Environmental and Experimental Botany xxx (2004) xxx–xxx Bacterial populations on the leaves of Mediterranean plants: quantitative features and testing of distribution models R.K.P. Yadav , J.M. Halley , K. Karamanoli , H.-I. Constantinidou , D. Vokou a Department of Ecology, School of Biology, Aristotle University, GR-541 24 Thessaloniki, Greece b Laboratory of Agricultural Chemistry, School of Agriculture, Aristotle University, GR-541 24 Thessaloniki, Greece Abstract
We studied the bacterial colonization of the phyllosphere of eight perennial species occurring in a Mediterranean ecosystem in Sithonia (Halkidiki), northern Greece, over a period of 2 years. The plant species were Arbutus unedo, Quercus coccifera,Pistacia lentiscus, Myrtus communis, Lavandula stoechas, Calamintha nepeta, Melissa officinalis and Cistus incanus. They differin a number of morphological features, mainly in habit and leaf trichome. The bacterial colonization of their leaves is highlyvariable. Over all species and sampling dates, observed values ranged from non-detectable to a maximum of 1.4 × 107 CFU g−1in C. nepeta. The average size of the microbial community varied among species by a factor of about 10, from 1.3 × 104 CFU g−1in A. unedo and L. stoechas to 1.3 × 105 CFU g−1 in M. officinalis and C. nepeta. Within species variability was far larger thanthat among species or among seasons. Apart from the fact that low values were recorded in summer, the marked seasonality ofthe Mediterranean climate was not reflected in the phyllosphere bacterial populations. Essential-oil producing species were notless colonized than the others. The hemicryptrophytes, M. officinalis and C. nepeta, shorter than all other species and equippedwith both glandular and non-glandular trichome, consistently sustained high bacterial populations on their leaves. Ice-nucleationactive (INA) bacteria were absent from all species, except for C. nepeta, on which a very low population was recorded in winter.
Given these results and additional literature information, we argue that perennial species of Mediterranean-climate areas are notsystematic hosts of INA bacteria. We tested the statistical distribution of the phyllosphere bacterial populations of these speciesfor lognormality using the Kolmogorov–Smirnov (K–S) test. Using the Akaike information criterion (AIC), we compared thelognormal, gamma and Weibull distributions, as well as their compound (Poisson-sampled) versions. The results clearly favourthe lognormal hypothesis for these data. This may have important implications for our understanding and interpretation ofbacterial population dynamics.
2004 Elsevier B.V. All rights reserved.
Keywords: Phyllosphere bacteria; INA bacteria; Mediterranean shrubs; Aromatic plants; Trichome; Lognormal distribution 1. Introduction
The total leaf area of terrestrial vegetation amounts Corresponding author. Tel.: +30-2310-998323; Nevertheless, interest in leaves as a distinct ecologi- E-mail address: [email protected] (D. Vokou).
cal milieu and potential habitat of microbes has only 0098-8472/$ – see front matter 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.envexpbot.2004.01.004 R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx This finding provided a basis for the development of The leaf is unique as a habitat for epiphytic microbes.
appropriate sampling techniques for epiphytic bacteria It is ephemeral, lasting only few weeks for many an- and also important insights into their epidemiology.
nuals up to a few years for woody perennial species; it is highly dynamic, exposed to pronounced cyclic and non-cyclic variation of environmental conditions rial populations of the rhizosphere also approximated a lognormal distribution. However, this is not univer- edge is more or less arbitrarily defined, the leaf mar- gin clearly delineates the boundary of the microbial found that the Weibull distribution gave better agree- community. Epiphytic communities are subjected to ment with their observations for the bacterial popula- frequent and rapid alternation between highly varying tions on the leaves of Phaseolus vulgaris. Departures states of environmental factors, such as temperature, from lognormality had also been observed by relative humidity, wind speed, radiation, any one of which may be considered stressful to at least some for using lognormal distribution in this context has High variability in space and time is a typical fea- not been formally developed beyond a hypothesis ture of epiphytic bacterial populations. Population that bacterial counts are the results of unidentified sizes can vary enormously even among adjacent, visu- ally identical leaves of the same individual argued that reasons governing frequency distributions in nature usually favour the lognormal distribution.
