Effects of Variation on Harvest Limits for Nontimber ... · Ticktin et al. Harvest Limits for...

691

Conservation Biology, Pages 691–705Volume 16, No. 3, June 2002

Effects of Variation on Harvest Limits for Nontimber Forest Species in Mexico

TAMARA TICKTIN,*†‡** PATRICK NANTEL,* FERNANDO RAMIREZ,‡AND TIMOTHY JOHNS§

*Department of Plant Science, McGill University, 21 111 Lakeshore Road, Ste-Anne de Bellevue, Quebec H9X 3V9, Canada †Department of Botany, University of Hawaii at Manoa, 3190 Maile Way, Honolulu, HI 96822–2279, U.S.A., email [email protected]‡Proyecto Sierra Santa Marta A.C., Cúahtemoc 10A, Xalapa, Veracruz 91000, México§Center for Indigenous Peoples’ Nutrition and Environment, McGill University, 21 111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec H9X 3V9, Canada

Abstract:

Successful conservation of nontimber products and their rainforest habitats requires the identifica-tion of optimal harvest regimes, the accurate estimation of maximum harvest limits, and the implementationof those limits by local harvesters. We used a combination of participatory research techniques and demo-graphic modeling to determine maximum sustainable harvest rates of the bromeliad

Aechmea magdalenae

inthe buffer zone of the Los Tuxtlas Biosphere Reserve in Mexico. We examined the effects of three types of vari-ation on maximum harvest rates: variation between forest types, between harvest regimes, and over time. Wealso tested the accuracy of estimating maximum harvest limits using matrix-model projections of unhar-vested populations. Maximum harvest rates of ramets from secondary forest populations were much higherthan from primary-forest populations. Likewise, variation in local harvest regimes had a large effect on max-imum harvest rates. Populations concurrently harvested for leaves and ramets had higher maximum sustain-able levels of ramet harvest than those harvested for ramets only. Simulations using harvested and unhar-

vested populations yielded significantly different estimates of maximum sustainable harvest limits, indicatingthat methods for calculating maximum harvest limits that assume linear responses to harvest may lead to er-

roneous conclusions. Active participation in the research process enabled local harvesters to accept as valid theharvest limits determined in this study, to switch to using a more sustainable harvest regime, and to pass alocal law prohibiting the destruction of their remaining primary forest because of its potential as

A. magdale-nae

habitat.

Efectos de la Variación Sobre los Límites de Cosecha de Especies Forestales No Maderables en México

Resumen:

La conservación exitosa de productos no maderables y sus hábitats boscosos requiere de la identi-ficación de regímenes de cosecha óptimos, la estimación precisa de límites de cosecha máximos y la instru-mentación de esos límites por los recolectores locales. Utilizamos una combinación de técnicas de investi-gación participativa y modelaje demográfico para determinar las tasas máximas de cosecha sostenible de labromeliácea

Aechmea magdalenae

en la zona de amortiguamiento de la Reserva de la Biosfera Los Tuxtlas enMéxico. Examinamos los efectos de tres tipos de variación en las tasas máximas de cosecha: variación entretipos de bosque, entre regímenes de cosecha y en el tiempo. También probamos la precisión de la estimaciónde límites máximos de cosecha utilizando modelos de proyección matricial de poblaciones no cosechadas.Las tasas máximas de cosecha de rámulas en poblaciones de bosque secundario fueron mucha más altas queen poblaciones de bosque primario. De igual modo, la variación en los regímenes de cosecha local tuvo unefecto notable en las tasas de cosecha máxima. Las poblaciones concurrentemente cosechadas para hojas y

rámulas tuvieron niveles de máxima cosecha sostenible de rámulas más altos que las cosechadas para rámulas

**

Address for correspondence University of Hawaii at Manoa.Paper submitted August 28, 2000; revised manuscript accepted August 2, 2001.

692

Harvest Limits for Nontimber Forest Species Ticktin et al.

Conservation BiologyVolume 16, No. 3, June 2002

solamente. Simulaciones utilizando poblaciones cosechadas y no cosechadas produjeron estimaciones delímites de cosecha máxima sostenible significativamente diferentes, lo que indica que los métodos para calcu-lar los límites máximos de cosecha que asumen respuestas lineales a la cosecha pueden conducir a conclu-siones erróneas. La participación activa en el proceso de investigación posibilitó que los cosechadores localesaceptaran como válidos los límites de cosecha determinados por este estudio, que cambiaran a utilizar unrégimen de cosecha más sostenible y aprobaran un ley local que prohibe la destrucción de los bosques prima-

rios debido a su potencial como hábitat de

A. magdalenae

.

Introduction

In many parts of the world, human communities livingin buffer zones or around nature reserves extract a largenumber of nontimber forest products ( NTFP ) for bothtrade and subsistence. An increasing number of reportshave documented the overharvest of NTFP and its nega-tive effects on plant and animal populations (e.g., Cun-

ningham & Milton 1987; Vasquez & Gentry 1989; Pinedo-Vasquez et al. 1992; O’Brien & Kinnaird 1996; Clay 1997).

Participatory research on establishing harvest limits forNTFP extracted from buffer zones may help ensure theconservation of overharvested NTFP and the integrity ofthe reserves. Participatory research involves the coopera-tion of local harvesters in a simultaneous research and edu-cation process. It can be a critical component of conserva-tion efforts, because when NTFP species are overharvestedin buffer-zone forests, harvesters often meet their eco-nomic needs by illegally harvesting them in the reserve.

Sustainable harvest regimes combined with forest cul-tivation can maximize yields in buffer zones and there-

fore decrease economic pressure for illegal harvestingin adjoining protected areas. Higher economic returnsfrom nontimber extraction provide greater incentives forbuffer-zone harvesters to maintain forest cover (e.g., Nep-

stad & Schwartzman 1992), which decreases edge effectsin the reserve. Still, forest cultivation may increase pres-sure on wild populations as vegetative propagulesneeded for cultivation are collected. There is therefore agreat need to design novel and feasible sustainable har-vest strategies for NTFP species.

At least three things are necessary to protect NTFP spe-cies from overharvest and for NTFP extraction in bufferzones to contribute to forest conservation: ( 1) identifica-tion of optimal harvest regimes, (2) accurate estimationof maximum harvest limits, and (3) implementation ofthose limits among local harvesters. The first and thirdtasks require the participation and cooperation of localharvesting communities. The accurate estimation of maxi-mum harvest limits poses more technical problems. First,it necessitates a sound description of the effects of envi-ronmental variation on maximum sustainable harvest rates( MSH ). Second, the methods used to estimate MSH mustbe validated.

The effects of environmental variation on MSH are farfrom completely described. For instance, we know of no

studies that have examined how MSH for a given speciesmay vary among forest types or ages. Likewise, althoughharvest regimes may vary greatly among cultures, regions,and even individual harvesters, few studies have simulatedMSH for different harvest regimes ( Nantel et al. 1996 ),and none that we know of have done so using empiricallyderived data.

