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e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 189–199

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

nalyzing the time-course variation of apple and pear treeates of flowering stages in the global warming context

ann Guédona, Jean Michel Legaveb,∗

CIRAD, UMR DAP and INRIA, Virtual Plants, TA A-96/02, 34398 Montpellier Cedex 5, FranceINRA, UMR DAP, Architecture et Fonctionnement des Espèces Fruitières, 2 place Viala, 34060 Montpellier Cedex 1, France

r t i c l e i n f o

rticle history:

eceived 6 March 2008

eceived in revised form

2 August 2008

ccepted 22 August 2008

eywords:

hange-point detection

hilling requirement

limate change

ruit tree

eat requirement

henology

a b s t r a c t

Over the last 40 years, perceptible advances in dates of flowering stages have been observed

in apple and pear trees growing in three cropping areas in France and one in Switzerland. The

time-course variation of dates of flowering stages was established for eight chronological

sequences. Our aim was to propose a statistical modelling framework for such sequences

with the objective of characterizing the relationship between flowering advances in fruit

trees and global warming. After an exploratory analysis, change-point models were applied

to multivariate and univariate sequences. The results clearly support the occurrence of a

significant abrupt change in the time-course variation of flowering dates at the end of the

1980s toward more frequent early dates, the most probable change instant being between

1988 and 1989. The coincidence between this abrupt change in phenological variations and

marked increases in temperature recorded particularly in France at the end of the 1980s led

us to consider the flowering advances in apple and pear trees as impacts of global warm-

ing. The suddenness in the response to global warming could be explained by changes in

rates for completion of chilling and heat requirements, successively essential to the devel-

opment of floral primordia within buds. In all cropping areas, annual mean temperatures

had suddenly increased since 1988 (1.1–1.3 ◦C), but including noticeable monthly differences.

Particularly, warming was clearly more pronounced in February and March (mean temper-

ature increases of 1.6 ◦C) corresponding to the main period of heat requirements, than in

November and December (0.8 ◦C) corresponding to the main period of chilling requirements.

So marked temperature increases during the heat phase would have suddenly resulted in

more frequent years with relatively short duration for completion of the heat requirements

and consequently more frequent early flowering years, despite some years with relatively

long duration of chilling requirements.

nario (IPCC, 2007). As plant phenology is mainly influenced by

. Introduction

lobal warming of the climate system is unequivocal, as is

ow evident from observations of increases in average airemperatures in many parts of the world. Eleven of the last2 years (1995–2006) rank among the 12 warmest years since

∗ Corresponding author. Tel.: +33 499612784; fax: +33 499612616.E-mail addresses: guedon@cirad.fr (Y. Guédon), legave@supagro.inra

304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2008.08.010

© 2008 Elsevier B.V. All rights reserved.

1850. Mean temperature will probably rise between 1.8 ◦C and4.0 ◦C for the end of the 21st century, according to climatic sce-

.fr (J.M. Legave).

temperature, climate warming has caused renewed interestin phenological methods and observations. Long-term phe-nological records at specific sites provide useful measures of

i n g

190 e c o l o g i c a l m o d e l l

species-level biological responses to climate changes accord-ing to Schwartz (1999). A lot of phenological studies focusedon changes in natural systems (Parmesan and Yohe, 2003;Menzel et al., 2006), while few studies dealt with phenolog-ical changes in perennial horticultural crops (Schultz, 2000).Changes in tree phenology have been observed in Europeancountries where earlier onsets of leafing dates were associ-ated with global warming (Chmielewski and Rötzer, 2001). Infruit tree orchards, changes in the timing of flowering phenol-ogy could have important impacts on production, because ofthe indirect influences of phenology on spring frost damage,pollination and fruit set efficiency (Cannell and Smith, 1986;Zavalloni et al., 2006).

Over the last 40 years, similar evolutions toward an advancein dates of flowering stages have been observed for severalfruit species in distant countries in the northern hemisphereand related to global warming (Omoto and Aono, 1990; Kai etal., 1993; Chmielewski et al., 2004; Legave and Clauzel, 2006;Miller-Rhushing et al., 2007; Legave et al., 2008). Nevertheless,it is less clear how these evolutions might be described torightly characterize the response to global warming and howthey might be explained by changes in temperature condi-tions during the flowering process. Thus, this study aimed toanalyze the time-course variation of dates of flowering stagesthrough a statistical modelling approach over ranges of yearsincluding the end of the 1980s when a marked increase inair temperature has been recorded worldwide (IPCC, 2007).For this aim, we collected and analyzed long-term chronolog-ical sequences of dates of flowering stages for apple and peartrees in three cropping areas in France and one in Switzer-land. After an exploratory analysis of these data, we choseto estimate change-point models on the basis of these phe-nological sequences. It was thus assumed that there weretwo periods within which the flowering dates follow thesame or nearly the same distribution and between which theflowering dates have different distributions. This statisticalmodelling of phenological sequences was completed by ananalysis of temperature changes during the successive chill-ing and heat phases up to flowering dates in the case of appletrees.

