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(American Journal of Botany. 2003;90:1064-1070.)
© 2003 Botanical Society of America, Inc.


Tropical Biology

Drought constraints on leaf gas exchange by Miconia ciliata (Melastomataceae) in the understory of an eastern Amazonian regrowth forest stand1

Lucas B. Fortini2, Stephen S. Mulkey3, Daniel J. Zarin2,5, Steel S. Vasconcelos2 and Claudio J. R. de Carvalho4

2School of Forest Resources and Conservation, Institute of Food and Agricultural Sciences, University of Florida, P.O. Box 110760, Gainesville, Florida 32611-0760 USA; 3Department of Botany, College of Liberal Arts and Sciences, University of Florida, P.O. Box 118526, Gainesville, Florida 34002-8526 USA; 4Laboratório de Ecofitologia e Propagação de Plantas, Empresa Brasileira de Pesquisa Agropecuária-Amazônia Oriental, Trav. Dr. Enéas Pinheiro S/N-Marco, CX.POSTAL 48, Belém, Pará CEP-66095-100, Brazil

Received for publication November 1, 2002. Accepted for publication February 13, 2003.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Analyses of the effects of drought stress on Amazonian regrowth stands are lacking. We measured leaf gas exchange and leaf water potential of Miconia ciliata (Melastomataceae) in a dry-season irrigation experiment in 14-yr-old regrowth. In the dry season, irrigated plants maintained significantly higher leaf water potentials, photosynthetic capacity at light saturation (Amax), stomatal conductance (gs), internal CO2 concentration (Ci), and lower Amax/gs than control plants. The degree of dry-season down-regulation of control plant Amax, along with its fast recovery following rain, reveals the importance of occasional dry-season rains to the carbon budget of M. ciliata. During the wet season, we observed higher Amax for control plants than for plants that had been irrigated during the dry season. We hypothesize that reduced drought constraints on photosynthesis of irrigated plants advanced the flowering and fruiting phenology of irrigated plants into the dry season. Flowers and fruits of control plants developed later, during the wet season, potentially stimulating a compensatory reproductive photosynthesis response in nearby leaves. The relative drought intolerance of M. ciliata may be a deciding factor in its ability to survive through the dynamic successional development of the regrowth stand studied.

Key Words: Amazon • compensatory (reproductive) photosynthesis • dry-season irrigation • leaf water potential • Melastomataceae • Miconia ciliata • phenology • secondary forest • tropical forests


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Drought stress in Neotropical forests has been shown to reduce net primary productivity (Nepstad et al., 2002 ), increase forest flammability (Uhl and Kauffman, 1990 ), and increase understory mortality (Mulkey et al., 1991 , 1993 ), while extreme seasonal droughts have been linked to increased tree mortality (Becker and Wong, 1994 ; Condit et al., 1995 ; Williamson et al., 2000 ). Modeling exercises for Amazonia suggest that extended droughts during El Niño Southern Oscillation (ENSO) events may shift the entire basin from a carbon sink to a carbon source (Tian et al., 1998 ) and that dry season length may constrain stand-level biomass accumulation following abandonment of agriculture or pasture (Zarin et al., 2001 ). Although concerns about the ecological consequences of drought in the region are growing (e.g., Nepstad et al., 2002 ) and regrowth forms an increasingly prominent part of the Amazonian landscape, offsetting roughly 20% of the carbon loss associated with deforestation (Fearnside, 1996 ; Houghton et al., 2000 ), there are very few analyses of the effects of drought stress on Amazonian regrowth forests (Dias-Filho and Dawson, 1995 ). In addition, Ellsworth and Reich (1996) have noted that we lack a fundamental understanding of the underlying physiological impacts of droughts on these forests. Long-term leaf gas exchange studies yield important information on the potential for recovery of individuals following drought (Montagu and Woo, 1999 ) and reflect how plants deal with asynchronic carbon supply and demand (Tissue and Wright, 1995 ).

