term demographic data limits our current understanding of processes that may correlate with age, such as senescence. Senescence is of particular interest here because shrinkage may be a consequence (Salguero-Gómez & Casper 2010; chapter IV).

Multiple censuses per year would also help us understand the causes of shrinkage, when it occurs, by providing information on the demographic fates of shoot apical

meristems over an annual cycle. Are plants smaller when they begin growth than they were the preceding year or does shrinkage occur during the growing season? Is plant size reduced following a year of heavy investment in reproduction or due to the death of semelparous meristems—when apical vegetative meristems are converted to flowering meristems? Does shrinkage coincide with or follow adverse environmental conditions? A multi-seasonal sampling effort would help narrow down these possibilities and

underlying environmental factors. Most demographic censuses of perennial species in COMPADRE II were carried out on annual visits to the field, coinciding with the flowering peak and resulting in annual projection matrices, which may not offer the temporal resolution needed to understand the role of shrinkage in the life cycle of the species.

The inclusion of seasonal demography in perennial studies is feasible. For instance, Goodman matrices (Le Corff & Horvitz 2005) can be used to incorporate seasonal sub-matrices into a larger annual matrix. In addition, periodic projection matrices, a standard tool in annual and biennial plant demography (Caswell & Trevisan 1994), can model seasonal dynamics in a battery of matrices that, when back-multiplied, generates the annual projection matrix. Both tools allow for the same eigen-analyses

employed for annual projection matrices (Ramula, Rees & Buckley 2008; Bacaer 2009). Nonetheless, we know of only three cases in which periodic matrices have been

employed in long-lived herbaceous species; these reveal different seasonal timings of shrinkage, and suggest different underlying mechanisms: during spring in Taraxacum officinale (Vavrek, McGraw & Yang 1997), in late winter in Lobularia maritima (Picó, de Kroon & Retana 2002) and both during the growing and during the dormant seasons in Cryptantha flava (Salguero-Gómez & Casper, unpublished).

But perhaps the most important field-based limitation to the true understanding of the effect of size on plant fitness in demographic studies, and the role of shrinkage in such a relationship, is how size is measured. Size-based matrix models vary a great deal in the state variable that is measured in the field and consequently used in the matrix models: number of tillers (Guardia, Raventos & Caswell2000), shoot height (Fröborg & Eriksson 2003), total leaf area (Fiedler 1985), height (Olmsted & Alvarez-Buylla 1995), stem length (Esparza-Olguin 2005), rhizome diameter (Pino, Sans & Masalles1998), tuft circumference or area (O’Connor 1993), number of rosettes (Lucas, Forseth & Casper 2008), trunk diameter in trees, making inter-specific demographic comparisons tricky. That no annual species in our database exhibits shrinkage is not surprising, since their optimal life history strategy is to maximize fecundity, not survival. However, we would expect shrinkage to be more frequent in larger, longer-lived growth forms, such as trees and palms, a hypothesis that is not supported by our results when compared to

intermediate growth forms like herbaceous perennials and succulents.

We think the problem lies in how woody plants are typically measured. Tree and palm demography is typically based on DBH (diameter at breast height; Zuidema et al.