Statistical analysis and code for: A high-throughput and sensitive method for food preference assays in walking insects

Thomas Wagner^1*, Henrique Galante¹, Tomer J. Czaczkes¹

¹ Animal Comparative Economics Laboratory, Department of Zoology and Evolutionary Biology, University of Regensburg, 93053 Regensburg, Germany

^* Corresponding Author: t.wagner.science@gmail.com

This document contains the statistical analysis output for the manuscript. https://doi.org/10.5281/zenodo.10953783 provides the entire raw data on which this analysis is based and the code used to process it. Note that much of the analysis is divided into sections using tabs. Click on the section you wish to inspect, and scroll down for the full analysis.

1 Setup

Load packages

require(betareg) # For beta regression
require(car) # To assess model fit
require(DHARMa) # To evaluate model fit
require(dplyr) # For data wrangling
require(emmeans) # For post-hoc analysis
require(ggplot2) # For plots
require(lme4) # Linear mixed-effects models
require(lmtest) # To assess model fit
require(MuMIn) # For adjusted R^2
require(stringr) # For handling strings
require(tidyr) # For data wrangling

Clean-up

rm(list = ls()) # Remove all variables/objects
graphics.off() # Close any open graphics
set.seed(11122) # Ensure all results are reproducible

Load data

linear_spoiling = read.csv2("../Data/DF_D1_Linear_Runway_Spoiling.csv")
dualfeeder = read.csv2("../Data/DF_D2_Sucrose_Quinine_Controls.csv")

2 Linear Runway Spoiling

Specify variable class

linear_spoiling$Collection_Date = as.factor(linear_spoiling$Collection_Date) # Data collection date
linear_spoiling$Experimenter = as.factor(linear_spoiling$Experimenter) # Experimenter who collected the data
linear_spoiling$Ant_ID = as.factor(linear_spoiling$Ant_ID) # Ant ID
linear_spoiling$Colony_ID = as.factor(linear_spoiling$Colony_ID) # Which colony did the ant belong to
linear_spoiling$Solution = as.factor(linear_spoiling$Solution) # What solution was the ant given
linear_spoiling$Quinine_Concentration = factor(linear_spoiling$Quinine_Concentration, levels = c("0", "0.31", "0.63", "0.94", "1.25"))  # How much quinine was the ant given (mM)
linear_spoiling$Spoiled_Status = as.factor(linear_spoiling$Spoiled_Status)  # Was the ant spoiled? 0 = No | 1 = Yes
linear_spoiling$Acceptance_First_10_sec = as.factor(linear_spoiling$Acceptance_First_10_sec) # Did the ant touch/drink the solution in the first 10 seconds? 0 = No | 1 = Yes
linear_spoiling$Acceptance_90_sec = as.factor(linear_spoiling$Acceptance_90_sec) # Did the ant have a visibly expanded gaster after 90 seconds? 0 = No | 1 = Yes

Linear Runway Spoiling Data

Biological model

Hide

Initial 10s

Sample size

	0	1
1M Sucrose	39	39
1M Sucrose + 0.31mM Quinine	20	40
1M Sucrose + 0.63mM Quinine	29	40
1M Sucrose + 0.94mM Quinine	25	40
1M Sucrose + 1.25mM Quinine	30	40

Define biological model

bio_mod = glmer(Acceptance_First_10_sec ~ Solution * Spoiled_Status + (1 | Ant_ID/Colony_ID) + (1|Experimenter), data = linear_spoiling, family = "binomial")

Model validation

Goodness of fit

R2m: Variation explained by fixed effects (%)

R2c: Variation explained by fixed + random effects (%)

	R2m	R2c
theoretical	94.36261	94.36261
delta	90.79887	90.79887

Model summary - Fixed effects

	Chisq	Df	Pr(>Chisq)
Solution	55.18474	4	0.0000000
Spoiled_Status	39.31174	1	0.0000000
Solution:Spoiled_Status	1.63065	4	0.8032731

Model summary - Random effects

grp	var1	var2	sdcor
Colony_ID:Ant_ID	(Intercept)	NA	0.0001378
Ant_ID	(Intercept)	NA	0.0000705
Experimenter	(Intercept)	NA	0.0000000