Drought affects leaf, flower, and fruit phenology (Wright, 1991 ; Mulkey and Wright, 1996 ) primarily by reducing leaf gas exchange and, consequently, carbon gain (Mulkey and Wright, 1996 ). The few studies that examine the effects of drought limitation on leaf gas exchange in Amazonian pioneer species focus only on canopy trees (e.g., Dias-Filho and Dawson, 1995 ). Understory plants in early regrowth forests are more susceptible to drought than larger trees due to their smaller root systems (Wright, 1992 ). Their susceptibility to drought stress is further enhanced by the generally tenuous carbon balance that exists under low-light conditions characteristic of the understory (Gentry and Emmons, 1987 ; Mulkey et al., 1991 ). Understory composition of regrowth forests is also influenced by water availability (Gentry and Emmons, 1987 ; Wright, 1992 ) and the selective environment created by highly degraded soils arising from repeated cycles of burning and cultivation (McGrath et al., 2001 ). Here we report on the effects of reducing moisture stress on dry season leaf gas exchange by Miconia ciliata, a common understory species in eastern Amazonian regrowth forests.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Site description
The experimental site is located at the FCAP (Faculdade de Ciências Agrárias do Pará) field station near the city of Castanhal, Pará, Brazil. Annual precipitation in the region is 2000–2500 mm, with a rainy season that extends from December to May. Mean daily temperatures fluctuate between 24° and 27°C. The soils are classified as dystrophic yellow latosols, stony phase I (concretionary, lateritic) in the Brazilian Classification, corresponding to Sombriustox in U.S. Soil Taxonomy (Tenório et al., 1999 ). Regrowth forests, annual crops, and active and degraded pastures characterize the landscape surrounding the field station. Our dry-season irrigation experiment was conducted in a 2-ha patch of 14-yr-old fallow, abandoned to regrowth after multiple cycles of shifting cultivation that began about 60 yr ago when the old-growth forest was first cleared. Each cycle included cultivation of corn, manioc, and beans, for 1–2 yr followed by a fallow stage. Typical shifting cultivation cycles lasted 7–10 yr (G. Silva e Souza and O. L. Oliveira, personal communication, local resident and field station personnel, respectively).

Study species
Melastomataceae is an abundant family occurring primarily in the Neotropics, generally as understory shrubs (Ellison et al., 1993 ), and is especially prevalent in regrowth forest stands. The genus Miconia includes over 1000 species (most as shrubs and small trees), comprising one of the most abundant Neotropical plant genera (Gentry, 1993 ). Miconia ciliata is a woody understory shrub with most individuals below 2 m tall, and very few have branches that reach heights greater than 3–4 m. Miconia ciliata is the third most abundant understory species at our study site, comprising 8% of all understory individuals (J. M. Tucker, University of Florida, personal communication).

Study design
The study was conducted in eight 20 x 20 m treatment plots separated by 10-m buffer strips. Four plots were randomly selected to receive dry-season irrigation; the other four served as untreated controls. Nested 10 x 10 m measurement plots were located in the center of each 20 x 20 m plot. An irrigation tape system provided the equivalent of 5 mm of daily precipitation during rainless dry-season days, corresponding to regional estimates of daily evapotranspiration (Shuttleworth et al., 1984 ; Lean et al., 1996 ; Jipp et al., 1998 ). Irrigation was initiated at the beginning of the 2001 dry season in July. Measurements of gravimetric soil moisture content indicate that during the dry season irrigated plots had about twice as much moisture as control plots (22% vs. 10%). Wet-season gravimetric soil moisture content was 27% for both treatments (Vasconcelos, 2002 ).

Gas exchange
Data were collected from October 2001 to May 2002. We picked three M. ciliata individuals in each measurement plot for leaf gas exchange measurements (N = 24). A portable gas exchange system (LI-6400, LI-COR, Lincoln, Nebraska, USA.) supplied with ambient air was used to measure the photosynthetic capacity at light saturation (Amax) and construct light response curves of fully expanded leaves. Photosynthetic capacity at light saturation was reached by exposing leaves to a predetermined 800–1000 µmol · m–2 · s–1 photosynthetic photon flux density (PFD), ambient CO2 and H2O concentrations, a flow rate of 400 µmol/s and chamber temperatures kept under 32°C until the photosynthetic rate stabilized. Replicate Amax measurements on each plant were done monthly with some additional measurements during exceptionally dry periods and early wet season (total N = 346). For light response curves, leaves were subjected to decreasing levels of light from saturation through darkness. Variables derived from these data include Amax, dark respiration, apparent quantum yield, light compensation point, light saturation point, and convexity (Photosyn Assistant, Dundee Scientific, Dundee, Scotland, UK). Replicate light response curve measurements were made three times per season on all study plants. All leaf gas exchange measurements were done between 0900 and 1500. To avoid time-of-day bias, measurements alternated between control and irrigated plots.