tions of P. syringae pathovar mors-prunorum on indi- Representation of large bacterial populations by a vidual cherry leaves ranged from the non-detectable continuous distribution as the lognormal, in spite of to 1.3 × 105 CFU per leaf within a set of 60 individ- the discrete nature of bacterial cells, is a convenient ual leaves. As a consequence of this high variability, approximation that facilitates mathematical and sta- he suggested the testing of large numbers of leaves if tistical analysis. The advantage of this distribution is bulked samples are being used. Apart from problems that by making a simple logarithmic transformation of arising from our limited capacity in elucidating the bacterial counts obtained from a leaf sample or bulked sources of such variability, there are also method- samples, individual data points will follow a normal ological problems associated with it, regarding both collecting and analysing relevant data.
prevalent but inconsistent reporting of lognormality Accurate estimates of bacterial population sizes are mentioned above, the current state of our knowledge needed if we are to safely predict phenomena related to them, including, for example, disease or frost dam- Because of their impact on world-wide agriculture, age. Because of the variability of epiphytic bacterial most studies of the microbiology of the phyllosphere populations in space and time and the procedural com- concern phytopathogens, and concomitantly cultivated plexity of their estimation, quantitative studies of phyl- plants, mostly with short-lived leaves, which account losphere bacterial populations must address the statis- tical distribution (i.e. probability density function) of these populations. This is very important because this may offer new insight as to the importance of the distribution dictates the statistical methods that can be phyllosphere as a habitat for microorganisms. Further- employed. Apart from the statistical issue, knowledge more, studies of the microbiology of leaves of peren- of the distribution may cast light upon the type of nial or non-deciduous plants may reveal patterns in dynamics controlling the population. This is because the ecology of the phyllosphere microbial community different types of distributions are associated with dif- Mediterranean ecosystems have not been consis- tently investigated as natural habitats for epiphytic time that epiphytic bacterial populations of various microorganisms in general, and bacteria in particu- crop plants approximated a lognormal distribution.
lar. There is only scarce information regarding fungi R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx a Mediterranean ecosystem, to examine whether the features differentiating them play a decisive role in determining epiphytic bacterial colonization, and fur- a few species found in them. The Mediterranean en- ther to assess the lognormal model and compare it vironment is unique in that factors favouring growth with a number of other models so as to have an under- do not coincide for a considerable part of the year. In standing of the distribution of phyllosphere bacterial summer, when the prevailing high temperatures can populations on Mediterranean perennial plants.
enhance growth, water is scarce. When water is avail-able, temperatures are not always favourable. Maquis(syn. choresh in Israel, monte bajo in Spain, macchia 2. Materials and methods
in Italy, chaparral in California) and phrygana (syn.
batha in Israel, tomillares in Spain, gariga in Italy, coastal sage in California) are major ecosystem typesin areas with Mediterranean-type climate. They are Our study site is a typical Mediterranean ecosystem, dominated by woody species with different prominent in Sithonia peninsula, Halkidiki (northern Greece).
features: evergreen and sclerophyll in maquis, season- Eight perennial plant species of different life form, ally dimorphic in phrygana. A number of features of major components of this ecosystem, were chosen as their component species can be considered of adap- our experimental material Four species (A. tive nature to face the shortage of water during the unedo, Q. coccifera, P. lentiscus, M. communis) make the group of evergreen-sclerophyll species and are of the species are also aromatic; in fact, 49% of the main components of maquis. Another four produce es- genera with representatives falling within the group sential oils (C. nepeta, L. stoechas, M. communis, and of aromatic plants are found in Mediterranean-climate We made a total of 10 samplings during a 2-year world where this climatic type prevails.
period (November 2000–November 2002). Sampling In this paper we study the size of the phyllosphere always took place early in the morning. Samples were bacterial population of eight co-occurring perennial placed in sterile plastic bags, were transported to the Mediterranean species that differ in a number of laboratory in an icebox, and were analysed within morphological features, mainly in plant habit and 24 hrs. The sampling protocol was the following: leaf trichome, glandular or non-glandular. We fur- Three individuals from each species were marked.
ther examine the statistical distribution of bacteria Mature leaves were collected at random from each on their leaves. Our objective is to estimate the level marked individual. Leaf samples consisted of one leaf of bacterial colonization of species participating in for A. unedo, which has the largest leaves, while for all Table 1Maximum, median (log CFU) and average values [log(CFU + 1)] over all sampling dates of total bacterial populations on the leaves ofeight Mediterranean perennial species, their life form and essential oil content of their leaves (average ± standard error) The minimum values are not given as for all species, there were samples with non-detectable bacterial populations.