Estimated Marginal Means

Solution	Spoiled_Status	prob	SE	df	asymp.LCL	asymp.UCL	Prop
1M Sucrose	0	100.0	0.0	Inf	0.0	100.0	10s
1M Sucrose + 0.31mM Quinine	0	100.0	0.0	Inf	0.0	100.0	10s
1M Sucrose + 0.63mM Quinine	0	96.6	3.4	Inf	61.7	99.8	10s
1M Sucrose + 0.94mM Quinine	0	92.0	5.4	Inf	59.2	98.9	10s
1M Sucrose + 1.25mM Quinine	0	90.0	5.5	Inf	62.0	98.0	10s
1M Sucrose	1	87.2	5.4	Inf	63.9	96.3	10s
1M Sucrose + 0.31mM Quinine	1	90.0	4.7	Inf	67.2	97.5	10s
1M Sucrose + 0.63mM Quinine	1	80.0	6.3	Inf	56.9	92.4	10s
1M Sucrose + 0.94mM Quinine	1	37.5	7.7	Inf	19.3	60.0	10s
1M Sucrose + 1.25mM Quinine	1	20.0	6.3	Inf	7.6	43.1	10s

Contrasts

contrast	odds.ratio	SE	df	null	z.ratio	p.value
1M Unspoiled / 1M Spoiled	1.256074e+08	8.442406e+09	Inf	1	0.2774577	1.0000000
0.31mM Q Unspoiled / 0.31mM Q Spoiled	9.489767e+07	1.728302e+10	Inf	1	0.1008568	1.0000000
0.63mM Q Unspoiled / 0.63mM Q Spoiled	6.999998e+00	7.642394e+00	Inf	1	1.7823427	0.3734669
0.94mM Q Unspoiled / 0.94mM Q Spoiled	1.916666e+01	1.546111e+01	Inf	1	3.6609568	0.0012564
1.25mM Q Unspoiled / 1.25mM Q Spoiled	3.600001e+01	2.614798e+01	Inf	1	4.9337159	0.0000040

Initial 90s

Sample size

	0	1
1M Sucrose	39	39
1M Sucrose + 0.31mM Quinine	20	40
1M Sucrose + 0.63mM Quinine	29	40
1M Sucrose + 0.94mM Quinine	25	40
1M Sucrose + 1.25mM Quinine	30	40

Define biological model

bio_mod = glmer(Acceptance_90_sec ~ Solution * Spoiled_Status + (1 | Ant_ID/Colony_ID) + (1|Experimenter), data = linear_spoiling, family = "binomial")

Model validation

Goodness of fit

R2m: Variation explained by fixed effects (%)

R2c: Variation explained by fixed + random effects (%)

	R2m	R2c
theoretical	92.29295	92.29295
delta	0.00000	0.00000

Model summary - Fixed effects

	Chisq	Df	Pr(>Chisq)
Solution	17.0628645	4	0.0018793
Spoiled_Status	6.0149006	1	0.0141856
Solution:Spoiled_Status	0.2924738	4	0.9902948

Model summary - Random effects

grp	var1	var2	sdcor
Colony_ID:Ant_ID	(Intercept)	NA	2.57e-05
Ant_ID	(Intercept)	NA	4.24e-05
Experimenter	(Intercept)	NA	0.00e+00

Estimated Marginal Means

Solution	Spoiled_Status	prob	SE	df	asymp.LCL	asymp.UCL	Prop
1M Sucrose	0	97.4	2.5	Inf	68.9	99.8	90s
1M Sucrose + 0.31mM Quinine	0	100.0	0.0	Inf	0.0	100.0	90s
1M Sucrose + 0.63mM Quinine	0	96.6	3.4	Inf	61.7	99.8	90s
1M Sucrose + 0.94mM Quinine	0	100.0	0.0	Inf	0.0	100.0	90s
1M Sucrose + 1.25mM Quinine	0	90.0	5.5	Inf	62.0	98.0	90s
1M Sucrose	1	94.9	3.5	Inf	70.7	99.3	90s
1M Sucrose + 0.31mM Quinine	1	92.5	4.2	Inf	69.6	98.5	90s
1M Sucrose + 0.63mM Quinine	1	87.5	5.2	Inf	64.7	96.4	90s
1M Sucrose + 0.94mM Quinine	1	70.0	7.2	Inf	47.0	86.0	90s
1M Sucrose + 1.25mM Quinine	1	67.5	7.4	Inf	44.6	84.3	90s