The effects of year-to-year environmental variation onmaximum sustainable harvest of NTFP have been exam-ined through stochastic population projections based ontransition matrices ( Nantel et al. 1996 ). Stochastic andperiodic population projections take into account someinterannual variability in vital rates, such as mortality andfecundity, by including a number of different yearly ma-trices in the projections. Environmental variations mayinteract in various ways with the effects of harvest ( Na-tions & Boyce 1997 ), and the annual rate of harvest itself

may vary from year to year. For the two species they stud-ied, Nantel et al. ( 1996 ) found that stochastic simulationspredicted MSH to be much lower than those estimatedunder the assumption of a favorable and unchanging envi-ronment, but it remains unknown how this may apply toother NTFP.

More important, current methods for estimating maxi-mum sustainable harvest for NTFP have not been validated.All reported studies have estimated MSH by describingthe dynamics of unharvested populations and using matrixmodels to simulate increasing harvest rates (e.g., Peters1990; Charron & Gagnon 1991; Nantel et al. 1996; Ratsirar-son et al. 1996; Bernal 1998). The harvest rate at which the

finite rate of population increase,

�

, drops below one is theoperational definition of the MSH. Most of these studiesrecognize that matrix models rely on a number of as-sumptions, in particular that population growth is inde-

pendent of density. But because solving for

�

is consid-ered a good way of characterizing the present environment(Caswell 1989), it has been assumed that this approach canprovide a realistic assessment of MSH in the short term. Inreality, harvest simulations with matrix-model projectionsbased on unharvested populations have never been tested,and their accuracy remains unknown ( Boot & Gullison1995). We used data from harvested and unharvested pop-

ulations of

Aechmea magdalenae

(Andre) Andre ex Bakerto (1) examine the effects on MSH of three sources of varia-tion, variation in forest age ( primary vs. secondary forests),variation among harvest regimes, and interannual envi-


Ticktin et al. Harvest Limits for Nontimber Forest Species

693

ronmental variation and (2) test the accuracy of estimat-ing MSH from matrix-model projections of unharvestedpopulations.

A. magdalenae

, a typical NTFP species, is a clonal un-derstory bromeliad harvested from the buffer zone of theLos Tuxtlas Biosphere Reserve in the state of Veracruz,Mexico. The strong, silky fiber extracted from its leavesis used to embroider expensive leather articles in an art

known as

el piteado.

The ramets are also harvested foruse in forest cultivation programs. Although nongovern-mental and governmental agencies have been promotingthe harvest of

A. magdelanae

as a strategy to encouragelocal harvesters to conserve the standing forest, the ele-vated economic value of

A. magdalenae’

s fiber has alsoresulted in high harvesting pressure on wild popula-tions. The species, collected by local harvesters through-out southeastern Mexico and Guatemala, is reported tohave disappeared from several regions due to overhar-vest ( Ticktin 2000).

Specifically, our objectives were (1) to compare theMSH of

A. magdelanae

ramets from primary and sec-ondary forest populations; (2) to compare the MSH of

A.magdelanae

populations under two different local fiber-harvest regimes; (3) to compare the MSH calculated fromtime-invariant models with MSH simulations that includeyear-to-year variation in vital rates; and (4 ) to test the ac-curacy of MSH estimates based on the dynamics of unhar-vested populations.

Methods

Species and Study Area

A. magdalenae

is a terrestrial bromeliad with long, spinyleaves up to 3 m in length. It is monocarpic and found indense and usually monospecific patches along streams,in swampy areas, and on hillsides in humid Neotropicalrainforests from Mexico to Ecuador (Croat 1978).

In the communities along the eastern coastal plain ofthe buffer zone of the Los Tuxtlas Biosphere Reserve,harvesters extract

A. magdalenae

from lowland regions(0–800 m ) of humid, tropical rainforest dominated by

Terminalia amazonica, Brosimium alicastrum

, and

Di-alium guianense.

The average annual temperature of this

region is 25

�

C, and average precipitation is about 2700mm. There is a heavy rainy season from May to Octoberand a short dry season from March to May.

In the buffer zone of Los Tuxtlas Biosphere Reserve,

A. magdalenae

populations are subject to four harvestregimes: ( 1) ramet harvest ( RH ) in primary forest, (2) RHin secondary forest, (3) combined leaf harvest and rametharvest ( LRH ) in primary forest, and (4) combined adult-plant harvest and ramet harvest ( PRH ) in primary forest.

There are also some populations that have not beenharvested. The ramets harvested from all populations are

�

120 cm wide and are used to initiate

A. magdalenae

plantations in new areas of forest. This form of extrac-tion has been practiced only over the past 5 years, start-

ing when cultivation of

A. magdalenae

was first pro-moted by regional conservation organizations. Populationsharvested for only ramets are often young and have regen-erated after fire, with few plants large enough to be har-vested for their fiber.

The LRH and PRH are two different harvest regimesused to obtain the long, fiber-containing leaves. In LRHpopulations, harvesters cut the longest leaves off the plantwith a machete and leave the individual to regenerate untilits new leaves reach harvestable length (160 cm long). InPRH populations, harvesters extract entire adult plantsby cutting the plant at the base. This regime, which killsthe plant, is quicker and easier than the LRH regime andhas been practiced only as a result of the high demandfor

A. magdalenae

from the piteado industry.

Matrix Construction

Prior to initiating harvesting simulations, we carried outsome analyses and comparisons of transition matrices forharvested and unharvested

A. magdalenae

populations( Ticktin 2000). We recorded the dynamics of three pop-ulations for each harvest regime. For each population,all

A. magdalenae

plants within an area of 4

�

10–20 mwere labeled with aluminum tags and mapped. This cor-responded to approximately 100 plants per population.All labeled plants were surveyed biannually for plant width,which was measured in two directions: the distance be-tween the tip of one of the outermost leaves to the tip ofthe longest leaf that lay at 180

�

to it, and the distance be-tween the two longest leaves that lay at 90

�

to those. All

plots were established between September 1996 and March1997 and were surveyed every 6 months until September1999.

Our basic matrix model consisted of a population di-vided into stage classes and a matrix of transition proba-bilities from one class to another across one time inter-val (Lefkovitch 1965). Multiplication of the transitionmatrix by an initial population at time

t

results in a col-umn vector representing the population size and stage

structure at time

t

�

1. Repeated multiplication ofthe matrix by the column vector will eventually pro-duce lambda (

�

), the dominant latent root of the matrix,and the roots-associated left and right eigenvectors. Anyinitial population described by a transition matrix whenprojected to its stable stage distribution will increase bythe value

�

during each time interval. Lambda is equal to

e

r

, the finite rate of increase of a population.To establish stage classes, we combined reproductive

criteria with size criteria ( following Horvitz & Schmen-ske 1995) because reproduction and vegetative propaga-tion were found to vary significantly with size. We esti-mated size by measuring plant width because this was

694

Harvest Limits for Nontimber Forest Species Ticktin et al.


the best predictor of total leaf area (

r

2

�

0.84,

n

�

40).Within reproductive (including vegetative propagation)categories, stages were divided according to the algorithmproposed by Vandermeer (1978), which minimizes bothsample and distribution errors. Ramets connected tomother plants were put in separate classes from discon-nected ramets because they had different rates of sur-vival and growth.

