Impact of fungi on control of bollworms Chrysodeixis includens and - PowerPoint PPT Presentation

Impact of fungi on control of bollworms Chrysodeixis includens and Helicoverpa armigera Eduardo Elias Ribeiro Junior 1 Celeste P. D’Alessandro 2 Clarice Garcia Borges Demétrio 1 1 Department of Exact Sciences (ESALQ-USP) 2 Department of Entomology (ESALQ-USP) 22nd November 2018 VIII Encontro dos Alunos em Estatística e Experimentação Escola Superior de Agricultura Luiz de Queiroz jreduardo@usp.br | edujrrib@gmail.com

Outline 1. Introduction 2. Models and methods 3. Results and discussion 4. Final remarks Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 0

Introduction 1 Introduction Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 0

Introduction Entomological motivation Species of interest: ◮ Chrysodeixis includens : the “soybean looper”; ◮ Helicoverpa armigera : the “cotton bollworm”; ◮ They feed feed on a wide range of plants, including many important cultivated crops (agronomic crops: soybean, cotton, maize, etc. and also vegetable and floricultural crops). Biological pest control: ◮ Controlling pest population using other organisms; ◮ An important biological control agents are pathogenic fungi. Research question: ◮ The inoculation of fungi in soybean plants may inhibit the development of bollworms Chrysodeixis includens and Helicoverpa armigera ? Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 1

Introduction Design of the experiment Treatments: ◮ Three species of fungi: Metarhizium anisopliae ESALQ-1638 ( Met 1638 ); Beauveria bassiana ESALQ-3399 ( Bb 3399 ); and Isaria fumosorosea ESALQ-3422 ( If 3422 ); ◮ Control (Tween 80). Experiment with whole plants : ◮ The fungi were inoculated on the commercial subtracts to cultivate the soybean plants. ◮ 30 bollworms (for each treatment) were confined in a pot with a plant, where the substrate was isolated. ◮ The plots were evaluated every three days during 18 days for Chrysodeixis includens and 21 days for Helicoverpa armigera . ◮ This design were repeated two times in different periods. Outcomes: ◮ Weight of bollworms over time (longitudinal data) and ◮ Time to death of the bollworms (time-to-event data). Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 2

Introduction Design of the experiment Figure: Pictures of the experiment: (a) Helicoverpa armigera , (b) soybean plants, (c)-(b) bollworms confined in the pots. Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 3

Introduction Descriptive analysis (longitudinal data) Death Pupa ● 0 5 10 15 0 5 10 15 Control Met 1638 Bb 3399 If 3422 300 Experiment 1 ● ● ● : ● ● 200 ● ● ● ● ● Weight (milligrams) ● ● 100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● ● ● ● ● ● ● ● ● 300 Experiment 2 : 200 100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 0 5 10 15 0 5 10 15 Time (days) (a) Specie: Chrysodeixis includens Figure: Data on weights of the Chrysodeixis includens bollworms over time. The symbols • and � indicate death and pupa stage, respectively. Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 4

Introduction Descriptive analysis (longitudinal data) Death Pupa ● 0 5 10 15 20 0 5 10 15 20 Control Met 1638 Bb 3399 If 3422 300 250 Experiment 1 : 200 ● 150 ● ● Weight (milligrams) 100 ● ● ● ● ● ● 50 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● 300 250 Experiment 2 : 200 ● 150 ● ● 100 ● ● ● ● ● ● 50 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 0 5 10 15 20 0 5 10 15 20 Time (days) (b) Specie: Helicoverpa armigera Figure: Data on weights of the Helicoverpa armigera bollworms over time. The symbols • and � indicate death and pupa stage, respectively. Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 5

Introduction Descriptive analysis (time-to-event data) Control Met 1638 Bb 3399 If 3422 5 10 15 20 5 10 15 20 Chysodeixis includens Chysodeixis includens Helicoverpa armigera Helicoverpa armigera (experiment 1) (experiment 2) (experiment 1) (experiment 2) 1.0 Estimated survival probability 0.8 0.6 0.4 0.2 Log−rank test: p−value=0.004 Log−rank test: p−value=0.04 Log−rank test: p−value=0.05 Log−rank test: p−value=0.3 0.0 5 10 15 20 5 10 15 20 Time (days) Figure: Kaplan-meier survivor function estimates for the times to death of the bollworms. Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 6

Models and methods 2 Models and methods Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 6

Models and methods Non-linear models (logistic growth) To model the weight growth of bollworms ( Y ) over time ( t ), we consider the logistic growth, θ A E ( Y ) = f ( t ) = 1 + exp [( θ M − t ) / θ S ] , where ◮ θ A is the horizontal asymptote ( f ( t ) when t → ∞ , if θ S > 0), ◮ θ M is the inflection point of the curve and ◮ θ S is the scale parameter. Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 7

