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Impact of fungi on control of bollworms Chrysodeixis includens and Helicoverpa armigera Eduardo Elias Ribeiro Junior 1 Celeste P. DAlessandro 2 Clarice Garcia Borges Demtrio 1 1 Department of Exact Sciences (ESALQ-USP) 2 Department of

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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

1Department of Exact Sciences (ESALQ-USP) 2Department 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

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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

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Introduction

1

Introduction

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

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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

  • f bollworms Chrysodeixis includens and Helicoverpa armigera?

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

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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

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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

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Introduction

Descriptive analysis (longitudinal data)

(a) Specie: Chrysodeixis includens

Time (days) Weight (milligrams)

100 200 300

  • Control

: Experiment 1

5 10 15

  • Met 1638
  • Bb 3399

5 10 15

  • If 3422

5 10 15

  • :

Experiment 2

  • 5

10 15

  • 100

200 300

  • Death

Pupa

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

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Introduction

Descriptive analysis (longitudinal data)

(b) Specie: Helicoverpa armigera

Time (days) Weight (milligrams)

50 100 150 200 250 300

  • Control

: Experiment 1

5 10 15 20

  • Met 1638
  • Bb 3399

5 10 15 20

  • If 3422

5 10 15 20

  • :

Experiment 2

  • 5

10 15 20

  • 50

100 150 200 250 300

  • Death

Pupa

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

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Introduction

Descriptive analysis (time-to-event data)

Time (days) Estimated survival probability

0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20

Control Met 1638 Bb 3399 If 3422 Chysodeixis includens

(experiment 1) Log−rank test: p−value=0.004

Chysodeixis includens

(experiment 2) Log−rank test: p−value=0.04

Helicoverpa armigera

(experiment 1) Log−rank test: p−value=0.05

Helicoverpa armigera

(experiment 2) Log−rank test: p−value=0.3

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

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Models and methods

2

Models and methods

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 6

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Models and methods

Non-linear models (logistic growth)

To model the weight growth of bollworms (Y) over time (t), we consider the logistic growth, E(Y) = f (t) = θA 1 + exp[(θM − t)/θS], where

◮ θA is the horizontal asymptote (f (t) when t → ∞, if θS > 0), ◮ θM is the inflection point of the curve and ◮ θS is the scale parameter.

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 7

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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 (yijk, tijk) 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 yijk = θAj + bAi 1 + exp[(θMj + bMi − tijk)/θSj] + εijk, Variance components

◮

  • bAi

bMi

  • ∼ N
  • , Σ =
  • σ2

A

σAM σAM σ2

M

  • ,

◮ Var(εijk) = σ2δ2 1jδ2 2K.

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 8

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Models and methods

Accelerated failure time models

Let Tij 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 Tij = exp(x⊤

ij β)εσ

log(Tij) = x⊤

ij β + σω.

The distributional assumption of Tij implies distribution of ω

(e.g. Tij ∼ 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

  • bserved time.

L(θ | t) =

n

∏

i=1

[ f (ti; θ)]censi [S(ti; θ)](1−censi) ,

◮ ti is the i-th recorded time, i = 1, . . . , n, ◮ censi = 0, if ti is a censored time and 1 otherwise.

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 9

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Results and discussion

3

Results and discussion

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 9

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Results and discussion

Non-linear models (Chrysodeixis includens)

(a) Fitted curves

Time (days) Weight (milligrams)

50 100 150 200 5 10 15

: Experiment 1

5 10 15

: Experiment 2 Control Met 1638 Bb 3399 If 3422

(b) Multiple comparisons

Control Met 1638 Bb 3399 If 3422 100 150 200 250

  • 240.13 b

139.15 a 154.78 a 182.86 ab

: Experiment 1 θA

100 150 200

  • 184.8 b

103.82 a 120.25 a 99.78 a

: Experiment 2

Control Met 1638 Bb 3399 If 3422 9.0 9.5 10.0 10.5 11.0

  • 10.35 a

9.26 a 9.89 a 9.92 a

θM

8.0 8.5 9.0 9.5 10.0

  • 9.19 a

9.01 a 9.51 a 8.64 a

Control Met 1638 Bb 3399 If 3422 1.90 1.95 2.00 2.05 2.10 2.15

  • 2.02 a

2.01 a 2 a 2.09 a

θS

1.8 2.0 2.2 2.4 2.6 2.8

  • 1.9 a

2.21 ab 2.66 c 2.47 bc

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

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Results and discussion

Non-linear models (Helicoverpa armigera)