A. magdalenae

genets could not be distinguished vi-sually and matrix model analysis was performed on theramets, which have independent transition probabilitiesand should therefore be regarded as demographically rel-evant. Transition matrices were built by following thefate of stage-classified plants over 1-year periods. That is,we recorded the number of plants that grew to a largerstage class, regressed to a lower stage class, stayed in thesame stage class, or died. We also summed the number ofnew ramets of a given stage class so that we could calculaterates of vegetative propagation. The transition matricestherefore combined the proportion of plants that were instate

i

at time

t

and had the fate

j

at time

t

�

1 with therates of vegetative division in each class.

We summed the transitions of the plants from thethree plots per harvest type to build the annual matrices( Ticktin 2000; Appendix). Matrices were solved for

�

bythe power method (Caswell 1989) in Microsoft Excelspreadsheets.

Quantification of Harvest Rates

To integrate the harvesting community into the researchprocess and to accurately document and quantify therates and patterns of harvest in each population and un-der each harvest regime, we used participatory researchmethods. Harvesters were involved in all stages of the re-search, from ideas for experiments to data collection, in-terpretation, and dissemination of results ( Ticktin 2000).

Harvesters kept a record of all ramets, leaves, and adultplants harvested in RH, LRH, and PRH populations. In LRHtransects, the number, length, and width of all leaves wererecorded for each plant before and after harvest. To en-sure that records of ramet harvest were accurate, we vis-ited all populations biweekly and marked all the newlyemerged ramets. This allowed us to account for rametsthat may have been stolen and therefore gone unrecorded.Harvesters also noted the date of harvest and the spatialpattern of harvest by recording the exact location of ev-ery harvested plant on population maps we provided forthem.

Data Analysis and Modeling

We estimated the maximum sustainable harvest for

A.magdalenae

populations under each harvest regime based

on ( 1 ) deterministic population projections and (2)periodic and stochastic projections. We used different ap-

proaches depending on whether the transition matriceswere built from survey data and harvest records of har-vested populations or from survey data of unharvestedcontrol populations ( Table 1). All simulations were runwith macros and worksheets designed and programmedby P.N. on Microsoft Excel.

Estimation of Maximum Sustainable Harvest with Average Matrices

For ramet-harvest populations in primary and in second-ary forests and for unharvested populations, transition co-efficients were averaged across periods to give one matrixper harvest regime. We documented two transition peri-ods involving harvests documented for RH populations inboth primary and secondary forests and two transitionperiods for the control population. The transition coeffi-cients were averaged to incorporate temporal heteroge-neity so that we could compare the MSH values obtainedby this method with those obtained with stochastic andperiodic simulations that were based on annual matrices.The MSH of ramets was estimated by simulating post-reproductive harvests of the ramet stage classes with thefollowing equation (Getz & Haight 1989):

(1)

For each simulated year (

t

), the vector

N

(

t

�

1) containedthe projected number of individuals per stage class afterharvest, vector

N

(

t

) contained the number of individuals

per stage class before harvest, the transition matrix

A

de-scribed the fates (with or without harvest, depending onthe population surveyed ) of all stage classes, and the

vector

h

s

a

1

N(

t

) represented the number of ramets har-vested per stage class for year

t

. The simulated harvestrate,

a

1

h

s

, was calculated as the proportion of harvestedramets relative to the total number of ramets before har-vest (

h

s

), multiplied by the proportion of harvestableramets in each stage class (vector

a

1

). Values of

a

1

werekept constant through time and were equal to {0, 1, 1, 1,0.4, 0, 0} because all plants in stage-classes 2–4 were har-vestable ramets, 40% of plants in stage-class 5 were ofharvestable size (

�

120 cm width), and no plants instage-classes 1, 6, and 7 were harvestable ramets.

The values for

h

s

ranged from 0 (no ramet harvested )to 1 (all ramets harvested ), and for each

h

, we computeda

�

value after running equation 1 over 50 years (i.e., as

N

(49)/

N

(50)). This resulted in a declining series of

�

val-ues as the harvest rate was increased. For all the harvestregimes, MSH was calculated as the rate of harvest atwhich the

�

values dropped below 1.0 ( Peters 1990).We used jack-knife resampling (Caswell 1989) to esti-

mate 95% confidence intervals for the

�

values obtainedwhen

h

s

�

0. We then obtained the confidence intervalsfor MSH by plotting the

�

values versus the simulatedharvest rates

a

1

h

s

and determining the harvest rates thatcorresponded to the

�

value’s outer confidence limits.

N t 1+( ) AN t( ) hsa1N t( ).–=


Ticktin et al. Harvest Limits for Nontimber Forest Species 695

Tabl

e 1.

Equa

tions

use

d fo

r es

timat

ing

max

imum

sus

tain

able

rat

es o

f har

vest

(M

SH)

of A

echm

ea m

agda

lena

e ra

met

s un

der

diffe

rent

har

vest

reg

imes

and

for

diffe

rent

type

s of

pro

ject

ion

mat

rice

s bu

ilt fr

om d

ata

from

har

vest

ed a

nd u

nhar

vest

ed p

opul

atio

ns.

Ma

trix

pro

ject

ion

Ha

rves

t re

gim

eP

opu

lati

on

su

rvey

edE

qu

ati

on

use

d f

or

esti

ma

tin

g M

SH o

f ra

met

sC

om

men

ts o

n k

ey p

ara

met

ers

Det

erm

inis

tica

ram

ets

on

lyco

ntr

ol

ram

et-h

arve

sted

N(t

� 1

) �

AN

(t)

� h

sa1N

(t)

N(t

� 1

) �

AN

(t)

� h

sa1N

(t)

Val

ues

of

hs,

the

pro

po

rtio

n o

f h

arve

sted

ra

met

s re

lati

ve t

o t

hei

r n

um

ber

bef

ore

h

arve

st, w

ere

allo

wed

to

var

y fr

om

0

(no

har

vest

) to

1 (

har

vest

of

all r

amet

s).

Vec

tor

a 1 w

as k

ept

con

stan

t th

rou

gh t

ime

�{0

, 1, 1

, 1, 0

.4, 0

, 0}.

leav

es a

nd

ram

ets

con

tro

lN

(t �

1)

� A

N(t

)� h

sa1N

(t)

Co

effi

cien

ts in

mat

rix

A d

escr

ibin

g th

e fa

te o

f d

efo

liate

d p

lan

ts w

ere

eith

er c

om

pu

ted

fro

m

dat

a fr

om

an

ex

per

imen

tal d

efo

liati

on

ca

rrie

d o

ut o

n s

ite

or

assu

med

to b

e th

e sa

me

as in

th

e LR

Hb p

op

ula

tio

n.

leaf

-har

vest

edN

(t �

1)

� A

N(t

) �

hsa

1N

(t)

Effe

ct o

f le

af h

arve

st w

as a

cco

un

ted

fo

r (e

mp

iric

ally

) in

mat

rix

A.

adu

lt p

lan

ts a

nd

ram

ets

con

tro

lN

(t �

1)

� {

A [

N(t

) �

haa 2

N(t

)] }

– h

sa1N

(t)

Har

vest

was

pre

-rep

rod

uct

ive

for

adu

lt p

lan

ts

and

po

st-r

epro

du

ctiv

e fo

r ra

met

s. V

ecto

r a 2

h

ad n

on

-zer

o v

alu

es o

nly

fo

r ad

ult

sta

ge-

clas

ses

and

ha, t

he

emp

iric

ally

rec

ord

ed

har

vest

rat

e w

as k

ept

con

stan

t.p

lan

t-h

arve

sted

N(t

� 1

) �

AN

(t)

� h

sa1N

(t)

Har

vest

of w

ho

le a

du

lt p

lan

ts w

as a

cou

nte

d fo

r (e

mp

iric

ally

) in

mat

rix

A.