R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx other species, they consisted of more, approximating the area of one A. unedo leaf; three or five leaf sam- sprayed with 3% paraffin in xylene, was folded into ples were collected per individual. Thus, there were a flat-bottomed boat, which was floated on polyethy- always 9 or 15 samples from each species. An excep- lene glycol solution maintained at −5 ◦C in a refrig- tion was for April 2002; for this date, there were no erated constant temperature bath. Discrete fluorescent samples of C. incanus, C. nepeta, L. stoechas and M. colonies from KB plates were removed with sterile officinalis, whereas for the rest, four leaf samples were inoculation loop and suspended in 0.25 ml phosphate collected from the marked three plus an additional buffer to yield a turbid suspension. Twenty 10 ␮l individual (in total 16 leaf samples). In consequence, droplets of suspension from each colony were placed there are in total 76 data sets (8 plant species × 10 on the −5 ◦C test surface. A colony was considered sampling times − 4 species in one sampling time).
to contain nucleus activity at −5 ◦C, if half or more A meteorological station close to our study site had been operating only for the years 1968–1975. To havean estimate of the climatic variability during the study period, we used data from the meteorological stationof Thessaloniki, the closest major city. We concluded Air-dried leaves (30–50 g) of C. nepeta, L. stoechas, that data from this station adequately reflect the cli- M. communis, and M. officinalis were water-distilled matic situation in the study area because comparison in a Clevenger apparatus for three hours. Essential of temperature data from the two stations over the pe- oil content was expressed in ml per 100 g of dry leaf riod 1968–1975 showed a very high degree of correla- tion (R = 0.99, P < 0.001), while rainfall data werealso considerably correlated (R = 0.54, P < 0.001).
CFU data were log transformed (log10) and sub- jected to the Kolmogorov–Smirnov (K–S) test for nor- mality for each species and for each season. Since no bacterial population was detected in several sam- placed in 100-ml Erlenmeyer flasks containing 25 ml ples, integer 1 was added to all CFU counts before sterile phosphate buffer (0.01 M, pH 7.3) supple- log transformation. These data were also standardized mented with 0.1% peptone, and washed for 10 min to a mean of zero and a standard deviation of unity.
on an ultrasonic cleaner; the temperature of water did In order to improve the power of our tests, the stan- not exceed 20 ◦C. Portions (100 ␮l) from the original dardised data sets of each species were pooled over all wash and appropriate serial dilutions thereof, prepared seasons, and those of each season were pooled over in 0.01 M phosphate buffer (pH 7.3), were plated onto all species. These were then also checked for normal- a) nutrient agar medium supplemented with 2.5% ity using the K–S test When the pooled set (v/v) glycerol (NAG), b) Kings B medium (KB), both of data is found to deviate from normality, this im- amended with natamycin (30 ␮g ml−1) to prevent plies that one or more of the individual sets are not fungal contamination. The dilutions examined were 1:1, 1:10 and 1:100. Total bacterial populations were In order to compare the goodness of fit of the lognor- enumerated from the NAG plates, and ice-nucleation mal to our CFU data with that of other distributions, active (INA) bacteria from the KB plates, after incu- we used the Akaike information criterion (AIC). This bation for 2–5 days at 24 ◦C; they were expressed as is a likelihood-based comparison and is widely used as colony forming units (CFU) per gram fresh weight.
an alternative to hypothesis-testing (The AIC works 2.3. Testing for ice-nucleation active bacteria by comparing the data with a probability model: thelower the value of the AIC, the better the model fit.
Ice-nucleation activity of bacterial colonies, ob- The models with which we compared the lognormal tained from KB plates, was tested following the were the Normal, gamma and Weibull distributions.
R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx All of these are encountered commonly in biological this procedure is bias. Specifically, it might happen that situations. In addition, the lognormal and Weibull have in small datasets like ours, the AIC shows a preference been used in studies of populations of epiphytic bacte- for the “wrong” distribution. For example, datasets {k1, k2, . . . , kn} generated from a gamma distribution normal and Weibull, respectively). While the gamma may on average yield a better fit (lower AIC) for a log- distribution has not been used in the latter context, it that the AIC could be biased towards one of the dis- tributions, we also generated sets of simulated data, of CFU = 0 is zero, the AIC cannot be computed which act as “controls”. For each of the 76 data sets, for datasets that include zeroes, and therefore we re- 10 replicates were generated using the estimated pa- placed CFU by CFU + 1, as in the earlier analysis.
