Journal of Fungi Article Incidence, Spatial Pattern and Temporal Progress of Fusarium Wilt of Bananas Daniel W. Heck 1,† , Miguel Dita 2 , Emerson M. Del Ponte 1 and Eduardo S. G. Mizubuti 1,* 1 Departmento de Fitopatologia, Universidade Federal de Viçosa, Viçosa 36570-900, Brazil; dwinterheck@gmail.com (D.W.H.); delponte@ufv.br (E.M.D.P.) 2 Bioversity International, Cali 763537, Colombia; m.dita@cgiar.org * Correspondence: mizubuti@ufv.br † Current address: Plant Pathology and Plant-Microbe Biology, College of Agriculture and Life Sciences, Cornell University, Geneva, NY 14456, USA. Abstract: The effective management of Fusarium wilt of bananas (FWB) depends on the knowledge of the disease dynamics in time and space. The objectives of this work were: to estimate disease intensity and impact, and to investigate the spatial and temporal dynamics of FWB. Fields planted with Silk (n = 10), Pome (n = 17), or Cavendish (n = 3) banana subgroups were surveyed in Brazil, totaling 95 ha. In each field, all plants were visually assessed, and diseased plants were georeferenced. The incidence of FWB and the impact of the disease on the yield on a regional scale were estimated. Spatial patterns were analyzed using quadrat- and distance-based methods. FWB incidence ranged from 0.09% to 41.42%, being higher in Silk fields (median = 14.26%). Impacts of epidemics on yield ranged from 18.4 to 8192.5 kg ha−1 year−1, with an average of 1856.7 kg ha−1 year−1. The higher economic impact of the disease was observed on Silk cultivar with an average loss of USD 1974.2 ha−1 year−1.   Overall, estimated losses increased on average by USD 109.8 ha−1 year−1 at each 1% of incidence. Aggregation of FWB was detected by all analytical methods in 13 fields (1 of Cavendish, 11 of Pome, Citation: Heck, D.W.; Dita, M.; Ponte, E.M.D.; Mizubuti, E.S.G. and 1 of Silk). In the other 17 fields, at least one analytical method did not reject the null hypothesis Incidence, Spatial Pattern and of randomness. One field (5 ha), composed of six plots, was selected for spatial and temporal studies Temporal Progress of Fusarium during two years with bi-monthly assessments. A sigmoidal curve represented the FWB progress Wilt of Bananas. J. Fungi 2021, 7, and the Gompertz model best-fitted disease progress. The level of aggregation varied over time, and 646. https://doi.org/10.3390/ evidence of secondary infection to neighboring and distant plants was detected. FWB is a widespread jof7080646 problem in Brazil and yield losses can be of high magnitude. Epidemiology-based management strategies can now be better established. Academic Editor: Kuang R. Chung Keywords: Fusarium oxysporum f. sp. cubense; Panama disease; epidemiology; disease impact; loss; Received: 13 July 2021 yield; management Accepted: 6 August 2021 Published: 8 August 2021 Publisher’s Note: MDPI stays neutral 1. Introduction with regard to jurisdictional claims in published maps and institutional affil- Banana plants with symptoms of Fusarium wilt were first reported in Australia in iations. 1874 [1]. In 1890, wilted plants were investigated in Cuba where Erwin F. Smith reported the soil-borne fungus Fusarium oxysporum associated with symptomatic banana plants [2]. It has been suggested that more than one species of Fusarium may be involved with the Fusarium wilt of banana (FWB), also known as Panama disease. Fusarium oxysporum f. sp. cubense (E. F. Smith) W. C. Snyder and H. N. Hansen has been traditionally reported as the Copyright: © 2021 by the authors. causal agent of FWB, but another species, F. odoratissimum N. Maryani, L. Lombard, Kema Licensee MDPI, Basel, Switzerland. This article is an open access article & Crous, was nominated to describe one of the lineages of F. oxysporum capable of causing distributed under the terms and the disease [3–5]. The taxonomy of F. odoratissimum is under debate [6] and we prefer to conditions of the Creative Commons use the traditional and most widely accepted nomenclature for the causal agent of FWB: Attribution (CC BY) license (https:// F. oxysporum f. sp. cubense (Foc). creativecommons.org/licenses/by/ Fusarium wilt is widespread in all banana-growing areas. The movement of infected 4.0/). planting material was responsible for the fast spread of the disease worldwide [7]. This J. Fungi 2021, 7, 646. https://doi.org/10.3390/jof7080646 https://www.mdpi.com/journal/jof J. Fungi 2021, 7, 646 2 of 19 practice is still common among banana farmers, mainly, but not exclusively, in subsistence systems. Despite the long history of damage by FWB on banana crops, there are important knowledge gaps about basic epidemiological features of FWB, such as intensity, impact, and the spatio-temporal dynamics of epidemics. Disease spatial pattern is primarily determined by biological and ecological factors correlated to the pathogen life-cycle [8], especially those related to the distribution of the primary inoculum [9]. Knowledge gained from the analysis of spatial patterns may help generate sound scientific hypotheses about pathogen dispersal mechanisms [10,11], and then can support mitigation strategies in the case of introduction of new variants of a pathogen into an area. Additionally, spatial analyses are useful for several purposes including the study of pathogen population dynamics [12], design of experiments [13], sampling programs for disease or pathogen monitoring [14–16], assessment of crop losses about disease intensity [13], and the development of management strategies [9]. Disease patterns can be the realization of the dispersal of propagules [17] and despite the epidemiological implications of the understanding of spatial dynamics to disease management, to date, only three studies provided information on the spatial pattern of FWB [15,18,19]. The aggregated pattern of FWB was detected in six banana plots (1334 m2 each) assessed in China. The higher the disease intensity, the higher was the aggregation level [15]. FWB was also reported to have an aggregated pattern in banana fields in Australia, but random diseased plants could also be found in some fields [18]. Weevil borers were allegedly involved in the spread of FWB [18]. In Brazil, weevil borers were detected affecting the spatial pattern of FWB [19]. The disease was more aggregated in a field where the population of weevil borers was managed and kept at lower numbers than in the unmanaged field [19]. Another important biological fact is the potential aerial dispersal of the pathogen [20]. If secondary infections could occur from airborne inoculum, a lower degree of aggregation and a higher number of diseased plants scattered in the field would be expected. Other forms of spore dispersal cannot be ruled out, such as transport by animals, wa- ter, soils, substrates, and anthropogenic factors [21]. Cultural practices, such as desuckering (destroying unwanted suckers which develop from the corm of a banana plant) and fertil- ization of asymptomatic but infected plants and sharing contaminated planting materials and tools, are common practices in banana plantations and contribute to the spread of FWB within and between fields. The movement of symptomless seedlings, infected fruit crowns, leaf trash through shipments, or infested soil adhered to any object used by workers may have facilitated the introduction of Foc tropical race 4 (TR4) from Southeast Asia to Africa or the Middle East [22] and even to South America. Spatial analysis may help elucidate whether an observed pattern emerged only by chance or due to an underlying process that may or may not be known. To succeed in such endeavor, it is necessary to use analytical methods based on different approaches for inspecting spatial patterns at different scales since the impact of a pattern on a process can vary with the scale [23]. Classic and current texts emphasize the potential large contribution of infected plants or contaminated tools to the spread of FWB in fields [21,24]. By examining the pattern of FWB epidemics in fields it is possible to infer that autochthonous inoculum of Foc would most likely result in random or regular distribution of wilted banana plants, whereas external inoculum from