Directory UMM :Data Elmu:jurnal:E:Ecological Economics:Vol31.Issue3.Dec1999:

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ANALYSIS

Enriching the rainforest with native fruit trees: an ecological

and economic analysis in Los Tuxtlas (Veracruz, Mexico)

Martin Ricker

_{*, Robert O. Mendelsohn}

_{, Douglas C. Daly}

_,

Guillermo A

´ ngeles

a_{Jardıń Botańico del Instituto de Biologıá}_,_Uni₆_{ersidad Nacional Autońoma de Me´xico}_,_{Apartado postal}₇₀_-₆₁₄_, Delegacioń Coyoacań,D.F.04510,Mexico

b_{School of Forestry and En}₆_{ironmental Studies}_,_{Yale Uni}₆_ersity_,₃₆₀_{Prospect Street}_,_{New Ha}₆_{en CT}₀₆₅₁₁_,_USA c_{The New York Botanical Garden}_,_Bronx_,_{New York}_,_NY₁₀₄₅₈_-₅₁₂₆_,_USA

d_{Estacioń de Biologıá}_‘_{Los Tuxtlas}_’_,_Uni₆_{ersidad Nacional Autońoma de Me´xico}_,_{Apartado postal}₉₄_,_{San Andre´s Tuxtla}_, Veracruz95700,Mexico

Received 23 October 1998; received in revised form 14 June 1999; accepted 14 June 1999

Abstract

Tropical forests continue to be deforested because forest owners believe they can earn more income through land uses involving forest conversion. A case study in a Mexican rainforest revealed that enrichment planting with the native tree speciesPouteria sapota(‘mamey’) is a management approach that can increase the commercial value of the forest enough to compete with these destructive land uses. Depending on the land value, planting more than 40 – 200 seedlings per hectare into the natural forest is expected to have a higher net present value than one hectare of existing cattle pasture. To arrive at this conclusion, we were able to project long-term tree growth and fruit production from a few years’ increment measurements, based on a new method for estimating ages of tropical trees without annual growth rings. This approach facilitates rather rapid cost-benefit analysis of tropical forest management with native species. © 1999 Elsevier Science B.V. All rights reserved.

Keywords:Forest economics; Fruit trees;Pouteria sapota; Rainforest; Tree growth; Valuation

www.elsevier.com/locate/ecolecon

1. Introduction

As tropical deforestation continues (Dirzo and Garcı´a, 1991; Cairns et al., 1995), the future of

those tropical forests not under effective protec-tion of conservaprotec-tion units hinges on the applica-tion of forest management strategies that can yield economic returns comparable if not superior to destructive land uses. The implicit challenge is to develop and apply methods, both in economics and in forest ecology, that potentiate cost-benefit

* Corresponding author. Fax: +52-5-6229046. E-mail address:[email protected] (M. Ricker)

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analyses in a relatively short time-frame. In the forest, this means being able to project long-term production levels for a given management regime, founded on empirical data over only a few years. Our study utilized this approach to calculate the commercial value of enrichment planting with data collected over three years. Such enrichment planting consists of planting and managing com-mercially valuable tree species inside the existing forest. The study was carried out in the rainforest at the biological research station of the Universi-dad Nacional Auto´noma de Me´xico in Los Tuxt-las (Veracruz, Mexico), about 30 km from the city of San Andre´s Tuxtla (for more information see Ibarra-Manrı´quez et al., 1997). The employed tree species, Pouteria sapota (Jacquin) H.E. Moore and Stearn (‘mamey’; Sapotaceae), is native to this forest but occurs naturally only in low densi-ties of about one tree per hectare. Its sweet fruits of 200 to over 600 g are found in local markets in southern Mexico, as well as in Mexico City’s supermarkets. The native range of P. sapota is probably southern Mexico to Nicaragua (Pen-nington, 1990), but it has been introduced in Florida, the Caribbean, South America, and Southeast Asia (Morton, 1987; Oyen, 1991).

The seedlings ofP.sapotahave their maximum growth rate in the forest understory. In an ecolog-ical analysis, the optimal canopy openness during the first 2 years after germination and transplant-ing was 60% (Ricker, 1998). Furthermore, existtransplant-ing adult trees can produce high fruit yields both inside and outside the forest environment. These ecological characteristics make the species suitable for forest enrichment.

2. Methods and results

The commercial value of a planted Pouteria sapotaseedling was calculated as its expected net present value (NPV), a standard concept in eco-nomics and business administration:

NPV=%i=1

MA _[_F

iSi(P−C)e

−ri_]

−K. (1)

In this equation,i is the age as a discrete integer number (the harvest is once a year). Planting

occurs at i=0, and MA is the maximum age of production. The variableFiis the expected annual fruit yield of the tree at age i (Fi=0 in the first years), whileSiis the expected survivorship at age

i as a proportion of the initial cohort size (Si ranges between 0 and 1). The economic parame-ters are the per-unit market price P, the per-unit cost C for harvesting, transportation and com-mercialization, the discount rate r, and the ex-pected present value K of all planting and management costs of the tree. Eq. (1) calculates the expected net return of the annual fruit yield in a given year FiSi(P–C), and discounts it by multiplying with e–ri

to take the time delay for future harvests into account from an investor’s perspective. Then it sums up the present values of all net returns, and subtracts the present value of the management costs K. The separation of per-unit costs at harvestCand management costsKis convenient because Cmust be paid per kilogram fruit at the time of harvest, whileK must be paid per tree or per hectare at times that are indepen-dent from the harvesting times. Consequently, it would be difficult to convert Kinto a component of C.