rameters associated with each of the six models. Thus, Given that the number of zeroes in our data is substan- there was one simulated group of data sets, containing tial, such a transformation is open to legitimate criti- 760 simulated data sets, associated with each distribu- cism. Also, these distributions, which are continuous, tion. Each of these groups of data sets was subjected neglect the basic fact that in practice we measure an to the same testing procedure as the real data.
integer number of colonies. The best way of dealing This maximum-likelihood fit provides an alterna- with these concerns is to use the associated compound tive means of estimating the average population values models, Poisson-lognormal, Poisson-gamma and the without recourse to the devices of adding 1 to CFU before log-transforming (or ignoring 0 values entirely, as many researchers do). It was, therefore, used as set of distributions, as they are intrinsically integer a check on the averages computed by our CFU + 1 valued, and in addition account for zero naturally. For these reasons we used them in spite of the technicaldifficulties in their calculation, which have led to theirnot being so widely applied.
3. Results
The AIC takes into account the number of parame- ters in each distribution. For all the distributions con- The bacterial colonization of the phyllosphere of sidered in this paper, the AIC has exactly two param- the species examined was highly variable. Taking all samples together (of all species and samplingtimes), the size of the phyllosphere microbial popu- lation ranged from non-detectable up to a maximumof 1.4 × 107 CFU g−1 in C. nepeta For where ˆ is the maximum value of the log-likelihood all species, there were samples in which no bacterial population was detected (A. unedo contained the largest proportion of samples with non-detectable 1)f(k2)f(k3) · · · f(kn)] bacterial populations (13.5%), whereas C. nepeta and for the given data set of CFU counts {k1, k2, . . . , kn} M. officinalis contained the smallest (3.9 and 1.5%, and probability function, f(k), the calculation of which respectively). Leaf samples with non-detectable bacte- is explained in For most distributions of rial populations were most frequent in summer; in four interest, there is no formula that gives the parameters species, for more than 30% of the August samples, that maximize ˆ, so we used a Monte-Carlo search there was no detectable population Given the to find the best parameters. We first parameterize the high number of zero values encountered in our data, distribution crudely, then we search for the parameter transformations of the form log(CFU) will cause seri- values giving a higher ˆ, using the method described ous concern. If we exclude zero values and transform the rest, we ignore a considerable and valid segment each of the 76 data sets for each of the models tested.
of our data. For this reason, we adopted the alternative For each data set, the model with the lowest AIC was solution of using the log(CFU + 1) transformation in declared the ‘winner’. A possible complication with order to calculate averages and standard errors.
R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx Table 2Proportion of leaf samples (%) of the plant species studied with non-detectable bacterial populations, at each sampling date The average total bacterial population of the phyl- Analysis of variance showed that the species and losphere (over all sampling times) ranged between season factors accounted for only 27% of the to- 1.3 × 104 CFU g−1 in A. unedo and L. stoechas to tal variance of the phyllosphere bacterial population 1.3 × 105 CFU g−1 in M. officinalis and C. nepeta, [log(CFU + 1)]. This means that within-species vari- varying by a factor of 10. Regarding the highest values ability is far larger than that among species or among recorded in leaves of each species, they ranged from 106 to 1.4 × 107 CFU g−1 leaf (The leaves Ice-nucleation active bacteria were practically ab- of M. officinalis and C. nepeta consistently sustained sent in this Mediterranean ecosystem. Only in one high total bacterial populations throughout the study case, in the February 2001 sampling, a low popula- tion of INA bacteria was recorded on the leaves of C. hemicryptophytes in nature, are the most heavily col- nepeta (0.93 ± 0.6 log CFU g−1).
onized, followed by Q. coccifera and P. lentiscus, two ws the results of testing the null hypothe- sis of lognormality (i.e. the normality of log(CFU+1)), The average size of the phyllosphere microbial pop- using the Kolmogorov–Smirnov goodness-of-fit test.