Leaf water potentials
We selected three M. ciliata individuals per plot for leaf water potential. Two sets of measurements were made on a monthly basis (November through April) using a PMS pressure bomb (Corvalis, Oregon, USA), one set in the mid-afternoon (1400–1500) and one set at pre-dawn (0300–0400). Because individuals were small and leaves were removed monthly for leaf water potential sampling, we did not do these measurements on the individuals used for leaf gas exchange.

For both leaf gas exchange and water potential one leaf per individual per measurement was used since individuals were small and leaf-to-leaf variation for same individuals was low.

Phenology
Plants used for leaf gas exchange measurements were observed for variation in phenology. At the beginning of the wet season, each time leaf gas exchange was measured, we recorded the presence and absence of flowers and fruits for the whole plant. Additionally, one branch from each leaf gas exchange plant was used to monitor leaf phenology.

Data analysis
Data analysis was performed with JMP version 3.2.6 software (SAS Institute, Cary, North Carolina, USA). A repeated measures MANOVA model was fitted to the Amax and water potential data with treatment as the only effect, each monthly measurement set as dependent variables and time as the effect between dependent variables. We use the Wilks' lambda test statistic to evaluate the MANOVA results. Preliminary statistical analysis showed that plot as a random nested variable was not a significant factor (P > 0.25) in the univariate model and was therefore excluded from subsequent analysis. The Geisser and Greenhouse (G-G) adjustment, which allows for univariate repeated measures ANOVA on data that fail the univariate sphericity assumption (SAS Institute, 1998 ), was performed along with the multivariate analysis. Light curve variables such as apparent quantum yield, dark respiration, and convexity were derived using a nonrectangular hyperbola fit with Photosyn Assistant software (Dundee Scientific, Dundee, UK). Derived variables were analyzed using the same MANOVA model described above.

Because treatment response for most variables varied greatly among measurement dates and more broadly between seasons, we assessed the significance of treatment differences as the interaction between treatment and time factors in our ANOVA and MANOVA models. Some measurement dates and plants were excluded from the multivariate analysis to conform to the requirement of no missing values.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Leaf gas exchange and leaf water potential
During the dry season, irrigated plants exhibited significantly higher Amax, stomatal conductance (gs), and internal CO2 concentration (Ci) and lower Amax/gs than control plants. Photosynthetic capacity at light saturation and gs were 3–4 times higher for irrigated plants than control plants during especially dry periods (Fig. 1 and Table 1). The treatment differences in leaf gas exchange disappeared at the onset of the wet season. Later wet-season leaf gas exchange measurements showed that Amax and gs of control plants increased significantly above values for plants that had been irrigated during the dry season, while Ci and Amax/gs were essentially the same for both treatments.



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Fig. 1. Leaf gas exchange of Miconia ciliata and daily precipitation across the 2001 dry season and 2002 wet season (±1 SE). Amax, photosynthetic capacity at light saturation; gs, stomatal conductance; Ci, internal CO2 concentration

 

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Table 1. Statistical results for leaf gas exchange and leaf water potential (treatment by time interaction term)

 
Light response curves showed no treatment differences for apparent quantum yield, light compensation point, convexity, and dark respiration (Fig. 2 and Table 2). Light curve derived Amax was consistent with results from Amax measurements, showing highly significant treatment and time effects (P < 0.0001) for both multivariate and univariate tests. Significant time differences in apparent quantum yield (P < 0.001) for both tests reflect the increase in values from dry to wet season for both treatments. In the dry season, the light saturation point was slightly higher for irrigated plants than control plants (F = 3.82, df = 1.57, 31.48, P < 0.04) only for the univariate G-G adjusted test.



