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Population Biology |
2Niwot Ridge Long-Term Ecological Research Program, University of Colorado, Boulder, Colorado 80309 USA; 3Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, California 95064 USA
Received for publication November 13, 2003. Accepted for publication March 20, 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Key Words: demography • elasticity • life history • longevity • matrix model • perennial • seedling • trade-off
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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). Organisms must allocate limited resources to competing functions in order to maximize lifetime reproductive value (Williams, 1966
), an individual's lifetime contribution to population growth. The resulting trade-offs between life history functions include a positive correlation between fecundity and adult mortality (Charnov, 1991
). This trade-off may be the result of two related phenomena: (1) limitations on reproduction due to physiological costs of survival and/or (2) the necessity to evolve high survival rates in environments where fecundity is low.
The extent to which the strength and form of trade-offs are shaped by environmental differences is a general question in population ecology (Rees, 1994
; Pfister, 1998
; Heppell et al., 2000
). If physiological limitations determine these trade-offs, the relationship between reproductive success and survival may be strongly altered in different environments, potentially resulting in weak correlations and a pattern in which trade-offs in some environments lie off the expected curve. Alternatively, if life history correlations primarily result from the necessity to maintain population growth, or at least stability, then one would predict that the fecundity/survival correlation should lie on a single trade-off curve in all environments. Here we examine these two alternatives in the context of alpine plant recruitment and longevity.
Alpine tundra plant communities are dominated by long-lived perennials (Billings and Mooney, 1968
), a life history that is predicted to feature low fecundities and rates of offspring survival (Silvertown et al., 1993
). Having high longevity is one strategy that allows persistence in an environment with high interannual climate variation (Morris and Doak, 1998
). This strategy has likely evolved in alpine plant species because the climate is unfavorable for sexual reproduction in a high proportion of years (Bell and Bliss, 1980
). Some studies have shown that tundra seedlings are abundant at times (Söyrinki, 1938
; Forbis, 2003
) and that seedling survival rates fall within the range for perennial species of other habitats (Forbis, 2003
) but the demographic importance of seedling establishment in tundra plant life histories is still largely undetermined. Therefore, it is not clear how important a role fecundity and seedling survival play in the persistence of alpine plant populations.
We examined two long-lived nonclonal alpine fellfield species, Paronychia pulvinata Gray, and Minuartia obtusiloba (Rydb.) House, to determine (1) the role of recruitment in alpine plant population dynamics and (2) whether the fecundity/mortality trade-off for these two alpine species follows the same relationship as that seen in perennial species from other ecosystems or whether the trade-off is particularly strong for these alpine plants. If the fecundity/mortality trade-off for our focal species deviates from this general trade-off curve, it would lend support to the theory that the alpine environment plays a unique role in shaping plant life histories.
To address these questions, we used static data on population size distributions for Minuartia and Paronychia in combination with detailed demographic data on recruitment and seedling survival probabilities to estimate size-based population projection matrices and elasticity values. Elasticities are a useful tool for determining which demographic rates are most important for the growth or persistence of a population, because the elasticity (eij) of a matrix element aij (where aij is the probability of a transition from stage j to stage i over one time step) is a measure of the relative contribution of that element to 
, the annual population growth rate (de Kroon et al., 1986
). Using seedling establishment elasticities allowed us to determine the importance of recruitment in maintaining alpine plant populations. Using these elasticities in combination with longevity calculations also allowed us to test the alternative hypotheses that alpine plants lie on or off of the expected fecundity/mortality trade-off curve.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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).
Both species studied here, Paronychia pulvinata and Minuartia obtusiloba, are in the Caryophyllaceae and both are caespitose, perennial herbs with branched, woody caudices. In both species, each branch terminates in an apical meristem surrounded by a rosette of leaves. Therefore, cushions are made up of many rosettes. Both species lack mechanisms for vegetative reproduction and rely entirely on sexual reproduction for population maintenance. Because both are cushion-forming, their size can be accurately measured as a two-dimensional area (Morris and Doak, 1998
).