ulations of essential-oil producing plants ranged be- For all the individual datasets, the null hypothesis was tween 1.3 × 104 and 1.3 × 105 CFU g−1. The highest accepted. However, when the standardized data were value was recorded in M. officinalis, which is the poor- pooled by species, the hypothesis was rejected for est in essential oil of the species examined ( A. unedo, M. communis and L. stoechas, and when whereas the lowest in L. stoechas, with an essential oil they were pooled by season, it was rejected for Au- concentration in its leaves more than 10 times higher noting that species exhibiting the largest deviations There was no obvious seasonal pattern of change from lognormality were those for which the median in the population of phyllosphere bacteria. Neverthe- and the mean of log(CFU + 1) differed substantially less, for most species, the summer values were among (Given these deviations from lognormality, the lowest (The climatic variability during the there was a need to examine more closely the relation- study period is shown in Analysis of data of ship between the data and the models being used to a 60-year period (1931–1990) show that August is fit them. ws the results of the model com- the driest month of the year with a mean rainfall of parisons using the Akaike information criterion. The 14.3 mm; 2002 was an exceptional year in that rainfall was unusually high during summer. Comparison of tributions. We can see that the lognormal-generated the two figures show that the bacterial populations on data most closely approximate the results for the ob- the phyllosphere do not follow the seasonal climatic served data. Note that the AIC tends to be biased; it discriminates in favour of the lognormal, even if the R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx Fig. 1. Total bacterial population [log(CFU + 1)] of the leaves of the Mediterranean species examined during the period November2000–November 2002. Error bars represent standard errors. A. unedo, Q. coccifera, P. lentiscus and M. communis are evergreen-sclerophyllspecies; L. stoechas, C. nepeta, M. officinalis and M. communis are aromatic plants.
data themselves are not lognormally distributed. If we idence that the population itself is best described by the lognormal distribution. Further evidence is sup- clearer picture, since the AIC is not so biased. Here, plied by the fact that the number of zeroes predicted for the simulated data, the best fitting models corre- by this model is consistent with the number observed.
spond to the models used to generate the data. The There were a total of 93 zeros in the observed 952 Poisson-lognormally generated data are more similar samples, and over the 10 simulated replicates an av- to the real data than either those Poisson-gamma or erage of 101.5 (ranging between 89 and 110). There- Poisson–Weibull generated. This provides strong ev- fore, the observed number of zeroes is well within the R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx Fig. 2. Climatic variability during the study period; data from the meteorological station of Thessaloniki.
typical range of behaviour for a sampled lognormal an evergreen oak also participating in maquis. They reported an average size of 3.13 × 104 CFU cm−2.
This value is much higher than the respective one adding 1 to CFU prior to taking logarithms, we tested (after transforming it on a per-area basis) for Q. coc- the effects of these potentially distorting transforma- cifera and may be due to the presence of tufted hairs tion by comparison with results derived from the supe- on the abaxial surface of Q. ilex. However, results for rior maximum-likelihood method. We found that the Q. ilex are not in fact comparable to our results for average error for each of the 76 population datasets Q. coccifera, as the authors used an entirely different was about 4% in excess of the value calculated by technique to recover bacteria from the leaves. maximum likelihood (and never exceeded 10% in any a minimum of 1.7 × 104 CFU cm−2 and dataset). Thus, we concluded that results in a maximum of 3.4 × 105 CFU cm−2 on the leaves of Olea europaea L. ‘coratina’. The olive tree, in its wildform, is also a typical component of maquis. Thesevalues are much higher than those of the four related 4. Discussion
species that we examined. There are two possiblereasons explaining this higher colonization of the In the present study we examine the bacterial col- olive leaves. (a) Our study was carried out in a natu- onization of the phyllosphere of eight Mediterranean ral ecosystem without major disturbances. Ercolani’s species, components of a Mediterranean ecosys- study area was an olive grove subjected to cultivation tem, that differ in a number of features. For the techniques which may affect the concentration of air- evergreen-sclerophyll species, the average size of the phyllosphere bacterial community ranged from (b) Olive leaves bear non-glandular scales on 1.3 × 104 to 4.6 × 104 CFU g−1, with A. unedo and M. communis being less colonized than Q. coccifera chomes have been repeatedly suggested to consist appropriate sites for bacterial colonization ( surfaces of Quercus ilex, which, like Q. coccifera, is R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx of 3.8–4.7 log CFU g−1. For Q. coccifera, it fluc- Normality of total bacterial population [log(CFU + 1)] of the tuated between a minimum of 2.5 to a maximum phyllosphere of (a) each species pooled for all seasons and(b) each season pooled for all species, as determined by the of 5.2 log CFU g−1, thus extending even further of the lower end of the range reported for the genus,possibly reflecting the more arid conditions of the Of all species, the hemicryptophytes C. nepeta and M. officinalis were the most heavily colonized (105 CFU g−1), sustaining high bacterial populations 0.007 (127)
throughout the study period. According to ground usually have bacterial populations larger and 0.003 (127)
0.02 (111)
less variable in size than taller ones. This is because leaves closest to the soil surface are likely to expe- rience more uniform physical conditions and higher relative humidity than are leaves located at a range becomes a more direct source of epiphytic bacteria.