Models and methods Heteroscedastic non-linear mixed models Statistical challenges ◮ Model the correlation between measures of the same bollworm and ◮ Model the heteroscedastic within-error. Fitted model ◮ Let ( y ijk , t ijk ) denote the weight and time (days) of the i -th bollworm on the j -th treatment at the k -th time, the fitted model can be expressed as θ A j + b A i y ijk = 1 + exp [( θ M j + b M i − t ijk ) / θ S j ] + ε ijk , Variance components σ 2 � � �� � � �� b A i 0 σ AM ∼ N A , Σ = , ◮ σ 2 b M i 0 σ AM M ◮ Var ( ε ijk ) = σ 2 δ 2 1 j δ 2 2 K . Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 8

Models and methods Accelerated failure time models Let T ij be the time-to-death of the i -th treatment and j -th bollworm, the AFT model can be expressed (where ω = log ( ε ) ) as T ij = exp ( x ⊤ ij β ) ε σ log ( T ij ) = x ⊤ ij β + σω . The distributional assumption of T ij implies distribution of ω (e.g. T ij ∼ Weibull ( α , λ ) = ⇒ ω ∼ E.V. ( λ , α ) ). Censoring times ◮ The time of event endpoint is not observed exactly; ◮ Right-censoring: the censored time-to-death will be a time beyond the observed time. n [ f ( t i ; θ )] cens i [ S ( t i ; θ )] ( 1 − cens i ) , L ( θ | t ) = ∏ i = 1 ◮ t i is the i -th recorded time, i = 1, . . . , n , ◮ cens i = 0, if t i is a censored time and 1 otherwise. Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 9

Results and discussion 3 Results and discussion Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 9

Results and discussion Non-linear models ( Chrysodeixis includens ) Control Experiment 1 : Experiment 2 : Met 1638 Bb 3399 182.86 ab 99.78 a If 3422 ● ● If 3422 154.78 a 120.25 a 5 10 15 ● ● Bb 3399 θ A Experiment 1 : Experiment 2 : 139.15 a 103.82 a Met 1638 ● ● 240.13 b 184.8 b Control ● ● 100 150 200 250 100 150 200 200 9.92 a 8.64 a If 3422 ● ● Weight (milligrams) 9.89 a 9.51 a Bb 3399 ● ● 150 θ M 9.26 a 9.01 a Met 1638 ● ● 10.35 a 9.19 a Control ● ● 100 9.0 9.5 10.0 10.5 11.0 8.0 8.5 9.0 9.5 10.0 2.09 a 2.47 bc If 3422 ● ● 50 2 a 2.66 c ● ● Bb 3399 θ S 2.01 a 2.21 ab ● ● Met 1638 2.02 a 1.9 a 0 Control ● ● 5 10 15 1.90 1.95 2.00 2.05 2.10 2.15 1.8 2.0 2.2 2.4 2.6 2.8 Time (days) (a) Fitted curves (b) Multiple comparisons Figure: Results for Helicoverpa armigera . (a) fitted logistic curves and (b) parameter estimates and multiple comparisons (5% significance level). Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 10

Results and discussion Non-linear models ( Helicoverpa armigera ) Control Experiment 1 : Experiment 2 : Met 1638 Bb 3399 111.6 a 157.63 a If 3422 ● ● If 3422 108.14 a 172.63 ab 5 10 15 20 ● ● Bb 3399 θ A Experiment 1 : Experiment 2 : 123.06 a 163.76 a Met 1638 ● ● 198.4 b 213 b Control ● ● 200 100 150 200 140 160 180 200 220 240 8.51 a 11.86 c If 3422 ● ● Weight (milligrams) 150 9.4 a 10.6 b Bb 3399 ● ● θ M 9.12 a 9.2 a Met 1638 ● ● 9.12 a 10.01 b 100 Control ● ● 8.0 8.5 9.0 9.5 10.0 9 10 11 12 2.07 a 3.17 c If 3422 ● ● 50 2.08 a 2.58 b ● ● Bb 3399 θ S 2.24 a 2.22 a ● ● Met 1638 2.2 a 2.55 b 0 Control ● ● 5 10 15 20 2.0 2.1 2.2 2.3 2.4 2.2 2.4 2.6 2.8 3.0 3.2 Time (days) (a) Fitted curves (b) Multiple comparisons Figure: Results for Helicoverpa armigera . (a) fitted logistic curves and (b) parameter estimates and multiple comparisons (5% significance level). Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 11