2. Materials and methods

2.1. Plant material and temperature conditions

The flowering data are mainly issued from a French database(called ‘PhénoClim’) devoted to fruit trees and vine. Floweringdates of one apple tree cultivar (‘Golden Delicious’) and threepear tree cultivars (‘Williams’, ‘Passe Crassane’, ‘Doyenné duComice’) were selected owing to their economic importance.Dates of flowering stages are recorded since a long time andin various locations in France for such main cultivars for vari-ous agronomic purposes like parasitism control, breeding andmodelling. Such dates are commonly assessed from obser-vations on several adult trees growing in long-term orchards

managed by commercial practices. The assessments of floraldates by experienced observers are made with an inaccuracyof 2–3 days. Among the different phenological stages con-sidered in past observations, we selected stages that were

2 1 9 ( 2 0 0 8 ) 189–199

subjected to reliable recording dates over the longest rangesof years.

Thus, the date when about 10% of flower buds are opened(F1 stage) was chosen for apple tree cultivar ‘Golden Delicious’,while the date when nearly 100% are opened (F2 stage) waschosen for the three pear tree cultivars. F1 dates for ‘GoldenDelicious’ were recorded during different periods at three loca-tions representative of the main cropping areas of France:from 1963 to 2006 at INRA research station near Angers (47◦

28 N, 0◦ 33 W) in Pays de Loire, from 1976 to 2002 at Domainede Castang (grower farm) near Bergerac (44◦ 51 N, 0◦ 29 E) inAquitaine and from 1974 to 2006 at Ctifl professional stationnear Nîmes (43◦ 50 N, 4◦ 21 E) in Languedoc. Regarding F2 datesfor pear trees, data were recorded mainly at Angers from 1959to 2006 for ‘Williams’ and ‘Passe Crassane’ and from 1972 to2006 for ‘Doyenné du Comice’. Data were also recorded at Berg-erac from 1972 to 2003 for ‘Williams’. In addition to Frenchdata, F2 dates collected for ‘Williams’ from 1971 to 2003 at theAgroscope Changins-Wädenswil research station near Nyonin Switzerland (46◦ 24 N, 6◦ 14 E) were used. This was achievedwith the collaboration of Doctor Danilo Christen, in order tocompare French phenological sequences with one sequencerepresentative of those collected in another European country.

The temperature conditions of the four locations involvedwere studied on the basis of mean daily temperature of 30years (1973–2002) covering an appropriate period to highlighttemperature increases. The data were issued from databasesmanaged by INRA in France and Météo Suisse in Switzerland.Moreover, in order to analyze the change in flowering stagedate in relation to temperature changes, mean temperatureswere assessed respectively during the phase of chilling effectsrequired to break bud endodormancy (Lang et al., 1987) andthe successive phase of heat effects required to active growthresulting in flower bud opening. To do this, we determined thecorresponding periods of these two phases for each annualflowering process (chilling onset in the autumn of year n − 1to heat completion in the spring of year n). In practical terms,this analysis was applied to F1 stage of ‘Golden Delicious’ forwhich previous work provided parameters to estimate a dateof completion of the chilling requirement for each year at eachlocation (Legave et al., 2008). Moreover the 1st of October ofyear n − 1 was found in France as an appropriate date to sit-uate the onset of chilling effects for each flowering year (n)and location (Bidabé, 1967). Thus, the mean temperature ofthe chilling phase was calculated from this fixed date to theestimated date of chilling completion for the flowering years1976–2002 for which F1 dates were recorded at all three loca-tions. The mean temperature of the heat phase was calculatedfrom the estimated date of chilling completion to the observedF1 date for the same situations (year × location).

2.2. Statistical models

Multiple change-point models are used to delimit segmentsfor which the data characteristics are homogeneous withineach segment while differing markedly from one segment to

another. In a probabilistic framework, the observed sequenceof length T, x0, . . ., xT−1 is modelled by T random variablesX0, . . ., XT−1 which are assumed to be independent. In thefollowing xT−1

0 is a shorthand for x0, . . ., xT−1.

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We made the assumption of Gaussian multiple change-oint models. Gaussian multiple change-point models differ

n the parameters assumed to be constant within segmentsi.e. between change points). This can be the mean or the meannd the variance. The two associated models are denoted by

m (for mean), and Mmv (for mean/variance). For model Mm,e suppose that there exist some J − 1 instants �1 < · · · < �J−1

with the convention �0 = 0 and �J = T) such that the mean isonstant between two successive change points and the vari-nce is assumed to be constant:

f �j ≤ t < �j+1,

{E(Xt) = �j,

V(Xt) = �2.

or model Mmv, the modelling of the variance is different sincet is also affected by the J − 1 change points:

f �j ≤ t < �j+1,

{E(Xt) = �j,

V(Xt) = �2j.

