## Loading required package: readxl
## Loading required package: lubridate
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:data.table':
## 
##     hour, isoweek, mday, minute, month, quarter, second, wday, week,
##     yday, year
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
## Loading required package: solartime
## - Winter data excluded.
## - The counts of all passing / wintering species (not breeding in the sampled unit) were set to zero. Abreed_and_non_breed contains the non-breeders as well.
## - Species less likely to be interacting with sampling location were EXCLUDED
## - observations with counts greater than or equal to 10 standard deviations AND greater than or equal to 60 individuals were set to 1,
## under the assumption that these are migrating or local wandering phenomena.
## No outliers found in unit Arid South.
## 2 outliers set equal to 1 in Herbaceous and Dwarf-Shrub Vegetation unit.
##                                     unit    point_name year
## 1: Herbaceous and Dwarf-Shrub Vegetation  Gamla Near 3 2014
## 2: Herbaceous and Dwarf-Shrub Vegetation Yavneel Far 2 2018
##                  SciName count_under_250  Z_score
## 1:     Passer domesticus              62 11.90316
## 2: Passer hispaniolensis              60 11.35733
## No outliers found in unit Inland Sands.
## No outliers found in unit Loess Covered Areas in the Northern Negev.
## No outliers found in unit Mediterranean-Desert Transition Zone.
## 5 outliers set equal to 1 in Mediterranean Maquis unit.
##                    unit           point_name year             SciName
## 1: Mediterranean Maquis     Beit Oren Near 1 2019     Curruca curruca
## 2: Mediterranean Maquis     Beit Oren Near 3 2019     Curruca curruca
## 3: Mediterranean Maquis Kerem Maharal Near 3 2021     Chloris chloris
## 4: Mediterranean Maquis Kerem Maharal Near 3 2021 Garrulus glandarius
## 5: Mediterranean Maquis    Nir Etzion Far 11 2021       Columba livia
##    count_under_250  Z_score
## 1:              99 11.94535
## 2:             142 17.16927
## 3:              80 19.19266
## 4:             150 20.50138
## 5:             100 14.85118
## 2 outliers set equal to 1 in Negev Highlands unit.
##               unit           point_name year                  SciName
## 1: Negev Highlands  Yeruham Far Slope 5 2018 Carpospiza brachydactyla
## 2: Negev Highlands Bislach Near Slope 6 2020    Passer hispaniolensis
##    count_under_250  Z_score
## 1:              70 14.34802
## 2:             100 10.61343
## No outliers found in unit Planted Conifer Forest.

Med-Desert Transition Zone

Factors are proximity to settlements and time. Total 5 campaigns. 5 sites with 6 plots per site. Raw data Total abundance: 6574 Number of observations: 1841 Total richness: 102

Filtered data Total abundance: 3339 Number of observations: 1029 Total richness: 51

Model gma, abundance and richness

Richness done with rare species. Abundance and mean abundance done without rare species. Full models include cosine and sine of the time difference from June 21st (in radians).

richness

Explore data and plot mean-variance plot. There is a strong relationship, indicating that employing GLMs is the proper way to analyze, rather than OLS (assumption of homogeneity is violated).

## [1] "RICHNESS WITH RARE SPECIES"
richness year_ct site settlements td_sc cos_td_rad sin_td_rad h_from_sunrise cos_hsun sin_hsun monitors_name wind precipitation temperature clouds
Min. : 1.00 Min. :0.000 Beit Yatir:24 Far :75 Min. :-2.06451 Min. :-0.2009 Min. :-0.99677 Length:150 Min. :0.4726 Min. :-0.2411 Eyal Shochat: 25 0 : 0 0 : 0 0 : 0 0 : 0
1st Qu.: 4.00 1st Qu.:2.000 Dvir : 6 Near:75 1st Qu.:-0.41912 1st Qu.: 0.5142 1st Qu.:-0.85766 Class :difftime 1st Qu.:0.8607 1st Qu.: 0.1797 Other : 5 1 : 0 3 : 0 1 : 0 1 : 0
Median : 6.00 Median :4.000 Har Amasa :29 NA Median : 0.07688 Median : 0.6917 Median :-0.72216 Mode :numeric Median :0.9336 Median : 0.3584 Adi Domer : 0 2 : 0 NA’s:150 2 : 0 2 : 0
Mean : 6.86 Mean :3.987 Lahav :31 NA Mean :-0.03383 Mean : 0.6007 Mean :-0.69390 NA Mean :0.8946 Mean : 0.3483 Asaf Mayrose: 0 3 : 0 NA 3 : 0 3 : 0
3rd Qu.: 9.00 3rd Qu.:6.000 Lehavim :30 NA 3rd Qu.: 0.22473 3rd Qu.: 0.7383 3rd Qu.:-0.67444 NA 3rd Qu.:0.9828 3rd Qu.: 0.5090 Eliraz Dvir : 0 NA’s:150 NA NA’s:150 NA’s:150
Max. :18.00 Max. :8.000 Meitar : 6 NA Max. : 1.90350 Max. : 1.0000 Max. : 0.01721 NA Max. :1.0000 Max. : 0.8813 (Other) : 0 NA NA NA NA
NA NA Mirsham :24 NA NA NA NA NA NA’s :61 NA’s :61 NA’s :120 NA NA NA NA

no observation for all 4 weather variables. many NAs (61) for sampling time of day variables. exclude from model.

## Warning in cor(P.anal[, lapply(X = .SD, FUN = as.numeric), .SDcols =
## IVs[1:11]], : the standard deviation is zero
richness year_ct site settlements td_sc cos_td_rad sin_td_rad h_from_sunrise cos_hsun sin_hsun monitors_name
richness 1.0000000 0.0024429 0.1326347 0.6790665 0.0423691 0.0857132 -0.0086319 -0.0973908 0.1999944 -0.0757602 0.0440223
year_ct 0.0024429 1.0000000 0.0000166 -0.0047063 -0.4784485 -0.4613745 -0.4697934 -0.4334083 0.3814165 -0.4327722 NA
site 0.1326347 0.0000166 1.0000000 0.0035169 -0.2288120 -0.1363567 -0.3069781 -0.1032496 0.1542517 -0.0901054 0.0447214
settlements 0.6790665 -0.0047063 0.0035169 1.0000000 0.0121481 0.0062718 0.0170858 0.0349726 0.0873478 0.0587772 0.2683282
td_sc 0.0423691 -0.4784485 -0.2288120 0.0121481 1.0000000 0.9576971 0.9330875 -0.0786776 0.0634242 -0.0849265 -0.1529258
cos_td_rad 0.0857132 -0.4613745 -0.1363567 0.0062718 0.9576971 1.0000000 0.7938914 -0.1011147 0.0827235 -0.1075303 -0.1580054
sin_td_rad -0.0086319 -0.4697934 -0.3069781 0.0170858 0.9330875 0.7938914 1.0000000 0.0563677 -0.0500522 0.0519939 -0.0915087
h_from_sunrise -0.0973908 -0.4334083 -0.1032496 0.0349726 -0.0786776 -0.1011147 0.0563677 1.0000000 -0.9216766 0.9965659 0.2604084
cos_hsun 0.1999944 0.3814165 0.1542517 0.0873478 0.0634242 0.0827235 -0.0500522 -0.9216766 1.0000000 -0.8880762 -0.2261490
sin_hsun -0.0757602 -0.4327722 -0.0901054 0.0587772 -0.0849265 -0.1075303 0.0519939 0.9965659 -0.8880762 1.0000000 0.2583855
monitors_name 0.0440223 NA 0.0447214 0.2683282 -0.1529258 -0.1580054 -0.0915087 0.2604084 -0.2261490 0.2583855 1.0000000

Fit Poisson glm, check for existence of overdispersion

## [1] "Estimating overdispersion parameter phi: (Res. Dev.)/(n-p) where n=number of observations; p=number of parameters in the model."
## [1] "od = 0.894821514091859"

Overdispersion parameter is <1 (underdispersion) and therefore Poisson is preferable to negative binomial.