contaminated transplants or tools would result in aggregation or clusters of diseased plants. Pattern analysis and the study of spatio-temporal dynamics of epidemics can shed light on the contribution of the origin of the inoculum of FWB epidemics in banana plantations. However, these studies are largely absent for the Foc-banana pathosystem. The objectives of this study can be summarized by the following research questions: (i) What is the intensity and (ii) the impact of FWB in different production regions and cultivars in Brazil? (iii) What is the predominant spatial pattern of FWB epidemics at different scales? (iv) What is the temporal dynamic? Lastly, (v) how does the spatial distribution change over time? J. Fungi 2021, 7, x FOR PEER REVIEW 3 of 19 J. Fungi 2021, 7, 646 3 of 19 epidemics at different scales? (iv) What is the temporal dynamic? Lastly, (v) how does the spatial distribution change over time? 2.. Matteriialls and Metthods 2..1.. Fiieelldss Thiirrtty banaannaa fifieeldldssw witihthr erecocordrdsso foFf WFWBBin icnicdiednecnecwe wereeraes asesssseesdsefdro fmromM aMrcahrc2h0 1260t1o6 Atop Aripl r2i0l 1270.17T.h Tehfiee flidelsdws wereerge rgoruopuepdedb absaesdedo nong geoeoggrarapphhicicl oloccaatitoionn: : Vaalleed doo Riibbeeiirraa ((VR;; N == 44 fifieellddss));; SSããoo JJoosséé ddoo Riioo PPrreettoo aanndd Arraaççaattuubbaa ((SSJJA;; N == 88)),, iinn SSããoo PPaauulloo ssttaattee;; SSeerrrraa ddaa Maannttiiqquueeiirraa aanndd ZZoonnaa ddaa Maattaa ((SSMZZM;; N == 66)),, iinn SSããoo PPaauulloo aanndd Miinnaass Geerraaiiss ssttaatteess,, rreessppeeccttiivveellyy;; Noorrttee ddee Miinnaass aanndd VVaalleed dooS SããooF Frraanncciissccood daaB Baahhiiaa( (NMSSFF;;N = = 55)),, iinn Miinnaass GGeerraaiiss aannddB Baahhiaias tsattaetse,sr,e rsepsepceticvteivlye;lyN; oNrtoerCtea tCaaritnaerninseen(sNeC (;NNC=; N5) ,=i n5S),a innt aSCanattaar iCnaatsatraintea; astnadteN; aonrdte NPioorntee iProioPnaeriraon aPeanrasena(NenPsPe; (NNP=P2; )N, i n= P2)a,r iann Páasrtaanteá (sFtiagtue r(eFi1gAu)r.eT 1hAe)fi. eTlhdes fwieeldres l ◦ ′ ◦ ′ ◦ ′ ◦ ′wocearete ldocwatitehdi nw1it3hi1n4 13S°t1o4′2 S6 t2o8 26S°2la8t′i tSu ldaetitaundde 4a3nd2 143W°21to′ W50 to5 050W°50l′o Wng liotundgeit.uAdlet.i tAudltei- rtuandgee rdanfrgoemd 4fr5omma 4s5l imn VasRl itno V11R5 0tom 1a1s5l0i nmSaMslZ iMn S. MThZeMse. fiTvheesstea tfeivsea cstcaotuens taecdcofourn4te3d% foofr t4h3e%p loafn ttheed parlaenataendd a5re3a% aonfdt h5e3%to toalf Bthraez tiolitaanl Bbaranzainliaanp rboadnuacntiao npriond2u0c1t7io[n2 5i]n. F2i0e1l7d [s2iz5e]. rFainelgde dsizfero rman0g.e8d5 ftroo6m.6 07.8h5a taon 6d.6w7 ahsap alnandt wedasw pitlhanStieldk (wNit=h S1i0lkfi e(Nld s=; 1a0t ofitealldos;f a3 4to.7tahl ao)f, P34o.m7 eha(N), P=o1m7;e 5(1N.4 =h 1a7);, 5o1r.C4 ahvae),n odri sCha(vNen=d3is;h8 .(5Nh a=) 3b; a8n.5a nhaa)s buabngaronua pssu.bgroups. Fiigurree 11.. (A) Location of the 30 sampled fifields distributed in fifive states of Brazil.. Mesoregions are shaded in gray,, aand tthee eexacctt lloccaattiion off tthee fifieellddss waass iiddeennttiififieedd bbyy ggeeoomeettrriiccaall sshhaappeess tthhaatt ccoorrrreessppoonndd ttoob baannaannaac cuullttiivvaarrss.. FFiieelldss llooccaatteed cclloossee ttoo eeaacchh ootthheerr aappppeeaarr ssuuppeerriimppoosseed oonn tthhee maapp aannd ggeeoomeettrriicc sshhaappeess aarree daarrkkeerr.. ((B)) BBooxxpplloottss iilllluussttrraattee tthhee iinncciideennccee ooff FFuussaarriiuumm wwiilltt oonn bbaannaannaa fifieellddss iinn ddiiffffeerreenntt rreeggiioonnsso off BBrraazziill aanndd ((CC)) ffoorr ddiiffffeerreenntt ccuullttiivvaarrss.. TThhee aavveerraaggee aanndd mmeeddiiaann vvaalluueess aarree rreepprreesseenntteeddb byyd daasshheedda anndds soolliiddl liinneess,,r reessppeeccttiviveelyly. . 22..22.. DDiisseeaassee IInntteennssiittyy IInn eeaacchh fifieelldd,, aallll bbaannaannaa ppllaannttss wweerree vviissuuaallllyy aasssseesssseedd ffoorr ttyyppiiccaall eexxtteerrnnaall aanndd iinntteerrnnaall ssyymmppttoommss ooff FFWWBB.. EExxtteerrnnaall ssyymmppttoommss ccoorrrreessppoonnddeedd ttoo ppllaanntt wwiillttiinngg,, yyeelllloowwiinngg ooff oollddeerr lleeaavveess,, tthhee ccoollllaappssee ooff lleeaavveess aatt tthhee bbaassee ooff tthhee ppeettiioollee,, ffaalllleenn aanndd ddrriieedd lleeaavveess aarroouunndd tthhee ppsseeuuddoosstteemm,,w wrirninkklilningga nadndd idstiosrtotirotnioonf loefa flebalaf dbelsa,daensd, aspnldit tsipnlgitatitntgh eabt atsheeo bf passee uodfo pstseemu-. Idnotestrenmal. sIynmteprtnoaml ssywmepretoombsse rwveerdew ohbesnerevxetder nwahlesny mexptteormnaslw seyrme pntootmevsi dweenrte, bnuottt heveipdleanntt, abpupt ethaere pdlainntf eacptpedea. rAeds imnfaelcltceudt. Ain stmhealpl csueut idno tshtee mpsweuadsomstaemde wtoasv meraifdye ytoe lvloewrif,yr eydedllioswh-, brerodwdinsh, o-brrbolwacnk, doirs cbolalocrka tdioisncsoilnorvaatisocnusl airnt ivsasusceusl[a2r6 t]i.sIsfueexst e[r2n6a].l Iafn edxitnertenranl aalnsdym inptteormnasl wsyemrepptoremses nwt einrea tplreeassetnot nine palta lnetaostf othnee mplaatn, tth oef wthheo mleamt,a tthwe awshcoolnes imdeart ewdadsi sceoansseiddearnedd wdiasseagseeodre afenrden wceads ugseionrgefaehreanncdehde ludsGinPgS ad ehandheld ®vice (GPS GMPASP d®e6v4i,cGe a(GrmPiSnM, OAlPath 6e,4K, GS,aUrmSAin),. When symptoms were not clearly assigned to FWB, samples were collected for further confirmation using morphological and molecular analyses (Heck et al., in preparation). For J. Fungi 2021, 7, 646 4 of 19 each field, data sets containing the polygon used to delimit the field perimeter and the diseased plants’ geographic coordinates were used for spatial analyses. The number of diseased plants (y) in each field was recorded, and the estimated incidence (p̂) was calculated as p̂ = y/n̂i, where n̂ is the estimated number of plants. The n̂i was calculated using the polygon representing the field perimeter (used to estimate the area) and plant spacing (plant distance within and between rows). Disease intensity was compared among regions and cultivars. The data were submitted to Shapiro–Wilk and Bartlett’s tests and transformed by log(x) before analysis of variance (ANOVA). Multiple comparison was performed by Tukey HSD test with the stats package in the R Software Version 3.6.1 [27]. All the following spatial and temporal statistics were calculated using disease incidence as proportion and in the same version of the R Software. The incidence values were presented as the percentage of infected plants. 2.3. Estimated Losses Yield loss (L) per unit area (ha) for each field was calculated based on L = W ∗ p̂, where W is the actual yield of the banana crop per year (ton ha−1 year−1) and p̂ is the estimated incidence (proportion) [17]. The actual yield is the average yield of the municipality in which a field was located (Table S1) [25]. Economic loss was calculated as L (US$) = L ∗ P̄s, where P̄ is the average price for each banana subgroup (s). Monthly prices from 2013 to 2016 for each banana variety were obtained from Fala.BR (https: //www.gov.br/acessoainformacao/, accessed on 17 March 2021). Linear regression was used to analyze the relationships between yield loss and the disease incidence, L = β0 + β1 ∗ p̂, where β0 and β1 are regression parameters [17]. Yield losses were also compared among regions and banana subgroups. The data were analyzed as in Section 2.2. 2.4. Spatial Pattern Analyses Analytical methods based on quadrats and distances were used to investigate the spatial patterns at different spatial and temporal scales. 