The problem now is to estimate the parameters of theseaussian multiple change-point models: the number of seg-ents J, the instants of the J − 1 change points �1, . . ., �J−1,

he J within-segment means �j and, the global variance �2

for model Mm) or the J within-segment variances �2j

(forodel Mmv). We shall adopt here a retrospective or off-line

pproach where change points are detected simultaneously.et us denote by � the set of mean and variance parame-ers. For model Mm, � = {�0,. . ., �J−1, �2} while for model Mmv,= {�0, . . . , �J−1, �2

0 , . . . , �2J−1}. In a first step, we suppose that

he number of segments J is known and the purpose is tobtain the optimal segmentation of the sequence into J seg-ents. We discuss in a second step the choice of J which can

e put into a model selection framework.Once the change points have been fixed, the mean and vari-

nce parameters are estimated by maximum likelihood. Forodel Mmv, we obtain the empirical mean and variance for

ach segment:

ˆ j =∑�j+1−1

t=�jxt

�j+1 − �jand �̂2

j =∑�j+1−1

t=�j(xt − �̂j)

2

�j+1 − �j. (1)

or model Mm, the estimated global variance is given by:

ˆ 2 =∑J−1

j=0

∑�j+1−1t=�j

(xt − �̂j)2

T. (2)

Then, if we denote by LJ the likelihood of a J-segment model,he estimation of the J − 1 change points �1, . . ., �J−1, whichorresponds to the optimal segmentation into J segments, isbtained as follows:

ˆ1, . . . , �̂J−1 = arg max0<�1<···<�J−1<T

log LJ(xT−10 ; �̂),

ith

log LJ(xT−10 ; �̂) = − T

2(log �̂2 + log 2� + 1) for model Mm,

log LJ(xT−10 ; �̂) = − 1

2

J−1∑j=0

(�j+1 − �j)(log �̂2j + log 2� + 1) for model Mmv.

9 ( 2 0 0 8 ) 189–199 191

For this optimisation task, the additivity in j of the sumof squared deviations from the means (see (2)) for model Mm,or the additivity in j of the log-likelihood for model Mmv (seeabove) allows us to use a dynamic programming algorithm(Auger and Lawrence, 1989) which reduces the computationalcomplexity from O(TJ) to O(JT2) in time.

The Gaussian multiple change-point models can be directlygeneralized to multivariate sequences. In our context, the Nvariables correspond to different locations or to different cul-tivars and the elementary random variables at a given time tare assumed to be independent. In the multivariate case, thelog-likelihood of the J-segment model is given by:

log LJ(xT−10 ; �̂) = −NT

2(log �̂2 + log 2� + 1)

with �̂2 =∑J−1

j=0

∑N

a=1

∑�j+1−1t=�j

(xa,t − �̂j,a)2

NT,

for model Mm and

log LJ(xT−10 ; �̂) = −1

2

J−1∑j=0

(�j+1 − �j)

N∑a=1

(log �̂2j,a + log 2� + 1)

where �̂2j,a is given by (1),

for model Mmv. In the multivariate case, we introduce asupplementary model which is intermediate between mod-els Mm and Mmv. In this new model denoted by Mmsv (formean/segment variance), the variance is common to theN variables within a segment. The log-likelihood of the J-segment model Mmsv is given by:

log LJ(xT−10 ; �̂) = −N

2

J−1∑j=0

(�j+1 − �j)(log �̂2j + log 2� + 1)

with �̂2j =

∑N

a=1

∑�j+1−1t=�j

(xa,t − �̂j,a)2

N(�j+1 − �j).

Once a multiple change-point model has been estimatedfor a fixed number of segments J, the question is then tochoose this number. Indeed, in real situations this number isunknown and should be estimated. In a model selection con-text, the purpose is to estimate J by maximizing a penalizedversion of the log-likelihood defined as follows:

J = argmaxJ≥1

{log LJ(xT−10 ; �̂1, . . . , �̂J−1, �̂) − Penalty(J)}.

The principle of this kind of penalized likelihood criterionconsists in making a trade-off between an adequate fitting ofthe model to the data (given by the first term) and a reasonablenumber of parameters to be estimated (control by the secondterm: the penalty term). The most popular information criteriasuch as AIC and BIC are not adapted in this particular con-text since they tend to underpenalize the log-likelihood andthus select a too large number of segments J. New penalties

have therefore been proposed in this context; see for exampleLavielle (2005) used in Picard et al. (2005), and Lebarbier (2005)and Zhang and Siegmund (2007) used in Guédon et al. (2007).Zhang and Siegmund proposed a modified BIC criterion in the

i n g

lighted differences in flowering date according to location andcultivar. For apple tree cultivar ‘Golden Delicious’, marked dif-ferences are observed between the three regional sequencesduring the period 1976–2002 (Fig. 1). The F1 date is consistently

192 e c o l o g i c a l m o d e l l

case of the univariate model Mm. This criterion is given by

mBICJ = 2 log LJ(xT−10 ; �̂1, . . . , �̂J−1, �̂) − 2J log T

−J−1∑j=0

log(�̂j+1 − �̂j), (3)

where

min0<�1<···<�J−1<T

J−1∑j=0

log(�̂j+1 − �̂j)

= log(T − J + 1) ≈ J log T − (J − 1) log T if J � T,

max0<�1<···<�J−1<T

J−1∑j=0

log(�̂j+1 − �̂j) = J logT

J= J log T − J log J.

Hence each change point contributes between 1 and 2dimensions to the penalty term (instead of systematically 1dimension for each mean or variance parameter) and thispenalty term is maximized when the change points are evenlyspaced.

A model selection procedure leads generally to a uniquesolution. However, it could be of interest to rank the mod-els allowing full consideration of other possible models. Theposterior probability of the J-segment model MJ, given by

P(MJ|xT−10 ) = exp(1/2�mBICJ)∑Jmax

k=1 exp(1/2�mBICK),

with

�mBICJ = mBICJ − maxK

mBICK,

can be interpreted as the weight of evidence in favour of theJ-segment model (among the Jmax models).