Because of their life form, C. nepeta and M. officinalis are shorter than all other species. In addition, they are equipped with leaf hairs, glandular and non-glandular.
The combination of these factors could explain the fact that they consistently sustain high bacterial pop- 0.007 (120)
Essential-oil producing plants differed in the size of the microbial populations on their phyllosphere. Re- 0.001 (120)
garding the essential oil in their leaves, L. stoechas and C. nepeta had on average similar concentration, 1.5 ml 100 g−1 d.w., whereas M. officinalis and M.
had a much lower concentration, of 0.12 Given are the probability values obtained from the K–S test. Valuesin bold italics are significant at P < 0.05. The number of samples and 0.28 ml 100 g−1 d.w., respectively. In spite of their after they were pooled is given in parenthesis. Since each datum resemblance in terms of the essential oil concentra- participates in two tests, a BF correction requires P-values to be tion in their leaves, L. stoechas and C. nepeta differed increased by a factor of 2. We show this for significant values, all markedly in the bacterial colonization of their phyllo- sphere; C. nepeta (along with M. officinalis) was mostheavily colonized and L. stoechas least colonized.
of the evergreen-sclerophyll species that we studied In another study of four Mediterranean aromatic are waxy and devoid of hairs (personal observations).
plants, different to the ones that we examined plants tend to have lower bacterial population than tions on their phyllosphere ranged between 2.4 and 5.4 log CFU g−1. This range is comparable to the one Various other Quercus species, which unlike Q. we found here, yet extended at both ends. Also, like coccifera are deciduous, have been studied regard- in this study, the richer in essential oil species were ing the bacterial colonization of their phyllosphere.
Essential oils are known to possess antimicro- reported a total bacterial population for Q. virgini- ana of 5.7 log CFU g−1, for Q. macrocarpa a range of 3.8–6.4 log CFU g−1, and for Q. rubra a range phyllosphere microbial population, this activity is R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx Table 4Goodness of fit (with AIC) to observed and simulated data for different (a) simple distribution models and (b) compound distribution models The values (given as percentages) are the proportion of data sets, for which the corresponding model fitted best. Numbers in parenthesesare the numbers of data sets.
not clearly expressed. Essential-oil producing species and C. incanus. Apart from these, the marked season- were not on average less colonized than non-producing ality of the Mediterranean climate was not reflected in species. Also, in some cases, species richer in es- the phyllosphere bacterial populations.
sential oil were more heavily colonized than poorer Reported average population densities of epi- ones. These findings show that the nature of the re- phytic bacteria cover a huge range, from 104 to lationship between essential oils and microbes is not a simple one. The qualitative and quantitative com- are often encountered in sizes averaging 106 to position of the essential oil may be very important, 107 CFU cm−2 (up to 108 CFU g−1) of leaf ( as some compounds have much higher antimicrobial also found on the leaves of the species that we may be equally or even more important in determin- examined but only as maximum values; averages ing the level of microbial colonization. In addition, never attained these levels. According to although the antimicrobial activity of essential oils leaves in the field are subject to bacterial is very well known, it is not universal against all immigration of about 104 cells per month, and there- microbes. A number of them can use isoprenoid com- fore a substantial proportion of epiphytic bacteria are pounds making the mixture of essential oils as carbon just temporary immigrants and not real colonizers.
Thus, he argued, plant species with epiphytic bacterial populations less than 104 CFU per average sized leaf some phyllosphere bacteria also have such a property.
should be only incidental hosts. All eight species that The lowest phyllosphere bacterial populations were we examined supported population sizes higher than recorded for most species in summer. Others have this threshold, but there are numerous instances where observed this pattern for some but not all perennial the population falls well below this level, not only for individual leaves but also for monthly averages.
example, no significant differences were found in the As for the ice-nucleation active bacteria, their pres- size of bacterial populations on the mango phyllo- ence was incidental; only on one species and only on sphere, in South Africa, among the different seasons one sampling date did we find any of them, and this in very low numbers. Various authors suggest a broad with non-detectable bacterial populations were most distribution of INA bacteria on leaf surfaces ( frequent in summer, accounting even for 40% or more of the samples of the species A. unedo, Q. coccifera, R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx on the leaves of woody species belonging to the genus of the AIC (in favour of the lognormal) at low sam- Quercus. For example, Q. macrocarpa had INA bacte- ple sizes. A second possible cause of departures from rial populations ranging from 2.1 to 5.9 log CFU g−1.