2.4.1. Quadrat-Based Methods Incidence maps were transformed into quadrats using the quadratcount function of the spatstat package in R software [28]. The exact number of plants in each quadrat could not be computed because the rows were not regularly spaced or straightly set in most fields. The maximum number of plants in a quadrat was assumed to vary from 4 plants in 2 × 2 to 36 plants in 6 × 6 quadrat-sizes. The sampling unit area varied among fields because the different spacing between plants was observed, but the relationship of the distance within and between rows was the same. The number of diseased plants in each quadrat was determined and used in the spatial analysis. Spatial hierarchy. Initially, sampling units were set at four hierarchical levels: 2 × 2 (lowest), 3 × 3, 4 × 4, and 6 × 6 (highest) estimated plants per quadrat. Analyses of β-binomial curves were used to assess aggregation within-sampling-unit. The spatial hierarchy analy- sis was performed using spatial_hier from epiphy package [29]. Dispersion index. The index of dispersion (D) for binomial data was calculated for each field as the ratio of the observed and the estimated variances [13]. A χ2 test was performed to test if the dispersion index equals 1 (D = 1). The analysis was conducted using the agg_index function from the epiphy package. Fitting distributions. The binomial and β-binomial distributions were fitted to the disease incidence data for each field. The χ2 goodness-of-fit test for both distributions and a log-likelihood ratio test (LRS) was used to determine whether the β-binomial better fits the observed frequency than the binomial distribution. This analysis was performed using the fit_two_distr function from the epiphy package. Binary power law. The binary power law was used to evaluate the relationship between the observed variance and the corresponding variance on the assumption of a binomial distribution of FWB incidence using an intermediate quadrat-size (3 × 3) [17]. The categor- J. Fungi 2021, 7, 646 5 of 19 ical values referring to the different banana subgroups—Cavendish, Pome, or Silk—were included in data sets. A modified t-test compared the model’s parameter estimates against the null hypothesis and between them [30]. 2.4.2. Distance-Based Methods Spatial Analysis by Distance IndicEs (SADIE). This method uses the location of the sampling units (quadrats) and the number of diseased individuals inside the unit to analyze the spatial arrangement of the diseased individuals by the distance to regularity (Dr) [31]. The modified index developed by Li et al. [32] was computed by the sadie function from epiphy package. Events and intervals. The distance-based statistic [17] was used as an alternative to quadrat-based methods. In this analysis, patterns of points were described based on intervals in space among events. The goodness-of-fit of the point process model was performed using a cdf.test function from spatstat package. L(d) function. Ripley’s K(d) function is a cumulative distribution function useful to analyze completely mapped spatial point process data [33]. K(d) considers the entire distribution of distances rather than just the mean of neighbor events [17,33]. L(d) is a transformed version of K(d), on which the expected K value is equal to distance [34]. The analyses were performed using Lest, envelope, and mad.test functions from spatstat package. Semivariance. The semivariance (γ) is a measurement of one-half of the variance between values separated by the same distance in a specific direction. Samples separated at distances greater than the range, may be considered spatially independent [17]. The semivariance and the parameters (range, nugget, and sill) were calculated using the variog and variofit functions from geoR [35]. 2.4.3. Concordance Analyses The fields were classified in aggregated or random as result of spatial statistic and tested by Cohen’s kappa for agreement between pairs of statistical methods and Fleiss’s kappa for an overall agreement among all methods used. The analysis was performed using the kappa2 and kappam.fleiss functions from the irr package [36]. 2.5. Temporal Analyses One Prata (Pome subgroup) banana field with 4.4 ha established in 2012 in Teixeiras, Minas Gerais state (Brazil), was selected to study the disease dynamics in space and time. The area has been cultivated in a low-input system, with minimal cultural practices. Six plots delimited by dirty roads, ranging from 0.3 to 1.0 ha, were set in the field. The number of plants per plot ranged from 171 to 649. Plants were spaced approximately 3× 5 m, within and between rows, respectively. The plots were assessed from April 2017 to February 2019 every two months, resulting in 12 disease assessments. Disease incidence was assessed as described above. Hourly records of temperature, relative humidity, and precipitation data were obtained from the closest standard weather station located at 14.4 Km from the field. Data were provided by Instituto Nacional de Meteorologia (INMET) of Ministério da Agricultura, Pecuária e Abastecimento (MAPA). The cumulative incidence was calculated for each plot in different assessment times. The monomolecular, logistic, and Gompertz models were fitted to the disease incidence and plotted over time by nonlinear regression analysis using the nlsLM function from the minpack.LM package [37]. The best model was chosen based on the lower root mean square error (RMSE), independence and homogeneity of variances, and higher coefficient of determination (R2). 2.6. Spatio-Temporal Dynamics Spatio-temporal analyses were performed for the same six plots assessed in Teixeiras for temporal analyses. The index of dispersion, SADIE, binary power law, and spatio- J. Fungi 2021, 7, 646 6 of 19 temporal association analyses were used to describe the spatial pattern of the disease on the plots over time. A spatio-temporal association study assesses the significance of the correlation coefficient between two spatially autocorrelated processes [38,39]. The measure- ment of the degree of local clustering in sampling units was used to calculate the similarity in the cluster indices of two sequential assessments. The local clustering (χp) was obtained by SADIE analysis [32], and the overall association, X, was acquired by the correlation coefficient of the local clustering between pairs of assessments. The t-test corrected for the spatial association was used to analyse the significance of χ2 distribution [39]. The analysis was performed using the sadie and modified.ttest functions from epiphy and SpatialPack [40] packages, respectively. 3. Results 3.1. Disease Intensity FWB incidence ranged from 0.09 to 41.4% across the fields located in different regions in Brazil (Table S1). The mean and median incidence values were 10.7% and 5%, respectively (Figure 1B, Table 1). The incidence varied among regions (p = 0.036). The highest average incidence was 22.1% in NPP (n = 2 fields) followed by SJA (n = 8) with an average of 17.8%. In other regions, the average incidence was lower than the overall average of 10.7% (Figure 1B). Table 1. Percentage of fields with significant aggregation by the index of dispersion (D), β-binomial parameter (θ), log-likelihood ratio statistic (LRS), index of aggregation (Ia) of the Spatial Analysis by Distance IndicEs procedure (SADIE), events and intervals (DK-S), and linear transformation of Ripley’s K function (L(d)) to each region assessed for incidence of Fusarium wilt of banana in Brazil a. Region b D c θ c LRS c I c da DK-S L(d) Function d SMZM (n = 6) 100 100 100 66.7 100 100 SJA (n = 8) 100 75 100 37.5 50 100 NPP (n = 2) 100 100 100 50 100 100 VR (n = 4) 100 100 100 100 100 100 NMSF (n = 5) 80 80 80 80 80 80 NC (n = 5) 100 100 100 80 40 100 Overall (N = 30) 96.7 90 96.7 66.7 73.3 96.7 a The aggregated pattern was inferred when the null hypothesis of randomness was rejected (p < 0.05). The null hypothesis of the β-binomial parameter (θ) is aggregation (p > 0.05). b SMZM—Serra da Mantiqueira and Zona da Mata; SJA—São José do Rio Preto and Araçatuba; NPP—Norte Pioneiro Paranaense; VR—Vale do Ribeira; NMSF—Norte de Minas and Vale do São Francisco da Bahia; NC—Norte Catarinense. c Quadrat-based statistics with quadrat-size of 3 × 3 plants. d Distance-based statistics. The incidence of FWB varied among cultivars (p = 0.017). The highest value of average incidence was observed for Silk (n = 10 fields), 18.62%. The widest range of incidence values was recorded on Silk fields: minimum of 4% and a maximum of 41.4%. Pome fields (n = 17) had intermediate incidence values: average of 7.5%, and ranging from 0.1% to 33.4%. The lowest disease incidence values were recorded on fields planted with Cavendish (n = 3) with an average of 2.4% and ranging from 1.8% to 2.8% (Figure 1C). 