For models Mmv and Mmsv, the maximum log-likelihood ofthe J-segment model can be written as:

log LJ(xT−10 ; �̂1, . . . , �̂J−1, �̂)

= max0<�1<···<�J−1<T

J−1∑j=0

log f (x�j, . . . , x�j+1−1; �̂j),

where log f (x�j, . . . , x�j+1−1; �̂j) is the maximum log-likelihood of

parameter �̂j attached to segment x�j, . . . , x�j+1−1. It is often of

interest to quantify the uncertainty concerning the instant ofchange points. In the case of a single change point, the poste-rior probability of entering the second segment at time �1 for�1 > 0 is given by:

f (x0, . . . , x�1−1; �̂0)f (x�1 , . . . , xT−1; �̂1)∑tf (x0, . . . , xt−1; �̂0)f (xt, . . . , xT−1; �̂1)

,

This computation can only be performed for models for which

the log-likelihood is additive in j (hence models Mmv andMmsv but not model Mm). This is the main justification of theintroduction of the parsimonious model Mmsv for multivariatesequences.

2 1 9 ( 2 0 0 8 ) 189–199

3. Results

3.1. Exploratory analysis of temperature conditions

In France, similar patterns were observed between the threelocations regarding the annual evolution for monthly meantemperatures. However, for each monthly temperature, grad-ual ranges according to the latitude degree of location wereobvious (data not shown). Thus, Angers is characterized bythe coldest monthly temperatures with a mean annual tem-perature of 11.9 ◦C and Nîmes the warmest (mean annualtemperature of 14.5 ◦C), while intermediate monthly temper-atures are observed at Bergerac (mean annual temperature of12.8 ◦C). Changins is characterized by a relatively cold climatewith a mean annual temperature of 9.7 ◦C.

Temperature increases have been clearly marked fromthe year 1988 in the three French growing locations asexpressed by the comparison of means of annual temper-atures between the two successive periods 1973–1987 and1988–2002. The mean increases of annual temperatures inthe second period were +1.1 ◦C at Angers, +1.2 ◦C at Berg-erac and +1.3 ◦C at Nîmes. A similar change has beenobvious at Changins (+1.2 ◦C during the period 1988–2002).Nevertheless, these increases include noticeable monthly dif-ferences for the months involved in the annual floweringprocess. Particularly, in France warming was clearly morepronounced in the period February–March (mean tempera-ture increases of 1.4–1.8 ◦C according to location), than in theperiod November–December (0.6–0.8 ◦C).

3.2. Exploratory analysis of the variability within theflowering dates

The time-course variation of flowering dates was establishedfor each of the eight selected sequences (Figs. 1–3). This high-

Fig. 1 – Segmentation of three chronological sequences ofF1 date for apple tree, cultivar ‘Golden Delicious’ at threelocations.

e c o l o g i c a l m o d e l l i n g 2 1

FF

eifA7vts1SoliS

dtwg12

FF

ig. 2 – Segmentation of three chronological sequences of2 date for pear tree, cultivar ‘Williams’ at three locations.

arlier at Nîmes than at Angers, while most of the time anntermediate date is observed at Bergerac. The mean F1 datesor this period are April 22 at Angers, April 14 at Bergerac andpril 7 at Nîmes (8 days earlier at Bergerac than at Angers anddays earlier at Nîmes than at Bergerac). The same range of

ariability in mean dates is observed between the three loca-ions when means are considered separately for the 1976–1988ub-period (April 25, April 19, April 11, respectively) and the989–2002 sub-period (April 18, April 11, April 4, respectively).uch data clearly underline a constant influence of locationn the date of stage F1 for ‘Golden Delicious’ apple trees. The

ower the latitude of location, the earlier the flowering daten the apple tree growing area extending from North-West toouth-East of France.

For pear tree cultivar ‘Williams’, slight differences in theate of stage F2 are observed between the two French loca-ions of Bergerac and Angers during the period 1972–2003,

hile later dates are clearly observed most of time at Chan-

ins in Switzerland (Fig. 2). The mean F2 dates for the period972–2003 are April 7 at Bergerac, April 9 at Angers and April0 at Changins. The differences in mean dates are unchanged

ig. 3 – Segmentation of three chronological sequences of2 date for three pear tree cultivars at Angers.

9 ( 2 0 0 8 ) 189–199 193

when means are considered separately for the 1972–1988 sub-period (April 11, April 13 and April 25, respectively) and the1989–2003 sub-period (April 2, April 4 and April 15, respec-tively).

Differences in flowering date according to cultivar arehighlighted by the comparison of sequences of three peartree cultivars growing at Angers during the period 1972–2006(Fig. 3). The F2 date is consistently earlier for ‘Passe Cras-sane’ than for ‘Doyenné du Comice’, while ‘Williams’ showsan intermediate date most of the time. The mean F2 datesfor the period 1972–2006 are April 8 for ‘Passe Crassane’ andApril 14 for ‘Doyenné du Comice’. This difference of 6 daysis unchanged when means are considered separately for the1972–1988 sub-period (April 12 and April 18, respectively) andthe 1989–2006 sub-period (April 3 and April 9, respectively).