Eq. (1) models the expected or average com-mercial value per tree of one cohort, planted at present, and without any replanting to replace dead trees. Prices and costs are assumed to remain constant over time. Fruit prices (P) were observed in the regional market of San Andre´s Tuxtla, approximately every two weeks between March 1995 and April 1997. The average price was Mex$4.52/kg [US$1=Mex$9 – 10 (‘pesos’) in May 1999; n=28 times the fruits were found in the market]. The per-unit cost of harvesting, trans-portation, and marketing costs (C) was estimated to be Mex$1.62/kg. Of this amount, the compo-nent for harvesting was Mex$0.61 (37.7%) after measuring an average harvesting time of 3.7 min/

kg with two persons and using a labor cost of Mex$30.00/person for 8 h. The component for transportation to San Andre´s Tuxtla was Mex$0.56/kg (34.6%), when using a public pickup-truck service with a cost of Mex$28.00 for one person plus Mex$28.00 for 100 kg freight. Finally, the component for comercialization was estimated to be Mex$0.45/kg (27.8%), assuming

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that 12 h of labor on the market would sell 100 kg of fruits.

The discount rate (r) reflects the value of time for an investor (e.g. a year is worth a 5% increase of invested money). Empirical analysis shows that a 5% discount rate is accurate in the long-run, i.e. considering decades in forestry (Berck, 1979; Ricker and Daly, 1998). Finally, K sums up the present values of all planting, management and equipment costs. Costs in later years are discounted in the same way as fruit harvests in later years.K

was estimated to be Mex$30.00/tree. This includes Mex$2.23/seedling (7.4%) nursery costs, Mex$4.77/

seedling (15.9%) site preparation and planting costs, Mex$6.36/tree (21.2%) present value of the watering costs over the first three years, and Mex$13.27/tree (44.2%) present value of weeding costs [present values were calculated by multiplying costs withe–ri_{; for more details see Ricker (1998)].} These components forKsum up to Mex$26.63/tree (88.7%), which, however, was rounded up to Mex$30.00 to leave a margin for uncontemplated costs. Watering was considered to become unneces-sary after 3 years, once the trees have established themselves with sufficient roots and within a hu-midity-conserving forest environment. Weeding was considered to be necessary every 3 months for the first 3 years, and once a year thereafter.

To determine annual fruit yield (Fi) and sur-vivorship (Si), we inventoried 100 naturally occur-ringP.sapotatrees of varying trunk diameter over 3 years (1995 – 1997). The 100 trees were found in an area of about 5×5 km, both inside the forest and in the open. Of these, we were able to measure the trunk circumference increments of 93 trees and the annual fruit yield of 79 trees in at least 1 of the 3 years. Two trees were cut down in the study period (one of which formed part of the 93 trees), while six trees died or disappeared and in the latter case were assumed to have died naturally. In a number of cases, tree owners did not give their permission to measure fruit yield.

2.1. A new method to determine tree ages and project yield

Studies of forest ecology and management depend heavily on knowing the ages of trees,

for example, to know at what age timber trees reach their harvestable size. In temperate zones, annual growth rings in the trunk wood can be counted, but in the winterless lowland tropics no reliable annual growth rings are formed (Jacoby, 1989). We have developed a new method for determining expected tree ages from annual incre-ment data, based on the Bertalanffy – Richards – Chapman (BRC) growth model (Pienaar and Turnbull, 1973; Zeide, 1993). The method can be applied with data collected over only one year, though several years are preferable (here 3 years; see point 1 below).

The basic functional form of the BRC model for diameter growth is:

D=DMax(1−e –aAge

. (2)

In Eq. (2), Dis the trunk diameter, and DMax, a,

andbare regression coefficients. DMaxis the

max-imum possible diameter reached at infinity age (here in cm); note that it is also a regression coefficient and not a measured value. The coeffi-cientacan be interpreted as a growth rate parame-ter (per year), andbas a shape parameter (without a unit).

Following, an equivalent functional form of the BRC model is developed that relates trunk diameter and relative growth, without includ-ing age as a variable. First, Eq. (2) is solved for Age:

Age=ln [1−(D/DMax)1/b]/–a. (3)

Next, an equation for the instantaneous relative growth (dD/dAge)/D is derived from Eq. (2) by taking the derivative with respect to Age and dividing by D:

RG=(dD/dAge)/D

=[abDMax(1−e–aAge)b– 1/eaAge]/[DMax(1−e–aAge)b]

=ab/(eaAge

−1).