lognormality is due to the fact that our data come However, in another study of four woody species oc- in the form of integers (including a large number of curring in Mediterranean-type ecosystems (all four be- zeroes), whereas the simple distributions examined ing representatives of aromatic plants), INA bacteria are continuous and do not allow zeroes. The only were found in half of them, and again in very low num- reliable way to deal with this was to upgrade the bers (<0.5 log CFU g−1) ().
simple models (lognormal, gamma, Weibull) to com- These results combined provide substantial evidence pound models (Poisson-lognormal, Poisson-gamma, that perennial species of Mediterranean climate areas Poisson–Weibull), where the sampling process is ac- are not systematic hosts for INA bacteria.
tually included in the distribution. Using the com- Authors have been divided on whether the lognor- pound distributions, a very clear picture in favour of mal hypothesis can be accepted as a general rule for a lognormally-distributed population emerged on the epiphytic bacterial populations. Since most of our data basis of the AIC. The number of zeroes was also con- sets are small, departures from lognormality were not sistent with the picture that would be expected with a always easy to detect. They showed up only when we lognormal distribution of the epiphytic bacterial pop- standardised and pooled our data, either by species ulation. Thus, we believe that the zeroes arise mostly or by season. Two possible causes could be respon- from the sampling process. They are more a conse- sible for departures from lognormality. Firstly, there quence of the failure of the measurement process to might be a systematic departure from lognormality to- detect very low populations rather than an indication wards an alternative distribution (gamma or Weibull), of true absence of bacteria on leaves.
which suggested to us to use the AIC for compar- The incidence of lognormality is a matter of ing different distributions. Using this technique, we importance, because it provides clues as to the found that the lognormal was somewhat better fit than population-dynamic processes that drive the sys- the other plausible alternatives. However, the picture was not a clear one, mainly due to the strong bias (1988) explained how population models can give Fig. 3. A model of bacterial population growth in a limited environment, subject to normally-distributed environmental variability. Theheavy line is the average population size for 1000 simulated population trajectories using the logistic approximation (while the inset panels are histograms of population size, for three different times. Notice that although the variability is normal, in therapid-growth phase the distribution is lognormal.
R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx rise to lognormal distributions. An example of this is fully understood yet, in semi-arid environments as the shown in which is a model of a population that grows in size from a small colony to a popu-lation that fully exploits the available resources, ac-cording to the well-known logistic model Acknowledgements
The expected probability distributions associ-ated with population growth are also shown. The de- The authors wish to thank Dr. Pablo Inchausti for mographic rates in this model are normally-distributed helpful suggestions. R.K.P. Yadav was supported by a grant from the State Scholarships Foundation (IKY), growing slowly at first, its distribution is almost nor- Greece. He is currently on study leave from Tribhuvan mal. Once it enters the phase of rapid exponential University, Nepal. This project was also supported by growth, the distribution becomes skewed and typically the Greek Ministry of Environment (01 ED 317).
lognormal. However, when it finally saturates at thecarrying capacity of the environment, it returns to thesymmetric normal form once again. The lognormal Appendix A. Calculation of compound
distribution, in most models, tends to be associated distributions
with periods of temporary exponential growth, whilepopulations that have reached “equilibrium” with Various models useful for describing population their environment tend to have a more symmetric sizes, such as the lognormal, gamma and Weibull dis- distribution. In a large study of 544 ecological time tributions, run into the problem that often the estimates of population size appear as a series of low-valued ecological distributions were less skewed than log- integers, even though the population itself may be normal and that the gamma distribution was at least very large. This is the case for the data appearing in as good a fit as the lognormal. This is in contrast to this paper. To estimate a bacterial population size X, the distributions found for bacteria on leaves, which we measure a number k of colony-forming units. In conform more closely to the lognormal distribution.
effect, we are measuring a small proportion δ of the This may reflect a more ephemeral “boom and bust” total population. Thus k is approximately δX, rounded type of population-dynamics than for macroscopic to the nearest integer. So, if k is simply re-scaled by organisms. Bacterial populations, dominated by ex- the factor 1/δ, we have an estimate of population X, ponential growth at first, tend to be wiped out before namely X k/δ. But information is lost, especially when the population is low, because different pop- In concluding, the perennial species that we ex- ulations are represented by the same integers. For amined, commonly found in Mediterranean ecosys- example, if δ = 10−3, then all populations between tems, are not systematic hosts for INA bacteria; often 500 and 1500 are represented by k = 1.