Per

iod

ic a

nd

sto

chas

ticc

ram

ets

on

lyco

ntr

ol

N(t

� 1

) �

AtN

(t)

� h

saN

(t)

ram

et-h

arve

sted

N(t

� 1

) �

max

imu

m o

f [A

tN(t

) �

haaN

(t)

� h

saN

(t)]

or

0M

atri

ces

At e

mp

iric

ally

acc

ou

nte

d f

or

ram

et

har

vest

. Fo

r ea

ch s

imu

late

d y

ear,

th

e m

od

el

firs

t p

ut

the

har

vest

ed r

amet

s b

ack

in t

he

po

pu

lati

on

bef

ore

sim

ula

tin

g th

e h

arve

st

and

nev

er h

arve

sted

mo

re r

amet

s th

an t

her

e ac

tual

ly w

ere

in e

ach

sta

ge c

lass

.le

aves

an

d r

amet

sco

ntr

ol

N(t

� 1

) �

AtN

(t)

� h

saN

(t)

leaf

-har

vest

edN

(t �

1)

� A

tN(t

) �

hsa

N(t

)St

och

asti

c an

d p

erio

dic

pro

ject

ion

s u

sed

th

ree

mat

rice

s: t

wo

fro

m le

af-h

arve

st p

erio

ds

sep

arat

ed b

y o

ne

fro

m a

no

nh

arve

st p

erio

d.

adu

lt p

lan

ts a

nd

ram

ets

con

tro

lN

(t �

1)

� {

At [

N(t

) �

haa 2

N(t

)] }

– h

sa 1

N(t

)P

erio

dic

on

lyd

pla

nt-

har

vest

edN

(t �

1)

� A

tN(t

) �

hsa

N(t

)aC

oef

fici

ents

of

ma

trix

A w

ere

ave

rage

s of

yea

rly

ma

tric

es.

bC

om

bin

ed lea

f a

nd r

am

et h

arv

est

(LR

H).

c Ma

trix

At w

as

cha

nge

d e

ach

sim

ula

ted y

ear

an

d d

raw

n f

rom

a p

erio

dic

or

a r

an

dom

ser

ies

of

tra

nsi

tion

ma

tric

es.

dO

nly

tw

o m

atr

ices

wer

e a

vail

able

, on

e fo

r a

ha

rves

t per

iod a

nd o

ne

for

a n

on

ha

rves

t per

iod, a

nd h

arv

ests

wer

e bie

nn

ial.

696 Harvest Limits for Nontimber Forest Species Ticktin et al.


This method assumes a constant jack-knife variance of �values across harvest rates.

Throughout, we use the term post-reproductive to re-fer to production of ramets. Our models did not includereproduction by seeds, because we did not observe flow-ering in any of the populations over the 3-year study. De-mographic analyses of flowering populations indicate,however, that sexual reproduction probably plays a mi-nor role in the population dynamics of this species ( Ville-gas 1997 ). Harvesting of ramets was assumed to be post-reproductive because most ramets were collected in oneevent per year, just after the wet season when ramet pro-duction was highest and several months after the popula-tions had been surveyed ( Ticktin 2000).

Concurrent Harvest of Leaves and Ramets

In LRH populations, leaves were collected at the timeof, or just after, our surveys. Once every 1.5–2 years, allleaves of commercial value (160 cm long) were col-lected from all plants with a width of 230 cm. We con-sidered this to be the maximum rate of leaf harvest, be-cause harvesters never collected leaves without commercialvalue. The MSH for concurrent leaf and ramet harvest wastherefore simulated in LRH populations by increasing therate of ramet harvest only (the harvest rate of leaves waskept constant at the empirical value).

To estimate MSH for concurrent leaf and ramet harvestwith data from the unharvested populations, we usedtwo methods to estimate the effect of leaf harvest on thefates of plants. For the first method, hereafter referredto as the “size” method, we assumed the fates of leaf-har-vested plants to be the same as those of unharvestedplants of equal size. Simulations were run so that afterleaf harvest 55% of all leaf-harvested plants went into theadult 2 stage class and 45% of them went into the adult 1stage-class. These transition coefficients were obtainedby measuring the length and width of 110 plants imme-diately after their leaves had been collected. For the sec-ond method, hereafter referred to as the “experimental”method, we assumed the fates of leaf-harvested plants tobe the same as those of plants experimentally defoliatedand monitored outside the surveyed portion of the pop-ulation ( Ticktin 2000).

Concurrent Harvest of Whole Adult Plants and Ramets

In PRH populations, all plants with more than four leavesof commercial value were harvested. This resulted in re-moval from the surveyed populations of all plants with awidth of 260 cm. As in the case of LRH populations,this rate of adult plant harvest was assumed to be themaximum. Harvests were usually carried out during oneevent about every 2 years, but they could have been lessfrequent depending on how fast the harvested plantswere replaced through natural regeneration. We simu-

lated the concurrent harvest of adult plants and rametsusing survey data from the PRH populations. We kept theadult-plant harvest rate constant (at the recorded empiri-cal value) and increased the rate of ramet harvest until �values fell below 1.

We considered the harvest of adult plants to be pre-reproductive because plants were collected immediatelyafter the surveys, before they could have contributed topopulation growth. Therefore, our simulations based ondata from unharvested populations assumed pre-repro-ductive harvests for adult plants and post-reproductiveharvest for ramets. We used the following equation torun the simulation:

(2)

where vector a2 had non-zero values only for adult stageclasses, ha was the harvest rate observed in harvested pop-ulations, vector a1 had the same values as in equation 1,and hs was allowed to vary from 0 to 1.

Estimation of Maximum Sustainable Harvest with Periodic and Stochastic Matrices

For each harvest regime, we also estimated maximum sus-tainable harvest with variable transition matrices using (1)periodic series of yearly matrices alternating in the sameorder in which they were observed and (2) stochastic se-ries consisting of the random alternation of the sameyearly matrices. These projections assumed that the meanand variance of each transition coefficient in a limited setof matrices were representative of their mean and vari-ance in a much larger set (Nantel et al. 1996 ). The meangrowth rate, �, was defined as the slope of the regres-sion of log10( N( t )) against time after 100 simulated years,following Nantel et al. ( 1996 ). This number of iterationsgave stable �. A series of annual �(t ) values, computed asN(t � 1)/N(t ), was also calculated. We computed the vari-ance of �(t ) and associated 95% confidence intervals usingthe standard formulas for random variables as rough esti-mates of the true confidence intervals for �. We estimatedconfidence limits for MSH by determining the harvestrates that corresponded to the outer confidence intervalsfor the � values.