Then, in this equation of relative growth, the variable Age is replaced with Eq. (3). Finally, the logarithm is taken to spread the data points and to avoid a nonlinear regression that would unrealistically predict negative values of relative growth:

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ln [RG]=ln {ab/[1/(1−(D/DMax) 1/b₎

−1]}. (4)

The empirical relative growth (RG) was calculated for each tree as the annual diameter increment divided by the diameter (D). Trunk diameters were determined from their circumferences (circ), measured at a marked height with a measurement tape (D=circ/p). Circumference increments were

measured at the beginning and the end of a year. The final measurements were not taken exactly 365 days after the initial ones. Therefore, the increment measurements were slightly inter- or extrapolated linearly to 365 days [annual incre-ment=(365)(measured increment)/(number of days)]. Furthermore, in such data sets from tape measurements of irregular trunks with buttresses, the measurement error can be large. Conse-quently, there are unrealistic outliers. Here, di-ameter increments appearing to be \6.0 cm and

50 cm were eliminated. In this way, 13 (4.6%) of 282 original data points were eliminated.

The SYSTAT 5.03 software was used to adjust the parameters DMax, a, and b of Eq. (4) with

nonlinear regression and ordinary least squares. The result is shown in Fig. 1 (R2₌_0.61, _n₌₂₆₉

increments for 93 trees and 3 years). The software also estimates standard errors. Having determined the parameters a,b, and DMax, the estimated age

of each tree can be calculated from its diameter

(D) with Eq. (3). The largest tree was estimated to be 191 years old (diameter at breast height=131 cm). This age was set as the maximum age (MA) for fruit production. However, there was no con-tribution of yields after 150 years to the seedling’s net present value; from a commercial viewpoint it was too far in the future.

Fruit production was measured by actually har-vesting all fruits in the period from May to July of each year over three years, and weighing them on a market scale. The annual fruit yield was graphed over the estimated tree ages, and the BRC model employed a second time with nonlin-ear regression to determine an average growth curve for the expected annual fruit yield per tree

F=FMax(1−e

–cAge₎d_. ₍₅₎ Similar to the regression coefficients in Eq. (2),

FMax is the maximum possible annual fruit yield

reached at infinity age (here in kg; again not a measured value), c represents a growth rate parameter (per year), and b a shape parameter (without a unit). Eq. (5) represents a continuous function (therefore the notationFrather thanFi). However, it may be applied only with ages that are 1 year apart in order to predict the annual fruit yields as discrete events.

The result of adjusting Eq. (5) to the data with nonlinear regression is shown in Fig. 2 (R2

=0.33,

n=225 harvests for 79 trees). Note that the BRC-model captures well the typical pattern of the development of annual fruit yield, taking an aver-age path and remaining conservative without be-ing unduly influenced by outliers.

A few precautionary notes are in place for applying this new method to estimate ages and to project yields:

1. The new method for determining tree ages relies on the assumption that the years of increment measurements are representative of other years. In particular, climate fluctuations are of concern, as they can cause lower or higher increments in some years. In this study, the average increments over 3 years were at least relatively consistent, 1.1 cm in 1995, 0.8 cm in 1996, and 1.0 cm in 1997 for the 81 trees.

Fig. 1. Nonlinear regression adjustedDMax,a, andbin Eq. (4) for 93 trees ofPouteria sapota, measured over 3 years in Los Tuxtlas (R2₌_0.61,_n₌_{269). The diameter is at breast height.}

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Fig. 2. Measured and expected annual fruit yield ofPouteria sapotaat Los Tuxtlas.FMax,c, anddof Eq. (5) were adjusted with nonlinear regression and using the average age estimates for the 79 trees measured over 3 years (R2₌_0.33, _n₌_225). Note that the continuous function of expected yield represents a discrete process, i.e. yields occur only once a year.

the sample size improves the estimate), each error term has to be uncorrelated with its corresponding X-variable, here D and Age, respectively (Maddala, 1992, chapter 9.1). We calculated Pearson correlation coefficients for each of the three cases, none of which was statistically significant [ru4−u5=0.02 (n=221),

ru4-D=– 0.02 (n=269), ru5-Age=0.04 (n=

225)]. Thus, there is no evidence that these assumptions were violated.

4. Finally, the three regression coefficients of the BRC model are correlated with each other in Eqs. (4) and (5). The SYSTAT software calcu-lated automatically these correlations, the re-sult being rD_Max-a=– 0.44, rD_Max-b=0.70,

ra-b=0.11 (n=269); andrF_Max-c=– 0.72,rF_Max

-d=– 0.69, rc-d=0.99 (n=225). Highly corre-lated parameters may cause misleading confidence intervals when these are con-structed on the assumption that each parame-ter individually presents a normal distribution independently from the other two parameters. Here, the confidence intervals constructed un-der this assumption in Table 1 lead to negative

c and d, an impossibility in the BRC model. Truncating c and d to zero leads to extreme situations that are of interest, but that do not reflect 95% confidence limits: Withc=0, there is no fruit yield at all, and with d=0, from year 1 to the last year the fruit yield is the maximum one (FMax).