The exploratory analysis clearly shows constant influencesof location and cultivar on the date of flowering stage. Nev-ertheless, as it is obviously apparent in the data (Figs. 1–3),it was not possible to extract regularly decreasing trends (i.e.long-term changes in the mean level) using various symmet-ric smoothing filters with different filter widths (results notshown). Hence, we chose to apply multiple change-point mod-els.

3.3. Analysis of the changes in the flowering datesusing multiple change-point models

A multivariate sequence was built taking each location (threefor apple tree cultivar ‘Golden Delicious’ and for pear tree cul-tivar ‘Williams’) or cultivar (three pear tree cultivars growing atAngers) as a variable. Applying multiple change-point detec-tion method to one of these multivariate sequences consiststhen in detecting change points common to the individualsequence (while the means are estimated for each segmentand each variable, and the global variance is estimated formodel Mm, the variances are estimated for each segment formodel Mmsv and for each segment and each variable for modelMmv); see Figs. 1–3. Since the variances estimated for each seg-ment and each variable are close, the modified BIC of Zhangand Siegmund (2007) always ranks the models from the moreto the less parsimonious for a fixed number of segments, i.e.Mm followed by Mmsv and Mmv (results not shown); see thecorresponding standard deviations estimated for the differ-ent two-segment models in Table 1. We thus chose to focus onmodels Mm for the selection of the number of segments. Themodified BIC favoured the two-segment model for apple tree,cultivar ‘Golden Delicious’ and for pear tree, cultivar ‘Williams’and the three-segment model for pear tree at Angers (Table 2).In this last case, both the two-segment and the three-segmentmodels are possible models according to their posterior prob-abilities. It should be noted that the penalty used in (3) islikely to slightly underpenalized the log-likelihood (and thusto select a too large number of segments) since this penaltywas derived in the case where the global variance � is known(instead of being estimated); see Zhang and Siegmund (2007).

In the case of the two-segment models, we obtained the

same instant for the change point (1988 → 1989) in the threecases with a low uncertainty (posterior probability between0.67 and 0.87 for the change point 1988 → 1989 computed usingMmsv models; see Fig. 4). The change-point magnitudes as

194 e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 189–199

Table 1 – Apple tree, cultivar ‘Golden Delicious’ atAngers, Bergerac and Nîmes (1976–2002); pear tree,cultivar ‘Williams’ at Angers, Bergerac and Changins(1972–2003); pear tree cultivars ‘Williams’, ‘PasseCrassane’ and ‘Doyenné du Comice’ at Angers(1972–2006): estimated multivariate two-segment modelparameters (�̂1 = 1989 for models Mm, Mmsv and Mmv inthe three cases).

Sequence �̂1,a − �̂0,a �̂0,a �̂1,a

Apple tree, cv. ‘Golden Delicious’, 1976–2002Angers −7.46 7.49 7.66Bergerac −7.97 7.99 5.85Nîmes −7.67 5.89 7.33

�̂j 7.18 6.99�̂ 7.08

Pear tree, cv. ‘Williams’, 1972–2003Angers −9.54 8.47 7.19Bergerac −9.33 7.48 7.84Changins −9.97 6.25 6.04

�̂j 7.46 7.06�̂ 7.27

Pear tree, Angers, 1972–2006Williams −8.25 8.47 7.44Passe Crassane −8.97 8.79 7.7Doyenné du Comice −8.96 7.83 7.41

Fig. 4 – Multivariate two-segment models Mmsv: posteriorchange-point probabilities.

Table 3 – Apple tree, cultivar ‘Golden Delicious’ (Angers,Bergerac and Nîmes) and pear tree, cultivars ‘Williams’(Angers, Bergerac and Changins), ‘Passe Crassane’(Angers) and ‘Doyenné du Comice’ (Angers) (1976–2002):choice of the number of segments for multivariate modelMm.

J 2log LJ Free param. mBICJ P(MJ|xT−10 )

1 −1555.99 9 −1607.67 0

�̂j 8.37 7.52�̂ 7.94

given by the mean difference between the two segments �̂1,a −�̂0,a are very similar (between −7.5 and −10; see Table 1). Thesample autocorrelation function computed from the resid-ual sequences obtained by subtracting the two successivesegment means from the original sequences (Lavielle, 1998)showed that the residual sequences were stationary and closeto white noise sequences (results not shown).

If all the data are gathered in a single multivariate sequence[apple tree, cultivar ‘Golden Delicious’ (Angers, Bergerac andNîmes) and pear tree, cultivar ‘Williams’ (Angers, Bergerac andChangins), ‘Passe Crassane’ (Angers) and ‘Doyenné du Comice’

Table 2 – Apple tree, cultivar ‘Golden Delicious’ at Angers, Bergat Angers, Bergerac and Changins (1972–2003); pear tree cultivaat Angers (1972–2006): choice of the number of segments for m

Sequence J 2log

Apple tree, cv. ‘Golden Delicious’, 1976–2002 1 −5672 −5463 −5324 −525

Pear tree, cv. ‘Williams’, 1972–2003 1 −6882 −6533 −6354 −629

Pear tree, Angers, 1972–2006 1 −7602 −7333 −7124 −702

2 −1475.15 18 −1577.11 0.993 −1435.14 27 −1586 0.014 −1416.19 36 −1615.35 0

(Angers)], the two-segment model Mm is by far the best modelwith very few uncertainty (posterior probability of 0.99 for thismodel; see Table 3) and there also remains almost no uncer-tainty for the instant of the change point 1988 → 1989 with aposterior probability of 0.99.