Seedling censuses and measurements of population structure
Germination and seedling survival were measured in a single 1-m2 plot at each of the three sites. Germination and survival were censused at 2–3 wk intervals from snowmelt through snowfall. New cohorts were marked in each of three years (1998 through 2000), and survival was censused for four years (1998 through 2001).
In 2001, by searching expanding areas until 100 individuals were located (range of search = 1.5–7.6 m2 per site), we measured the size of these 100 individuals of each species at each of the three sites. Seedlings were not included because seedling survival is lower than adult survival and contributes to the low probability of detecting seedlings in a one-time census. Instead, seedling data were based on the repeated censuses described above. To minimize measurement error for small plants, we counted rosette number for plants with 20 or fewer rosettes and then converted these counts to sizes using species-specific mean rosette sizes. One-rosette plants were distinguished from seedlings by the absence of cotyledons, which both species retain through their first growing season. For larger plants, an outline was drawn and digitized. Percentage of dead area for each cushion was subtracted from the total area.
Estimation of population matrices and elasticity values
To determine whether size distributions differed significantly between plots or species, we used two-sample Kolmogorov-Smirnov (K-S) tests (Sokal and Rohlf, 1995
). Because there were not significant differences between most plots (K-S, P < 0.05 for five of 15 possible species–plot combinations), further analyses do not consider plots separately.
Construction of a demographic matrix model requires estimates of age- or size-dependent fecundity, survival, growth, and shrinkage probabilities for all life stages. To estimate fecundity, we assumed a linear relationship between plant size and seed production, estimating the number of new seedlings produced per square centimeter of adult plant by dividing average seedling density by average area covered by adult plants for each species (Table 1). This is an untested assumption. However, fecundity values were extremely low and did not make a large contribution to so this assumption is unlikely to affect our model significantly. We used the repeated seedling survey data, in combination with Kendall's (1998)
method to account for sampling variation, to estimate mean seedling and one-rosette survival rates.
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). In contrast, we used maximum likelihood fitting to infer the growth, shrinkage, and survival probabilities of larger size classes. The basic approach used to make these estimates is to match the predicted size distribution of a population matrix with the observed population size distributions seen in the field. To merge our data on seedling numbers with the observed population size structure of larger plants, we used area-adjusted estimates of seedling numbers with all data on adult sizes to generate a single size distribution (Table 1). The growth, shrinkage, and survival rates that, when included in a matrix model, yield the best prediction of the observed size distribution of plants are judged as the best estimates of these rates. Because we have only a single population size distribution, we estimate only a single deterministic matrix model for each species.
To construct a matrix model and estimate these vital rates, we first divided the populations into nine size classes following Morris and Doak's (1998)
classification for Alaskan populations of another alpine cushion plant in the Caryophyllaceae, Silene acaulis. Rather than estimate separate rates for each class, we fit size-dependent functions for the probabilities of survival (s) and of growth (g) and shrinkage (h) to adjacent size classes as logistic functions (Doak and Morris, 1999
):
 | (1) |
To quantify how well a model constructed using particular parameter values predicted the observed size distribution, we calculated the likelihood of seeing the observed distribution, given the predicted stable stage distribution from the model, using the formula for multinomial probabilities (see Doak and Morris, 1999
, and Monson et al., 2000
, for details of this calculation). For each species, we searched for the parameter values that yielded the best (maximum likelihood) prediction of observed population size distribution. In making these fits, we initially constrained parameter combinations to those predicting between 0.99 and 1.01, but found that model fits did not differ when these constraints were removed, indicating that observed values did not differ from one. We show results only for the described logistic function; a wide range of other model forms, including quadratic effects of size in logistic and linear equations, were all less supported by the data (Akaike Information Criterion results not shown). Elasticity matrices were calculated from the resulting population matrices using Matlab code from Morris and Doak (2002
, pp. 223, 335; "eigenall" and "vitalsens").