2.2. Predicting tree sur6i6orship

Turning to survivorship (S), the simplest model that has been employed is the negative exponen-tial function (Lieberman et al., 1985; Condit et al., 1995):

S=e–mAge

. (6)

In this model, the expected annual mortality rate

mof a cohort is assumed to be constant through-out the tree’s life. Though this model is not accurate for very early and very late tree ages when mortality is high, it is useful for the type of data employed here. One has to assume that at

i=1 year, the seedling stock is well-established in the field, thus having passed already through the 2. A statistical problem arises from measuring

the same trees repeatedly over years because these measurements are generally expected to be correlated. A tree that grows well in one year tends to grow well in other years. Here, the Pearson correlation coefficients for loga-rithmic relative growth of the trunk diameters between years 1995 – 97 were all statistically highly significant [r95 – 96=0.78 (n=92), r95 –

97=0.67 (n=84),r96 – 97=0.82 (n=85)]. To a

lesser extent, significant correlations existed also for fruit yields of the same trees between years [r94−95=0.50 (n=72), r94−96=0.45

(n=71), r95−96=0.31 (n=74)]. While

parameter estimates remain unaffected by these correlations, variance estimators may be biased, and confidence intervals may be inac-curate (Sullivan and Reynolds, 1976; West, 1995). However, here the key objective was to estimate the regression parameters, and this problem is only of secondary concern. 3. Carrying out the two nonlinear regressions for

Eqs. (4) and (5) independently assumes that their error terms (i.e. residualsu) are uncorre-lated (Borders, 1989). Furthermore, to get a consistent regression estimate (i.e. increasing

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Ricker

Ecological

Economics

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439

–

448

444

Sensitivity analysis forPouteria sapotafruit production

Parameter Explanation Original Changed Confidence % Change of New NPV in % Change of Ratio of % NPV

parameter parameter value changes

parameter value interval Mex$

value

a(year–1₎ _{Growth rate} _0.0026237 _0.0023363 _{Lower 95%} _–11.0 _25.19 _–51.0 _4.7

0.0029111 Upper 95% +11.0 81.61 +58.8 5.4

parameter for age determina-tion

1.0590 0.9479 Lower 95% –10.5 143.13 +178.5 –17.0

Growth form b

parameter for 1.1701 Upper 95% +10.5 7.21 –86.0 –8.2

age determina-tion

Lower 95% –19.6

DMax(cm) Maximum pre- 351.19 282.47 7.63 –85.2 –4.4

419.90 Upper 95% +19.6 108.01 +110.1 5.6

dicted average diameter

0 Truncated –100.0

c Growth rate 0.093059 –30.00 –158.4 1.6

0.190115 Upper 95% +104.3 410.12 +697.9 6.7

parameter for annual fruit yield

87.318 0 Truncated –100.0 2453.81 +4673.9 –46.7

Growth form d(year–1₎

488.586 Upper 95% +459.5 –7.58 –114.7

parameter for –0.2

annual fruit yield

49.093 Lower 95%

FMax(kg) Maximum pre- 62.102 –20.9 34.34 –33.2 1.6

75.112 Upper 95% +20.9 61.05 +18.8 0.9

dicted average annual fruit yield

No –50.0 120.34 +134.1 –2.7

m Constant an- 0.02 0.01

No +100.0 –4.10 –108.0

0.04 –1.1

nual mortality rate

32.03 –37.7

P(Mex$/kg) Per-unit price 4.52 3.83 Lower 95% –15.3 2.5

70.76 +37.7 2.5

+15.3 Upper 95%

5.21

Per-unit cost 1.62 0.62 –61.7 79.46 +54.6 –0.9

C(Mex$/kg) No

23.33 –54.6 –0.9

+61.7 No

2.62

–40.0 258.22 +402.4 –10.1

r Annual discount 0.05 0.03 No

+40.0 –4.10 –108.0 –2.7

rate 0.07

K(Mex$/tree) Present value 30.00 10.00 No –66.7 71.40 +38.9 –0.6

50.00 No +66.7 31.40 –38.9 –0.6

per tree of all management costs

a_NPV₌_{net present value, calculated with Eq. (1); US$1}₌_{Mex$9–10 in May 1999; ‘% change of parameter value’: 100%}₌_{original parameter value; ‘% change of} NPV’: 100%=Mex$51.40, the result with the original parameter values; ‘Ratio of % changes’=elasticity of NPV to parameter=(% change of NPV)/(% change of parameter value).

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initial phase of relatively high mortality. An early constantly low mortality can also be supported by management. Late ages are of no concern because the discounting factor e–ri _{results in very low or} no contributions of old trees to the net present value.

The critical parameter to be adjusted in Eq. (6) for a specific site and species is the constant annual mortality rate m. Over the three study years, 6 of 100 individuals of a wide range of diameters (i.e. ages) died naturally at different times (4 in the first year, 0 in the second, and 2 in the third). Therefore,m was estimated to be 0.02 for a planted cohort [ln [1+(4/100+0/96+2/

96)/3]. Mortality data on adult trees is difficult to obtain in rainforest species with low densities because large survey areas are required to analyze several populations of, say, 100 trees. However, our estimated annual mortality rate of 2% is consistent with results from other studies on rain-forest trees involving larger tree propulations as well as varying site and climate conditions (Lieberman et al., 1985; Condit et al., 1995).

2.3. Sensiti6ity analysis

To analyze which parameters are critical in determining the net present value, a sensitivity analysis for each model parameter is provided in Table 1. The first column (‘Parameter’) shows the 11 input parameters, and the second column (‘Ex-planation’) a short explanation about their mean-ing. The third column (‘Original parameter value’) presents the original input parameter values, re-sulting together in an average estimate for the net present value of Mex$51.40. Next, in column 4 (‘Changed parameter value’) an upper and lower bound is chosen. When possible, 95% confidence intervals based on a normal distribution were chosen to get these bounds (column 5, ‘Confi-dence interval’). In two cases (for c and d), the lower confidence limits were unrealistically less than zero, and were truncated to be zero (see point 4 in Section 2.1). For parameters without standard errors (m, C, r, K), ranges were chosen so as to be realistically possible.