3.2. Estimated Losses The yield losses in the 30 fields ranged from 18.4 to 8192.5 kg ha−1 year−1 (Figure 2A). The mean value was 1856.5 kg ha−1 year−1 with a median of 935.2 kg ha−1 year−1. Yield losses did not vary among banana subgroups (p = 0.10). Economic losses reached a maxi- mum of USD 5244.8 ha−1 year−1, with an average value of USD 1010.4 ha−1 year−1 and a median of USD 405.1 ha−1 year−1 (Figure 2B). Differences were observed for economic losses (p = 0.01) among banana subgroups. Silk differed (p = 0.016) from the Pome subgroup with median loss of USD 910.6 ha−1 year−1 and USD 343.1 ha−1 year−1, respectively. J. Fungi 2021, 7, x FOR PEER REVIEW 7 of 19 3.2. Estimated Losses The yield losses in the 30 fields ranged from 18.4 to 8192.5 kg ha−1 year−1 (Figure 2A). The mean value was 1856.5 kg ha−1 year−1 with a median of 935.2 kg ha−1 year−1. Yield losses did not vary among banana subgroups (p = 0.10). Economic losses reached a maximum of USD 5244.8 ha−1 year−1, with an average value of USD 1010.4 ha−1 year−1 and a median of J. Fungi 2021, 7, 646 USD 405.1 ha−1 year−1 (Figure 2B). Differences were observed for economic losses (p =7 0o.0f 19) among banana subgroups. Silk differed (p = 0.016) from the Pome subgroup with median loss of USD 910.6 ha−1 year−1 and USD 343.1 ha−1 year−1, respectively. Figure 2. Estimated values of yield and economic losses and its relationship with the incidence of Fusarium wilt of banana aasssseesssseedd iinn 3300 fifieellddss ffrroom ddiiffffeerreenntt ccuullttiivvaarrss aanndd rreeggiioonnss ooff BBrraazziill.. ((A)) FFrreeqquueennccyy ooff eessttiimaatteedd vvaalluueess ooff yyiieelldd lloosssseess,, aanndd ((BB)) eeccoonnoommiicc lloosssseess bbyy ccuultlitvivaar.r .EEstsitmimataetde dvavlauleuse fsofro eraechac ahssaesssseesds efdielfide (lsdy(msybmolbs)o alsn)da onvdeoravlel rraelglrreesgsrioesns (isoonli(ds oblliadckb)l aacnkd) acunldticvualrt irveagrrersesgiroens sliionnesl i(ndeassh(dedas choeldorceodl)o rfeodr )thfoer rtehlaetiroenlasthioipn sbheitpwbeeetnw FeWenBF iWncBidiennccide eanncde (aCn)d y(iCel)dy lioesldselso, sasneds, (aDn)d e(cDo-) nomic losses. Confidence intervals (CI95%) is presented in C and D as shaded areas. economic losses. Confidence intervals (CI95%) is presented in (C,D) as shaded areas. AA ppoossiittiivvee lliinneeaarrt rternenddw wasasd edteectetecdtedfo rfothr ethreel arteiloantisohnipshsibpest wbeetewneFeWn BFWincBi dinencicdeeanncde abnodth btohteh etshteim esattiemdayteiedl dyiaenldd aencdo neocomniocmloiscs leosss(Fesig (uFirgeu2rCe ,2DC).,DT)h. eTihnet einrcteerpcteppat rpaamraemteertoerf obfo bthotrhe greregsrseisosniomn omdoedlse,lβs, β0yield= =− −111122..33 ((SSEE == 225500.3.3)) aanndd ββ0US$ = −=16−21.46 2(S.4E = 151.4), did not 0yield 0US$ (SE = 151.4), did dnioftfedri fffreormfr 0o m(p 0> (0p.2>9)0.. 2T9h)e. Tslhoepesl oppareapmaertaemr eotfe brootfhb roetghreresgsiroenss mioondmelos,d βe1lysie,ldβ = 184.4 (SE = 1yield = 184.4 1(S5E.8)= a1n5d. 8β)1UaSn$ d= 1β019U.S8$ (S=E1 =0 99..853()S, Edi=ffe9r.e5d3) f,rdoimff ezreerdo f(rpo o0t.1s6ig).n ificant (p > 0.16). 3.3. Spatiiall Pattern Analyses 33..33..11.. QQuuaaddrraatt--BBaasseedd Meetthhooddss AAtt aallll ffoouurr hhiieerraarrcchhiiccaall lleevveellss,, tthhee ββ--bbiinnoommiiaall ccuurrvveess ffeellll uunnddeerr tthhee bbiinnoommiiaall ccuurrvveess ((FFiigguurree 33)).. VVaalluueess ooff vv,, iinntteerrpprreetteedd aass tthhee eeffffeeccttiivvee ssaammppllee ssiizzee,, wweerree lloowweerr tthhaann tthhee rreeaall nnuummbbeerr ooff ininddivivididuuaalsls (n(n) f)ofro arlla hlliehriaerrcahrcichailc alelvleelvse (lps <( p0.<0001.)0. 0E1f)f.ecEtifvfeec staivmepslaem sipzeles swizeeres ewsetirme aestetidm aatt evd a t= v22.×729 =(±2 0.7.192()± fo0r. 1t2h)ef o2r ×t h2e q2u×ad2raqtu-saidzera cto-sniztaeincoinntaining 4 individuals,2×2 g 4 individuals, v3×3 = v3×3 = 5.22 (±0.32) for quadrats of 9 individuals, v4×4 = 7.95 (± 0.67) for quadrats of 16 individuals, and v6×6 = 13.73 (± 1.48) for the 6× 6 quadrat-size containing 36 individuals at the highest level (Figure 3). These values of v correspond to 69.8%, 57.9%, 49.7%, and 38.2% of n in the four hierarchical levels, respectively. Only the intermediate quadrat-size (3 × 3) was used in subsequent quadrat-based analyses. J. Fungi 2021, 7, x FOR PEER REVIEW 8 of 19 5.22 (±0.32) for quadrats of 9 individuals, v4×4 = 7.95 (± 0.67) for quadrats of 16 individuals, and v6×6 = 13.73 (± 1.48) for the 6 × 6 quadrat-size containing 36 individuals at the highest J. Fungi 2021, 7, 646 level (Figure 3). These values of v correspond to 69.8%, 57.9%, 49.7%, and 38.2% of8 nof i1n9 the four hierarchical levels, respectively. Only the intermediate quadrat-size (3 × 3) was used in subsequent quadrat-based analyses. Figure 3. Relationships between the incidence of Fusarium wilt of banana at (A) 2 × 2; (B) 3 × 3; (C) 4 × 4; and (D) Fi×gure 3. Relationships between the incidence of Fusarium wilt of banana at (A) 2 × 2; (B) 3 × 3; (C) 4 × 4; and (D) 6 × 6 q6uad6rqatu addimraetndsiimonesn siino n3s0 inba3n0abnaan fainealdfise. lTdhs.eT shaemspalminpgl inugniut n(iqtu(qaduaradtr)a wt) awsa tshteh ehihgihghesets t(p(phihgihg)h h) iheirearracrhchiciacla llelevveel laanndd tthhee iinnddiivviidduuaall ((ppllaannttss)) wwaass tthhee lloowweesstt ((pplow)).. BBiinnoommiiaall ((ddaasshheedd--lliinneess)) aanndd ββ--bbiinnoommiiaall ((ssoolliidd--lliinneess)) ddiissttrriibbuuttiioonnss wweerree ffiitttteeddlow ttoo tthhee ddaattaa.. TThhee nnuummbbeerr ooff iinnddiivviidduuaallss ((nn)) aanndd tthhee eeffffeeccttiivvee ssaammppllee ssiizzee ((vv)) eessttiimmaatteedd aatt eeaacchh lleevveell aarree pprreesseenntteedd iinn tthhee ggrraapphhss.. TThhee ddiissppeerrssiioonn iinnddeexx( D(D))r arnangegdedfr formom1 1to t6o. 56.a5n adntdh ethme emdieadniavna lvuaeluwea sw2a.3s 2(F.3ig (uFrieg4uAre). 4OAv)e. rOalvl,etrhaellr,e thweerree wneored inffoe rdeinffceerseanmceosn agmroengigo nresgrieognasr dreingagrDdin(pg= D0 (.1p1 =9 )0.a1n1d9)a agngdre aggagtiroen- gwaatisoinn fwerarse dinifnerarelldfi ienl daslla fniedldrse gainodn sr,ebguiotnfso,r bausti nfogrl ea fisienldgl(eo fuietlodf (5o)uitn otfh 5e)N inM thSFe NreMgioSFn rweghieorne awrhaenrde oam rapnadtotemrn poafttFeWrnB owf FaWs dBe wtecatse dde(tTeacbteled 1()T.able 1). TThhee ffrreeqquueennccyy ooff ddiisseeaasseedd ppllaannttss iinn qquuaaddrraattss wwaass wweellll ddeessccrriibbeedd ffoorr 9900%% ooff tthhee ffiieellddss bbyy tthhee ββ--bbiinnoommiiaall ddiissttrriibbuuttiioonn ((pp >> 00.0.055)) ((TTaabbllee 11)).. FFoorr oonnee ffiieelldd tthhee ffrreeqquueennccyy wwaass bbeetttteerr ddeescridisstcrriibb beedd bbyy tthhee bbiinnoomial distribution (data not shown). The θ parameter of the β-binomialution ranged frommia0l. 0d2isttori2b.u01tio(mn e(ddiaatna =no0t. 2s0h)o(wFing)u. rTeh4eB )θ. Tphaerraemweeterer onfo tdhieff βer-benincoes- mamiaol ndgistrreigbiuotniosnf orranthgeed fproamra m0.0e2te tro( 2p.0=1 0(m.26e)d. iaTnh =e 0d.i2s0tr) i(bFuigtiuorne o4fB)d. iTsehaesreed wpelraen ntso wdiθ afs- fbeertetnecredse asmcroibnegd rbeygitohnes f-obri nthoem θia plathraamn ebtyert h(pe =b i0n.o26m).i aTlhdei sdtrisibtruibtiuotnioinn o96f .d7i%seoafsethde pfilanβ eldtss w(pa 0.05). J. Fungi 2021, 7, x FOR PEER REVIEW 9 of 19 general, the level of aggregation was higher and more influenced by incidence in Silk J. Fungi 2021, 7, 646 (log(Ap) = 2.77 ± 0.41, b = 1.40 ± 0.09) than in Pome fields (log(Ap) = 2.37 ± 09.4o5f 1; 9b = 1.26 ± 0.07). Cavendish fields did not differ from Silk and Pome for both parameters (log(Ap) and b; p > 0.05). Figure 4F. iHguisreto4g.raHmissto ogfr a(mAs) tohfe( Ain)dtheex ionfd dexisopfedrsisipoenr s(iDon); ((DB)); β(B-b) iβn-obminoiaml ipalapraamrameteetre r(θ(θ)) frfroomm ddiissttrriibbuutitoionnfi fttiitntign;g(;C ()C) aggre- gation indaeggxr (eIgatia) froonmin Sdpexa(tIiaa)lf AronmaSlypsaitsia bl yA nDailsytsaisnbcye DInisdtaicnEces I(nSdAicDEsIE(S);A (DDI)E e);v(Den) tesv aenntds ainndteirnvtearlvsa (lDs (DK);- S()E; ()E M) MaxaixK-S mimuumm Absolute DeviationA (bMsoAluDte)D teesvti aotifo Ln((dM) fAuDn)ctteiostno;f aLn(dd) (fFu)n crtaionng;ea fnrdom(F) sreamngievfarroimansceem aivnaarliyanscees aonfa FlyusseasroifuFmu swariilutm ofw bialtnoafnbaa.n Tanhae. frequen- cies were Tbhaesferdeq ounen 3c0ie fsiewledrse absasseedssoend3 f0ofir eilndcsiadsesnescsee doff oFruinscairdieunmce wofilFtu osfa rbiuamnawnialt ionf Bbaranzanila. Min eBdraizainl. vMaelduiea nofv athluee coofrtrheesponding corresponding statistic is presented numerically on the graphs (dashed line). The classification of fields is represented as statistic is presented numerically on the graphs (dashed line). The classification of fields is represented as random (gray) random (gray) or aggregated (black). or aggregated (black). J. Fungi 2021J,. 