Observations 89 (61 missing obs. deleted)
Dependent variable richness
Type Generalized linear model
Family poisson
Link log
χ²(7) 119.84
Pseudo-R² (Cragg-Uhler) 0.74
Pseudo-R² (McFadden) 0.23
AIC 407.38
BIC 427.29
Est. S.E. z val. p
(Intercept) 2.12 1.45 1.46 0.14
settlementsNear 0.35 0.35 0.99 0.32
year_ct -0.01 0.05 -0.26 0.79
cos_td_rad -0.35 0.40 -0.88 0.38
sin_td_rad 1.62 0.96 1.69 0.09
cos_hsun 0.94 0.98 0.96 0.34
sin_hsun -0.02 0.45 -0.04 0.97
settlementsNear:year_ct 0.08 0.06 1.47 0.14
Standard errors: MLE

cosine and sine of hours from sunrise are not significant. remove them because of many NAs.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: richness ~ settlements * year_ct + cos_td_rad + sin_td_rad +  
##     (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##    690.8    711.9   -338.4    676.8      143 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.12699 -0.74859 -0.03467  0.52894  2.53237 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  site   (Intercept) 0.0006558 0.02561 
## Number of obs: 150, groups:  site, 7
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              0.95430    0.27969   3.412 0.000645 ***
## settlementsNear          0.59575    0.11320   5.263 1.42e-07 ***
## year_ct                 -0.02016    0.02033  -0.992 0.321354    
## cos_td_rad               0.49938    0.20321   2.457 0.013993 *  
## sin_td_rad              -0.44147    0.22517  -1.961 0.049924 *  
## settlementsNear:year_ct  0.03750    0.02348   1.597 0.110238    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_td_ sn_td_
## settlmntsNr -0.292                            
## year_ct     -0.254  0.613                     
## cos_td_rad  -0.903  0.021  0.090              
## sin_td_rad   0.871 -0.032  0.113 -0.771       
## sttlmntsN:_  0.233 -0.807 -0.781 -0.013  0.021

center time of year (cosine and sine) variables - highly correlated with intercept

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: richness ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c +  
##     (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##    690.8    711.9   -338.4    676.8      143 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.12698 -0.74858 -0.03468  0.52895  2.53237 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  site   (Intercept) 0.0006556 0.0256  
## Number of obs: 150, groups:  site, 7
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              1.56061    0.09581  16.289  < 2e-16 ***
## settlementsNear          0.59576    0.11320   5.263 1.42e-07 ***
## year_ct                 -0.02016    0.02033  -0.992   0.3214    
## cos_td_rad_c             0.49937    0.20321   2.457   0.0140 *  
## sin_td_rad_c            -0.44148    0.22517  -1.961   0.0499 *  
## settlementsNear:year_ct  0.03750    0.02348   1.597   0.1102    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_t__ sn_t__
## settlmntsNr -0.772                            
## year_ct     -0.811  0.613                     
## cos_td_rd_c -0.105  0.021  0.090              
## sin_td_rd_c -0.072 -0.032  0.113 -0.771       
## sttlmntsN:_  0.630 -0.807 -0.781 -0.013  0.021

perform stepwise model selection of poisson mixed model.

## Single term deletions
## 
## Model:
## richness ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c + 
##     (1 | site)
##                     npar    AIC
## <none>                   690.79
## cos_td_rad_c           1 694.73
## sin_td_rad_c           1 692.67
## settlements:year_ct    1 691.35

drop settlements * year.

## Single term deletions
## 
## Model:
## richness ~ settlements + year_ct + cos_td_rad_c + sin_td_rad_c + 
##     (1 | site)
##              npar    AIC
## <none>            691.35
## settlements     1 822.30
## year_ct         1 689.51
## cos_td_rad_c    1 695.37
## sin_td_rad_c    1 693.35

drop year.

## Single term deletions
## 
## Model:
## richness ~ settlements + cos_td_rad_c + sin_td_rad_c + (1 | site)
##              npar    AIC
## <none>            689.51
## settlements     1 820.50
## cos_td_rad_c    1 693.37
## sin_td_rad_c    1 692.00

settlements and time of year remain. Final model:

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: richness ~ settlements + cos_td_rad_c + sin_td_rad_c + (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##    689.5    704.6   -339.8    679.5      145 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.18315 -0.75018 -0.04449  0.60796  2.82290 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  site   (Intercept) 0.0004421 0.02103 
## Number of obs: 150, groups:  site, 7
## 
## Fixed effects:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      1.48240    0.05569  26.620   <2e-16 ***
## settlementsNear  0.74384    0.06671  11.150   <2e-16 ***
## cos_td_rad_c     0.49152    0.20254   2.427   0.0152 *  
## sin_td_rad_c    -0.46595    0.22093  -2.109   0.0349 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN cs_t__
## settlmntsNr -0.811              
## cos_td_rd_c -0.046  0.019       
## sin_td_rd_c  0.040 -0.025 -0.824
## $site
##              (Intercept)
## Beit Yatir -0.0079097816
## Dvir        0.0007649121
## Har Amasa  -0.0030138047
## Lahav       0.0078284551
## Lehavim    -0.0036991931
## Meitar     -0.0001437228
## Mirsham     0.0062593182
## 
## with conditional variances for "site"
## $site

## Registered S3 methods overwritten by 'broom':
##   method            from  
##   tidy.glht         jtools
##   tidy.summary.glht jtools
Observations 150
Dependent variable richness
Type Mixed effects generalized linear model
Family poisson
Link log
AIC 689.513
BIC 704.566
Pseudo-R² (fixed effects) 0.517
Pseudo-R² (total) 0.518
Fixed Effects
exp(Est.) S.E. z val. p
(Intercept) 4.403 0.056 26.620 0.000
settlementsNear 2.104 0.067 11.150 0.000
cos_td_rad_c 1.635 0.203 2.427 0.015
sin_td_rad_c 0.628 0.221 -2.109 0.035
Random Effects
Group Parameter Std. Dev.
site (Intercept) 0.021
Grouping Variables
Group # groups ICC
site 7 0.000
## Loading required package: extrafont
## Registering fonts with R
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.

## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
##        1        2 
## 4.403495 9.264964
## [1] 110.4002

There is a statistically significant effect for proximity to settlements and time of year.

Near plots have on average 4.8614687 more species than far plots, which is 110.4002235 percent higher.