For each upper or lower parameter, the whole net present value calculation was carried out,

keeping all other parameters at their original value. In the case of a, b and DMax, lower and

upper ages for each of these three parameters were re-calculated for the fruit yield data of the 79 trees (i.e. a total of six possible ages for each tree). Subsequently, the second nonlinear regression with Eq. (5) was carried out for each of the six cases, and the corresponding net present value was calculated each time with the new FMax, c,

and d combined.

The sixth column of Table 1 (‘% change of parameter value’) calculates the percent deviation of changed parameters from their original value. The seventh column (‘new NPV’) gives the new net present value, and the eighth column (‘% change of NPV’) the percent change relative to the original net present value of Mex$51.40 per seedling. Finally, the last column (‘Ratio of % changes’) divides the ‘% change of NPV’ by the ‘% change of parameter value’. This ratio indi-cates the sensitivity of the net present value to the parameter, i.e. the average percent change of the net present value resulting from a 1% parameter change. In economic terms, this ratio would be called the elasticity of the net present value to the parameter.

a=0.0023363 instead of 0.0026237, with all other parameters remaining at their original values, the net present value is Mex$25.19 (‘New NPV’). The column ‘% change of NPV’ shows that Mex$25.19 is 51.0% lower than the original net present value of Mex$51.40 [(51.40−25.19)(100)/51.40]. Fi-nally, the last column ‘Ratio of % changes’ shows that the elasticity of the net present value to the parameter a is 4.7. Each one percent-decrease of the value of a decreases the net present value on average by 4.7% (note that calculations were car-ried out with more than one decimal so that 4.7 rather than −51.0%/– 11.0%=4.6 resulted).

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One may be concerned about several parameters varying at the same time. However, given multiple and independent factors influencing the parameter values, one can expect that when one parameter is above its predicted average value, another parameter is likely to be below its predicted aver-age value. In this way, the effect of stochastically varying parameters on the net present value is expected to be buffered to some extent. Neverthe-less, the determination of the distribution and confidence limits for the net present value will be an interesting future research topic.

3. Discussion

The expected net present value per planted seedling was calculated at Mex$51.40 or approxi-mately US$5.40. The positive net present value indicates that planting seedlings ofPouteria sapota

is expected to be an economically viable enterprise from a commercial viewpoint. The results confirm the conclusion of previous studies that non-timber forest products such as edible fruits can be com-mercially valuable assets of tropical forests (Peters et al., 1989; Schulze et al., 1994).

The land value of existing cattle pastures in the region is Mex$2000 – 10 000 per hectare, and this is also approximately the net present value of pas-ture (Ricker and Daly, 1998, pp. 221 – 223, 249). For an enrichment system to be competitive with that value, one would have to plant about 40 – 200 seedlings per hectare (2000/51.40=40 – 10 000/

51.40=195). This comparison is valid for two different situations. First, a land owner may have a forest that could either be enriched or converted into pasture. In order to maintain that 40 – 200 seedlings per hectare make enrichment competi-tive, one would have to assume that the costs of the conversion from forest to pasture (labor, buy-ing pasture seeds, fences and a mother cow) and the benefits (selling or using existing timber) cancel each other out. Second, a land owner may have a pasture that could either be maintained or refor-ested. In this case, existing cattle and fences could be sold to provide an additional benefit, and less seedlings per hectare would already make refor-estation competitive.

Planting 40 – 200 seedlings per hectare is possible within a semi-natural forest management system that conserves much biodiversity. While commer-cial fruit production may require tree selection, grafting and pruning, and the development of a wide crown rather than a high stem, such require-ments should not be prohibitive of a successful implementation of a semi-natural enrichment sys-tem. There is a continuum of possibilities, with the extremes being extracting fruits from the wild on the one hand, and establishing an intensive mono-culture on the other. Note that these calculations include an expected annual mortality rate of 2% so that each year there will be fewer of the planted trees, i.e. each year the forest becomes more natu-ral again (at age 30, 55% of the planted trees are expected to remain).

Table 1 provided the sensitivity analysis. The column ‘New NPV’ shows that one may be confi-dent of the economic viability of enrichment plant-ing in Los Tuxtlas withP.sapota: only 4 of the 22 bounds in the column ‘Changed parameter values’ contain a negative net present value in the column ‘New NPV’. The second-last column, ‘% change of NPV’, indicates the level of uncertainty. One can see which parameters should be estimated more accurately to get a ‘safer’ estimate of the net present value (i.e. with less variance). To compare parameters in the second-last column, one can look at the range between the lower and upper value (51.0+58.8=109.0 for a). Ordering parameters according to decreasing range of un-certainty, the resulting sequence starts with the growth form parameter for fruit yield (d) with the highest range, followed by the growth rate parameter for fruit yield (c), the discount rate (r), the growth form parameter for age determination (b), and the annual mortality rate (m). Note that the confidence limits are inaccurate for the parameters b and d, as discussed in point 4 of Section 2.1.