Contrasts

contrast	odds.ratio	SE	df	null	z.ratio	p.value
1M Unspoiled / 1M Spoiled	2.054054e+00	2.559691e+00	Inf	1	0.5776243	1.0000000
0.31mM Q Unspoiled / 0.31mM Q Spoiled	6.827367e+07	1.526103e+10	Inf	1	0.0807017	1.0000000
0.63mM Q Unspoiled / 0.63mM Q Spoiled	4.000000e+00	4.497527e+00	Inf	1	1.2329391	1.0000000
0.94mM Q Unspoiled / 0.94mM Q Spoiled	3.609000e+08	7.708684e+10	Inf	1	0.0922494	1.0000000
1.25mM Q Unspoiled / 1.25mM Q Spoiled	4.333333e+00	3.015699e+00	Inf	1	2.1070165	0.1755807

Proportion of acceptance at initial 10sec and 90sec

3 Dual-Feeder

Proportion of time spent at initial choice

dualfeeder$time_initial_choice_s = ifelse(dualfeeder$Initial_Decision == "L", dualfeeder$Drinking_Time_Left_s, dualfeeder$Drinking_Time_Right_s)

dualfeeder$prop_time_initial_choice = dualfeeder$time_initial_choice_s / (dualfeeder$Drinking_Time_Left_s + dualfeeder$Drinking_Time_Right_s)

If an ant spent 100% of the time at one feeder it is likely it didn’t perceive both and therefore we cannot be sure the ant made a choice. Therefore, these points are excluded.

dualfeeder$prop_time_initial_choice = ifelse(dualfeeder$prop_time_initial_choice == 1, NA, dualfeeder$prop_time_initial_choice)

Initial choice solution

dualfeeder$solution_initial_choice = ifelse(dualfeeder$Initial_Decision == "L", dualfeeder$Solution_Left, dualfeeder$Solution_Right)
dualfeeder$solution_initial_choice = ifelse((dualfeeder$Solution_Left == "1M Sucrose") & (dualfeeder$Solution_Right == "1M Sucrose"), "1M_L", dualfeeder$solution_initial_choice)
dualfeeder$solution_initial_choice = ifelse((dualfeeder$Solution_Left == "1M Sucrose") & (dualfeeder$Solution_Right == "1M Sucrose") & (dualfeeder$Initial_Decision == "R"), "1M_R", dualfeeder$solution_initial_choice)

Is initial choice random?

Number of times each solution was placed on the left

Var1	Freq
0.5M Sucrose	63
0.75M Sucrose	32
1M Sucrose	443
1M Sucrose+ 0.156mM Quinine	38
1M Sucrose+ 0.313mM Quinine	39
1M Sucrose+ 0.625mM Quinine	38

Number of times each solution was placed on the right

Var1	Freq
0.5M Sucrose	77
0.75M Sucrose	33
1M Sucrose	427
1M Sucrose+ 0.156mM Quinine	39
1M Sucrose+ 0.313mM Quinine	38
1M Sucrose+ 0.625mM Quinine	39

Ants seem to have a side bias towards the right especially in the 0.75M VS 1M and 1M VS Quinine experiments. However, all experiments were balanced regarding how many times each solution was placed on which side of the feeder.

Var1	Freq
L	283
R	370

	0.5M_1M	0.75M_1M	1M_1M	1M_Quinine
L	66	21	110	86
R	74	44	107	145

## 
##  Chi-squared test for given probabilities
## 
## data:  table(dualfeeder$Initial_Decision)
## X-squared = 11.591, df = 1, p-value = 0.0006627

Specify variable class

dualfeeder$Collection_Date = as.factor(dualfeeder$Collection_Date) # Data collection date
dualfeeder$Experimenter = as.factor(dualfeeder$Experimenter) # Experimenter who collected the data
dualfeeder$Ant_ID = as.factor(dualfeeder$Ant_ID) # Ant ID
dualfeeder$Colony_ID = as.factor(dualfeeder$Colony_ID) # Which colony did the ant belong to
dualfeeder$Experiment = as.factor(dualfeeder$Experiment) # What experiment is the data referent to
dualfeeder$Set = as.factor(dualfeeder$Set) # Some experiments were conducted in multiple sets
dualfeeder$solution_initial_choice = factor(dualfeeder$solution_initial_choice, levels = c("0.5M Sucrose", "0.75M Sucrose", "1M_L", "1M_R", "1M Sucrose", "1M Sucrose+ 0.156mM Quinine", "1M Sucrose+ 0.313mM Quinine", "1M Sucrose+ 0.625mM Quinine"))  # Which solution was first touched
dualfeeder$prop_time_initial_choice = as.numeric(dualfeeder$prop_time_initial_choice) # Proportion of time spent drinking the first solution touched