No statistically significant effect for the other factors tested.

geometric mean of abundance

Explore data. Exclude time of day because of high number of NAs.

## [1] "GEOMETRIC MEAN ABUNDANCE WITHOUT RARE SPECIES"
gma year_ct site settlements td_sc cos_td_rad sin_td_rad
Min. : 1.000 Min. :0.000 Lahav :31 Far :75 Min. :-2.06451 Min. :-0.2009 Min. :-0.99677
1st Qu.: 1.646 1st Qu.:2.000 Lehavim :30 Near:75 1st Qu.:-0.41912 1st Qu.: 0.5142 1st Qu.:-0.85766
Median : 2.285 Median :4.000 Har Amasa :29 NA Median : 0.07688 Median : 0.6917 Median :-0.72216
Mean : 2.432 Mean :3.987 Beit Yatir:24 NA Mean :-0.03383 Mean : 0.6007 Mean :-0.69390
3rd Qu.: 2.860 3rd Qu.:6.000 Mirsham :24 NA 3rd Qu.: 0.22473 3rd Qu.: 0.7383 3rd Qu.:-0.67444
Max. :10.247 Max. :8.000 Dvir : 6 NA Max. : 1.90350 Max. : 1.0000 Max. : 0.01721
NA NA (Other) : 6 NA NA NA NA

Fit glm, compare gamma, gaussian (poisson inappropriate because response is not discrete)

Gamma seems better than gaussian. Remove rows 80 and 19 (1 species with abundance of 5 and 2 species with abundance of 38, respectively). Fit fixed and mixed models.

Mixed model converged:

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( inverse )
## Formula: gma ~ settlements * year_ct + cos_td_rad + sin_td_rad + (1 |  
##     site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##    316.0    339.9   -150.0    300.0      140 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5813 -0.7148 -0.1712  0.6185  3.5987 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  site     (Intercept) 2.729e-07 0.0005224
##  Residual             9.584e-02 0.3095743
## Number of obs: 148, groups:  site, 7
## 
## Fixed effects:
##                          Estimate Std. Error t value Pr(>|z|)    
## (Intercept)              0.507804   0.093741   5.417 6.06e-08 ***
## settlementsNear         -0.047911   0.029549  -1.621   0.1049    
## year_ct                  0.036045   0.006260   5.758 8.52e-09 ***
## cos_td_rad              -0.155633   0.074803  -2.081   0.0375 *  
## sin_td_rad               0.087974   0.069988   1.257   0.2088    
## settlementsNear:year_ct -0.011281   0.007612  -1.482   0.1384    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_td_ sn_td_
## settlmntsNr -0.213                            
## year_ct     -0.269  0.523                     
## cos_td_rad  -0.939  0.025  0.179              
## sin_td_rad   0.877 -0.027  0.033 -0.770       
## sttlmntsN:_  0.139 -0.717 -0.738 -0.004  0.003

center time of year (cosine and sine) variables - highly correlated with intercept

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( inverse )
## Formula: gma ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c + (1 |  
##     site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##    316.0    339.9   -150.0    300.0      140 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5813 -0.7148 -0.1712  0.6185  3.5987 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. 
##  site     (Intercept) 2.679e-07 0.0005175
##  Residual             9.584e-02 0.3095743
## Number of obs: 148, groups:  site, 7
## 
## Fixed effects:
##                          Estimate Std. Error t value Pr(>|z|)    
## (Intercept)              0.352631   0.025026  14.090  < 2e-16 ***
## settlementsNear         -0.047912   0.029549  -1.621   0.1049    
## year_ct                  0.036045   0.006260   5.758 8.53e-09 ***
## cos_td_rad_c            -0.155633   0.074815  -2.080   0.0375 *  
## sin_td_rad_c             0.087974   0.070029   1.256   0.2090    
## settlementsNear:year_ct -0.011281   0.007612  -1.482   0.1384    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_t__ sn_t__
## settlmntsNr -0.702                            
## year_ct     -0.746  0.523                     
## cos_td_rd_c -0.216  0.025  0.179              
## sin_td_rd_c -0.045 -0.028  0.033 -0.770       
## sttlmntsN:_  0.508 -0.717 -0.738 -0.004  0.003

perform stepwise model selection of Gaussian model.

## boundary (singular) fit: see help('isSingular')
## Single term deletions
## 
## Model:
## gma ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c + (1 | 
##     site)
##                     npar    AIC
## <none>                   315.97
## cos_td_rad_c           1 318.34
## sin_td_rad_c           1 315.55
## settlements:year_ct    1 316.15

drop settlements * year.

## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## Single term deletions
## 
## Model:
## gma ~ settlements + year_ct + cos_td_rad_c + sin_td_rad_c + (1 | 
##     site)
##              npar    AIC
## <none>            316.15
## settlements     1 328.41
## year_ct         1 349.53
## cos_td_rad_c    1 318.46
## sin_td_rad_c    1 315.72

drop sine of time of year

## Single term deletions
## 
## Model:
## gma ~ settlements + year_ct + cos_td_rad_c + (1 | site)
##              npar    AIC
## <none>            315.72
## settlements     1 327.61
## year_ct         1 347.79
## cos_td_rad_c    1 316.81

drop cosine because \(\Delta AIC<2\).

## Single term deletions
## 
## Model:
## gma ~ settlements + year_ct + (1 | site)
##             npar    AIC
## <none>           316.81
## settlements    1 328.23
## year_ct        1 373.72

Settlements and year remain. This is the final model:

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( inverse )
## Formula: gma ~ settlements + year_ct + (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##    316.8    331.8   -153.4    306.8      143 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.4865 -0.7138 -0.1938  0.6896  3.8425 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev.
##  site     (Intercept) 0.0001207 0.01099 
##  Residual             0.1000007 0.31623 
## Number of obs: 148, groups:  site, 7
## 
## Fixed effects:
##                  Estimate Std. Error t value Pr(>|z|)    
## (Intercept)      0.356323   0.020849  17.090  < 2e-16 ***
## settlementsNear -0.078152   0.021059  -3.711 0.000206 ***
## year_ct          0.032875   0.003891   8.449  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN
## settlmntsNr -0.640       
## year_ct     -0.536  0.054
## $site
##              (Intercept)
## Beit Yatir  0.0015694547
## Dvir        0.0016137637
## Har Amasa   0.0028023650
## Lahav      -0.0060807603
## Lehavim     0.0021981925
## Meitar      0.0001680174
## Mirsham    -0.0028066602
## 
## with conditional variances for "site"
## $site

Observations 148
Dependent variable gma
Type Mixed effects generalized linear model
Family Gamma
Link inverse
AIC 316.807
BIC 331.793
Pseudo-R² (fixed effects) NA
Pseudo-R² (total) NA
Fixed Effects
Est. S.E. t val. p
(Intercept) 0.356 0.021 17.090 0.000
settlementsNear -0.078 0.021 -3.711 0.000
year_ct 0.033 0.004 8.449 0.000
Random Effects
Group Parameter Std. Dev.
site (Intercept) 0.011
Residual 0.316
Grouping Variables
Group # groups ICC
site 7 0.001
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.

## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
##        1        2 
## 2.048067 2.438350
## [1] 19.0562
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.

## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
##        1        2        3        4        5        6        7        8 
## 2.806445 2.785677 2.765214 2.745049 2.725176 2.705589 2.686281 2.667247 
##        9       10       11       12       13       14       15       16 
## 2.648481 2.629977 2.611730 2.593734 2.575985 2.558477 2.541205 2.524165 
##       17       18       19       20       21       22       23       24 
## 2.507352 2.490761 2.474389 2.458230 2.442281 2.426537 2.410996 2.395652 
##       25       26       27       28       29       30       31       32 
## 2.380502 2.365543 2.350770 2.336181 2.321772 2.307539 2.293480 2.279591 
##       33       34       35       36       37       38       39       40 
## 2.265869 2.252312 2.238916 2.225678 2.212596 2.199666 2.186887 2.174256 
##       41       42       43       44       45       46       47       48 
## 2.161769 2.149426 2.137222 2.125156 2.113226 2.101429 2.089763 2.078225 
##       49       50       51       52       53       54       55       56 
## 2.066815 2.055529 2.044365 2.033323 2.022398 2.011591 2.000898 1.990319 
##       57       58       59       60       61       62       63       64 
## 1.979851 1.969492 1.959241 1.949097 1.939057 1.929119 1.919283 1.909547 
##       65       66       67       68       69       70       71       72 
## 1.899910 1.890369 1.880923 1.871571 1.862312 1.853144 1.844066 1.835076 
##       73       74       75       76       77       78       79       80 
## 1.826173 1.817357 1.808625 1.799977 1.791411 1.782926 1.774521 1.766195 
##       81       82       83       84       85       86       87       88 
## 1.757947 1.749775 1.741679 1.733658 1.725710 1.717835 1.710031 1.702298 
##       89       90       91       92       93       94       95       96 
## 1.694635 1.687040 1.679513 1.672053 1.664658 1.657329 1.650065 1.642863 
##       97       98       99      100 
## 1.635724 1.628647 1.621631 1.614675
## [1] 42.46546
## [1] 0.4246547
## [1] 1.738087

Very significant temporal decrease in gma as well as lower gma far from settlements.

Near plots have on average 0.3902837 more individuals per species than far plots, which is 19.0561994 percent higher. GMA is decreasing on average in 0.1489713 individuals per species per year.

abundance

Explore data

## [1] "ABUNDANCE WITHOUT RARE SPECIES"
abundance year_ct site settlements td_sc cos_td_rad sin_td_rad
Min. : 2.00 Min. :0.000 Lahav :31 Far :75 Min. :-2.06451 Min. :-0.2009 Min. :-0.99677
1st Qu.: 7.25 1st Qu.:2.000 Lehavim :30 Near:75 1st Qu.:-0.41912 1st Qu.: 0.5142 1st Qu.:-0.85766
Median :16.00 Median :4.000 Har Amasa :29 NA Median : 0.07688 Median : 0.6917 Median :-0.72216
Mean :21.25 Mean :3.987 Beit Yatir:24 NA Mean :-0.03383 Mean : 0.6007 Mean :-0.69390
3rd Qu.:30.00 3rd Qu.:6.000 Mirsham :24 NA 3rd Qu.: 0.22473 3rd Qu.: 0.7383 3rd Qu.:-0.67444
Max. :93.00 Max. :8.000 Dvir : 6 NA Max. : 1.90350 Max. : 1.0000 Max. : 0.01721
NA NA (Other) : 6 NA NA NA NA

Outlier with total abundance >80. Examine:

##                                    unit subunit    site year year_ct
## 1: Mediterranean-Desert Transition Zone    <NA> Lehavim 2012       0
##    settlements agriculture habitat dunes land_use     point_name       date
## 1:        Near        <NA>    <NA>  <NA>     <NA> Lehavim Near 4 2012-04-25
##    datetime      td_sc     td_rad cos_td_rad sin_td_rad timediff_Jun21
## 1:     <NA> -0.3094269 -0.9812098  0.5560174 -0.8311706       -57 days
##    monitors_name wind precipitation temperature clouds h_from_sunrise cos_hsun
## 1:          <NA> <NA>          <NA>        <NA>   <NA>       NA hours       NA
##    sin_hsun pilot richness abundance    gma
## 1:       NA  TRUE       10        93 4.8029

Decided to keep point with abundance of 93 (Lehavim Near 4 from 2012). Nearest total abundances are 72 and 69.

PHI>1, hence choose negative binomial. Fit fixed and mixed models. Choose mixed model if possible, otherwise choose a model with fixed-effects only.

Mixed model converged:

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Negative Binomial(4.8393)  ( log )
## Formula: abundance ~ settlements * year_ct + cos_td_rad + sin_td_rad +  
##     (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##   1077.3   1101.4   -530.7   1061.3      142 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6391 -0.7596 -0.1664  0.7179  3.4342 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  site   (Intercept) 4.075e-05 0.006383
## Number of obs: 150, groups:  site, 7
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              1.67793    0.35924   4.671 3.00e-06 ***
## settlementsNear          0.84785    0.14199   5.971 2.36e-09 ***
## year_ct                 -0.12846    0.02475  -5.190 2.10e-07 ***
## cos_td_rad               0.93204    0.26342   3.538 0.000403 ***
## sin_td_rad              -0.77776    0.30449  -2.554 0.010641 *  
## settlementsNear:year_ct  0.08170    0.02994   2.729 0.006352 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_td_ sn_td_
## settlmntsNr -0.165                            
## year_ct     -0.229  0.585                     
## cos_td_rad  -0.917 -0.037  0.098              
## sin_td_rad   0.879  0.089  0.120 -0.774       
## sttlmntsN:_  0.153 -0.789 -0.745  0.024 -0.039

center time of year (cosine and sine) variables - highly correlated with intercept

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Negative Binomial(4.8393)  ( log )
## Formula: abundance ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c +  
##     (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##   1077.3   1101.4   -530.7   1061.3      142 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6391 -0.7596 -0.1664  0.7179  3.4342 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  site   (Intercept) 4.081e-05 0.006388
## Number of obs: 150, groups:  site, 7
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              2.77750    0.11360  24.449  < 2e-16 ***
## settlementsNear          0.84785    0.14199   5.971 2.36e-09 ***
## year_ct                 -0.12846    0.02475  -5.190 2.10e-07 ***
## cos_td_rad_c             0.93204    0.26341   3.538 0.000403 ***
## sin_td_rad_c            -0.77776    0.30447  -2.554 0.010636 *  
## settlementsNear:year_ct  0.08170    0.02994   2.729 0.006352 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_t__ sn_t__
## settlmntsNr -0.737                            
## year_ct     -0.810  0.585                     
## cos_td_rd_c -0.066 -0.037  0.098              
## sin_td_rd_c -0.160  0.089  0.120 -0.774       
## sttlmntsN:_  0.591 -0.789 -0.745  0.024 -0.039

Perform stepwise model selection of mixed model.