7F,u nxg Fi 2O0R21 ,P7E, 6E4R6 REVIEW 10 of 19 10 of 19 F𝑙i𝑜g𝑔u r𝑠e 5. RFeiglau(trieo5n).sRheilpat iboentswhipeebn ( )et twheee nlotghearloitgharmith omf tohf eth oebosbesrervveed varriiaanncece(l o(𝑙g𝑜𝑔s2o bs𝑠 ) and) athnedlo tghaer iltohmgaorfithemor eotfic tahlevoarieatniceal variance ( )( lfoogr si2bninci)dfeonr cinec iddaentace odf aFtauosfaFruiusamri uwmilwt ioltf obfabnaanannaa iin 30 fifieeldlds sin inBr Bazrial.z(iAl.) (LAin)e Larinregarre srseiognrefosrsiaolln3 0fofire ladlsl a3s0s efsieselds assessed for diseasefo irndciisdeaesnecien c(isdoelnicde d(saolrikd dlianrek)l;i naen);da n(Bd)( Bfo) fro Sr iSliklk ((nn == 1100 fifieeldlds)s, )C, aCvaenvdeinshd(insh= (3n) o=r 3P)r aotar (Pnr=at1a7 )(cnu =lt i1v7ar)s c. uBilntiovmairasl. Binomial lines are relipnersesaerenrteepdre bseyn tdeadsbhyedda sghreadyg lrianyelsin. eBsi.nBainryar ypopowweerr llaaww ppaararmameteertse(rlso g((lAogp)(aAnpd) ba)nwde rbe) pwreesreen tpedre. sented. 3.3.2.3 D.3.i2s.taDnisctaen-Bcea-sBeadse dMMeeththooddss The distance to regularity (Dr), computed by SADIE, was calculated for all fields. TheTaghger edgiasttioannicned teox r(Iea)grualnagreidtyf r(oDmr)0,. 9c3otmo p3.u86teadnd btyh eSmAeDdIiaEn, vwaaluse cwaalcsu1.l7a5te(Fdig fuorre a4lCl )f.ields. The aggreDgiaffteiroenc iens damexo n(gIa)re rgaionngsewde frreonmot o0b.9se3r vtoed 3f.o8r6I aa(npd= t0h.1e1 4m).eCdoinasnid verainlugeth we a30s fi1e.7ld5s (inFigure 4C). Diffesriexnrceegiso nasm, tohne gra nredgomionpast twerenroef nFWotB owbasseirnvfeerdre fdofro rIa1 0(pfi e=l d0s.1(3134.3).% C) (oTnabslied1e)r.iFnigve tohfe 30 fields in sixt hreemgiownerse, tlohcea treadnadt oSJmA ,paalltptelarnnt eodf wFiWthBSi lwk acus litnivfaerr. red for 10 fields (33.3%) (Table 1). Five The maximum difference (DK-S) between the observed and expected distributionsof therman gwedefrreo mlo0c.a0t6e4dto a0t. 5S6J6A(m, aeldli apnla=n0t.e18d7 )w(Fiitghu Sreil4kD c).uTlhtievhayrp. othesis of randomness for TKholem mogaoxroimv–uS mir ndoivffsetraetinstcice w(DasKr-eS)je cbtedtwfoere7n3 .3t%heo fotbhesefirevldesd( Taanblde 1e).xTpheectsemda lldeissttributions rangevdal ufreosmof D0.K0-S64w etore 0o.b5s6e6rv (emd eindSiaJAn a=n d0.N18C7()m (eFainguofre0 .143D0)).. ITnhSeJA haynpdoNthCesairsa nodf ormandomness for KpoalmtteorngoofroFvW–BSmwairsninofver sretadtiinstaiclm wosatsa rllefijeecldtesda nfodrt h7e3r.e3%wa os fn toheev fidieelndcse (tTo arebjelec t1t)h.e The small- est vanluullehs yopfo Dthesi swiner5e0 %obansedr6v0e%do ifnt hSeJAfie ladns,dr eNspCec (tmiveelay.nI notfh 0e.N13M0S).F region, a randompattern of FKW-SB was inferred in a single field with an intermediate val uIne fSoJrAD andK-S (0 .N21C4) a random pattearnnd otfh eFlWowBe swt FaWs Bininfecirdreendc ein(0 .a09lm%)o. st all fields and there was no evidence to reject the null hypoTtheeseisco ind 5-o0r%de ar npdoi n6t0-p%a totefr nthaen faileylsdiss,u rsedspReicptlievye’slyK. Ian dththee NliMneSarFiz reedgfiornm, a random patteLrn(d )offu nFcWtioBn .wThaes minafxeimrruemd ainbs aol usitengdelev ifaiteioldn (wMiAthD )atnes tinratenrgmedefdroiamte1 .6v1atloue58 f.3o4r mDK-S (0.214) and twheit hloawmeesdti aFnWofB6 .i9n1cmid(eFnigcuer e(04.E0)9.%Th)e. observed values of L(d)-d for 96.7% of the fields were higher than the critical values of the simulated envelope and resulted in aggregation T(Fhigeu sreec6Aon).dO-nolrydoenre pfieolidnrte-spualttetderinna arnanadlyosmisp uatsteerdn R(pi=pl0e.3y4’)s. TKh aisnfidel tdhwea lsincuelatirviazteedd form L(d) functwioitnh. ‘TPhome em’ cauxlitimvaur,mha adbasololwutien cdideevniacetiofnF W(MBA(0D.4)9 %te)s, ta nradnthgedra nfrdoom p1.a6tt1e rtno w58as.34 m with a medalisaonin ofef r6re.9d1b ymtw (Foiqguuarder a4t-Eb)a.s eTdhset aotibstsiecsrv(Dedan vdaLluRSe)s. Tohf eLd(ids)ta-dn cfeotrh a9t6r.e7s%ul toedf tinheth feields were highehri gthheasnt s tchalee corfiatigcgarle gvaatliounes(m oafx tLh(ed )s-dim) fourlaeatechd fieenldveisloshpoew annidn Friegsuurelt6eAd. in aggregation (Fig- ure 6A). OSenmliyv aorniaen cfeiewlda srseuscucletsesdfu lilny ap errafonrdmoemd b pyatht e spherical model in 27 of 30 fields(Figure 4F). Three fields (10%) had higher spatial vateriranb il(ipty =a 0t .s3c4al)e. sTshmisa llfeireltdha wn athse cultivated with d‘Pisotamncee’b ceutwlteievnasra, mhpaldin ga ulnoiwts ainndcitdheesnecmei voafr iFanWceBp a(0ra.4m9e%ter)s, caonudld tnhoet breancodmopmut epda. ttern was also iSnefmerivraerdia nbcye tpwaroa mqeuteardsrvaatr-ibedasaemdo nstgafitiesltdisc.sT (hDo saenwdit hLhRiSg)h.e rTihneci deinstcaenhcaed thhigahte resulted in the hvigalhueessto sfcsaemlei voafr iaagncger(eRg=at0i.o8n7; (dmataaxn oLt(sdh)o-wd)n f).oTrh eeancuhg gfieetlpda riasm shetoerwrann igned Ffirgoumr0e t6oA. 4.62 with a median of 0.40 and sill ranged from 0.01 to 5.06 (median of 0.46) (Figure 6B). The observed values of the range parameter varied from 9.36 to 154.61 m with a median of 30.80 m (Figures 4F and 5B). J. Fungi 2021, 7, x FOR PEER REVIEW 10 of 19 F𝑙i𝑜g𝑔u r𝑠e 5. Relationship between the logarithm of the observed variance (𝑙𝑜𝑔 𝑠 ) and the logarithm of theoretical variance ( ) for incidence data of Fusarium wilt of banana in 30 fields in Brazil. (A) Linear regression for all 30 fields assessed for disease incidence (solid dark line); and (B) for Silk (n = 10 fields), Cavendish (n = 3) or Prata (n = 17) cultivars. Binomial lines are represented by dashed gray lines. Binary power law parameters (log(Ap) and b) were presented. 3.3.2. Distance-Based Methods The distance to regularity (Dr), computed by SADIE, was calculated for all fields. The aggregation index (Ia) ranged from 0.93 to 3.86 and the median value was 1.75 (Figure 4C). Differences among regions were not observed for Ia (p = 0.114). Considering the 30 fields in six regions, the random pattern of FWB was inferred for 10 fields (33.3%) (Table 1). Five of them were located at SJA, all planted with Silk cultivar. The maximum difference (DK-S) between the observed and expected distributions ranged from 0.064 to 0.566 (median = 0.187) (Figure 4D). The hypothesis of randomness for Kolmogorov–Smirnov statistic was rejected for 73.3% of the fields (Table 1). The small- est values of DK-S were observed in SJA and NC (mean of 0.130). In SJA and NC a random pattern of FWB was inferred in almost all fields and there was no evidence to reject the null hypothesis in 50% and 60% of the fields, respectively. In the NMSF region, a random pattern of FWB was inferred in a single field with an intermediate value for DK-S (0.214) and the lowest FWB incidence (0.09%). The second-order point-pattern analysis used Ripley’s K and the linearized form L(d) function. The maximum absolute deviation (MAD) test ranged from 1.61 to 58.34 m with a median of 6.91 m (Figure 4E). The observed values of L(d)-d for 96.7% of the fields were higher than the critical values of the simulated envelope and resulted in aggregation (Fig- ure 6A). Only one field resulted in a random pattern (p = 0.34). This field was cultivated J. Fungi 2021, 7, 646 with ‘Pome’ cultivar, had a low incidence of FWB (0.49%), and the random patter1n1 wofa19s also inferred by two quadrat-based statistics (D and LRS). The distance that resulted in the highest scale of aggregation (max L(d)-d) for each field is shown in Figure 6A. Figure 6. Distance-based statistics of the incidence of Fusarium wilt of banana in 30 fields in Brazil. (A) L(d)-d against d (solid line), superimposed envelopes (shaded area) and the random pattern (dashed line) are presented. (B) Semivariance (γ) in a range of distances was represented by spherical model fitted to the data. Fields were represented by solid lines. Distances are presented in meters (m). 