For unharvested populations, we ran stochastic and peri-odic simulations with two yearly matrices. We used theseto simulate the MSH for harvests of (1) ramets only, (2)leaves and ramets, and (3) adult plants and ramets. We car-ried out stochastic and periodic projections by projectingthe equation for the post-reproductive harvest of rametsthrough time:

(3)

The difference between equations 1 and 3 is that inequation 3 the transition matrix A t varied for each simu-lated year and was drawn from either a periodic or a ran-dom series of transition matrices.

N t 1+( ) A N t( ) haa2N t( )–[ ]{ } hsa1N t( ),–=

N t 1+( ) AtN t( ) hsaN t( ).–=



The stochastic and periodic projections for RH popu-lations in primary and secondary forests were run withtransition matrices from three different transition peri-ods. Harvest intensity varied over these periods, so tokeep the harvest rate constant among simulated years,for each iteration we used a model that first put the har-vested ramets back into the population and then simu-lated harvest. We did this by running the following equa-tion over time:

(4)

This model never permitted the harvest of moreramets than there were in each stage class. We calculatedthe number of ramets actually harvested in each stageclass at time t was by multiplying the number of harvest-able ramets (aN(t ), as in equation 1) by the actual harvestrate ha. The ha was a fixed parameter associated with eachyearly transition matrix, whereas hs was the simulated har-vest rate. Both parameters ranged from 0 (no rametsharvested) to 1 (all ramets harvested) and were computedas the proportion of ramets harvested relative to the totalnumber of ramets in the previous survey.

For the LRH populations, stochastic and periodic pro-jections were run with three matrices: two from leaf har-vest periods, separated by one from an unharvested pe-riod. For the PRH populations, only two matrices wereavailable: one for a harvest period and one for a nonhar-vest period (fire destroyed two of the three populationsafter the second year of monitoring). In both LRH andPRH populations, the periodic alternation of matricessimulated biennial harvests of adult plants and leaves,respectively, and we used equation 3 to simulate an an-nual harvest of ramets. Because harvests of adult plantswere biennial, only periodic projections were run forPH populations.

Projections of Fiber Yield

To assess the economic implications of different harvestregimes for local harvesters, we used periodic simulationsto estimate maximum fiber yields for both PRH and LRHharvests over 5 years (three harvests). These populationswere harvested biennually at their maximum rates of leafor plant harvest and had a similar annual ramet harvestrate of about 25%. We estimated yield by multiplying thenumber of harvestable plants in the projected populationstructures by the average fiber yield per plant, as calcu-lated by T.T. ( Ticktin 2000). Leaf yield was assumed toremain stable over the three consecutive harvests, giventhat experimental harvests showed that it did not de-crease from the first to second harvest ( Ticktin 2000).

We also compared estimates of maximum fiber yieldsobtained from simulations based on data from unharvestedpopulations with those based on data from harvested pop-ulations. To do so, we repeated the same method we used

N t 1+( )maximum of AtN t( ) haaN t( ) hsaN t( )–+[ ]or 0.

=

to calculate yields in the harvested populations, but theprojected population structure was obtained with a peri-odic projection of matrices from the unharvested popu-lations that were simulated for the MSH of leaves andplants and calculated yields as above.

Results

Maximum Sustainable Rates of Ramet Harvest

The average transition matrix of the RH primary-forestpopulations had a � � 1.000. The average harvest rate ofthese populations over the 3-year period was about 38%,so we considered this the MSH for ramets of RH primaryforest populations ( Table 2). When ramet harvest wassimulated from the unharvested populations, the MSH waspredicted to be only 22%. When the 95% confidence inter-vals of the � value for the RH population were taken intoaccount, the two values were not significantly different.

The stochastic and periodic simulations did not differfrom each other, and although the MSH they predictedwas about 15% higher than that of the average matrix,the values were not significantly different. Likewise, MSHcalculated from the stochastic, periodic, and average pro-jections that simulated ramet harvest using the unharvestedpopulation matrix showed no significant differences. TheMSH of the RH secondary forest populations was morethan twice that of the RH primary forests: 100% of the har-vestable ramets could be sustainably harvested accordingto average, periodic, and stochastic simulations (Table 2).

Maximum Sustainable Rates of Concurrent Leaf andRamet Harvest

Leaf harvest was already at its maximum in LRH popula-tions because we considered the maximum rate equal tothe harvest of all leaves with commercial value. For all

Table 2. Comparison of maximum sustainable rates of ramet harvest ( MSH ) in Aechmea magdalenae populations simulatedin two types of forest and with harvested and unharvested populations.*

MSH of ramets(% of harvestable ramets)

Population average periodic stochastic

Ramet harvest in primaryforest 38 25 55 15 55 15

Ramet harvest in secondaryforest 100 100 100

Unharvested in primary forest 22 11 20 10 20 10

*Values are to the proportion of harvestable ramets (40–120 cmwidth or connected to mother plant) 95% confidence intervalsand were determined from projections using time series of three an-nual transition matrices.



populations and projections, the MSH of leaves was 100%of individuals of 230 cm width. For these individuals,harvest implies that 75% of the total leaves are removed.

The MSH for concurrent leaf and ramet harvest basedon the average matrix for LRH populations was esti-mated as 100% harvest of ramets ( Table 3). This is abouttwice the MSH of ramets calculated from the RH popula-tions in primary forests ( Fig. 1). Periodic and stochasticsimulations of LRH matrices showed that the MSH of rametscombined with a biennial leaf harvest ranged from 80% to100%.

The simulation of concurrent leaf and ramet harvestwith the unharvested population matrix by the experi-mental method gave MSH estimates that were closer toempirical values than those of the size method ( Table 3).Although both methods predicted that there could beadditional ramet harvest on top of maximum levels ofleaf harvest, the maximum additional ramet harvest de-termined by the experimental method was more thantwice that determined by the size method. Simulationswith average, periodic, and stochastic projections fromthe size method predicted a 10–15% MSH of additional

Table 3. Comparison of maximum sustainable rates of ramet harvest ( MSH ) for Aechmea magdalenae populations subject to concurrent leaf and ramet harvest simulated with harvested and unharvested populations.a

MSH of ramets (% of harvestable ramets)

Population average periodic stochastic biennial harvest

Leaf and ramet harvest 68 18b 100 100 100 20Unharvested (size method ) 13 7 12 2 12 2 15 4Unharvested (experimental method ) 18 12 28 7 26 7 30 3aValues represent the proportion of harvestable ramets (40–120 cm width or connected to mother plant) 95% confidence intervals and weredetermined from projections using time series of three annual transition matrices for harvested populations and two annual matrices for un-harvested populations. For all populations and projections, the MSH of leaves was 100% of individuals of commercial size.bThe MSH of ramets for defoliated populations in the year when there was no leaf harvest was 74 31%.