Comparison with other species
To compare our focal species with other perennials, we searched the literature for demographic studies of perennial forbs that included a seedling stage and either presented elasticities or allowed for their calculation. For each species, we summed elasticity values that contribute to reproduction (fecundities and germination; efecundity). The sum of efecundity and the elasticity of seedling survival (esdlsurv) provided seedling establishment elasticity (esdlest). We used this elasticity value to answer the two general questions presented in this paper: what is the relative importance of recruitment in alpine plant populations; and do these two alpine species follow the general fecundity/survival trade-off pattern set by other species?
We chose to use seedling establishment elasticity rather than using raw demographic values because the selective forces that create the trade-offs of interest are better represented by elasticities than by separate demographic rates. Most of the commonly accepted correlations between pairs of traits are only one of many ways to "solve" the same ecological problem, while life history theory rests on the concept of fitness as the product of processes occurring across all life history stages (Charnov, 1997
). The strength to which fitness is correlated with, or influenced by, any particular demographic rate is properly measured by its elasticity rather than raw demographic values, because elasticities account for effects across the entire life cycle. Additionally, the esdlest parameter incorporates several traits that contribute to recruitment— reproductive effort, reproductive output, seed bank, germination, and seedling survival. Viewing these reproductive traits as part of an integrated life history rather than in isolation allows us to look at the overall contribution of recruitment to population persistence in these species.
To estimate individual longevity, we used a starting vector consisting of one seedling and zero adults and multiplying this vector by each species' matrix with all fecundities set to zero (Caswell, 2001
). Matrices were iteratively multiplied by the resulting population vectors until the summed probability of survival for all age classes reached 0.01, providing a consistent measure of maximum longevity.
To date, the most comprehensive efforts to determine whether proposed life history trade-offs exist in plants have tested for negative correlations between elasticities (Silvertown et al., 1993
; Franco and Silvertown, 1996
). However, Shea et al. (1994)
pointed out that elasticities sum to one by definition; therefore, this system assumes trade-offs by default. Analyses of simulated data sets have shown that even attempts to deal with intercorrelations by using randomization tests find spurious negative correlations between most elements of the elasticity matrices (Shea et al., 1994
). Therefore, to ask whether the relationship between seedling establishment elasticity and longevity in Minuartia and Paronychia differs from the relationship seen in other herbaceous perennials, we performed a linear regression of esdlest on raw longevities for our focal species in combination with the species from the literature (both variables were first log-transformed).
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RESULTS |
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Elasticity values, longevities, and comparisons
Elasticity matrices for the two species were similar (Table 2). Both had the highest elasticity values (e) for stasis (survival without growth) of intermediate classes. For Minuartia, elasticity of stasis of individuals in stages 4–7 ranged from 0.1839 to 0.2993. For Paronychia, elasticity of stasis of individuals in stages 4–8 ranged from 0.1244 through 0.2430. Conversely, both species had low elasticity values for fecundities, most growth elements, and survival of individuals in the largest size class. Minuartia had the lowest elasticity values for the fecundity of individuals in classes 3, 4, 8, and 9 and for growth out of class 8. Paronychia had its lowest elasticity values for fecundities in classes 3, 4, and 9 and growth out of class 8 (Table 3).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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). That said, these species are very similar to one another when compared with other perennials—their esdlest values are within 0.001 of one another, and their life spans are well beyond the range of most other plant species surveyed.
The emphasis on stasis in our models suggests that if we were to measure growth and survival of adults over four years we would see little change in populations of Minuartia and Paronychia on Niwot Ridge. Therefore, the use of size distributions to indirectly estimate vital rates is a reasonable approach in this case. The incorporation of adult size distributions and four years of seedling establishment data into a single model might also serve to buffer high expected interannual variability in alpine seedling recruitment due to high interannual variability in seed output (Arft et al., 1999
), viability (Chambers, 1989
), and survival (Forbis, 2003
).