Fig. 2 shows clearly that there is much uncer-tainty about the increase of the annual fruit yield with age, and therefore about the parameters c

andd. Future research should focus on explaining this variation to find management that secures a rapidly increasing growth curve for annual fruit yield. Large fluctuations of annual fruit yield

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be-tween years for the same tree were notorious over the three study years. This phenomenon can also be noted in the statistical correlations between years of the same trees. As given in point 4 of Section 2.1, these are relatively low (though statis-tically significant), ranging between 0.31 and 0.50. The fluctuations between years made it difficult to compare habitats to find the optimal one because a single tree in a given habitat could produce a large yield in one year and a small one in another, hiding in this way any habitat effect.

The last column, ‘Ratio of % changes’, indi-cates the sensitivity or elasticity of the net present value to each parameter. For ordering the parameters from high to low sensitivity, one can calculate averages of the two values that corre-spond to lower and upper limits [(4.7+5.4)/2=

5.0 for a]. The resulting sequence in decreasing order starts with the growth form parameter for fruit yield (d) with the largest average of sensitiv-ity values, followed by the growth form parameter for age determination (b), the discount rate (r), the growth rate parameter for age determination (a), and the maximum predicted average diameter (DMax). These parameters should receive attention

from management because a small change in the parameter value has a large effect on the net present value. Note that the parameter a is also largely responsible for the age of first production in the model.

Interestingly, all parameters to which the net present value is highly sensitive are biological parameters, except the unmanageable, macroeco-nomic discount rater. The challenge to maximize the commercial value of the enrichment planting at this stage is primarily a biological one. While securing commercialization is important, the prices and cost parameters are at this point of lesser concern. First priority should be the selec-tion of high-quality, fast-growing varieties and growth improvements by fertilization.

In 1998, the geographic Los Tuxtlas area was declared a biosphere reserve by the Mexican fed-eral government. This has caused a renewed and increased interest to promote forestry and refor-estation, and to discourage the expansion of cattle ranching and agriculture. There are a number of tree species that should receive attention

(Ibarra-Manrı´quez et al., 1997). One of the most promis-ing native tree species besides Porteria sapota is probably Pimenta dioica (L.) Merr., whose fruits are well-known in the international market as ‘allspice’. The combination of several tree species for the local, national and possibly international market would secure income even under uncer-tainty about the biological and economic parame-ters: while the net return in a given year for a single species may be low (because of a low yield or price), it is unlikely to be low for all species at the same time. Such commercial diversification enriches the region not only biologically, but also culturally, when compared to complete specializa-tion on cattle ranching. Furthermore, the pro-posed enrichment requires mainly labor and almost no financial capital. Therefore, it is suit-able for poor farmers who own land but no capital.

Unfortunately, but not surprisingly, it is difficult to convince local farmers to change land use activities. One has to keep in mind that many of these people are illiterate and generally follow the activities of their family and neighbors. Poor farmers are not entrepreneurs. It should be noted that the proposed enrichment system is not meant to replace in a sudden move all other commercial activities on a farmer’s land. Rather, we recom-mend applying this management scenario in still existing forest that is threatened to be converted to cattle pasture. If farmers start managing these forests carefully at low intensity, they will con-sider them valuable and be interested in conserv-ing them. Pilot projects combined with extension services and commercialization support should be able to promote greatly such enrichment forestry. In conclusion, enrichment planting with com-mercially valuable tree species such as P. sapota

can be an economically viable alternative or com-plement to cattle ranching and other land uses that signify forest destruction. The analysis showed that maximization of the commercial value implies early rapid diameter growth and fruit production. Therefore, selection of high-quality, fast-growing varieties and fertilization should be the object of further research.

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Acknowledgements

We are grateful for the logistic and financial support provided by the Instituto de Biologıá (Universidad Nacional Autońoma de Me´xico, UNAM) — special thanks go to Hećtor M. Her-nańdez M., Robert Bye, Alfonso Delgado S., and Gonzalo Pe´rez H. Funds for the field work were obtained from the Programa Universitario de Ali-mentos (UNAM), under the direction of Ernesto Moreno M. Finally, we are grateful to Miguel A. Sinaca C. for assisting in the fieldwork.

References

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Cairns, M.A., Dirzo, R., Zadroga, F., 1995. Forests of Mexico — a diminishing resource? J. Forestry, July, 21 – 24. Condit, R., Hubbell, S.P., Foster, R.B., 1995. Mortality rates

of 205 neotropical tree and shrub species and the impact of a severe drought. Ecol. Monogr. 65, 419 – 439.

Dirzo, R., Garcı´a, M.C., 1991. Rates of deforestation in Los Tuxtlas, a neotropical area in southeastern Mexico. Con-serv. Biol. 6, 84 – 90.

Ibarra-Manrı´quez, G., Ricker, M., A´ ngeles, G., Sinaca C. S., Sinaca C., M.A., 1997. Useful plants of the Los Tuxtlas rain forest (Veracruz, Mexico): Considerations of their market potential. Econ. Bot. 51, 362 – 376.

Jacoby, G.C., 1989. Overview of tree-ring analysis in tropical regions. IAWA Bull. n.s. 10, 99 – 108.

Lieberman, D., Lieberman, M., Peralta, R., Hartshorn, G.S., 1985. Mortality patterns and stand turnover rates in a wet tropical forest in Costa Rica. J. Ecol. 73, 915 – 924. Maddala, G.S., 1992. Introduction to Econometrics.