Figure 1. Decline in mean popula-tion growth rate with increasing rates of ramet harvest for Aechmea magdalenae populations under dif-ferent harvest regimes. Stochastic simulations were run with three annual matrices for all popula-tions except for plant harvested and unharvested populations, which were run with two annual matrices. For leaf-and-plant harvest populations, simulations assumed biennial fiber harvest. Ramet har-vest refers to the percentage of ramets harvested relative to the number of harvestable ramets. The harvest rate at which � � 1 is the maximum sustainable harvest.



ramets. The experimental method predicted the MSH ofadditional ramets to be about 20–35% with the periodicand stochastic simulations. These were slightly higher thanthe value predicted from the average matrix, but not signif-icantly different.

Maximum Sustainable Rates of Adult and Ramet Harvest

As was the case with leaf harvest, plant harvest was al-ready at its maximum in PRH populations, because weconsidered the maximum rate equal to the harvest of allplants with commercial value (plants 260 cm width).The MSH for concurrent plant and ramet harvest in thePRH populations was estimated to be all plants of com-mercial value and about 40% of ramets ( Table 4 ). Peri-odic simulations of biennial plant harvests yielded simi-lar results.

Simulations of concurrent adult plant and ramet har-vest based on the dynamics of unharvested populationspredicted that those populations could not withstand therates of harvest currently found in the PRH populations( Table 4 ). The MSH was estimated at about 60% of plantswith commercial value with no additional ramet harvest( � � 1 for this rate of plant harvest). This was true forsimulations with the average matrix and for periodic andstochastic simulations.

Projections of Fiber Yield

The periodic projections of LRH and PRH matrices thatsimulated biennial leaf and adult plant harvests, respec-tively, showed that over 5 years (or three fiber harvests)LRH populations would yield about 1.5 times as much fi-ber as the PRH populations at MSH (Fig. 2). Similarly,leaf and plant harvests that were simulated with the un-harvested populations predicted that leaf harvest wouldyield about 1.5 times as much fiber as adult plant har-vest. However, leaf harvest simulations of the unhar-vested populations predicted a fiber yield that was only68% of that predicted by simulations with the LRH popu-lations. Likewise, simulations of adult plant harvest withthe unharvested populations showed a fiber yield that

was only 71% of that predicted from projections of thePRH populations.

Discussion

In the buffer-zone communities of nature reserves, theimplementation of participatory research projects to iden-tify harvest regimes that yield high maximum sustainableharvests can decrease economic pressure for illegal har-vesting of these resources within reserves and contributeto conservation initiatives in the buffer zone itself.

Maximum Rates of Ramet Harvest in Primary versus Secondary Forests

Our harvest simulations showed that the RH populationsof A. magdalenae in primary forests were able to toleratean MSH of about 40% on average. The average MSH roughlymatches the actual average harvest rate of the popula-tions over a period of 3 years. We cannot tell how this valuecompares with other understory species because wecould not find information on any other species in whichonly the smallest stage classes are harvested. This kind ofinformation will become particularly relevant as supple-mental cultivation becomes a necessity for many economi-cally important nontimber forest products whose wildpopulations are being depleted (e.g., Gunatilleke et al.1993; Mont et al. 1994). Establishing harvest limits for wildpopulations is important even when the species is culti-vated because harvesters who do not have access to landfor cultivation will continue to exploit wild populations.

The MSH of ramets in the RH secondary-forest popula-tions was twice that of the primary-forest populationsbecause of the higher rates of population growth in thesecondary forests ( Ticktin 2000). Although populationgrowth rates for other nontimber forest products havenot been compared in different forest types, for some un-derstory species population growth is higher in light gapsthan under the forest canopy (e.g., Horvitz & Schemske1986; Valverde & Silvertown 1997 ). For those nontim-ber forest products able to grow under secondary-forest

Table 4. Comparison of maximum sustainable rates of harvest ( MSH ) for Aechmea magdalenae populations subject to concurrent adult plant and ramet harvest simulated with harvested and unharvested populations.a

MSH

average periodic stochastic biennial harvest

Population plant ramet plant ramet plant ramet plant ramet

Plant and ramet harvest 100 39 9b — — — — 100 30 3

Unharvested 63 31 0 63 28 0 58 23 0 60 25 0aValues represent the proportion of harvestable ramets (ramet) (40–120 cm width or connected to mother plant) 95% confidence intervalsand harvestable adult plants ( plant) ( 260 cm width) and were determined from projections using time series of two annual transition ma-trices. Dash indicates “not calculated” because we had only 2 years of data: one harvest (of adult plants) year and one nonharvest year.bThe MSH of ramets in adult plant–harvested populations in the year when there was no adult plant harvest was 44 14%.



conditions, extraction in secondary forests can act as apowerful tool for reducing pressure on primary for-ests and for increasing the economic returns of harvest-ers. In the Los Tuxtlas buffer zone, this strategy hasserved as an incentive to conserve secondary forests thatare under threat of conversion to cattle pastures. In thecase of A. magdalenae in particular, management op-tions such as trimming of the overstory in primary for-ests or thinning of adult plants to increase incipient lightcan help prevent overharvesting in primary-forest popu-lations. Alternatively, ramets thinned from primary-for-est populations could be transplanted to secondary for-ests to initiate populations. These practices have nowbeen implemented in buffer-zone communities.

Maximum Rates of Harvest for Leaf-and-Ramet versus Plant-and-Ramet Harvest Regimes

Although LRH and PRH populations were harvested forall commercially valuable leaves, populations subject toboth types of harvest continue to increase in size ( Tick-tin 2000). For LRH populations, the harvest rate was equalto 75% defoliation of all harvest-sized plants, a value much

higher than the maximum 25% defoliation rate predictedfrom an experimental harvest of the tropical palmNeodypsis decaryi ( Ratsirarson et al. 1996 ). N. decaryiis the only species for which a maximum leaf harvestrate has been proposed in the literature. Because the dy-namics of leaf-harvested populations of N. decaryi werenot measured, however, it is difficult to draw any con-clusions about the large difference in MSH between thesetwo species.

For the PRH populations, about 10% of the total popu-lation was harvested. Northern populations of temper-ate understory herbs, such as Panax quinquefolius andAllium tricoccum, which also depend on adult survivalfor population maintenance, are able to withstand whole-plant harvests of 6–8% of harvestable plants (Charron &Gagnon 1991; Nault & Gagnon 1993; Nantel et al. 1996 ).

The MSH simulations in LRH populations predicted that,on top of leaf harvest, 100% of harvestable ramets couldalso be sustainably harvested. This is about twice as highas the MSH of ramets in the RH primary-forest populations.That is, defoliated populations actually permitted higherrates of ramet harvest than populations with leaves. Leafharvest appears to allow for increased survival of ramets,probably due to the increased light ( Ticktin 2000).

Harvest simulations also showed that the PRH popula-tions could tolerate only about one-third the quantity oframets that could be harvested in LRH populations. Theharvest of adults makes the growth of PRH populationsmore dependent on regeneration and therefore more sus-ceptible to overharvest of ramets. The PRH regime there-fore poses a high risk for A. magdalenae because any in-crease in ramet harvest could result in population decline.Indeed local extinctions after PRH harvest have beenreported in several regions of Mexico and Guatemala( Ticktin 2000). Moreover, projections of maximum fiberyields showed that adult plant harvest yielded about 35%less fiber than leaf harvest.