3.3.3. Concordance Analyses The FWB epidemics had either random or aggregated patterns. Cohen’s Kappa paired agreement was weak or non-significant for most of the spatial statistics (Table 2). Two pairwise tests had a significant agreement. One was a strong agreement (1; p < 0.001) between the aggregation index (D) and the MAD test on which all fields are classified in the same category (aggregated). The second was a weak agreement of SADIE’s aggregation index (Ia) with DK-S (0.37; p = 0.04), with 22 of 30 fields presenting the same spatial pattern. Fleiss’s Kappa (overall agreement) did not reject the null hypothesis for a random classification of all spatial analyses (p = 0.63). The agreement could not be detected by the test in 43.3% (13/30) for the fields that presented the aggregated patterns and none of them were classified as random for all spatial statistics (Table 2). Table 2. Cohen’s and Fleiss’s Kappa agreement and proportions of fields with the same classification for the index of aggregation (D), β-binomial distribution, index of aggregation (Ia) of Spatial Analysis by Distance IndicEs (SADIE), events and intervals (DK-S) and Maximum Absolute Deviation (MAD) test from L(d) function for 30 fields assessed for Fusarium wilt of banana (FWB) incidence in Brazil a. Spatial Statistic b θ Ia DK-S MAD D −0.05 (26/30) −0.06 (19/30) −0.06 (21/30) 1.00 (30/30) θ −0.18 (17/30) −0.17 (19/30) −0.05 (26/30) Ia 0.37 (22/30) −0.06 (19/30) DK-S −0.06 (21/30) Overall c −0.027 (13/30) a The pattern of FWB in the fields was classified as aggregated or random according to the spatial statistics. Kappa values in bold differed significantly from zero (random classification) by z statistic (p < 0.05). The proportion of fields classified in the same spatial pattern of FWB is shown in parentheses. b Cohen’s Kappa paired agreement between tests. c Fleiss’s Kappa overall agreement among the tests. 3.4. Temporal Analyses On the first assessment, the incidence ranged from 0 to 0.03 with a mean and median both of 0.01 (Figure 7). Five of six plots already had symptomatic FWB plants before the beginning of the assessments. After six assessments the incidence in all plots ranged from 0.02 to 0.09 with a median of 0.06 and in the last assessment the FWB incidence ranged from 0.05 to 0.15 with a median of 0.1. The Gompertz model best fitted the disease incidence data over time in all plots (Table S2). The estimated parameters of the model, as the initial J. Fungi 2021, 7, 646 12 of 19 J. Fungi 2021, 7, x FOR PEER REVIEW incidence (y0) ranged from 0.003 to 0.027 with an average of 0.015 and the disease pro 1g2r oefs 1s9 rate (r) from 0.096 to 0.148, with an average of 0.127 (Figure 7). FFiiggurree 77.. TThhee Goomppeerrttzz moodeell aaddjjuussttee?̂?d ttoo iinncciiddeennccee ddaattaa ooff FFuussaarriiuum wiilltt ooffb baannaannaa( (FFWBB))f frroomm Apprriill2 2001177t too FFeebbrruuaarryy2 2001199 iinn ssiixx plloottss lloccaatteed iin Teeiixxeeiirraass,, Miinnaass Geerraaiiss,,B Brraazziill.. SSyymbboollss rreepprreesseenntt tthee oobbsseerrveed iincciideenccee iin prroopoorrttiion ((p̂)) aannd ssoolliid lliinneess aarree tthhee pprreeddiicctteeddi inncciiddeennccee ooff FFWBBb byyt thhee GGoommppeerrttzz mmooddeell.. 33..55.. Spattiio--Teemppoorraall Dyynnaammiiccss Among tthee diiffffeerreenntt qquuaaddrraatt--bbaasseedd meetthhooddss,, tthhee aaggggrreeggaattiioonn iinnddeexx ((D)) waassc chhoosseenn tto aasssseessss tthee sspaattiiaall ppaatttteerrnno off FFWBBa att aa ssmaallll ssccaallee.. IIn 1111 off 1122 aasssseessssmeenttss,, bbaannaannaa ppllaannttss wiitthhs syymppttoomsso offF FWBB weerreea aggggrreeggaatteeddi nina alllls siixxp plloottss ((FFiigguurree8 8A))..I Inn tthhee fifirrsstt aasssseessssmeenntt ccoonndduucctteeddi ninA Apprirlil2 021071,7D, Dra rnagnegdedfr ofrmom1. 315.3t5o 3to.0 30.0w0i twh iathm ae dmiaendivaanlu veaolufe1 .o5f2 .1I.5n2t.h Ienl athste alassset sassmseesnstm, Feenbt,r uFaerbyru2a0r1y9 ,2D01r9a,n Dge rdanfrgoemd 2fr.5o5mt o2.55.50 6tow 5it.h06a wmiethd iaa nmoefd4i.a1n8 .oDf 4in.1c8r.e Das eind- lcinreeaasrelyd wliniteharthlye wFWithB tphreo FgWresBs p(pron 0(.p0 5>) .0.I0a5d).i dIa ndoidt cnhoatn cgheadnugeri ndgurtihneg ptherei opderoiofdst uofd sytu(pd=y 0(p.5 =1 )0. .I5n1)t.h Ien fitrhset faisrsset sassmseesnstm, Aenptr, iAl 2p0r1il7 ,2I0a1r7a, nIag erdanfgroemd f0r.o7m8 t0o.718.9 t8o w1.i9th8 wa mithe dai amnevdailaune voafl1u.e0 1o.f I1n.0F1e.b Irnu aFreybr2u0a1r9y, I2a0r1a9n,g Ieda rafnrogmed0 f.r8o6mto 02.8.261 two i2t.h21a wmietdhi aan moef- 1d.4ia7n. of 1.47. TThhee rreellaattiioonnsshhiipp bbeettwweeeenn tthhee llooggaarriitthhmm ooff oobbsseerrvveedd aanndd bbiinnoommiiaall vvaarriiaanncces2es ffoorr ssiixx pplloottss iinn bbiimmoonntthhllyy aasssseessssmmeennttss wwaass wweellll ddeessccrriibbeedd bbyy tthheeb bininaarryyp poowweerrl alaww( R(R2 == 00..991144)) ((FFiigguurree 8C). Overall, para±8C). Overall, param meetteerr eessttiimmaatteess ffoorr ppoowweerr lalaww, ,lologg(A(A)p ) = 0p = 0.88.828 2± 0±.002.90,2 a9n, da nbd = b1.=231 .±2 30.0405.,0 w45e,rwe esriegnsiigfinciafinctalyn tdlyifdfeifrfeenret nfrtofrmom 0 0anadn d1,1 r, erespspeecctitviveelyly,, wwhheenn aallll pplloottss wweerree jjooiinnttllyy aannaallyyzzeedd ((pp << 00..000011)).. AAss lloogg((AAp)) wwaass hhiigghhep err tthhaann 00 aanndd bb hhiigghheerr tthhaann 11,, tthhee ppaatttteerrnn ooff FFWWBB wwaass iinnffeerrrreedd ttoo bbee aaggggrreeggaatteedd aanndd tthhee ddeeggrreeee ooffa aggggrreeggaattiioonnv vaarriieeddw wiitthhd diisseeaassee iinncciiddeenncSpac e. tei.o -temporal associations were detected between the pairs of successive assess- mentsSpfoartitoh-etelmocpaol cralul satsesroincgia(tXion, sp wp < e0r.0e5 d) e(Fteigcuterde 8bDet)w. Ienetnh ethfier sptaainrsd osfe csouncdceassssiveses masesnestss,- Amperniltsa fnodr tJhuen leoocaf l2 c0l1u7s,tethrirnege (oXfpt, hpe se0c.0o7n)d. Aaststehsissmtiemntes,, tAheproivl earnadll Jausnseo coifa t2i0o1n7o, fththreeec oluf sttheer ifnivgei npdloetxs (hXa)dv nalou aesssroacniagteidonf r(opm > 00..4017)t.o A0t. 9t1hiws ittihmae, mtheed oiavneroafll0 a.7s1so. cAiafttieornt hoef tthheir dcluasstseorciinagti oinnd,eAxu (gXu) svta2l0u1e7s aranndgOedc tforboemr 200.4117 ,toa l0l.p91a iwrwitihs ea cmomedpiaarni soofn 0s.w71e.r Ae sftigern itfihcea nthtliyrda sassoscoicaitaetdiofno,r Aalul gpulostts 2(0p1<7 0a.0n5d) .OIncttohbeelra s2t0a1s7s, oaclila tpiaoinr,wthisee Xcovmalpuaersisroannsg ewdefrreo msig0n.i9f2ictaon0tl.y9 9a(sFsiogcuiartee8dD f)o.r all plots (p < 0.05). In the last association, the X values ranged from 0.92 to 0.99 (Figure 8D). J. Fungi 2021J., F7u, nxg iF2O02R1 ,P7E, 6E4R6 REVIEW 13 of 19 13 of 19 Figure 8. SFpigautrieo-8t.eSmpaptioor-taelm sptaortaisl tsitcasti swticesrew uerseeuds etdo tcohcahraaracctteerriizzeet thheed dynyanmaimcsiocfsF oufs aFruiusmarwiuilmt o fwbialnta onfa binansiaxnpalo itns assisxe spsleodts assessed in Teixeirains,T eMixieniraass, GMeinraasisG, eBrariasz, Bilr,a fzrilo, mfro mApArpirli l22001177 ttoo FFeebbruraurayr2y0 1290. 1(A9). D(Ais)p eDrsiisopneirnsdieoxn( Din);d(Be)xa (gDgr)e; g(aBti)o nagingdreexg(aIat)ioofn index (Ia) of Spatial SApnataiallyAsinsa blyysi sDbiystDainstcaen cIne dInidciEcEs s(S(SAADDIIEE));;( C(C) b) ibnainryarpyo wpeorwlaewr; laanwd ;( Dan) sdp a(tDio)- tsepmaptoiora-ltaesmsopcioartiaoln a(sXs)oocfisautciocens s(iXve) of succes- sive assesassmseesnsmtse notfs colfucslutesrteinrigng ininddiicceess.. OOppeenna nadncdlo csleodsdeodt sdwoetsre wpreersee npterdeswehnetnedth we nhuelnl h tyhpeo tnhueslils hoyf praontdhoemsinse sosf isrannodt omness is not rejecterdej e(cpte >d 0(p.0>50) .0o5r) roerjreecjetectded (p(p << 00..0055)),, rreespspecetcivteivlye. lAyv. eAravgeersatagteis tsitcaftoirstailcl pfolort sa(lslo plidloltisn e()saonliddc olinnfied)e anncedi nctoenrvfaidl (eCnIce interval (CI 95%; s9h5%ad; sehda daerdeaar)e aa)raer epprreesseenntteedd. .E qEuqautiaontioorns uomr msuarmy mstaatirsyti csstwateirsetpicrse sweneterde wphreenseapnptelidca bwleh. *e*n* Saigpnpifiliccaanbtllyed. i*ff*e*r eSnitgnificantly from zero (log(Ap)) or 1 (b) by the modified t-test (p < 0.001) [30].different from zero (log(Ap)) or 1 (b) by the modified t-test (p < 0.001) [30]. 