## boundary (singular) fit: see help('isSingular')
## Single term deletions
## 
## Model:
## abundance ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c + 
##     (1 | site)
##                     npar    AIC
## <none>                   1077.3
## cos_td_rad_c           1 1086.4
## sin_td_rad_c           1 1081.6
## settlements:year_ct    1 1082.8

all terms remain. The final model:

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Negative Binomial(4.8393)  ( log )
## Formula: abundance ~ settlements * year_ct + cos_td_rad_c + sin_td_rad_c +  
##     (1 | site)
##    Data: P.anal
## 
##      AIC      BIC   logLik deviance df.resid 
##   1077.3   1101.4   -530.7   1061.3      142 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6391 -0.7596 -0.1664  0.7179  3.4342 
## 
## Random effects:
##  Groups Name        Variance  Std.Dev.
##  site   (Intercept) 4.081e-05 0.006388
## Number of obs: 150, groups:  site, 7
## 
## Fixed effects:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)              2.77750    0.11360  24.449  < 2e-16 ***
## settlementsNear          0.84785    0.14199   5.971 2.36e-09 ***
## year_ct                 -0.12846    0.02475  -5.190 2.10e-07 ***
## cos_td_rad_c             0.93204    0.26341   3.538 0.000403 ***
## sin_td_rad_c            -0.77776    0.30447  -2.554 0.010636 *  
## settlementsNear:year_ct  0.08170    0.02994   2.729 0.006352 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sttlmN yer_ct cs_t__ sn_t__
## settlmntsNr -0.737                            
## year_ct     -0.810  0.585                     
## cos_td_rd_c -0.066 -0.037  0.098              
## sin_td_rd_c -0.160  0.089  0.120 -0.774       
## sttlmntsN:_  0.591 -0.789 -0.745  0.024 -0.039
## $site
##              (Intercept)
## Beit Yatir -3.549638e-04
## Dvir        1.980054e-05
## Har Amasa  -4.699015e-04
## Lahav      -4.879645e-05
## Lehavim     2.869112e-04
## Meitar     -1.190116e-04
## Mirsham     6.860578e-04
## 
## with conditional variances for "site"
## $site

Interpretation of abundance model:

Observations 150
Dependent variable abundance
Type Mixed effects generalized linear model
Family Negative Binomial(4.8393)
Link log
AIC 1077.349
BIC 1101.434
Pseudo-R² (fixed effects) 0.910
Pseudo-R² (total) 0.910
Fixed Effects
Est. S.E. z val. p
(Intercept) 2.777 0.114 24.449 0.000
settlementsNear 0.848 0.142 5.971 0.000
year_ct -0.128 0.025 -5.190 0.000
cos_td_rad_c 0.932 0.263 3.538 0.000
sin_td_rad_c -0.778 0.304 -2.554 0.011
settlementsNear:year_ct 0.082 0.030 2.729 0.006
Random Effects
Group Parameter Std. Dev.
site (Intercept) 0.006
Grouping Variables
Group # groups ICC
site 7 0.000

## [1] 31.2092
## [1] 0.3120919
## [1] 64.21687
## [1] 0.6421687

##  settlements year_ct.trend     SE  df asymp.LCL asymp.UCL
##  Far               -0.1285 0.0248 Inf   -0.1770  -0.07995
##  Near              -0.0468 0.0201 Inf   -0.0862  -0.00733
## 
## Confidence level used: 0.95
##  settlements year_ct.trend     SE  df z.ratio p.value
##  Far               -0.1285 0.0248 Inf  -5.190  <.0001
##  Near              -0.0468 0.0201 Inf  -2.324  0.0201
## 
## P value adjustment: fdr method for 2 tests
##  settlements year_ct emmean     SE  df asymp.LCL asymp.UCL
##  Far            3.99   2.27 0.0669 Inf      2.13      2.40
##  Near           3.99   3.44 0.0567 Inf      3.33      3.55
## 
## Results are given on the log (not the response) scale. 
## Confidence level used: 0.95
##  contrast   year_ct estimate     SE  df z.ratio p.value
##  Far - Near    3.99    -1.17 0.0875 Inf -13.405  <.0001
## 
## Results are given on the log (not the response) scale.

Significant higher abundance near settlements, and stronger relative decrease in total abundance far from settlements:

On average, a near plot has 20.763981 more individuals than a far plot, which is 67.4427346 percent higher.

The average rate of decrease in abundance far from settlements is NEARLY TRIPLE the rate near settlements, 12.0552769 vs. 4.5686008, respectively.

community analysis using package MVabund

## Overlapping points were shifted along the y-axis to make them visible.
## 
##  PIPING TO 2nd MVFACTOR
## Only the variables Passer.domesticus, Galerida.cristata, Columba.livia, Streptopelia.decaocto, Prinia.gracilis, Chloris.chloris, Pycnonotus.xanthopygos, Spilopelia.senegalensis, Corvus.monedula, Curruca.conspicillata, Cecropis.daurica, Alectoris.chukar were included in the plot 
## (the variables with highest total abundance).

start model specification:

##       nb       po 
## 246.6567 302.9650
## [1] "POISSON"

## [1] "NEGATIVE BINOMIAL"

negative binomial model is better than poisson according to residuals and AIC comparison.

##       nb       po      nb1 
## 246.6567 302.9650 239.5285

The addition of the explanatory variable ‘site’ is improving the AIC of the model. stepwise selection of model:

## Single term deletions
## 
## Model:
## spp_no_rare ~ settlements * year_ct + cos_td_rad + sin_td_rad + 
##     site
##                      Df    AIC
## <none>                  6706.8
## cos_td_rad           28 6687.6
## sin_td_rad           28 6701.8
## site                168 6906.4
## settlements:year_ct  28 6699.4

drop cosine.

## Single term deletions
## 
## Model:
## spp_no_rare ~ settlements * year_ct + sin_td_rad + site
##                      Df    AIC
## <none>                  6687.6
## sin_td_rad           28 6692.8
## site                168 6912.9
## settlements:year_ct  28 6681.4

drop interaction of settlements with year.

## Single term deletions
## 
## Model:
## spp_no_rare ~ settlements + year_ct + sin_td_rad + site
##              Df    AIC
## <none>          6681.4
## settlements  28 7535.2
## year_ct      28 6720.6
## sin_td_rad   28 6688.4
## site        168 6895.1

final model includes settlements, year, sampling time of year and site.

