Forest Ecology and Management 134 (2000) 249±256 Structure and population dynamics of Pinus lagunae M.-F. Passini Sara DõÂaz*, Carmen Mercado, Sergio Alvarez-Cardenas Centro de Investigaciones BioloÂgicas del Noroeste, Mar Bermejo No 195, Col. Playa Palo Santa Rita, A.P. 128, La Paz 23000, B.C.S. Mexico Accepted 27 August 1999 Abstract The pinÄon pine, Pinus lagunae, is a species endemic to the pine-oak forest in Sierra de La Laguna Biosphere Reserve, Baja California Sur, Mexico. In four 2500 m2 squares of forest, we recorded the height, crown cover, and basal area of pinÄon pines in 1989, 1992, and 1997. Using dendrochronological techniques, two cores each of 120 selected pines were used to estimate age. A linear model was obtained with the height and the age to estimate the age for each tree of the sampled population. The tree-ring widths were measured to identify mast years. The pine population structure and life tables for each year were compared. There are no differences in the recruitment of the youngest classes among the three years. The stand shows a population with the mode-class of the youngest pines and just few older trees. The light-wave-like age distribution is probably caused by the impact of hurricanes and ®res. More speci®c studies like fecundity analysis, identi®cation of the exact year of disturbances, and the evaluation of seed predators are suggested to gain more knowledge to preserve this rare species. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Pinus lagunae; Baja California Sur; Population structure; Mast years; Life-table 1. Introduction Within the pinÄon pines of Mexico, Pinus lagunae is a species endemic to Baja California Sur (Passini, 1987). It is considered rare (Perry, 1991). This pine is the dominant species in the pine-oak forest in the highest part of the Sierra de La Laguna, an area protected as a Biosphere Reserve (DõÂaz, 1995). The forest has a limited extension, 20 000 ha (Villa-Salas, 1968), and is the only forest in the state of Baja California Sur. Even though some work has been done in the Sierra de La Laguna pine-oak forest (Robert-Passini, 1981; Pinel, 1985; Passini and Pinel, 1987, 1989; DõÂaz and * Corresponding author.: Tel.: ‡52-112-536-33; fax: ‡52-11-25-53-43. E-mail address: sdiaz@cibnor.mx (S. DõÂaz) Arriaga, 1992), studies of the structure and dynamics of the pine population are necessary to provide to the managers of protected areas knowledge of the demographic mechanisms responsible for changes in population size. Demographic analysis for pines, as long-lived species, has to be done with the existing populations (survivors), with varying proportions of young and old individuals. The historical forces that shaped them must be inferred (Floyd, 1986). Population age structure may provide an insight into past and present regeneration (Agren and Zackarisson, 1990). Life tables are used for simplicity because they list, in a concentrated way, birth and death rates for each age or size class in a population (Holla and Knowles, 1988). Furthermore, the life table can show the chance the seedlings will be recruited into the population. The proportion of coniferous seedlings that can be incorporated into a population may vary year by year. 0378-1127/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 1 1 2 7 ( 9 9 ) 0 0 2 6 1 - 3 250 S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 Nevertheless, there are well-de®ned cycles of synchronized, higher seed production, called mast fruiting (Monroy and Trinidad, 1992). With this strategy, trees guarantee their existence during years of low seed production. The cost of reproduction during mast years is the restriction or depression of the capacity of vegetative investment (Lalonde and Roitberg, 1992) and, as a consequence, a narrow tree ring may be formed in the trunk. Our objectives were to (1) examine the stand structure differences of the Pinus lagunae population during three sampled years (2) analyze the survival curves and identify the age classes that suffer the highest mortality, and (3) try to infer the mast year frequency by the analysis of the stand structure and tree-ring widths. 