4. Discussion 4. DiscusTshieogna p of knowledge related to the spatio-temporal dynamics of FWB and the lack of eTshtiem gataeps oofft hkeneocwonloemdigceim replaactteodf tthoe tdhisee asspeahtaivoe-tbeemenproarisaeld dinynparemviiocuss ostfu FdWiesB[2 a1n].d the lack of esBtiamseadteosn tohfe tdhisee aesceodniostmribiuc tiiomnpwaicthti noffi etlhdes adnidseraegsieo nhsa, vhyep boetheense rsaciasnedbe idne vperloepveiodus studies [21]. toB oausnedderstand the ways plant pathogens can be dispersed. The dver tim oena nthdei ndfoisremaasteio dniosntrtihbeustoiocina lwanitdheinco fnioemldics iamnpda crteogfio ynnasm, hicyspof the diseasea plant disoetahseesaeres kceayn be devel- opedf otor iumnpdleemresntatindg rtehseo uwrcaeys sa npdlaenffot rptsattohgougiedness tcraatne gbiees dtoismpaenrasgeedp. lTahnted disyenasaems [i4c1s] .of the dis- ease Roevgearr dtiinmgeth aonseda sisnufmorpmtioantsi,otnhi sowno trhkea sssoescsieadl tahnedin etecnosnityo,minvice sitmigaptaedctt hoef sap aptilaalnant ddisease are key ftoerm ipmorpalledmyneanmtiincsg, arnedsoesutrimceaste adntdhe eyfifeoldrtasn tdoe gcouniodme isctirmapteagctieosf FtoW mB iann3a0gbea npalnaant diseases [41]. fiReeldgsa(94.6 ha) in six different production regionsvisuallrydaisnsges tshedo,saen ads7s9u4m1 spymtiopntosm, athtiicsp wlanotrskw as inseBsrsaezdil. tIhnet oitnal, 109,280 plants wereere georeferencedt.ensity, investigated the spa- tial and tTehme pinocirdaeln dceyonfaFmWiBcso,n atnheda esssetsismedafiteedld sthineB yraiezlildw aans dm oedceornatoem(avice riamgep=ac10t .7o%f )FWB in 30 banawnah efnieclodms p(9ar4e.d6 thoas)u irnve syisxp deirffoerrmeendt ipnrsoodmuecrteigoinon rseigniAonfrsic ian[ 4B2r,4a3z]i.lF. WInB toeptaidl,e m10ic9s,280 plants were visually assessed, and 7941 symptomatic plants were georeferenced. The incidence of FWB on the assessed fields in Brazil was moderate (average = 10.7%) when compared to surveys performed in some regions in Africa [42,43]. FWB epidemics reach up to 77% of incidence in Southwest Ethiopia, with an average of 17.8% and a prev- alence of 67% in plots (100 m2) studied in 180 peasant farms [42]. In East and Central Af- rica, disease incidence was greater than 40% in most of the fields [43]. Considering disease incidence, this study used a census to characterize the FWB epidemics in the fields. The highest FWB incidence was observed in NPP and SJA regions where there is a higher pro- portion of fields planted with the highly susceptible cultivar, Silk. Pome and Cavendish fields were significantly less affected by the disease, as these cultivars are moderately and J. Fungi 2021, 7, 646 14 of 19 reach up to 77% of incidence in Southwest Ethiopia, with an average of 17.8% and a prevalence of 67% in plots (100 m2) studied in 180 peasant farms [42]. In East and Central Africa, disease incidence was greater than 40% in most of the fields [43]. Considering disease incidence, this study used a census to characterize the FWB epidemics in the fields. The highest FWB incidence was observed in NPP and SJA regions where there is a higher proportion of fields planted with the highly susceptible cultivar, Silk. Pome and Cavendish fields were significantly less affected by the disease, as these cultivars are moderately and highly resistant, respectively, to the Foc populations present in Brazil [21,44]. However, this scenario might change if Foc TR4 surpasses the borders with Colombia [45] and Peru [46], or if it is accidentally introduced in Brazil in other ways. Despite occurring at moderate intensity, FWB may have socio-economic impacts be- cause many affected fields in the study are in low- or moderate-input farms, where the resource access to manage and reduce the disease impact is limited [41]. Overall, at each 1% of FWB incidence detected in the fields resulted in a loss of 184 kg ha−1 year−1. The average value of ~10.7% of FWB incidence, which results in a yield loss of 1856.5 kg ha−1 year−1, or USD 1010.4 ha−1 year−1 can substantially reduce the revenue from the crop. Bananas are cultivated on 468,000 hectares in Brazil [25]. In a hypothetical scenario where 20% of the ba- nana fields in Brazil are affected by FWB with the average incidence observed on this study, the estimated losses would be 173,771.7 tons and USD 94.58 million yearly. Considering that Brazil has one of the highest per capita consumption (~60 kg; FAO: http://www.fao.org/ economic/est/est-commodities/bananas/bananafacts/en/#.YOnduejMPDc, accessed on 5 July 2021), the potential losses could feed 2.9 million people yearly. Unfortunately, some crucial information, such as local attainable yield and prices, and either the FWB prevalence in Brazil, were not available for a precise estimation of the social-economic impact of the disease for farmers and consumers. Thus, the estimates may be used as a baseline for farmers, industry, and policymakers. Most likely, the real impact of FWB in the banana industry is still underestimated. Regarding the spatial distribution of FWB, the aggregated pattern was detected in 43% of the fields by all spatial statistics and the random pattern was detected in 57% of the data sets by one or more analytical methods (Table 2). Some of the quadrat-based statistics (D and distribution fitting) resulted in a higher number of fields with an aggregated pattern compared to the distance-based methods (Table 2). The quadrat-based methods do not use the spatial information of the sampling units [31] and have limited capacity to describe the spatial pattern in the entire field. Inferences about heterogeneity are made at scales below the threshold at which the data were collected. However, these tests were important to detect the degree of heterogeneity within disease clusters when few clusters were present. When a quadrat-based method is used in association with distance-based methods the entire process of disease spread could be better studied. Notwithstanding, a clear relationship between quadrat- and distance-based methods was not expected because of the intrinsic features adjusted for the different physical scales set to study spatial heterogeneity [11,47]. Overall, FWB had an aggregated pattern, but clusters of diseased plants (foci) were randomly distributed in the field. Thus, the spatial distribution of the disease is largely driven by the distribution of the initial inoculum in the area. From a focus, neighboring plants are more likely to become infected originating the aggregated pattern. Consequently, a random pattern is likely to be detected at lower intensities, and aggregation may be detected after epidemics develop. These dynamics were revealed when analyzing the data with the binary power law: fields with lower incidences had weaker aggregation parameters than fields with higher incidence values observed in this study (Figure 5A). However, this fact was only observed because the highest incidence was 41%. For foliar pathosystems where disease incidence above 50% is commonly observed, the binary power law’s aggregation parameter is low in datasets with either very low or very high incidences [11,16]. Diseases caused by pathogens dispersed mostly from plant-to-plant usually present this pattern [48,49]. Coffee wilt, caused by F. xylarioides, and Fusarium J. Fungi 2021, 7, 646 15 of 19 crown and root rot of tomato, caused by F. oxysporum f. sp. lycopersici (Fol), illustrate this pattern of distribution [48,49]. An aggregated pattern of FWB was also found in Australia by the joint-count statistic [18]. The random pattern of FWB epidemics detected in some of the fields by one or more spatial statistics may also warn about other processes affecting the dispersal of Foc to sites far from the main foci. Based on the semivariance analysis, half of the fields had a range of values shorter than 30.8 m, meaning that the foci size on these fields are usually smaller than that. The range parameter is the maximum distance that the samples are spatially correlated [50]. The spread of Fusarium crown and root rot in tomatoes ranged from 1.1 to 4.4 m [49]. Tomatoes are an annual crop with a short cycle and fields are normally cultivated at distances