At the opposite, on the basis of two-segment modelsMm estimated from univariate sequences, the change point1988 → 1989 was detected for all the apple and pear treesequences. On the basis of two-segment models Mmv, the

erac and Nîmes (1976–2002); pear tree, cultivar ‘Williams’rs ‘Williams’, ‘Passe Crassane’ and ‘Doyenné du Comice’ultivariate models Mm.

LJ Free param. mBICJ P(MJ|xT−10 )

.93 4 −588.81 0.3

.98 8 −587.34 0.62

.86 12 −591.33 0.08

.8 16 −601.77 0

.11 4 −709.83 0

.42 8 −695.48 0.71

.57 12 −697.24 0.29

.26 16 −710.19 0

.89 4 −783.06 0.01

.19 8 −776.15 0.4

.58 12 −775.38 0.58

.38 16 −783.86 0.01

e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 189–199 195

Table 4 – Univariate two-segment models Mmv: posterior change-point probabilities.

Cultivar Location Year range 1988 → 1989 probability Maximum probability (change point)

Golden Delicious Angers 1963–2006 0.23Bergerac 1976–2002 0.27Nîmes 1974–2006 0.15 0.21 (2002 → 2003)

Williams Angers 1959–2006 0.24Bergerac 1972–2003 0.27Changins 1971–2003 0.46

Passe Crassane Angers 1959–2006 0.18 0.29 (1960 → 1961)0.32

c‘‘ctvaeaDaoauits

tomee1pht1db

Fig. 5 – Univariate two-segment models Mmv: posterior

Doyenné du Comice Angers 1972–2006

hange point 1988 → 1989 was detected for apple tree cultivarGolden Delicious’ at Angers and Bergerac, pear tree cultivarWilliams’ at Angers, Bergerac and Changins and pear treeultivar ‘Doyenné du Comice’ at Angers, but not for appleree cultivar ‘Golden Delicious’ at Nîmes and pear tree culti-ar ‘Passe-Crassane’ at Angers (Table 4). Nevertheless, there isstrong consensus among the univariate two-segment mod-

ls Mmv for the change point 1988 → 1989 since 1988 → 1989 ispossible change point even for apple tree cultivar ‘Goldenelicious’ at Nîmes and pear tree cultivar ‘Passe-Crassane’t Angers (Table 4 and Fig. 5). It should be noted that somef the univariate sequences are longer than the multivari-te sequences since only the common range of years can besed to build multivariate sequences. However, this increase

n length of the univariate sequence does not compensate forhe combination with another sequence in terms of sampleize for estimating change points.

Finally, despite usual yearly fluctuations, we may concludehat a change in the time-course variation of flowering datesccurred abruptly at the end of the 1980s (1988 → 1989) towardore frequent early dates. This evolution was similar for the

ight sequences analyzed, regardless of the respective influ-nces of location and cultivar (Figs. 1–3). When the period976–2002 common to all sequences is considered to com-are the advances in flowering date (Table 5), this clearlyighlights earlier mean dates of F1 and F2 stages during

he sub-period 1989–2002 in comparison with the sub-period976–1988, although higher mean advances in pear tree (10–11ays for F2 stage) than in apple tree (7–8 days for F1 stage) cane noted.

Table 5 – Mean dates of F1 stage (apple tree) or F2 stage (pear trto cultivar and location during the two successive observation p

Cultivar Location Sta

Golden Delicious Angers FBergerac FNîmes F

Williams Angers FBergerac FChangins F

Passe Crassane Angers FDoyenné du Comice Angers F

change-point probabilities.

3.4. Temperature changes related to flowering datechanges

Firstly, the changes in temperature during the chilling andheat phases for the three locations regarding apple tree cul-

tivar ‘Golden Delicious’ (Figs. 6 and 7) were analyzed withthe same approach used for the flowering dates. Multivari-ate sequences were built taking each location as a variablefor the ‘chilling temperatures’ and the ‘heat temperatures’.

ee), expressed in calendar day from 1st January, accordingeriods.

ge Observation period

1976–1988 1989–2002

1 115 1081 109 1011 101 94

2 105 942 102 922 115 105

2 104 932 109 98

196 e c o l o g i c a l m o d e l l i n g 2 1 9 ( 2 0 0 8 ) 189–199

Fig. 6 – Segmentation of three chronological sequences ofmean temperature during the chilling phase of theflowering process for cultivar ‘Golden Delicious’ at three

Table 6 – Mean temperatures during the chilling andheat phases of the flowering process for cultivar ‘GoldenDelicious’ at Angers, Bergerac and Nîmes (1976–2002):estimated multivariate two-segment model parameters(�̂1 = 1988 for models Mm, Mmsv and Mmv in the twocases).