2. Area descriptions The study was done in the Baja California Sur conifer forest at the highest part of the Sierra de La Laguna Biosphere Reserve (Fig. 1). This forest grows between 1800 and 2000 m.a.s.l. The climate corresponds to temperate subhumid in the classi®cation of GarcõÂa and MosinÄo (1968). The mean total annual precipitation in the region for a 15-year period was 762 mm, and has been frequently in¯uenced by the hurricanes and tropical storms during summer. The dry season extends from November to late June, although winter rains do occur. The mean annual temperature is 148C The soils, derived from granite parent rock, are slightly acid (pH from 5 to 7) and have an alluvial-sandy texture. Fig. 1. Location of the pine forest in the highest parts of Sierra de La laguna Biosphere Reserve. S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 The dominant species in the forest are Pinus lagunae, Quercus devia, Arbutus peninsularis, and Nolina beldingii. It also contains many annuals, and shortlived perennial species, like Calliandra peninsularis, Lepechinia hastata, Mimosa xanti, Arracacia brandegeei, and Desmodium prostratum (LeoÂn-de la Luz and DomõÂnguez-Cadena, 1989). 3. Methods Four local pine populations were selected to represent the range of conditions where the species survives. The total area covered by all these was a hectare. At each site, all the individuals were recorded, and their height, crown cover, and diameter were measured. These measurements were recorded in 1989, 1992, and 1997. During 1989, tree cores were taken, with an increment borer, from 120 individuals of different sizes. That samples were mounted and surface smoothed for study. The skeleton-plot technique was used to compare the specimens to each other by pattern matching. The crossdating was used for determining the exact year of formation for each treering (Stokes and Smiley, 1968). The precise measurements of the tree-ring widths were made with a sliding-stage micrometer interfaced to a computer. Standardization transforms the ring widths into a new series of ring indices, by a ®tted curve of the individual tree width series, and dividing each measured ring width by its expected value (Fritz, 1989). The master chronology was obtained by averaging the individual chronologies. The height-frequency distributions were obtained for each year of sampling to compare years. Because the highest densities are present in the smallest categories, we grouped the trees by 20 cm classes in the ®rst meter of height. The rest of the pines were grouped into 2 m classes. To determine tree age, a regression model (age± height) was used (Arriaga et al., 1994). The sizeclasses were transformed to age-classes and the density data were standardized to compare between classes (Krebs, 1989) according to the equation nx ˆ n0x ts =tx ÿ txÿ1 † where nx is standardized frequency; n0 x, the original frequency; ts, standardized interval; tx, time at x age-class. Time-speci®c life tables were constructed with the standardized values. To compare the results with other 251 studies, lx (survivorship) and qx (mortality) were multiplied by 1000 (Wratten and Fry, 1980). The survivorship and mortality curves were obtained for each year sampled. To determine if the age-class densities differed among the 3 years sampled, the densities were compared using an ANOVA. To ®nd some evidence of mast years, the height distribution was analyzed graphically and the chronology was analyzed by Fourier analysis to look for recurring frequency. The height structure data were ®tted to the power function, y is y0 xÿb , where y is the frequency of individuals of a given height, y0 the number of individuals established in each class, and x the height. This function assumes a constant recruitment rate, but the mortality changes with age, and b, determines the form (Agren and Zackarisson, 1990). 4. Results and discussion The master chronology for Pinus lagunae goes from 1840 to 1997 (DõÂaz, unpubl. data).Pine densities for the 3 years studied (Fig. 2) were 1712 in 1989, 2933 in 1993, and 1135 in 1997. These results were apparently caused by differences in recruitment recorded within the ®rst three height-classes. In 1993, 2318 pines (79%) were less than 20 cm height, equivalent to 0± 3-years-old (using the height-age regression model). The densities in the same height class in 1989 were 574 (33.5%), and only 294 (25.9%) in 1997. The small number of pines in the ®rst class for 1997 and the observation of very little seed production for 1988 suggests these could be crop-failure years, as has happened in longleaf pine production (Platt et al., 1988). The height distribution of the pine populations