Stochastic versus Periodic and Deterministic Simulations

Stochastic projections may differ from average matriceswhen temporal variation is high because increased varia-tion produces lower growth rates ( Nations & Boyce1997 ). In a study of the harvest of ginseng and wild leek,Nantel et al. ( 1996 ) found that stochastic simulationspredicted maximum sustainable harvests that were threeand two times lower, respectively, than those predictedby the best period matrices. For all types of A. magdale-nae harvest we evaluated, the maximum sustainable har-vests obtained from the stochastic projections did notdiffer significantly from those obtained from determinis-tic projections with average matrices. Given that climaticconditions varied substantially over the study period( in one there was an El Niño event), it appears that A.

Figure 2. Comparison of fiber yields calculated by ma-trix-model simulations with unharvested Aechmea magdalenae versus populations harvested under two different harvest regimes. Simulations assumed maxi-mum sustainable rates of harvest. All simulations started with the same stage-class distribution of 100 individuals and were run for 5 years ( 3 harvests).



magdalenae populations may have exhibited little tem-poral stochasticity because the vital rates of A. magdale-nae plants were robust to changing environmental con-ditions.

Harvest simulations of periodic and stochastic matri-ces showed almost no differences in their predictions ofMSH. Silva et al. (1991) found similar results for tropicalsavannah grasses. Again, this is likely to be the case whenthere is little temporal variation in vital rates.

Accuracy of Maximum Sustainable Harvest Estimates Obtained from Unharvested Populations

All published studies to our knowledge that have attemptedto estimate maximum rates of harvest for nontimber for-est products have simulated harvests with matrix-modelprojections of unharvested populations (e.g., Peters1990; Charron & Gagnon 1991; Nantel et al. 1996; Rat-sirarson et al. 1996; Bernal 1998). Our results, however,showed that this method can lead to highly inaccurate re-sults: stochastic, periodic, and average projections basedon data from unharvested populations consistently and sig-nificantly underestimated A. magdalenae’s tolerance toharvest in each of the four different harvest regimes weexamined. The maximum sustainable harvests estimatedfrom the unharvested populations for concurrent leafand ramet harvest and concurrent plant and ramet har-vest were significantly less than the current rates of har-vest found in the LRH and PRH populations, respec-tively, yet both LRH and PRH populations appeared tobe increasing ( � 1).

The matrix-model projections of A. magdalenae’s un-harvested populations lacked predictive ability largelybecause they did not include density dependence or anypossible stimulating effect of harvest. The lower densityof the RH, LRH, and PRH conditions stimulate signifi-cantly higher rates of survival and growth of ramets andsmall adults ( Ticktin 2000) and therefore allow higherrates of harvest. This type of density dependence appearsto be common in clonal species, including some tropicalunderstory plants growing at high densities (e.g., Martinez-Ramos et al. 1988; Condit et al. 1994 ). The inaccuracy ofMSH estimates based on density-independent models ofunharvested populations becomes particularly relevantwhen one considers that many nontimber forest products,and the majority of these products for which MSH hasbeen calculated, occur in dense stands (e.g., Peters 1990;Nault & Gagnon 1993; Nantel et al. 1996; Bernal 1998).

Effect on Conservation of A. magdalenae Populationsand Habitat

The underestimation of inaccurate MSH can be detri-mental to conservation efforts. Unharvested A. magdela-nae populations predicted maximum fiber yield for bothLRH and PRH regimes that were about 30% less than

those calculated from harvested populations. Low MSHtranslates into low economic returns for harvesters, whoare therefore more likely to abandon the harvest of non-timber forest products for more lucrative but destructiveland-use practices.

Aside from density dependence, factors such as varia-tion in physiological responses to leaf loss (e.g. Whithamet al. 1991), effects of the spatial patterning of harvest( Ticktin 2000), and ecological differences between har-vested and unharvested sites can also cause matrix pro-jections of unharvested populations to yield inaccurateestimates of MSH. Although the assessment of harvestsof nontimber forest products often requires the use ofminimal resources, incorporating these factors into ma-trix projections necessitates large amounts of data. Wetherefore suggest that MSH be estimated from analyses ofthe dynamics of harvested populations and coupled withprecise knowledge of harvesting rates and patterns. Thelatter requires the use of participatory research tech-niques and can include experimental manipulation byharvesters.

In our study, the use of participatory research had di-rect implications for the conservation of A. magdelanaeand its surrounding forest ( Ticktin 2000). For example,participation in the project enabled harvesters to acceptthe harvest limits determined in the study to be valid.Harvesters adopted the management plan that came outof the study and switched from the PRH to the LRH re-gime when they saw that it was more economically prof-itable over the long term. These populations are still mon-itored by the harvesters. Another result was that the mainharvester community with whom we worked passed a lo-cal law prohibiting the destruction of primary forest dueto its potential as A. magdelanae habitat. This forest wasunder high pressure to be cleared for cattle grazing.

Conclusions

The estimates of maximum sustainable harvest in our studyare subject to the shortcomings of matrix-model projec-tions based on a limited number of individuals and fol-lowed over a relatively short time span ( Bierzychudek1999). Although long-term monitoring will be essentialfor the validation of matrix projections, in the meantimewe must be able to estimate MSH with the short-termdata available. At the least, our results suggest that MSHmay vary greatly with local harvest regime and can bemore accurately estimated from harvested populations.This knowledge is fundamental to effective conservationof nontimber species and their habitat.

Acknowledgments

We are indebted to the A. magdalenae harvesters fromV. Carranza for their participation and support and to



the Proyecto Sierra Santa Marta A.C. ( PSSM ) for theircollaboration. Research was supported by scholarshipsto T.T. by the National Science and Engineering ResearchCouncil of Canada and a grant to T.T. by the Fondo Mexi-cano para la Conservación de la Naturaleza A.C throughthe PSSM.

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con

nec

ted

0.15

40.

000

0.00

00.

000

0.58

20.

000

0.31

70.

000

0.00

00.

000

0.42

40.

000

ram

et 1

0.00

00.

137

0.00

00.

094

0.19

00.

250

0.00

00.

233

0.18

20.

105

0.13

70.

071

ram

et 2

0.00

00.

020

0.00

00.

000

0.13

90.

375

0.00

00.

186

0.09

10.

053

0.11

00.

143

ram

et 3

0.03

80.

000

0.00

00.

019

0.00

00.

000

0.17

10.

000

0.09

10.

263

0.00

00.

000

adu

lt 1

0.01

90.

020

0.07

30.

075

0.48

10.

244

0.04

90.

209

0.09

10.

211

0.61

60.

214

adu

lt 2

0.00

00.

000

0.00

00.

000

0.02

50.

831

0.00

00.

000

0.00

00.

000

0.31

50.

928

Yea

r 2

dis

con

nec

ted

0.43

40.

000

0.00

00.

000

0.33

30.

000

0.33

70.

000

0.04

20.

000

0.02

50.

000

ram

et 1

0.03

80.

174

0.00

00.

000

0.15

80.

250

0.03

50.