Importance of recruitment
As expected, values of esdlest were lower for Minuartia and Paronychia than for virtually all other species from our literature survey. For at least these two alpine species, reproduction and the seedling stage contribute only a small part of the annual population change, which seems counterintuitive given the fact that these two species rely entirely on seedling establishment for recruitment. However, the esdlest values make sense in the context of reproductive value. The probability that a seedling will survive the many decades required to reach sexual maturity is low, whereas the probability that an established adult will contribute to future generations is high (Table 3).
Our results for esdlest are similar to those for Alaskan Silene acaulis (Morris and Doak, 1998
; Table 4), but due to the wide variation in life histories among alpine plants, our results on esdlest in these two species are not directly transferable to other high-elevation species. In the above-treeline grass-shrub paramos of the Andes, Espeletia timotensis and E. spicata (Silva et al., 2000
) have higher esdlest (Table 4) and values (1.24 and 1.13, respectively) than Minuartia ( = 1) and Paronychia ( = 1). Both the greater importance of young life stages and rapid population growth rates show that these paramo species have a faster life history than do our alpine cushions.
Fecundity/mortality trade-off
Using esdlest and longevity, we asked whether the extremity of the alpine environment causes the fecundity/mortality trade-off for alpine plants to fall on or off of the trade-off curve set by other perennial plant species. Our regression results showed that the relationship between seedling establishment and longevity for Minuartia and Paronychia is consistent with relationships seen for all other species in Table 4 (Fig. 3). These two alpine species are not outliers with regard to the fecundity/mortality trade-off. Therefore, seedling establishment patterns for these two species are concordant with what would be predicted for any extremely long-lived species, and the alpine environment itself is not disproportionately affecting survival dynamics.
It is worth mentioning that while most species from this data set fit well along this curve, there are a few species with short life spans whose seedling establishment elasticities fall outside the confidence intervals (although they were not outliers). Of the three species that fall below the lower confidence limit, two (Calathea ovandensis and Potentilla anserina) reproduce asexually. The occurrence of clonal reproduction might be another important predictor of the fecundity/longevity trade-off, and it might be more appropriate to develop separate trade-off curves for clonal and nonclonal species. Another reproductive life history trait, the formation of long-lived seed banks, was not considered here. Due to its potential to strongly influence population longevity, it doubtless plays a role. While seed dormancy does correlate with other life history traits, these relationships are generally quite weak (Rees, 1993
; Doak et al., 2002
).
Our data indicate that these two cushion pink species live for centuries in the alpine fellfields of Niwot Ridge. Comparison with other studies indicates that Minuartia and Paronychia are among the longest-lived forbs whose longevity has been estimated. Ehrlén and Lehtilä (2002)
estimated longevities of 71 perennial plant species; their highest estimate for any herbaceous species was Silene acaulis at 337.16 yr. Our estimates of up to 324 yr for Paronychia and 200 yr for Minuartia place them among the longest-lived herbaceous plants known.
The life history strategy seen in Minuartia and Paronychia is likely the product of a history of selection in an environment with wide, random interannual climate variation and the inability to reach reproductive sizes quickly. In environments where juvenile mortality can be high, a long life with repeated episodes of reproduction is predicted (Charnov and Shaffer, 1973
).
Previous results (Forbis, 2003
) have shown that many alpine plant species have per capita recruitment rates and seedling survival rates similar to those of perennial plants from other environments. This study has shown that the importance of seedling establishment to population maintenance in two particularly long-lived alpine species is lower than in other perennial species. However, when longevity is taken into account, these two alpine species do not differ from other perennials in their seedling survival probabilities. This result indicates that while the alpine environment can strongly shape life history, it does not appear to alter the shape or strength of general life history trade-offs.
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FOOTNOTES |
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4 Current address: The Nature Conservancy, P.O. Box 150266, Ely, Nevada 89315 USA (E-mail: tforbis{at}tnc.org
)
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LITERATURE CITED |
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