resembles a reverse J-shaped distribution for the 3 years (Fig. 2), where the smallest class was the modal class and the frequency of pine in the following height-classes dropped rapidly. These kinds of curves suggest a reduction in the probability of death with age or size, which happens when there is a strong relation between age and size (Harcombe, 1987), like the relationship between age and height reported by Arriaga et al., (1994) for this species (F1126 ˆ 1255.46; P < 0.0001; r2 ˆ 0.91). The step in the 300 cm height-class is because of the change between 252 S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 Fig. 2. Pine densities and relative frequencies. Densities are shown in bars, scale in each graphic is different. Relative frequency is shown with lines. height-class, rather than a period of successful pine regeneration. The left vertical scale in Fig. 2 varies between the years sampled. That is why there seem to be higher bars in medium and higher classes in 1997, even when there are little differences in these classes among the 3 years. A population of P. cembroides in San Luis Potosi, Mexico (Cetina et al., 1988) shows a different age- 253 S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 Table 1 Life table of the Pinus lagunae population of Sierra de La Laguna for 3 different yearsa 1989 1993 1997 x nx lx qx nx lx qx nx lx qx 4 6 7 9 10 22 35 48 60 73 85 98 110 123 135 148 160 1722 3065 2163 708 325 113 38 16 13 7 12 16 14 11 6 2 2 1000.00 1780.00 1255.91 411.23 188.94 65.57 22.23 9.45 7.78 3.89 7.22 9.45 8.34 6.67 3.33 1.11 1.11 0.00 294.43 672.57 540.54 652.94 661.02 575.00 176.47 500.00 0.00 0.00 117.65 200.00 500.00 666.67 0.00 0.00 6954 890 928 431 402 124 45 30 14 6 11 12 8 7 2 2 2 1000.00 127.91 133.48 61.92 57.80 17.89 6.47 4.27 2.06 0.83 1.51 1.79 1.10 0.96 0.28 0.28 0.28 872.09 0.00 536.08 66.67 690.48 638.46 340.43 516.13 600.00 0.00 0.00 384.62 125.00 714.29 0.00 0.00 0.00 883 1542 1276 930 478 128 37 29 13 9 13 14 11 10 8 2 1 1000.00 1746.70 1444.98 1053.63 541.87 144.50 42.15 33.11 15.17 9.75 15.05 16.26 13.00 10.84 8.67 2.17 1.13 0.00 172.74 270.83 485.71 733.33 708.33 214.29 541.82 357.14 0.00 0.00 200.00 166.67 200.00 750.00 477.50 0.00 a x±Age class; nx±standardized number of pines; lx±number of survivors from an original cohort of 1000 individuals; qx±proportion of individuals at age dying in the interval and x to x ‡ 1. frequency distribution, because between ages 25 and 125 the curve has a bell shape. That is because of high seed consumption by humans and of seedlings by goats. With the same species, Segura and Snook (1992) found a stand distribution different from the inverse J caused by human and natural disturbances, showing that population recruitment occurs at intervals rather than continuously. The life table for the 3 years sampled was obtained (Table 1), where X is the pine age class, nx the standardized number of pines, lx survival rate (x 1000), and qx the proportion of individuals at age x dying in the interval x to x ˆ 1. The standardization process changed the nx values from the original densities, making more apparent the differences between the ®rst three classes as can be seen when compared with the Fig. 1 values. In time-speci®c tables, as we are using, the frequency of pines does not necessarily decrease with the age; there can be negative values of qx. The negative qx values were replaced by zero during that intervals where there were no deaths. The survival curves (Fig. 3a) have almost the same tendency. That curve seems more Type II than Type III as we could expect, because Type III is most common among all organisms. The Type II curve suggests a constant risk of mortality over all ages (Harcombe, 1987). However, we observe more evident differences in mortality curves (Fig. 3b). Time-speci®c life-tables represent net survival, which is composed of each class's establishment minus all mortality of the intervening years (Knowles and Grant, 1983). The positive survival tendency for the 1989 and 1993 second age-class may not be related to differences in mortality. It could be caused by a lower production of seed during years before that census, and a mast year could have happened before the 1993 census. There is a risk in assuming differences in recruitment are caused only by mast years, because natural forest regeneration also depends on several factors like climate, pest, stand structure and