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Fig. 2. Treatment light response curves for 2001 dry season and 2002 wet season. Individual light curves are means of all individually measured curves by treatment and season (photosynthetic photon flux density [PFD] = 800, 400, 150, 40, 15, 5, 0)

 

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Table 2. Light response curve derived values from dry season (November) and wet season (March) measurements (1 SE in parenthesis). Curves from these dates were chosen for analysis because they represent the peak of the dry season (November) and a midpoint in the rainy season (March). They are representative of the seasonal differences in the entire data set

 
A subset of dry-season relative humidity and air temperature data measured with the LI-COR reference chamber showed irrigated plots had higher relative humidity and lower temperature during the day. These differences intensified as the day progressed from no differences in the morning to mid-afternoon values of 49% vs. 57% relative humidity and 32.9°C vs. 32.5°C, for control and irrigated plots, respectively. Full factorial two-way ANOVAs with time of day and treatment as factors applied on a representative subset of dry-season data showed time of day by treatment as a significant interaction term in air temperature (F = 5.05, df = 3, 18, P < 0.04) and relative humidity data (F = 24.49, df = 3, 23, P < 0.0001).

During very dry periods, M. ciliata individuals in control plots and the surrounding forest lost turgor, while irrigated plants maintained full turgor and horizontal leaf angles. The severity of drought stress was reflected in leaf water potential values as low as –3.0 MPa for some control plants during the dry season in comparison to a maximum wet-season leaf water potential of –0.2 (Fig. 3 and Table 1). One of our 12 control plants wilted and died after several days without rain during a critical drought period in December 2001.



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Fig. 3. Leaf water potential of Miconia ciliata across the 2001 dry season and 2002 wet season (±1 SE)

 
Differences between dry-season control and irrigated leaf water potentials were highly correlated to plot level leaf gas exchange during the dry season despite the fact that gas exchange and water potential measurements were done on separate sets of individuals (Fig. 4). The negative correlation between dry-season plot mean leaf water potential and plot mean Amax indicates that M. ciliata is an anisohydric species that matches its leaf gas exchange closely to leaf water status. No treatment effects on leaf water potential for the wet season were observed.



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Fig. 4. Plot level correlation between photosynthetic capacity at light saturation (Amax) and leaf water potential. Pearson product moment for dry-season data: R2 = 0.8877, P < 0.0001

 
For plants in the control plots, modest to steep drops in leaf gas exchange occurred during the dry-season periods of little or no rain while scattered rain events interrupted the dry spells, triggering immediate large rebounds in gas exchange. This contrasted with the relatively more constant gas exchange of irrigated plants across the dry season and was exemplified by leaf gas exchange measurements made up to 3 h before and 15 h after a 7.4-mm dry-season rain (Fig. 5). The Amax of control plants had a significant two- to threefold increase from pre-rain event values, while Amax of irrigated plants showed no significant differences (paired t tests; P = 0.002, P = 0.664, respectively). This dry-season event had a significant impact in the carbon balance of control plants, as prolonged drought would have meant a further reduction in control Amax, which was already three times smaller than irrigated Amax before the rain event.



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Fig. 5. Photosynthetic capacity at light saturation (Amax) and stomatal conductance (gs) immediately before and after a dry-season rain event (+1 SE)

 
Phenology
The amount and timing of leaf production and senescence during the wet season did not differ between treatments. Irrigated plants showed early onset of flowering and fruiting in the dry season, resulting in more flowering and fruiting on irrigated plants than on control plants. In contrast, in the wet season we recorded higher percentages of control plants than irrigated plants that had flower buds (58% vs. 25%), were flowering (58% vs. 8%), and bore unripe fruit (58% vs. 33%), respectively.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Drought impacts on leaf water potential and leaf gas exchange
The strong treatment effect on dry-season Amax contrasts with the results of another irrigation experiment where Amax of old-growth understory species was only mildly constrained by drought despite significant decreases in stomatal conductance (Mulkey et al., 1991 , 1993 ; Mulkey and Wright, 1996 ). However, declines in Amax in response to increased drought stress have been observed in several other recent studies (Zotz and Winter, 1994 ; Liang et al., 1997 ; Cao, 2000 ), supporting the supposition that reduced Amax is a prominent indicator of water stress (Lawlor and Cornic, 2002 ), especially in shaded understory plants (Valladares and Pearcy, 2002 ). Wilting in M. ciliata in response to drought stress may be a facultative response to minimize evaporative demand as has been observed in early successional rainforest herbs (Chiariello et al., 1987 ) and to avoid sustained damage to photosynthesis.