(a) Fitted curves

Time (days) Weight (milligrams)

50 100 150 200 5 10 15 20

: Experiment 1

5 10 15 20

: Experiment 2 Control Met 1638 Bb 3399 If 3422

(b) Multiple comparisons

Control Met 1638 Bb 3399 If 3422 100 150 200

  • 198.4 b

123.06 a 108.14 a 111.6 a

: Experiment 1 θA

140 160 180 200 220 240

  • 213 b

163.76 a 172.63 ab 157.63 a

: Experiment 2

Control Met 1638 Bb 3399 If 3422 8.0 8.5 9.0 9.5 10.0

  • 9.12 a

9.12 a 9.4 a 8.51 a

θM

9 10 11 12

  • 10.01 b

9.2 a 10.6 b 11.86 c

Control Met 1638 Bb 3399 If 3422 2.0 2.1 2.2 2.3 2.4

  • 2.2 a

2.24 a 2.08 a 2.07 a

θS

2.2 2.4 2.6 2.8 3.0 3.2

  • 2.55 b

2.22 a 2.58 b 3.17 c

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

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Results and discussion

AFT models

Table: Analysis of deviance for the models fitted to the time-to-death of the bollworms

Chrysodeixis includens and Helicoverpa armigera.

Specie Effect df Deviance Diff df 2 logLik p-value Chrysodeixis Null 187 679.9222 Treatment 3 23.4077 184 656.5144 0.00003 Experiment 1 7.7327 183 648.7817 0.00542 Interaction 3 1.1316 180 647.6501 0.76946 Helicoverpa Null 198 693.8224 Treatment 3 11.3926 195 682.4298 0.00978 Experiment 1 1.6096 194 680.8202 0.20455 Interaction 3 1.2429 191 679.5772 0.74272

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 12

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Results and discussion

AFT models

Estimated time (days) Survival probability

0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20

Chrysodeixis includens

5 10 15 20

Helicoverpa armigera

Letal time50%

[ a ] Control [ b ] Met 1638 [ b ] Bb 3399 [ b ] If 3422 [ a ] Control [ b ] Met 1638 [ b ] Bb 3399 [ b ] If 3422

Figure: Survival curves for the estimated times to death.

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 13

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Final remarks

4

Final remarks

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 13

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Final remarks

Data analysis results

◮ In this work, we evaluated the effect of fungus inoculation in soybean

plants on delayed development of bollworms;

◮ The data analysis has shown that inoculation of fungi may delay the

bollworm development. The weight gain and time-to-death were lower for bollworms fed with fungus inoculated plants. Methodological contributions

◮ Use of non-linear models with interpretive parameters and multiple

comparison tests for each parameter;

◮ Use of parametric models for time-to-event data with comparison of the

survival curves by using the likelihood ratio test. Future research

◮ Joint modelling longitudinal outcomes and time-to-event data

(Rizopoulos 2012).

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 14

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Bibliography

References

Benjamini, Y. & Yekutieli, D. (2001), ‘The control of the false discovery rate in multiple testing under dependency’, Annals of Statistics 29, 1165–1188. Bretz, F., Hothorn, T. & Westfall, P. (2016), Multiple comparisons using R, Chapman & Hall / CRC Press, New York. Kalbfleisch, J. D. & Prentice, R. L. (2002), The statistical analysis of failure time data, Vol. 360, 2nd edition edn, John Wiley & Sons, Hoboken, New Jersey. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D. & R Core Team (2018), nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-137. URL: https://CRAN.R-project.org/package=nlme Pinheiro, J. C. & Bates, D. M. (2000), Mixed-Effects Models in S and SPLUS, Springer Series in Statistics and Computing, New York. Rizopoulos, D. (2012), Joint models for longitudinal and time-to-event data: With applications in R, Chapman and Hall/CRC. Therneau, T. M. (2015), A Package for Survival Analysis in S. version 2.38. URL: https://CRAN.R-project.org/package=survival Verbeke, G. & Molenberghs, G. (2000), Linear mixed models for longitudinal data, Springer Series in Statistics, New York.

Ribeiro Jr, E.E. Impact of fungi on control of bollworms Slide 15