Sequence �̂1,a − �̂0,a �̂0,a �̂1,a

‘Chilling temperature’Angers 1 0.57 0.85Bergerac 1.08 0.67 0.91Nîmes 1.12 0.65 0.63

�̂j 0.63 0.81�̂ 0.73

‘Heat temperature’Angers 1.28 0.62 0.95Bergerac 0.98 0.76 1Nîmes 1.77 0.9 0.91

locations.

Since the variances estimated for each segment and eachvariable are close, the modified BIC of Zhang and Siegmund(2007) always ranks the models from the more to the less par-

simonious for a fixed number of segments, i.e. Mm followedby Mmsv and Mmv (results not shown); see the correspondingstandard deviations estimated for the different two-segment

Fig. 7 – Segmentation of three chronological sequences of meanfor cultivar ‘Golden Delicious’ at three locations.

Table 7 – Mean temperatures during the chilling and heat phasat Angers, Bergerac and Nîmes (1976–2002): choice of the numb

Sequence J 2log LJ

‘Chilling temperature’ 1 −213.782 −179.583 −174.024 −163.49

‘Heat temperature’ 1 −247.442 −208.853 −199.114 −172.27

�̂j 0.77 0.96�̂ 0.88

models in Table 6. We thus chose to focus on models Mm

for the selection of the number of segments. The modified

BIC favoured the two-segment model for the chilling tem-peratures and the heat temperatures (Table 7). We obtainedthe same instant for the change point (1987 → 1988) in the

temperature during the heat phase of the flowering process

es of the flowering process for cultivar ‘Golden Delicious’er of segments for multivariate models Mm.

Free param. mBICJ P(MJ|xT−10 )

4 −234.65 08 −219.92 1

12 −232.46 016 −240.5 0

4 −268.31 08 −249.2 0.53

12 −258.11 0.0116 −249.46 0.46

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wo cases with a very low uncertainty (posterior probabil-ty of 0.94 in the chilling temperature case, and of 0.93 inhe heat temperature case for the change point 1987 → 1988omputed using Mmsv models). The change-point magnitudess given by the mean difference between the two segments

ˆ 1,a − �̂0,a are very close for the three locations in the chill-ng temperature case while they are more variable in the heatemperature case (Table 6 and Figs. 6 and 7). The sample auto-orrelation function computed from the residual sequencesbtained by subtracting the two successive segment meansrom the original sequences (Lavielle, 1998) showed that theesidual sequences were stationary and close to white noiseequences (results not shown).

On the basis of two-segment models Mm estimated fromnivariate sequences, the change point 1987 → 1988 wasetected for all the chilling temperature sequences and forhe heat temperature sequences at Angers and Nîmes.

Since a single change point was detected at 1 year apartn both the flowering date sequence for apple tree cultivarGolden Delicious’ and the corresponding chilling and heatemperature sequences (and the ratios between the averagebsolute mean difference between the two segments and thelobal standard deviation

∑N

a=1|�̂1,a − �̂0,a|/N�̂ are relativelylose in the three cases; see Tables 1 and 6), the flower-ng date can be directly related to the corresponding chillingrespectively heat) temperature by a simple linear correla-ion coefficient. In the two cases, the correlation coefficientsre largely below the threshold of −0.22 corresponding to theypothesis of no correlation and clearly indicate negative cor-elation between the temperature and the flowering date. Ithould be noted that the heat temperature is far more corre-ated with the flowering date (correlation coefficient of −0.79)han the chilling temperature (−0.3).

. Discussion

ne difficulty with these data sets is the similar orders ofagnitude of the mean difference between the two segments

nd the standard deviation attached to each segment (seeable 1). Hence, the two underlying Gaussian distributionsstimated for the two segments exhibit a large recovering.or instance in the case of two Gaussian random variables

0 ∼ N(�0, �2) and X1 ∼ N(�1, �2) with common variance �2 suchhat �0 − �1 = �, we have P(�1 ≤ X0 ≤ �0) = P(�1 ≤ X1 ≤ �0) = 0.34nd P(X0 ≤ �1) = P(X1 ≥ �0) = 0.16.

Another source of difficulty lies in the relatively shortength of segments (between 13 and 18; see Figs. 1–3). Assum-ng a segment length of 16, the confidence interval for �j isoughly �̂j ± �̂/2. Hence, our statistical analysis clearly sup-orts the idea of abrupt change of the dates of flowering stagest the end of the 1980s, but the statistical model (a singlehange point between two stationary segments) is not fullyalidated because of the quite short length of the segments inonjunction with the recovering of the two Gaussian distribu-ions estimated for the two segments.

Despite some statistical uncertainties, our analysis of phe-ological sequences and their relationship with temperaturehanges provide elements for a right description and expla-ation of the impact of global warming on apple and pear