Stomatal limitation and limited acclimation
The combination of low Amax, gs, Ci, and leaf water potential in control plants during the dry season relative to both control plants in the wet season and irrigated plants during the dry season suggests that Amax is constrained by CO2 diffusion due to stomatal response to drought (Osmond et al., 1980 ) and is consistent with studies that show stomatal closure as the initial defense against turgor loss (Tenhuen et al., 1987 ; Schulze, 1993 ; Flexas et al., 1998 ). Stomatal response to drought is driven by reduction in both soil moisture and relative humidity (Ball and Farquhar, 1984 ; Reseman and Raschke, 1984 ; Reekie and Wayne, 1992 ), consistent with the results we have reported.

Control plants partially acclimated to drought by increasing Amax/g (indicative of water use efficiency [WUE]) as drought stress intensified, but not enough to prevent steep drops in carbon assimilation during dry periods. As gs decreases, transpiration decreases linearly, but Ci also drops since CO2 demand is unchanged. This decrease in Ci is compensated by a steeper internal/external CO2 concentration gradient that counteracts the drop in gs and increases CO2 diffusion. Not surprisingly, drought-stricken control plants with the lowest Amax generally had higher Amax/gs ratios (cf. Jones, 1993 ). These results are also consistent with other studies that link plant variation in WUE to ecological variation in atmospheric and soil drought conditions (Tenhuen et al., 1987 ; Mulkey et al., 1991 , 1992 ).

Wet-season recovery of leaf gas exchange
The abrupt start of the wet season in January provided a clear response of study plants to the change of water availability that occurs between the dry and wet season. There are very few data on the recovery of leaf gas exchange from drought stress as the wet season progresses (Montagu and Woo, 1999 ). Similar to our results, Montagu and Woo (1999) found fast recovery from stomatal limitation within the first 8 d of the wet season in Acacia auriculiformis in Australia, but full recovery was delayed for several weeks as foliar chlorophyll slowly rebounded from dry-season reductions. In contrast, the absence of dry-season treatment differences in apparent quantum yield and the quick recovery of leaf gas exchange in our study suggest that M. ciliata did not suffer from any sustained biochemical changes in its photosynthetic apparatus in response to drought. The dry-/wet-season transition signified a rapid and drastic change from drought-induced stomatal limits on carbon assimilation to a scenario in which water no longer limited leaf gas exchange. This is reflected in a drop in Amax/gs for both treatments and increases in Ci that signal the end of stomatal limitation to Amax.

Phenology and the impact of drought in the wet season
Water stress is closely linked to leaf, flower, and fruit phenology for a wide array of tropical species in seasonally dry forests (Opler et al., 1976 ; Alvim and Alvim, 1978 ; Augspurger, 1979 ; Reich and Borchert, 1984 ; Bullock and Solis-Magallanes, 1990 ; Wright et al., 1992 ; Wright, 1996 ). A similar study in Panama has shown irrigation to strongly influence understory phenology without affecting canopy phenology, presumably due to differential access to deeper sources of soil moisture (Wright, 1996 ). Irrigation disrupted the timing of leaf production in seven understory species (Wright, 1991 ) while advancing the flowering and fruiting phenology of three other species in Panama (Tissue and Wright, 1995 ). Although rainfall has been shown to function mainly as a cue to initiate growth and phenological changes (Opler et al., 1976 ; Reich and Borchert, 1984 ), dry-season drought likely regulated M. ciliata phenology by limiting carbon assimilation in control plants during the dry season and restricting their potential for flowering and fruiting. Our data suggest that the high potential assimilation rates of irrigated plants in the dry season advanced flowering and fruiting phenology, as observed in Panama (Tissue and Wright, 1995 ), creating the difference in flowering and fruiting phenology observed during the wet season between control and irrigated treatments.