Macmil-lan Publishing Company, New York, USA. 631 pp. Morton, J.F., 1987. Fruits of Warm Climates. J.F. Morton,

20534 SW 92 Ct., Miami, FL 33189, USA. 505 pp. Oyen, L.P.A., 1991.Pouteria sapota (Jacq.) H.E. Moore and

Stearn. In: Verheij, E.W.M., Coronel, R.E. (Eds.), Plant Resources of South-East Asia 2: Edible Fruits and Nuts. Pudoc, Wageningen, The Netherlands, pp. 259 – 262. Pennington, T.D., 1990. Flora Neotropica Monograph 52:

Sapotaceae. The New York Botanical Garden, Bronx, New York, USA. 770 pp.

Peters, C.M., Gentry, A.H., Mendelsohn, R.O., 1989. Valua-tion of an Amazonian rainforest. Nature 339, 655 – 656. Pienaar, L.V., Turnbull, K.J., 1973. The Chapman – Richards

generalization of Von Bertalanffy’s growth model for basal area growth and yield in even-aged stands. Forest Sci. 19, 2 – 22.

Ricker, M., 1998. Enriching the Tropical Rain Forest with Native Fruit Trees: A Biological and Economic Analysis in Los Tuxtlas (Veracruz, Mexico). Ph.D. thesis, Yale Uni-versity, School of Forestry and Environmental Studies; and Graduate School, New Haven, Connecticut, USA. UMI Dissertation Services, Ann Arbor, Michigan, USA, 262 pp. Ricker, M., Daly, D.C., 1998. Bota´nica econo´mica en bosques tropicales: principios y me´todos para su estudio y aprovechamiento. Editorial Diana, Me´xico D.F., Mexico, 293 pp.

Schulze, P.C., Leighton, M., Peart, D.R., 1994. Enrichment planting in selectively logged rain forest: A combined ecological and economic analysis. Ecol. Appl. 4, 581 – 592. Sullivan, A.D., Reynolds, M.R. Jr., 1976. Regression problems

from repeated measurements. Forest Sci. 22, 382 – 385. West, P.W., 1995. Application of regression analysis to

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M.Ricker et al./Ecological Economics31 (1999) 439 – 448 443

the sample size improves the estimate), each error term has to be uncorrelated with its corresponding X-variable, here D and Age, respectively (Maddala, 1992, chapter 9.1). We calculated Pearson correlation coefficients for each of the three cases, none of which was statistically significant [ru4−u5=0.02 (n=221),

ru4-D=– 0.02 (n=269), ru5-Age=0.04 (n=

225)]. Thus, there is no evidence that these assumptions were violated.

ra-b=0.11 (n=269); andrF_Max-c=– 0.72,rF_Max

-d=– 0.69, rc-d=0.99 (n=225). Highly

corre-lated parameters may cause misleading confidence intervals when these are con-structed on the assumption that each parame-ter individually presents a normal distribution independently from the other two parameters. Here, the confidence intervals constructed un-der this assumption in Table 1 lead to negative c and d, an impossibility in the BRC model. Truncating c and d to zero leads to extreme situations that are of interest, but that do not reflect 95% confidence limits: Withc=0, there is no fruit yield at all, and with d=0, from year 1 to the last year the fruit yield is the maximum one (FMax).

2.2. Predicting tree sur6i6orship

Turning to survivorship (S), the simplest model that has been employed is the negative exponen-tial function (Lieberman et al., 1985; Condit et al., 1995):

S=e–mAge

. (6)

In this model, the expected annual mortality rate mof a cohort is assumed to be constant through-out the tree’s life. Though this model is not accurate for very early and very late tree ages when mortality is high, it is useful for the type of data employed here. One has to assume that at i=1 year, the seedling stock is well-established in the field, thus having passed already through the 2. A statistical problem arises from measuring

97=0.67 (n=84),r96 – 97=0.82 (n=85)]. To a

lesser extent, significant correlations existed also for fruit yields of the same trees between years [r94−95=0.50 (n=72), r94−96=0.45

(n=71), r95−96=0.31 (n=74)]. While

Eqs. (4) and (5) independently assumes that their error terms (i.e. residualsu) are uncorre-lated (Borders, 1989). Furthermore, to get a consistent regression estimate (i.e. increasing

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Ricker

Ecological

Economics

(1999)

439

–

448

444

Sensitivity analysis forPouteria sapotafruit production

Parameter Explanation Original Changed Confidence % Change of New NPV in % Change of Ratio of %

NPV

parameter parameter value changes

parameter value interval Mex$

value

a(year–1₎ _{Growth rate} _0.0026237 _0.0023363 _{Lower 95%} _–11.0 _25.19 _–51.0 _4.7