Dual Feeder Data

3.1 Quinine Sensitivity

Sample Size

	0	0.156	0.313	0.625
0.156	33	29	0	0
0.313	26	0	34	0
0.625	19	0	0	38

Hide

0.156mM of quinine

Biological Model

bio_mod = betareg(prop_time_initial_choice ~ solution_initial_choice, data = subset(quinine, quinine$pair == "0.156"))

Model Summary

lrtest(bio_mod)

## Likelihood ratio test
## 
## Model 1: prop_time_initial_choice ~ solution_initial_choice
## Model 2: prop_time_initial_choice ~ 1
##   #Df LogLik Df  Chisq Pr(>Chisq)
## 1   3 17.330                     
## 2   2 16.884 -1 0.8912     0.3451

summary(bio_mod)

## 
## Call:
## betareg(formula = prop_time_initial_choice ~ solution_initial_choice, 
##     data = subset(quinine, quinine$pair == "0.156"))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -2.5554 -0.6991  0.0805  0.6587  1.5785 
## 
## Coefficients (mean model with logit link):
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    0.9689     0.1816   5.334 9.58e-08 ***
## solution_initial_choice0.156  -0.2395     0.2527  -0.948    0.343    
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   3.0704     0.5062   6.065 1.32e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 17.33 on 3 Df
## Pseudo R-squared: 0.01726
## Number of iterations: 15 (BFGS) + 2 (Fisher scoring)

joint_tests(bio_mod)

##  model term              df1 df2 F.ratio Chisq p.value
##  solution_initial_choice   1 Inf   0.895 0.895  0.3440

Anova(bio_mod)

## Analysis of Deviance Table (Type II tests)
## 
## Response: prop_time_initial_choice
##                         Df  Chisq Pr(>Chisq)
## solution_initial_choice  1 0.8983     0.3432

Estimated Marginal Means

solution_initial_choice	emmean	SE	df	asymp.LCL	asymp.UCL
0	0.7248925	0.0362199	Inf	0.6437092	0.8060758
0.156	0.6746629	0.0411192	Inf	0.5824982	0.7668276

Contrasts

contrast	estimate	SE	df	z.ratio	p.value
solution_initial_choice0 - solution_initial_choice0.156	0.0502296	0.053083	Inf	0.9462464	0.3440229

0.313mM of quinine

Biological Model

bio_mod = betareg(prop_time_initial_choice ~ solution_initial_choice, data = subset(quinine, quinine$pair == "0.313"))

Model Summary

lrtest(bio_mod)

## Likelihood ratio test
## 
## Model 1: prop_time_initial_choice ~ solution_initial_choice
## Model 2: prop_time_initial_choice ~ 1
##   #Df LogLik Df  Chisq Pr(>Chisq)    
## 1   3 29.535                         
## 2   2 22.951 -1 13.167  0.0002849 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(bio_mod)

## 
## Call:
## betareg(formula = prop_time_initial_choice ~ solution_initial_choice, 
##     data = subset(quinine, quinine$pair == "0.313"))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -2.6345 -0.6313  0.1156  0.5185  2.1822 
## 
## Coefficients (mean model with logit link):
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    1.5899     0.2025   7.850 4.17e-15 ***
## solution_initial_choice0.313  -0.9159     0.2454  -3.732  0.00019 ***
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   4.2975     0.7521   5.714  1.1e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 29.53 on 3 Df
## Pseudo R-squared: 0.2439
## Number of iterations: 13 (BFGS) + 1 (Fisher scoring)

joint_tests(bio_mod)

##  model term              df1 df2 F.ratio  Chisq p.value
##  solution_initial_choice   1 Inf  15.252 15.252  0.0001

Anova(bio_mod)

## Analysis of Deviance Table (Type II tests)
## 
## Response: prop_time_initial_choice
##                         Df  Chisq Pr(>Chisq)    
## solution_initial_choice  1 13.925  0.0001903 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated Marginal Means

solution_initial_choice	emmean	SE	df	asymp.LCL	asymp.UCL
0	0.8306056	0.0284987	Inf	0.7667286	0.8944826
0.313	0.6624081	0.0343740	Inf	0.5853622	0.7394540