## 
## Test statistics:
##                 wald value Pr(>wald)    
## (Intercept)         12.267     0.001 ***
## settlementsNear     23.289     0.001 ***
## year_ct             10.018     0.001 ***
## sin_td_rad           8.176     0.004 ** 
## siteDvir             7.240     0.001 ***
## siteHar Amasa        7.041     0.004 ** 
## siteLahav            8.997     0.001 ***
## siteLehavim          8.065     0.001 ***
## siteMeitar           6.484     0.001 ***
## siteMirsham          9.693     0.001 ***
## --- 
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Test statistic:  32.95, p-value: 0.001 
## Arguments:
##  Test statistics calculated assuming response assumed to be uncorrelated 
##  P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).
## Analysis of Deviance Table
## 
## Model: spp_no_rare ~ settlements + year_ct + sin_td_rad + site
## 
## Multivariate test:
##             Res.Df Df.diff   Dev Pr(>Dev)   
## (Intercept)    149                          
## settlements    148       1 757.8     0.01 **
## year_ct        147       1 106.8     0.01 **
## sin_td_rad     146       1  52.4     0.04 * 
## site           140       6 549.8     0.01 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Univariate Tests:
##             Acridotheres.tristis          Alectoris.chukar         
##                              Dev Pr(>Dev)              Dev Pr(>Dev)
## (Intercept)                                                        
## settlements               47.832     0.01            2.828     0.39
## year_ct                   19.477     0.01            1.321     0.97
## sin_td_rad                 2.853     0.92            3.177     0.87
## site                      18.048     0.15            8.687     0.91
##             Anthus.similis          Burhinus.oedicnemus         
##                        Dev Pr(>Dev)                 Dev Pr(>Dev)
## (Intercept)                                                     
## settlements         22.266     0.01                   0     0.94
## year_ct              0.023     1.00               0.071     1.00
## sin_td_rad           0.014     1.00               1.984     0.98
## site                 8.018     0.91               7.761     0.91
##             Cecropis.daurica          Chloris.chloris          Cinnyris.osea
##                          Dev Pr(>Dev)             Dev Pr(>Dev)           Dev
## (Intercept)                                                                 
## settlements           32.021     0.01          46.076     0.01        41.406
## year_ct                0.056     1.00           1.089     0.98         8.852
## sin_td_rad             0.415     1.00           1.543     1.00         6.317
## site                  27.913     0.01          16.681     0.16        18.063
##                      Columba.livia          Corvus.cornix         
##             Pr(>Dev)           Dev Pr(>Dev)           Dev Pr(>Dev)
## (Intercept)                                                       
## settlements     0.01            53     0.01        50.914     0.01
## year_ct         0.10         0.485     1.00         1.249     0.98
## sin_td_rad      0.37         0.265     1.00         0.961     1.00
## site            0.15        15.727     0.25        35.085     0.01
##             Corvus.monedula          Curruca.conspicillata         
##                         Dev Pr(>Dev)                   Dev Pr(>Dev)
## (Intercept)                                                        
## settlements           9.184     0.04                57.418     0.01
## year_ct                1.44     0.97                 4.035     0.63
## sin_td_rad             0.27     1.00                 0.912     1.00
## site                 44.159     0.01                   3.5     0.99
##             Curruca.melanocephala          Emberiza.calandra         
##                               Dev Pr(>Dev)               Dev Pr(>Dev)
## (Intercept)                                                          
## settlements                   5.2     0.15             0.961     0.69
## year_ct                     3.848     0.66             0.711     1.00
## sin_td_rad                  0.612     1.00             0.924     1.00
## site                       54.683     0.01            24.943     0.03
##             Falco.tinnunculus          Galerida.cristata         
##                           Dev Pr(>Dev)               Dev Pr(>Dev)
## (Intercept)                                                      
## settlements             1.443     0.65            37.532     0.01
## year_ct                 0.071     1.00            16.713     0.01
## sin_td_rad              0.544     1.00             1.284     1.00
## site                    4.054     0.99            35.053     0.01
##             Garrulus.glandarius          Lanius.senator         
##                             Dev Pr(>Dev)            Dev Pr(>Dev)
## (Intercept)                                                     
## settlements              27.928     0.01          7.661     0.06
## year_ct                   6.706     0.23          2.843     0.84
## sin_td_rad                 0.47     1.00          3.753     0.80
## site                      9.637     0.91          3.202     0.99
##             Oenanthe.melanoleuca          Parus.major         
##                              Dev Pr(>Dev)         Dev Pr(>Dev)
## (Intercept)                                                   
## settlements                2.775     0.39      22.544     0.01
## year_ct                    0.302     1.00       0.071     1.00
## sin_td_rad                 0.954     1.00       0.624     1.00
## site                      29.726     0.01      24.605     0.03
##             Passer.domesticus          Prinia.gracilis         
##                           Dev Pr(>Dev)             Dev Pr(>Dev)
## (Intercept)                                                    
## settlements            34.617     0.01            3.78     0.23
## year_ct                12.018     0.03           1.108     0.98
## sin_td_rad              4.031     0.80           1.665     1.00
## site                   23.604     0.06          22.037     0.06
##             Pycnonotus.xanthopygos          Spilopelia.senegalensis         
##                                Dev Pr(>Dev)                     Dev Pr(>Dev)
## (Intercept)                                                                 
## settlements                 24.463     0.01                  68.189     0.01
## year_ct                      4.364     0.63                  10.358     0.03
## sin_td_rad                   0.165     1.00                   7.402     0.26
## site                        22.544     0.06                  11.889     0.67
##             Streptopelia.decaocto          Streptopelia.turtur         
##                               Dev Pr(>Dev)                 Dev Pr(>Dev)
## (Intercept)                                                            
## settlements                81.258     0.01              17.901     0.01
## year_ct                      0.33     1.00               5.018     0.46
## sin_td_rad                  0.105     1.00               2.344     0.96
## site                        9.569     0.91              26.877     0.02
##             Turdus.merula          Upupa.epops          Vanellus.spinosus
##                       Dev Pr(>Dev)         Dev Pr(>Dev)               Dev
## (Intercept)                                                              
## settlements         41.91     0.01       0.355     0.76            16.373
## year_ct             3.432     0.76       0.506     1.00              0.33
## sin_td_rad          6.131     0.39       2.566     0.93             0.163
## site               15.523     0.25       5.663     0.95            22.515
##                     
##             Pr(>Dev)
## (Intercept)         
## settlements     0.01
## year_ct         1.00
## sin_td_rad      1.00
## site            0.06
## Arguments:
##  Test statistics calculated assuming uncorrelated response (for faster computation) 
## P-value calculated using 99 iterations via PIT-trap resampling.

All factors (settlements, year, time of year and site) have a statistically significant effect on community composition.

## Loading required package: ggnewscale
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## [1] "black arrow is median of synanthrope/invasive\ngreen arrow is median of batha specialists\nred arrow is median of endangered\n\n"

## [1] "black arrow is median of synanthrope/invasive\ngreen arrow is median of batha specialists\nred arrow is median of endangered\n\n"

Significant effect of settlement proximity: synanthrope / invasive species near settlements, endangered and / or batha specialists far from settlements.

Synanthrope local species decreasing while synanthrope invasive species increasing

Significant negative temporal effect on crested lark, house sparrow and laughing dove, and positive effect on common myna.