development, seed predators, disturbance, and germination (Cetina et al., 1988; Prieto and Martinez, 1993). Against our suppositions of differences in recruitment based on pine densities, the ANOVA results showed no differences between year-classes (F2,16 ˆ 0.4; P05 ˆ 0.6763). This result implies that recruitment has been constant for Pinus lagunae. The Fourier analysis had a recurring cycle with a frequency of 12.8 years that cannot be attributed to a mast year, because masting at intervals of every 5±10 years characterizes pine populations (Platt et al., 1988). It 254 S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 Fig. 3. (a) Curves of survival, and (b) mortality. does not imply that there are no mast years in this species, only that the mast years probably do not occur on a periodic way. That frequency could be attributable to environmental factors, like sunspots that are coincident with this frequency (Bartusiak, 1989). With the assumptions that the pine population has a constant recruitment, a power function was ®tted to the age structures (Table 2). The power function accounts for more than 84% of the total variation, suggesting that the age structures are compatible with the assumption of constant recruitment (Agren and Zackarisson, 1990). Deviations from the class frequencies predicted by the power function model can be identi®ed by an inspection of the residuals (Fig. 4). The age structure showed positive deviations from the ®tted power functions in the 3±6 and 12±15 year age-classes; this implies a larger number of trees than expected for these classes. Negative deviations occur in the 7±11 year age-classes. Table 2 Power function model adjusted with the age-structure values for the 3 studied yearsa y0 b r2 n a 1989 1993 1997 1330 ±1.99 0.87 8233 1642 ÿ2.19 0.88 9356 809 ÿ1.75 0.84 5384 y0 ±Number of individuals established in each class; b±determines the form of the mortality change with the age; r2±correlation coefficient and n±number of pines. S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 255 Fig. 4. Residuals curve fitted shows the class frequency deviations from the power function model. The deviations indicate distribution as a wave-like regeneration pattern that may commonly suggest populations that are recovering from a rare disturbance (Agren and Zackarisson, 1990). The disturbance agents reported for this forest are ®res (DõÂaz, 1995) and hurricanes (Arriaga, 1988). Hurricanes cause pronounced variation in mortality among certain age-and size-classes, in¯uencing pine population dynamics (Platt et al., 1988). 5. Conclusions Size and age structure of Pinus lagunae provides information about population dynamics. The stand shows a young population with the tendency to continue recruitment. The mode-class is with the youngest pines and there are just a few older trees, giving the impression of a balanced multi-age condition. There were no differences in the recruitment of 256 S. DõÂaz et al. / Forest Ecology and Management 134 (2000) 249±256 the youngest classes among the years. Analyzing the patterns of tree rings did not produce evidences of mast years for this species. To have a better understanding of these phenomena and the population demography, a fecundity study is suggested. Hurricanes and ®res have been reported for this forest, and the pine population has wave-like age distribution that could be produced those factors. It will be necessary to compare the year when those disturbances occurred to detect if they coincide with the negative deviations from the predicted class frequencies. An evaluation of the impact of seed predators is also needed. The limited distribution of this forest type, the limited volume of Pinus lagunae, and the `rare' status of the species make these kinds of studies very important to the successful management and preservation of this endemic species of the Sierra de La Laguna Biosphere Reserve. Acknowledgements This research was supported by the Mexican National Council of Science and Technology (CONACyT, Mexico, grant # 1471P-N9507). Thanks to Dr. Ellis Glazier for editing the English-language text. Thanks to Franco Cota and Miguel Dominguez for the ®eld assistance. References Agren, J., Zackarisson, O., 1990. Age and size structure of Pinus sylvestris populations on mires in Central and Northern Sweden. J. Ecol. 78, 1049±1062. Arriaga, L., 1988. 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