Contrasts

contrast	estimate	SE	df	z.ratio	p.value
solution_initial_choice0 - solution_initial_choice0.313	0.1681974	0.0430687	Inf	3.905325	9.41e-05

0.625mM of quinine

Biological Model

bio_mod = betareg(prop_time_initial_choice ~ solution_initial_choice, data = subset(quinine, quinine$pair == "0.625"))

Model Summary

lrtest(bio_mod)

## Likelihood ratio test
## 
## Model 1: prop_time_initial_choice ~ solution_initial_choice
## Model 2: prop_time_initial_choice ~ 1
##   #Df LogLik Df  Chisq Pr(>Chisq)   
## 1   3 18.376                        
## 2   2 13.071 -1 10.611   0.001124 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(bio_mod)

## 
## Call:
## betareg(formula = prop_time_initial_choice ~ solution_initial_choice, 
##     data = subset(quinine, quinine$pair == "0.625"))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -2.1806 -0.4001  0.1484  0.5056  2.4698 
## 
## Coefficients (mean model with logit link):
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    1.4113     0.2622   5.383 7.33e-08 ***
## solution_initial_choice0.625  -1.0034     0.3058  -3.282  0.00103 ** 
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   2.3756     0.4034    5.89 3.87e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 18.38 on 3 Df
## Pseudo R-squared: 0.2216
## Number of iterations: 14 (BFGS) + 1 (Fisher scoring)

joint_tests(bio_mod)

##  model term              df1 df2 F.ratio  Chisq p.value
##  solution_initial_choice   1 Inf  12.789 12.789  0.0003

Anova(bio_mod)

## Analysis of Deviance Table (Type II tests)
## 
## Response: prop_time_initial_choice
##                         Df  Chisq Pr(>Chisq)   
## solution_initial_choice  1 10.769   0.001032 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated Marginal Means

solution_initial_choice	emmean	SE	df	asymp.LCL	asymp.UCL
0	0.8039783	0.0413203	Inf	0.7113630	0.8965937
0.625	0.6006017	0.0415239	Inf	0.5075299	0.6936734

Contrasts

contrast	estimate	SE	df	z.ratio	p.value
solution_initial_choice0 - solution_initial_choice0.625	0.2033767	0.0568701	Inf	3.576163	0.0003487

Graph

3.2 Sucrose Sensitivity

Sample Size

	0.5	0.75	1	1_L	1_R
1M VS 0.5M	71	0	69	0	0
1M VS 0.75M	0	28	37	0	0
1M VS 1M	0	0	0	110	107

Hide

0.5M of sucrose

Biological Model

bio_mod = betareg(prop_time_initial_choice ~ solution_initial_choice * Set, data = subset(sucrose, sucrose$pair == "1M VS 0.5M"))

Model Summary

lrtest(bio_mod)

## Likelihood ratio test
## 
## Model 1: prop_time_initial_choice ~ solution_initial_choice * Set
## Model 2: prop_time_initial_choice ~ 1
##   #Df LogLik Df  Chisq Pr(>Chisq)    
## 1   5 70.389                         
## 2   2 53.366 -3 34.047  1.937e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(bio_mod)

## 
## Call:
## betareg(formula = prop_time_initial_choice ~ solution_initial_choice * 
##     Set, data = subset(sucrose, sucrose$pair == "1M VS 0.5M"))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -3.1385 -0.5033  0.1385  0.5866  2.2588 
## 
## Coefficients (mean model with logit link):
##                               Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                     0.5586     0.2012   2.777  0.00549 **
## solution_initial_choice1        0.5250     0.2936   1.788  0.07376 . 
## SetB                            0.1848     0.2575   0.718  0.47294   
## solution_initial_choice1:SetB   0.7477     0.3841   1.947  0.05158 . 
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   3.0702     0.3919   7.835 4.69e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 70.39 on 5 Df
## Pseudo R-squared: 0.3916
## Number of iterations: 19 (BFGS) + 2 (Fisher scoring)

joint_tests(bio_mod)