##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -3.19814420      2.89705871     -0.01238059      0.01275034     -0.86596715 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      1.04169767      1.11930105      1.41581895      0.86058066     -0.79193622
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -3.19813999      2.89705635     -0.01238155      0.01274407     -0.86597053 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      1.04169668      1.11929858      1.41581039      0.86057512     -0.79193710
## [1] 0.03852899 0.69817330
## [1] 1712.073

##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      1.25496613     -1.19594013     -0.06850155      0.45136555      1.52709323 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.31063784      0.26250633      0.89269549      0.72997866      0.80682753
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      1.25496619     -1.19593983     -0.06850164      0.45136495      1.52709237 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.31063778      0.26250653      0.89269494      0.72997832      0.80682702
##   [1] 2.564497 2.550341 2.536263 2.522262 2.508338 2.494492 2.480722 2.467028
##   [9] 2.453409 2.439866 2.426398 2.413003 2.399683 2.386436 2.373263 2.360162
##  [17] 2.347133 2.334177 2.321292 2.308478 2.295734 2.283062 2.270459 2.257925
##  [25] 2.245461 2.233066 2.220739 2.208480 2.196289 2.184165 2.172108 2.160117
##  [33] 2.148193 2.136334 2.124541 2.112814 2.101150 2.089552 2.078017 2.066546
##  [41] 2.055138 2.043793 2.032511 2.021291 2.010133 1.999037 1.988002 1.977028
##  [49] 1.966114 1.955261 1.944468 1.933734 1.923059 1.912444 1.901886 1.891388
##  [57] 1.880947 1.870564 1.860238 1.849969 1.839757 1.829601 1.819501 1.809457
##  [65] 1.799469 1.789535 1.779657 1.769833 1.760063 1.750347 1.740685 1.731076
##  [73] 1.721520 1.712017 1.702566 1.693168 1.683821 1.674526 1.665282 1.656090
##  [81] 1.646948 1.637856 1.628815 1.619823 1.610882 1.601989 1.593146 1.584352
##  [89] 1.575606 1.566908 1.558258 1.549656 1.541102 1.532595 1.524135 1.515721
##  [97] 1.507354 1.499033 1.490758 1.482529
## [1] 42.19027
## [1] 0.4219026
## [1] 1.9516386 0.5902138
## [1] 230.6664
## [1] 2.306664
## [1] 3.306664

##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -14.4769942      14.5363087      -0.2637631      -1.9187965     -11.9872840 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       0.2471728      -0.5600265      -0.5835720       0.1596259      -0.1256885
##   (Intercept)       year_ct    sin_td_rad      siteDvir siteHar Amasa 
##    0.05931718   -0.26376383   -1.91879680  -37.62480300    0.24717515 
##     siteLahav   siteLehavim    siteMeitar   siteMirsham 
##   -0.56002776   -0.58357131    0.15962450   -0.12569286
##   [1] 3.9831056 3.8991070 3.8168799 3.7363868 3.6575913 3.5804574 3.5049502
##   [8] 3.4310353 3.3586792 3.2878490 3.2185126 3.1506383 3.0841954 3.0191537
##  [15] 2.9554837 2.8931564 2.8321434 2.7724172 2.7139505 2.6567168 2.6006901
##  [22] 2.5458449 2.4921563 2.4396000 2.3881520 2.3377889 2.2884880 2.2402268
##  [29] 2.1929833 2.1467361 2.1014642 2.0571470 2.0137645 1.9712968 1.9297247
##  [36] 1.8890293 1.8491921 1.8101951 1.7720204 1.7346508 1.6980692 1.6622591
##  [43] 1.6272043 1.5928886 1.5592967 1.5264131 1.4942230 1.4627118 1.4318651
##  [50] 1.4016689 1.3721095 1.3431735 1.3148477 1.2871193 1.2599756 1.2334044
##  [57] 1.2073935 1.1819311 1.1570057 1.1326060 1.1087208 1.0853393 1.0624509
##  [64] 1.0400452 1.0181120 0.9966413 0.9756234 0.9550488 0.9349080 0.9151920
##  [71] 0.8958918 0.8769986 0.8585039 0.8403991 0.8226762 0.8053270 0.7883437
##  [78] 0.7717186 0.7554440 0.7395127 0.7239173 0.7086508 0.6937063 0.6790769
##  [85] 0.6647561 0.6507372 0.6370140 0.6235802 0.6104297 0.5975566 0.5849549
##  [92] 0.5726189 0.5605431 0.5487220 0.5371502 0.5258224 0.5147335 0.5038784
##  [99] 0.4932523 0.4828502
## [1] 87.87754
## [1] 0.9482312
## [1] 19.31665

##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -1.1106547       3.3180220      -0.3217530      -2.3706172       0.1593572 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.8070834      -1.1022411      -0.1485289      -1.7699350       1.1851742
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -1.1105960       3.3179648      -0.3217529      -2.3706068       0.1593137 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.8070914      -1.1022516      -0.1485468      -1.7699354       1.1851270
##   [1] 1.7063833 1.6625887 1.6199181 1.5783427 1.5378343 1.4983656 1.4599098
##   [8] 1.4224411 1.3859339 1.3503637 1.3157065 1.2819387 1.2490375 1.2169808
##  [15] 1.1857468 1.1553145 1.1256632 1.0967729 1.0686240 1.0411977 1.0144752
##  [22] 0.9884385 0.9630701 0.9383528 0.9142698 0.8908050 0.8679423 0.8456665
##  [29] 0.8239623 0.8028152 0.7822109 0.7621353 0.7425750 0.7235167 0.7049475
##  [36] 0.6868550 0.6692267 0.6520509 0.6353160 0.6190105 0.6031235 0.5876443
##  [43] 0.5725623 0.5578674 0.5435497 0.5295994 0.5160071 0.5027637 0.4898602
##  [50] 0.4772879 0.4650382 0.4531030 0.4414740 0.4301435 0.4191038 0.4083475
##  [57] 0.3978672 0.3876559 0.3777066 0.3680127 0.3585676 0.3493649 0.3403984
##  [64] 0.3316621 0.3231499 0.3148562 0.3067754 0.2989020 0.2912306 0.2837561
##  [71] 0.2764735 0.2693778 0.2624641 0.2557280 0.2491647 0.2427698 0.2365391
##  [78] 0.2304683 0.2245533 0.2187901 0.2131748 0.2077037 0.2023729 0.1971790
##  [85] 0.1921184 0.1871876 0.1823834 0.1777025 0.1731418 0.1686981 0.1643684
##  [92] 0.1601499 0.1560396 0.1520348 0.1481328 0.1443310 0.1406267 0.1370175
##  [99] 0.1335009 0.1300746
## [1] 92.37718
## [1] 0.9673434
## [1] 30.6217
## [1]  0.4731487 13.0608517
## [1] 2660.411
## [1] 26.60412
## [1] 27.60412

##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -15.60884159     13.74308689      0.30200051     -0.41611381     -9.72099927 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.05107192     -0.10752380      0.75720550     -9.92337525     -1.98612180
##   (Intercept)       year_ct    sin_td_rad      siteDvir siteHar Amasa 
##   -1.86575223    0.30200122   -0.41610429  -35.29106415    0.05107478 
##     siteLahav   siteLehavim    siteMeitar   siteMirsham 
##   -0.10751983    0.75720860  -35.49343545   -1.98612734
##   [1] 0.2062006 0.2112946 0.2165145 0.2218634 0.2273444 0.2329608 0.2387159
##   [8] 0.2446132 0.2506562 0.2568485 0.2631938 0.2696959 0.2763585 0.2831858
##  [15] 0.2901817 0.2973504 0.3046963 0.3122236 0.3199369 0.3278407 0.3359398
##  [22] 0.3442390 0.3527432 0.3614575 0.3703871 0.3795373 0.3889135 0.3985213
##  [29] 0.4083666 0.4184550 0.4287927 0.4393857 0.4502404 0.4613633 0.4727610
##  [36] 0.4844403 0.4964081 0.5086715 0.5212379 0.5341148 0.5473097 0.5608307
##  [43] 0.5746856 0.5888829 0.6034308 0.6183382 0.6336139 0.6492669 0.6653066
##  [50] 0.6817426 0.6985846 0.7158427 0.7335271 0.7516484 0.7702174 0.7892451
##  [57] 0.8087429 0.8287224 0.8491954 0.8701743 0.8916714 0.9136995 0.9362719
##  [64] 0.9594019 0.9831033 1.0073902 1.0322772 1.0577789 1.0839107 1.1106880
##  [71] 1.1381268 1.1662435 1.1950548 1.2245778 1.2548303 1.2858300 1.3175956
##  [78] 1.3501460 1.3835005 1.4176790 1.4527018 1.4885899 1.5253645 1.5630477
##  [85] 1.6016618 1.6412298 1.6817753 1.7233225 1.7658961 1.8095214 1.8542245
##  [92] 1.9000319 1.9469709 1.9950696 2.0443565 2.0948610 2.1466132 2.1996439
##  [99] 2.2539847 2.3096680
## [1] 1020.107
## [1] 10.20107
## [1] 11.20107