069

0.04

20.

130

0.15

30.

167

ram

et 2

0.00

00.

261

0.00

00.

000

0.15

80.

000

0.01

20.

069

0.00

00.

130

0.12

70.

167

ram

et 3

0.05

70.

000

0.06

30.

714

0.01

80.

000

0.24

40.

000

0.16

70.

435

0.00

80.

028

adu

lt 1

0.00

00.

130

0.31

30.

000

0.63

20.

237

0.03

50.

414

0.50

00.

478

0.55

90.

333

adu

lt 2

0.00

00.

000

0.00

00.

000

0.21

10.

713

0.00

00.

069

0.00

00.

000

0.45

80.

806

Yea

r 3*

dis

con

nec

ted

0.35

70.

000

0.00

00.

125

0.20

70.

000

0.28

10.

000

0.00

00.

000

0.06

30.

000

ram

et 1

0.04

80.

000

0.00

00.

125

0.05

70.

154

0.01

80.

000

0.00

00.

529

0.16

30.

093

ram

et 2

0.02

40.

143

0.00

00.

000

0.18

90.

231

0.00

00.

625

0.00

00.

176

0.22

50.

372

ram

et 3

0.16

70.

000

0.00

00.

625

0.00

00.

000

0.24

60.

000

0.12

00.

000

0.01

30.

000

adu

lt 1

0.00

00.

714

0.71

40.

125

0.81

10.

308

0.19

30.

125

0.56

00.

412

0.72

50.

558

adu

lt 2

0.00

00.

000

0.00

00.

000

0.15

10.

846

0.00

00.

125

0.08

00.

529

0.53

80.

930

Con

tin

ued



Appe

ndix

Cont

inue

d

Con

curr

ent

lea

f a

nd r

am

et h

arv

est, p

rim

ary

fore

stC

on

curr

ent

adu

lt p

lan

t a

nd r

am

et h

arv

est, p

rim

ary

fore

st

dis

con

nec

ted

ram

et 1

ram

et 2

ram

et 3

adu

lt 1

adu

lt 2

adu

lt 3

dis

con

nec

ted

ram

et 1

ram

et 2

ram

et 3

adu

lt 1

adu

lt 2

adu

lt 3

Har

vest

of

leav

es

and

ram

ets

Har

vest

of

adu

lt p

lan

ts a

nd

ram

ets

dis

con

nec

ted

0.43

40.

000

0.00

00.

000

0.32

00.

000

0.00

00.

422

0.14

30.

000

0.06

70.

320

0.00

00.

460

ram

et 1

0.00

00.

000

0.00

00.

000

0.08

60.

080

0.04

20.

024

0.00

00.

000

0.20

00.

115

0.10

00.

000

ram

et 2

0.00

00.

286

0.00

00.

000

0.05

70.

120

0.12

50.

000

0.28

60.

000

0.00

00.

154

0.05

00.

000

ram

et 3

0.00

00.

000

0.00

00.

222

0.00

00.

000

0.00

00.

253

0.00

00.

000

0.40

00.

026

0.00

00.

000

adu

lt 1

0.06

00.

571

1.50

00.

667

0.42

90.

240

0.16

70.

012

0.42

90.

357

0.20

00.

615

0.17

80.

000

adu

lt 2

0.00

00.

000

0.00

00.

000

0.45

70.

760

0.66

70.

000

0.00

00.

000

0.00

00.

359

0.68

10.

000

adu

lt 3

0.00

00.

000

0.00

00.

000

0.28

60.

160

0.25

00.

000

0.00

00.

000

0.00

00.

000

0.10

60.

000

No

leaf

har

vest

No

ad

ult

pla

nt

har

vest

dis

con

nec

ted

0.27

90.

045

0.00

00.

037

0.32

00.

000

0.00

00.

279

0.04

80.

000

0.02

60.

333

0.00

00.

000

ram

et 1

0.01

50.

000

0.00

00.

148

0.03

10.

077

0.11

10.

015

0.00

00.

000

0.20

00.

115

0.10

00.

111

ram

et 2

0.00

00.

136

0.00

00.

037

0.03

10.

154

0.00

00.

000

0.14

30.

000

0.00

00.

154

0.05

00.

000

ram

et 3

0.39

70.

000

0.00

00.

296

0.00

00.

000

0.00

00.

397

0.00

00.

063

0.34

20.

000

0.00

00.

000

adu

lt 1

0.01

50.

136

0.46

20.

370

0.39

40.

099

0.00

00.

015

0.14

30.

500

0.36

80.

554

0.09

40.

000

adu

lt 2

0.00

00.

000

0.00

00.

000

0.44

50.

849

0.88

90.

000

0.04

50.

000

0.00

00.

360

0.75

20.

538

adu

lt 3

0.00

00.

000

0.00

00.

000

0.00

00.

101

0.11

10.

000

0.00

00.

000

0.00

00.

000

0.13

70.

436

Har

vest

of

leav

es

and

ram

ets

dis

con

nec

ted

0.43

40.

067

0.00

00.

034

0.80

00.

000

0.00

0ra

met

10.

049

0.00

00.

000

0.00

00.

124

0.01

40.

154

ram

et 2

0.00

00.

267

0.00

00.

000

0.08

70.

042

0.09

6ra

met

30.

205

0.00

00.

063

0.20

70.

000

0.00

00.

000

adu

lt 1

0.04

80.

400

0.43

80.

379

0.46

10.

214

0.40

3ad

ult

20.

000

0.00

00.

000

0.00

00.

391

0.60

00.

442

adu

lt 3

0.00

00.

000

0.00

00.

000

0.01

60.

200

0.13

5

con

tin

ued



Appendix

Continued

Unharvested populations, primary forest

disconnected ramet 1 ramet 2 ramet 3 adult 1 adult 2 adult 3

Year 1disconnected 0.000 0.071 0.000 0.111 0.055 0.000 0.000

ramet 1 0.000 0.000 0.125 0.000 0.123 0.154 0.158ramet 2 0.000 0.357 0.125 0.037 0.055 0.077 0.105ramet 3 0.429 0.000 0.625 0.407 0.068 0.000 0.000adult 1 0.055 0.286 0.250 0.259 0.616 0.231 0.211adult 2 0.000 0.000 0.000 0.000 0.219 0.500 0.053adult 3 0.000 0.000 0.000 0.000 0.013 0.269 0.895

Year 2disconnected 0.444 0.237 0.000 0.205 0.063 0.000 0.000

ramet 1 0.000 0.000 0.000 0.026 0.099 0.186 0.135ramet 2 0.000 0.342 0.000 0.026 0.108 0.100 0.054ramet 3 0.111 0.000 0.136 0.410 0.081 0.000 0.000adult 1 0.063 0.026 0.455 0.333 0.757 0.386 0.108adult 2 0.000 0.000 0.091 0.000 0.117 0.614 0.676adult 3 0.000 0.000 0.000 0.000 0.000 0.071 0.270

*In year 3, the first column under “Ramet harvest, primary forest” is rhizome, not disconnected as it is for all others.

Effects of Variation on Harvest Limits for Nontimber ... · Ticktin et al. Harvest Limits for...

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