0.0029111 Upper 95% +11.0 81.61 +58.8 5.4

parameter for age determina-tion

1.0590 0.9479 Lower 95% –10.5 143.13 +178.5 –17.0

Growth form

parameter for 1.1701 Upper 95% +10.5 7.21 –86.0 –8.2

age determina-tion

Lower 95% –19.6

DMax(cm) Maximum pre- 351.19 282.47 7.63 –85.2 –4.4

419.90 Upper 95% +19.6 108.01 +110.1 5.6

dicted average diameter

0 Truncated –100.0

c Growth rate 0.093059 –30.00 –158.4 1.6

0.190115 Upper 95% +104.3 410.12 +697.9 6.7

parameter for annual fruit yield

87.318 0 Truncated –100.0 2453.81 +4673.9 –46.7

Growth form

d(year–1₎

488.586 Upper 95% +459.5 –7.58 –114.7

parameter for –0.2

annual fruit yield

49.093 Lower 95%

FMax(kg) Maximum pre- 62.102 –20.9 34.34 –33.2 1.6

75.112 Upper 95% +20.9 61.05 +18.8 0.9

dicted average annual fruit yield

No –50.0 120.34 +134.1 –2.7

m Constant an- 0.02 0.01

No +100.0 –4.10 –108.0

0.04 –1.1

nual mortality rate

32.03 –37.7

P(Mex$/kg) Per-unit price 4.52 3.83 Lower 95% –15.3 2.5

70.76 +37.7 2.5

+15.3 Upper 95%

5.21

Per-unit cost 1.62 0.62 –61.7 79.46 +54.6 –0.9

C(Mex$/kg) No

23.33 –54.6 –0.9

+61.7 No

2.62

–40.0 258.22 +402.4 –10.1

r Annual discount 0.05 0.03 No

+40.0 –4.10 –108.0 –2.7

rate 0.07

K(Mex$/tree) Present value 30.00 10.00 No –66.7 71.40 +38.9 –0.6

50.00 No +66.7 31.40 –38.9 –0.6

per tree of all management costs

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M.Ricker et al./Ecological Economics31 (1999) 439 – 448 445

no contributions of old trees to the net present value.

The critical parameter to be adjusted in Eq. (6) for a specific site and species is the constant annual mortality rate m. Over the three study years, 6 of 100 individuals of a wide range of diameters (i.e. ages) died naturally at different times (4 in the first year, 0 in the second, and 2 in the third). Therefore,m was estimated to be 0.02 for a planted cohort [ln [1+(4/100+0/96+2/

To analyze which parameters are critical in determining the net present value, a sensitivity analysis for each model parameter is provided in Table 1. The first column (‘Parameter’) shows the 11 input parameters, and the second column (‘Ex-planation’) a short explanation about their mean-ing. The third column (‘Original parameter value’) presents the original input parameter values, re-sulting together in an average estimate for the net present value of Mex$51.40. Next, in column 4 (‘Changed parameter value’) an upper and lower bound is chosen. When possible, 95% confidence intervals based on a normal distribution were chosen to get these bounds (column 5, ‘Confi-dence interval’). In two cases (for c and d), the lower confidence limits were unrealistically less than zero, and were truncated to be zero (see point 4 in Section 2.1). For parameters without standard errors (m, C, r, K), ranges were chosen so as to be realistically possible.

For each upper or lower parameter, the whole net present value calculation was carried out,

keeping all other parameters at their original value. In the case of a, b and DMax, lower and

and d combined.

As an example, take the parameterain Table 1. In nonlinear regression with Eq. (4), the parame-ter a was calculated to be 0.0026237 (‘Original parameter value’). The 95% confidence limits ofa, assuming here a normal distribution, are 0.0023363 and 0.0029111. The column ‘% change of parameter value’ indicates that 0.0023363 is 11.0% lower than the original value of 0.0026237 [(0.0026237−0.0023363)(100)/0.0026237]. Using a=0.0023363 instead of 0.0026237, with all other parameters remaining at their original values, the net present value is Mex$25.19 (‘New NPV’). The column ‘% change of NPV’ shows that Mex$25.19 is 51.0% lower than the original net present value of Mex$51.40 [(51.40−25.19)(100)/51.40]. Fi-nally, the last column ‘Ratio of % changes’ shows that the elasticity of the net present value to the parameter a is 4.7. Each one percent-decrease of the value of a decreases the net present value on average by 4.7% (note that calculations were car-ried out with more than one decimal so that 4.7 rather than −51.0%/– 11.0%=4.6 resulted).

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3. Discussion

The expected net present value per planted seedling was calculated at Mex$51.40 or approxi-mately US$5.40. The positive net present value indicates that planting seedlings ofPouteria sapota is expected to be an economically viable enterprise from a commercial viewpoint. The results confirm the conclusion of previous studies that non-timber forest products such as edible fruits can be com-mercially valuable assets of tropical forests (Peters et al., 1989; Schulze et al., 1994).

Fig. 2 shows clearly that there is much uncer-tainty about the increase of the annual fruit yield with age, and therefore about the parameters c andd. Future research should focus on explaining this variation to find management that secures a rapidly increasing growth curve for annual fruit yield. Large fluctuations of annual fruit yield

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be-M.Ricker et al./Ecological Economics31 (1999) 439 – 448 447

tween years for the same tree were notorious over the three study years. This phenomenon can also be noted in the statistical correlations between years of the same trees. As given in point 4 of Section 2.1, these are relatively low (though statis-tically significant), ranging between 0.31 and 0.50. The fluctuations between years made it difficult to compare habitats to find the optimal one because a single tree in a given habitat could produce a large yield in one year and a small one in another, hiding in this way any habitat effect.