less than 50 cm within a row. Bananas are a semi perennial crop cultivated at within row distances that range from 1.5 m to 7 m. In addition to the plant-to-plant spread, weevil borer, other animals, cultural practices, wind, runoff, or irrigation water may contribute to disease dissemination [21]. Aerial dispersal of Fol and F. oxysporum f. sp. cucumerinum has been reported [51,52]. Evidence of external sporulation of Foc in banana plants may suggest the potential role of wind and rain dispersion [20]. It is hypothesized that feral pigs surrounding the fields [53] and humans [54] are involved in the within and among field dispersal of Foc [7,21]. Insects as weevil borers can carry infective propagules of Foc [55] and their populations were driving FWB epidemics in banana fields [19]. Many biological, cultural, and ecological processes can directly affect the spatial pattern of plant diseases [8]. The study of the effect of cultivars in the distribution of FWB indicated that the disease has an aggregated pattern and the level of aggregation varied with incidence. The power law parameter, log(Ap), was significantly different between Silk and Pome cultivars. Silk is more susceptible than Pome, thus a clearer aggregated pattern was more often observed in fields planted to the latter. Based on this pattern, it is possible to infer that FWB can spread farther when epidemics occur in highly susceptible cultivars. Plants with intermediate resistance levels are less affected by FWB up to certain densities of inoculum [21]. In this way, the inoculum density: disease intensity (ID:DI) relationship may hold for FWB as reported in other F. oxysporum pathosystems [56–59]. Soilborne pathogens give rise, in general, to monocyclic diseases [60]. However, multiple cycles of infection may occur in banana plantations affected by Foc [7,61]. The sigmoidal pattern observed for the plots of incidence over time suggests that multiple infections may have occurred in the FWB epidemics along the two years of study. The semi-perennial nature of the banana plant and the impractical task of pathogen elimination from the soil means that once infected and infested by Foc, respectively, they may act as an inoculum source for an undetermined time. The intensive management to achieve high productivity and other mechanisms of dispersal during the growing season could affect the dynamics of the disease and were reported for other members of F. oxysporum [49,52,62]. A similar argument was suggested for Foc in banana plantations [18,49,52,62]. The field monitored was managed in a low-input system, so anthropogenic factors, such as cultural practices, were not performed before and during the study period. In this case, Foc dispersal is due to natural causes, such as root-to-root contact, vectors, floods, or wind. A critical point of this result is that the highest incidence value observed for the FWB epidemic was low (p̂ = 0.15), and the full temporal dynamic of the epidemic (0 to 1) could not be completely characterized. Future studies addressing the temporal dynamic in different cultivars, pathogen populations, abiotic factors, and management practices can complement the epidemiological knowledge of the disease. The spatio-temporal dynamics support the occurrence of secondary infection as in- dicated by the spatial and temporal analyses conducted separately. The ratio between the observed and expected variances (D) increased over time (Figure 8A). However, the aggregation index (Ia) of a geospatial statistic (SADIE) remained unaltered (Figure 8B). These facts showed a low level of aggregation, i.e., low number of diseased plants per sampling unit, at the beginning of the epidemics. Over time, the number of diseased individuals increased on the sampling units where diseased plants were already detected, J. Fungi 2021, 7, 646 16 of 19 increasing the ratio between the observed and expected variances, with no or little effect in the geospatial distribution of the foci. The observed pattern agrees with disease trans- mission to neighboring plants at a higher rate than to plants located farther apart in the field, mainly due to plant-to-plant spread. In addition, temporal associations of the local clustering indices indicated strong evidence of correlations between the successive pairs of assessments. Only in the beginning of the epidemic, when the incidence was low, there was no association in some plots (Figure 8D). However, a lack of association between the first and the intermediate, and the first and the last assessment was observed (data not shown). Mechanisms of Foc dispersal to long distances (beyond the borders of the sampling unit) also affected the epidemics and were evidenced in the long term. This fact may be associated with disease spread beyond the borders of sampling units, by the increase in foci size or spread to plants far from initial foci that could not be detected by other methods. Understanding how the inoculum arrives in the field and the mechanisms involved in Foc dispersal are key to propose efficient management strategies to reduce the impacts of FWB epidemics. In summary, the intensity of FWB in Brazil was moderate (average of 10.7%) with losses up to 8.19 ton ha−1 year−1. The disease distribution was predominantly aggregated with some fields presenting a random distribution of disease foci, which may be due to the way the initial inoculum was introduced and distributed. The polycyclic model best describes the initial development of the epidemic. After establishing the disease in the field, transmission to the neighboring plants seems to drive the epidemics in the short term, while the spatial distribution of foci is mainly affected by long-distance dispersal mechanisms. These insights about the epidemiology of FWB can help banana farmers improve their decisions to manage the disease and reduce crop losses. Assuming the general pattern of non-TR4 populations of Foc could be used as a proxy, this large-scale study is also useful to policymakers in charge of the formulation of actions to mitigate the consequences of the introduction of Foc TR4. Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/jof7080646/s1, Table S1: Description of fields assessed for Fusarium wilt of banana in Brazil, Table S2: Summary statistics used to study the progress of Fusarium wilt on bananas in six plots located in Teixeiras, Minas Gerais state, Brazil, from April 2017 to February 2019. Author Contributions: Conceptualization, D.W.H., M.D. and E.S.G.M.; Data curation, D.W.H. and E.S.G.M.; Formal analysis, D.W.H. and E.M.D.P.; Investigation, D.W.H.; Resources, M.D.; Supervision, E.M.D.P. and E.S.G.M.; Writing—original draft preparation, D.W.H., M.D., E.M.D.P. and E.S.G.M.; Writing—review and editing, D.W.H. and E.S.G.M. All authors have read and agreed to the published version of the manuscript. Funding: The scholarship of the first author was supported by the National Council for Scientific and Technological Development—CNPq, process number 141026/2015-4. This research was funded by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001; and by Brazilian Agricultural Research Corporation—Embrapa and The São Paulo Research Foundation—Fapesp. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: Special thanks to Francisco Laranjeira (Embrapa, Brazil), Fernando Haddad (Embrapa, Brazil), and Luiz Teixeira (IAC, Brazil) for their critical reading of the manuscript. Conflicts of Interest: The authors declare no conflict of interest. J. Fungi 2021, 7, 646 17 of 19 References 1. Bancroft, J. Report of the Board Appointed to Enquire into the Cause of Disease Affecting Livestock and Plants. Votes Proc. 1876, 3, 1011–1038. 2. Stover, R.H. Fusarial Wilt (Panama Disease) of Bananas and Other Musa Species; Stover, R.H., Ed.; Commonwealth Mycological Institute: Kew, Surrey, UK, 1962. 3. Snyder, W.C.; Hansen, H.N. The species concept in Fusarium. Am. J. Bot. 1940, 27, 64. [CrossRef] 4. Ploetz, R.C. Fusarium wilt of banana is caused by several pathogens referred to as Fusarium oxysporum f. sp. cubense. Phytopathology 2006, 96, 653–656. [CrossRef] 5. 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