9 ( 2 0 0 8 ) 189–199 197

tree phenology in France. In the case of apple tree ‘GoldenDelicious’, the advances in flowering date have been similarfrom North-West to South-East of France, i.e. without interac-tion with the location. Moreover, the mean range in floweringadvance (7–8 days) was similar to the mean difference in flow-ering date between adjacent locations (6–8 days). Thus, as aresult of the abrupt change in flowering date, ‘Golden Deli-cious’ is now flowering at the northern location of Angerswithin the same date range it was previously flowering fur-ther south at Bergerac. The same relative change was observedbetween Bergerac and Nîmes (Table 5). For pear tree culti-vars growing at Angers, similar mean flowering advances wereobserved, i.e. without interaction with cultivar. In compari-son with apple tree ‘Golden Delicious’ in the same Frenchlocations, pear tree cultivars showed higher mean flower-ing advances (10–11 days), exceeding the mean differencebetween adjacent locations (2–3 days between Angers andBergerac for ‘Williams’). A similar higher advance (10 days)was also found for ‘Williams’ at Changins in Switzerland.For each of the eight phenological sequences, there was aclear time coincidence between the beginning of markedincreases of annual temperatures and the most probableinstant (1988 → 1989, according to the statistical models) ofabrupt change of flowering dates. Thus, our results confirma general impact of global warming in Europe toward ear-lier flowering dates at the end of the 1980s (Chmielewski etal., 2004) and contribute to an accurate characterization ofthis impact (abrupt change, most probable change instant).In addition, they suggest genetic differences in phenologicalresponse between apple and pear trees, as already reportedfor cherry tree (Miller-Rhushing et al., 2007).

At present, such a phenological change do not affect fruittree production, but it is important to understand the mecha-nism by which climate warming exerts its influence, especiallybecause this was poorly investigated since the old works ofCannell and Smith (1986). An interesting feature to explainis why the flowering advance would have been expressedthrough an abrupt change and not in a progressive way. Oneexplanation would lie in different changes in the respectiverates of completion of the chilling and heat requirements.Indeed in the case of ‘Golden Delicious’ in France, previousworks (Legave et al., 2008) showed that a constant regionalgradient of annual F1 dates (the latest dates at Angers to theearliest dates at Nîmes) is determined by differences in lengthof the heat phase (the longest at Angers and the shortestat Nîmes) since an inverse gradient of the dates of chillingcompletion occurred constantly (the earliest at Angers andthe latest at Nîmes). Similarly, earlier F1 dates since 1989at all three locations have been explained by a major effectof warming in reducing the length of the heat phase (morefrequent years with relatively short lengths), in spite of notice-able trends, at the same time, toward some years with longerlengths of the chilling phase (Legave et al., 2008). In agreementwith these previous findings, the present study clearly showsthat the mean temperature during the heat phase has beenthe main climatic factor determining the F1 date (the higher

temperature, the earlier date), while the mean temperatureduring the chilling phase has been a less important factor(poorly linked to the F1 date). Indeed, the recent warmingwas non-uniform at all locations but particularly pronounced

i n g

r

198 e c o l o g i c a l m o d e l l

in months corresponding to the heat phase (February andMarch particularly), while warming was limited in monthscorresponding to the chilling phase (October to early January).Moreover, the mean temperature during the heat phase clearlyincreased from 1988 to 1990 at Angers and Nîmes and moreprogressively at Bergerac (Fig. 7). Then, from 1991 to 2002, themean temperatures during the heat phase remained relativelyhigh at all three locations (particularly from 1994) in compari-son with the mean temperatures prevailing before 1988 (Fig. 7).Such temperature changes led to a marked increase in therate of completion of the heat requirements since 1988 andcan explain the abrupt change of flowering dates. Neverthe-less, as previously mentioned, climate warming also affectedthe rate of completion of the chilling requirements which wasclearly decreased in some years (high temperatures duringthe chilling phase). In such cases, relatively long dormancytended to delay the flowering date despite the short lengthof the heat phase linked to a high rate of completion of theheat requirements. This was markedly the case for the annualcycle 1987–1988 characterized by relatively high temperaturesat the end of chilling process (January 1988), particularly atNîmes. Such a temperature feature a this time (Figs. 6 and 7)can explain that the most probable instant of abrupt changeof flowering date is detected only between 1988 and 1989, i.e.1 year after the beginning of the marked warming in Francewhich started in 1988 as confirmed by our results.

For pear tree cultivars, we may suppose that abrupt changeof flowering dates is explainable in the same way as for appletree ‘Golden Delicious’. However, higher mean advances inflowering dates for pear tree cultivars in same locations andperiods suggest that climate warming exerted a lower effect onthe lengthening of dormancy in the case of pear trees, due totheir lower chilling requirements (Atkinson and Taylor, 1994).

Finally, it may be emphasized that cultivars of fruit treeshave been suitable plants to highlight climatic change factorsduring the recent climate warming in France (temperatureincreases from autumn to early spring) as probably in otherEuropean countries. A first advantage of fruit trees is due to theconsiderable longevity of cultivars (clone) permitting analysesof phenological sequences over long terms. Another inter-esting feature lies in the fact that their flowering process ishighly linked to two temperature requirements, which allowsto highlight significant temperature changes during the differ-ent seasons. Therefore, it is important to continue to collectand analyze flowering data for some main cultivars of fruittrees, in order to detect new changes in main temperaturefactors and consequently select cultivars adapted to possiblephenological disorders in the future (Sunley et al., 2006).

The authors are grateful to Danilo Christen (SRA Changins-Wädenswil, André Bélouin (INRA Angers), Catherine Miny(Domaine de Castang) and Vincent Mathieu (Ctifl Nîmes) fortheir essential contribution to the collect of phenological data.Financial support is acknowledged from INRA Mission on Cli-mate Change (Bernard Seguin, INRA Avignon).

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