##  model term                  df1 df2 F.ratio  Chisq p.value
##  solution_initial_choice       1 Inf  18.373 18.373  <.0001
##  Set                           1 Inf   5.794  5.794  0.0161
##  solution_initial_choice:Set   1 Inf   1.625  1.625  0.2023

Anova(bio_mod)

## Analysis of Deviance Table (Type II tests)
## 
## Response: prop_time_initial_choice
##                             Df   Chisq Pr(>Chisq)    
## solution_initial_choice      1 24.5018  7.424e-07 ***
## Set                          1  7.3288   0.006786 ** 
## solution_initial_choice:Set  1  3.7892   0.051585 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated Marginal Means

solution_initial_choice	Set	emmean	SE	df	asymp.LCL	asymp.UCL
0.5	A	0.6361318	0.0465645	Inf	0.5198274	0.7524363
1	A	0.7471753	0.0413425	Inf	0.6439138	0.8504368
0.5	B	0.6777413	0.0360806	Inf	0.5876225	0.7678600
1	B	0.8824781	0.0212136	Inf	0.8294929	0.9354634

Contrasts

## NOTE: Results may be misleading due to involvement in interactions

contrast	estimate	SE	df	z.ratio	p.value
solution_initial_choice0.5 - solution_initial_choice1	-0.1578902	0.0368355	Inf	-4.286363	1.82e-05

0.75M of sucrose

Biological Model

bio_mod = betareg(prop_time_initial_choice ~ solution_initial_choice, data = subset(sucrose, sucrose$pair == "1M VS 0.75M"))

Model Summary

lrtest(bio_mod)

## Likelihood ratio test
## 
## Model 1: prop_time_initial_choice ~ solution_initial_choice
## Model 2: prop_time_initial_choice ~ 1
##   #Df LogLik Df  Chisq Pr(>Chisq)    
## 1   3 25.657                         
## 2   2 20.031 -1 11.252  0.0007956 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(bio_mod)

## 
## Call:
## betareg(formula = prop_time_initial_choice ~ solution_initial_choice, 
##     data = subset(sucrose, sucrose$pair == "1M VS 0.75M"))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -2.3031 -0.5965  0.1168  0.6589  1.4716 
## 
## Coefficients (mean model with logit link):
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                0.5770     0.2034   2.837  0.00455 ** 
## solution_initial_choice1   1.0396     0.2963   3.509  0.00045 ***
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   3.2680     0.6489   5.036 4.75e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 25.66 on 3 Df
## Pseudo R-squared: 0.2536
## Number of iterations: 13 (BFGS) + 2 (Fisher scoring)

joint_tests(bio_mod)

##  model term              df1 df2 F.ratio  Chisq p.value
##  solution_initial_choice   1 Inf  12.598 12.598  0.0004

Anova(bio_mod)

## Analysis of Deviance Table (Type II tests)
## 
## Response: prop_time_initial_choice
##                         Df  Chisq Pr(>Chisq)    
## solution_initial_choice  1 12.312    0.00045 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Estimated Marginal Means

solution_initial_choice	emmean	SE	df	asymp.LCL	asymp.UCL
0.75	0.6403743	0.0468367	Inf	0.5353943	0.7453542
1	0.8343259	0.0320770	Inf	0.7624284	0.9062234

Contrasts

contrast	estimate	SE	df	z.ratio	p.value
solution_initial_choice0.75 - solution_initial_choice1	-0.1939517	0.0546441	Inf	-3.549358	0.0003862

1M of sucrose

Biological Model

bio_mod = betareg(prop_time_initial_choice ~ solution_initial_choice * Set, data = subset(sucrose, sucrose$pair == "1M VS 1M"))

Model Summary

lrtest(bio_mod)

## Likelihood ratio test
## 
## Model 1: prop_time_initial_choice ~ solution_initial_choice * Set
## Model 2: prop_time_initial_choice ~ 1
##   #Df LogLik Df  Chisq Pr(>Chisq)
## 1   7 87.894                     
## 2   2 86.712 -5 2.3649     0.7967

summary(bio_mod)