The combination of phenology and leaf gas exchange treatment differences in the wet season is consistent with reproductive compensatory photosynthesis by control plants during this period. The increased demand for carbon in developing flowers and fruits can increase photosynthesis in source leaves (Watson and Casper, 1984 ; Bazzaz and Reekie, 1985 ; Reekie and Bazzaz, 1987 ). Although this may mean an increase in whole plant photosynthesis, this compensatory response is often observed on leaves near strong carbon sinks (Evans and Rawson, 1970 ; Hansen, 1970 ; Flinn, 1974 ; Chapin and Wardlaw, 1988 ). Because M. ciliata flowering and fruiting occurs at branch tips near fully developed mature leaves used for leaf gas exchange measurements, our findings may have captured this effect. In contrast, the broadened period of flowering and fruiting for irrigated plants likely limited compensatory photosynthesis in irrigated plants by spreading the demand for reproductive carbon over a longer time span.

An alternative or complementary explanation to the elevated wet-season leaf gas exchange of control plants relative to previously irrigated plants may be an early wet-season nutrient pulse in control plots (Lodge et al., 1994 ). A pulse of nutrients derived from leaf litter and the onset of microbial activity may supply control plants with nutrients necessary to markedly increase photosynthetic capacity. In contrast, irrigated plants would have consistent access to nutrients, but in smaller amount than experienced by control plants during a pulse following the onset of rains. Although previous studies have found limited evidence of effects of irrigation on nutrient pulses during early wet season in Panama (Yavitt et al., 1993 ; Yavitt and Wright, 1996 ), the seasonal variation in soil water content in those studies may not have been large enough to create sufficient water stress to induce microbial mortality in early wet season (Yavitt et al., 1993 ). Decreased microbial biomass and increased microbial respiration during the wet season at our site (Vasconcelos, 2002 ), along with increasing evidence that nutrient pulses occur more frequently on sites of increased drought seasonality (Lodge et al., 1994 ), support this explanation.

Conclusions
Leaf gas exchange of M. ciliata plants was influenced both directly and indirectly by dry-season irrigation. During the dry season, stomatal limitation in response to drought constrained gas exchange in control plants primarily through CO2 diffusion limitation. Irrigated plants exhibited advanced fruiting and flowering and, as a likely consequence, did not exhibit the compensatory photosynthetic response that appeared to have characterized wet-season leaf gas exchange for the control plants. Dry-season irrigation may have also prevented elevated leaf gas exchange rates in the wet season by suppressing an early wet-season nutrient pulse.

To the extent that Amax is a master integrator of stress, resource availability, and growth potential (Field, 1991 ), our study shows how Amax reflected plant water status, water stress, and whole plant carbon demand. The large drops in control Amax associated with critical dry periods during the dry season may be largely responsible for treatment differences in plant carbon status expressed through changes in phenology. These results illustrate the importance of the periodicity of dry-season rains in the carbon budget of this understory species. Miconia ciliata's sensitivity to water availability suggests that drought stress may be an important selective pressure in the understory during the successional development of this eastern Amazonian regrowth forest stand. Future studies will assess the impact of drought water stress on this and other species as the stand ages.


    FOOTNOTES
 
1 The authors thank Joanna M. Tucker for comments on earlier versions of the manuscript; Francisco de Assis Oliveira and Raimundo Nonato da Silva for logistical support; and Debora Viega Aragão, Evandro Rodrigues da Silva, Glebson A. da Silva Sousa, and Osório L. Oliveira for assistance with fieldwork. This research was conducted under cooperative agreements between the University of Florida, Faculdade de Ciências Agrárias do Pará and Empresa Brasileira de Pesquisa Agropecuária. This research was supported by the Florida Agricultural Experimental Station and by a grant from the Andrew Mellon Foundation and was approved for publication as Journal Series No. R-09314. Back

5 Author for reprint requests (zarin{at}ufl.edu ) Back


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 DISCUSSION
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D. V. Aragao, L. B. Fortini, S. S. Mulkey, D. J. Zarin, M. M. Araujo, and C. J. R. de Carvalho
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