they are not systematic hosts for epiphytic bacteria However, the really serious problem is that all pop- either. The total bacterial population on their phyllo- ulations less than 500 are undetectable, because the sphere is low during summer. A number of plant fea- nearest integer is zero. In such cases, X is estimated to tures are involved in determining the size of epiphytic be zero. This creates big problems, when testing for bacteria on their leaves, as is the leaf trichome. Yet, distributions such as the lognormal, for which we need plants with waxy cuticled leaves (e.g. Q. coccifera) are to calculate log(X). The usual way of getting around not always characterized by lower phyllosphere bac- this problem, is by replacing k with k + 1. This dis- terial population than rough, trichomatic leaved plants torts the distribution to an extent which is acceptable (e.g. C. incanus) that even produce essential oil in only when the number of zeroes in the data is small fair quantities (e.g. L. stoechas). Regarding the sta- tistical distribution of phyllosphere bacteria, our re- When the aim is to compare different distribution sults clearly support the lognormal hypothesis. This models or to test whether a sample is of a given distri- may have important implications about the underly- bution, the best solution is to estimate the compound ing population dynamic processes that are acting, not distribution. This is the distribution of k that arises R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx when small proportion of the population X (with a values (k > 20) we used the perturbation approxima- given distribution) is used as a sample ( If the population size itself can be described by theprobability density g(x) (e.g. the lognormal), then the probability that a randomly chosen leaf will be repre- sented by a count k in the data is given by a probability e−λ g(λ)dλ, k = 0,1,2,3. (A.1) A.2. Gamma and Poisson-gamma (negative binomial) The distributions thus formed are referred to as the The gamma random variable, with shape parameter corresponding Poisson-sampled distributions. Finding c and scale parameter b has the probability density the values f(0), f(1), f(2), f(3), etc. requires calcu- lating the integral in (A.1), which often is not possible in closed form. It is usually technically difficult and most of the rest of this appendix is devoted to speci- The parameters c and b are estimated from the meanM and variance V of the sample data by the formulas A.1. Lognormal and Poisson-lognormal M = bc and V = b2c, respectively.
For the Poisson-gamma, we use the formula (A.1) If a random variable X has a lognormal distribution, with g(x) = G(x). The Poisson-gamma is, in fact, with parameters µ and σ, then its probability density The parameters µ and σ are the mean and standard deviation of the corresponding normal distribution,which is obeyed by the random variable Y = ln k.
which means that the values f(k) for the observed sam- 1, k2, . . . , kN } of a lognormal distribution, µ and σ can be found simply by takingthe natural logarithm of all the observations {ln k A.3. Weibull and Poisson–Weibull distribution ln k2, . . . , ln kN} and getting the mean and standarddeviation of these.
The Weibull random variable, with shape parameter For the Poisson-lognormal, we use the formula c and scale parameter b has the cumulative distribution (A.1) with g(x) = L(x). However, for programming function (i.e. the probability of a value less than or purposes, it is best to transform the Poisson-lognormal integral (using φ = log λ) to the form ( k = F(k) = 1 − exp − b The probability density function is found by differen- tiating (A.7). A crude estimate of the parameters c and − eϕ − ln(k!) dϕ b is found first by rearranging (A.7): ln k = − 1cln[ln(1 − yk)] + ln b For small values of k, this integral can be evaluatednumerically (We carried out the We can find 1/c and ln b by regressing ln k against integration between the limits −5 and +5. For larger R.K.P. Yadav et al. / Environmental and Experimental Botany xxx (2004) xxx–xxx For the Poisson–Weibull, we use the formula (A.1) References
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School of Chemical and Biomedical Engineering Web: Sci. Tech. Process Engg. ETH Zurich, SwitzerlandM.Engg. Chem. Engg. National University of Singapore, SingaporeB.E Chem. Engg. Annamalai University, IndiaNanyang Technological University, SingaporeAssistant Professor, School of chemical and biomolecular engineeringSPIC Fertilizer Complex, Naptha base

DERMaTOlOGIa piante e sole: un mix E SE FOSSE allERGIa? In alcuni casi, meno frequenti, le stesse piante che provocano (a volte) pericoloso reazioni fototossiche possono indurre anche una reazione al- lergica. Ma che differenza c'è? a cura di Grazia Manfredi • La reazione fototossica dipen- de esclusivamente dal contatto con la sostanz

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