## 
## Call:
## betareg(formula = prop_time_initial_choice ~ solution_initial_choice * 
##     Set, data = subset(sucrose, sucrose$pair == "1M VS 1M"))
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -2.8080 -0.5817 -0.0247  0.6047  2.3207 
## 
## Coefficients (mean model with logit link):
##                                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                      1.05155    0.17267   6.090 1.13e-09 ***
## solution_initial_choice1_R       0.12469    0.25345   0.492    0.623    
## SetB                             0.30976    0.24121   1.284    0.199    
## SetC                             0.03364    0.23755   0.142    0.887    
## solution_initial_choice1_R:SetB -0.23179    0.34730  -0.667    0.505    
## solution_initial_choice1_R:SetC  0.04557    0.34121   0.134    0.894    
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)    4.649      0.484   9.604   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 87.89 on 7 Df
## Pseudo R-squared: 0.01629
## Number of iterations: 16 (BFGS) + 2 (Fisher scoring)

joint_tests(bio_mod)

##  model term                  df1 df2 F.ratio Chisq p.value
##  solution_initial_choice       1 Inf   0.236 0.236  0.6274
##  Set                           2 Inf   0.695 1.390  0.4992
##  solution_initial_choice:Set   2 Inf   0.412 0.824  0.6623

Anova(bio_mod)

## Analysis of Deviance Table (Type II tests)
## 
## Response: prop_time_initial_choice
##                             Df  Chisq Pr(>Chisq)
## solution_initial_choice      1 0.2075     0.6487
## Set                          2 1.3369     0.5125
## solution_initial_choice:Set  2 0.7926     0.6728

Estimated Marginal Means

## NOTE: Results may be misleading due to involvement in interactions

solution_initial_choice	emmean	SE	df	asymp.LCL	asymp.UCL
1_L	0.7615070	0.0184529	Inf	0.7201465	0.8028674
1_R	0.7735133	0.0181694	Inf	0.7327884	0.8142383

Contrasts

contrast	estimate	SE	df	z.ratio	p.value
1_L - 1_R	-0.0120064	0.0247355	Inf	-0.4853912	0.6273989

Graph

4 Session Information

R version 4.2.2 (2022-10-31) Platform: aarch64-apple-darwin20 (64-bit) Running under: macOS Ventura 13.2.1

Matrix products: default BLAS: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib

locale: [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages: [1] stats graphics grDevices utils datasets methods base

other attached packages: [1] tidyr_1.3.0 stringr_1.5.0 MuMIn_1.47.5 lmtest_0.9-40 zoo_1.8-12
[6] lme4_1.1-33 Matrix_1.5-4.1 ggplot2_3.4.2 emmeans_1.8.6 dplyr_1.1.2
[11] DHARMa_0.4.6 car_3.1-2 carData_3.0-5 betareg_3.1-4 knitr_1.43

loaded via a namespace (and not attached): [1] Rcpp_1.0.10 mvtnorm_1.2-1 lattice_0.21-8 digest_0.6.31
[5] utf8_1.2.3 R6_2.5.1 gap.datasets_0.0.5 stats4_4.2.2
[9] evaluate_0.21 coda_0.19-4 highr_0.10 pillar_1.9.0
[13] rlang_1.1.1 multcomp_1.4-23 rstudioapi_0.14 minqa_1.2.5
[17] nloptr_2.0.3 jquerylib_0.1.4 gap_1.5-1 rmarkdown_2.22
[21] splines_4.2.2 munsell_0.5.0 compiler_4.2.2 xfun_0.39
[25] pkgconfig_2.0.3 htmltools_0.5.5 nnet_7.3-19 tidyselect_1.2.0
[29] tibble_3.2.1 bookdown_0.34 codetools_0.2-19 fansi_1.0.4
[33] withr_2.5.0 MASS_7.3-60 grid_4.2.2 nlme_3.1-162
[37] jsonlite_1.8.5 xtable_1.8-4 gtable_0.3.3 lifecycle_1.0.3
[41] magrittr_2.0.3 scales_1.2.1 rmdformats_1.0.4 stringi_1.7.12
[45] estimability_1.4.1 cli_3.6.1 cachem_1.0.8 flexmix_2.3-19
[49] bslib_0.4.2 generics_0.1.3 vctrs_0.6.2 boot_1.3-28.1
[53] sandwich_3.0-2 Formula_1.2-5 TH.data_1.1-2 tools_4.2.2
[57] glue_1.6.2 purrr_1.0.1 abind_1.4-5 fastmap_1.1.1
[61] survival_3.5-5 yaml_2.3.7 colorspace_2.1-0 sass_0.4.6
[65] modeltools_0.2-23

Statistical analysis and code for: A high-throughput and sensitive method for food preference assays in walking insects