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -14.76379810     13.87675561     -0.14841723     -0.39927299     -0.32015486 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -0.79522939      0.40930269      1.12953042      1.97056489     -0.09860667
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -1.1105960       3.3179648      -0.3217529      -2.3706068       0.1593137 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.8070914      -1.1022516      -0.1485468      -1.7699354       1.1851270
## [1] 3.526405e-10 3.006890e-01

## Warning: glm.fit: fitted rates numerically 0 occurred
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -15.94540157     13.78748956     -0.04443269      0.20409935      2.50109902 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      1.89133568      3.30658511      2.77896378     -9.15701943      0.03772084
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -31.99689451     29.83896482     -0.04443280      0.20409925      2.50111822 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      1.89135476      3.30660493      2.77898337    -26.25815950      0.03772092

## Warning: glm.fit: fitted rates numerically 0 occurred
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -13.5890463      12.5621167      -0.1610875      -1.6624329     -11.0075650 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.2108969       0.1650222      -0.3427736       0.4594397     -11.0038973
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -34.0300817      33.0031558      -0.1610883      -1.6624397     -31.6652555 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.2108988       0.1650199      -0.3427768       0.4594354     -31.6412082
## [1] 2.773366e-15 5.971669e-01

## Warning: glm.fit: fitted rates numerically 0 occurred
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -12.9694905      12.5002301      -0.1172293       0.6727212       0.2467421 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       0.9006157       0.3756373       0.1239605       1.4902069     -10.0815474
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -34.0677475      33.5984927      -0.1172305       0.6727187       0.2467410 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       0.9006205       0.3756369       0.1239606       1.4902069     -31.1638780

## Warning: glm.fit: fitted rates numerically 0 occurred
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -14.17505368     11.94790980      0.00412469      0.52734606     -9.27293690 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      2.66224692      1.77128672     -0.06080704     -9.01646338     -9.06083834
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##   -34.543926351    32.316787345     0.004124596     0.527345614   -30.016785218 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     2.662253454     1.771289221    -0.060809508   -29.760311918   -29.803774313
## Warning: glm.fit: fitted rates numerically 0 occurred
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -13.51343635     11.65320800      0.07711059      1.92092987      2.67028539 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -8.98545269      3.40990316      1.43542922     -8.35716228     -8.84604330
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##    -34.55055160     32.69039054      0.07711744      1.92110268      2.67030268 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##    -30.02087486      3.40997492      1.43547703    -29.38222633    -29.87254372
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -2.09997307      3.50772911     -0.05143191     -0.58938946      1.53267517 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -1.89626110     -0.28967466     -0.48571467     -0.14901045      0.03804001
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -2.09994928      3.50770694     -0.05143300     -0.58939924      1.53263442 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -1.89626759     -0.28967817     -0.48572193     -0.14901898      0.03800344
## [1] 0.1501667 5.0113110
## [1] 3237.166
## [1] 32.37165
## [1] 33.37165
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -4.4595392       3.5917328       0.1934950       3.1739652     -11.4255596 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.8416089       2.5675920       3.1185990       4.7933308       2.4047970
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -4.4595422       3.5917351       0.1934950       3.1739715     -33.5063724 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -0.8416025       2.5675993       3.1186032       4.7933351       2.4048022
## [1] 0.002765395 0.100375562
## [1] 3529.7
## [1] 35.29701
## [1] 36.29701
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -1.79107320      2.59560051      0.01453756      0.47999242      0.46997224 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.57360737      0.96158393      0.32282073      0.99068065      0.68508944
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -1.79107286      2.59559857      0.01453838      0.47999454      0.46997713 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.57360973      0.96158533      0.32281947      0.99068714      0.68507610
## [1] 0.1266684 1.6979397
## [1] 1240.461
## [1] 12.4046
## [1] 13.4046
## Warning in glm.nb(formula = Pycnonotus.xanthopygos ~ settlements + year_ct + :
## alternation limit reached
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -1.6449156       1.9807003      -0.1179208       1.1895879      -0.2191414 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       0.6489535       1.2004035       1.1630775       1.2593246       2.4113083
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -1.6449036       1.9806887      -0.1179209       1.1895865      -0.2191424 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       0.6489537       1.2004003       1.1630763       1.2593237       2.4112913
## [1] 0.05284072 0.38297545
## [1] 624.7733
## [1] 6.247733
## [1] 7.247733
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -3.9724453       1.8103955      -0.1390345      -2.4669111       3.4137131 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -1.9043463       1.7773560      -2.3646211     -13.6189360       2.0544543
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -3.9724313       1.8103890      -0.1390337      -2.4668935       3.4137032 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      -1.9043429       1.7773578      -2.3646162     -35.7603308       2.0544496
## [1] 0.05990911 0.36621389
## [1] 511.2825
## [1] 5.112825
## [1] 6.112825
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -3.2927856       1.7980640      -0.1396831       1.2142572       1.2297556 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       2.8016678       2.7452205       0.1265903       1.8203068       3.0852608
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      -3.2927874       1.7980643      -0.1396830       1.2142553       1.2297571 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##       2.8016692       2.7452205       0.1265897       1.8203073       3.0852589
## [1] 0.009166199 0.055345034
## [1] 503.7948
## [1] 5.037948
## [1] 6.037948
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -0.99236961     -1.68347873     -0.04400099      1.90120228      1.31219156 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.85006123      0.34319109      0.52868215      1.15565273      1.28393220
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -0.99236961     -1.68347889     -0.04400106      1.90120201      1.31219205 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##      0.85006099      0.34319143      0.52868212      1.15565275      1.28393261
## [1] 0.08315593 0.01544428
## [1] 438.4255
## [1] 4.384254
## [1] 5.384254
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      1.04469141     -2.93776365     -0.10129974      0.54394420     -0.46908933 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -0.25043287      0.17860903     -0.02802894     -1.10254931     -0.18544890
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##      1.04469107     -2.93776395     -0.10129986      0.54394448     -0.46908844 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -0.25043130      0.17861053     -0.02802755     -1.10254854     -0.18544866
## [1] 1.30134374 0.06895049
## [1] 1787.36
## [1] 17.8736
## [1] 18.8736
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -0.69745551     -3.03356413     -0.08288675     -0.66836457    -12.84389449 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -0.57490952     -1.57163622     -0.52021075    -13.16895203     -0.81746168
##     (Intercept) settlementsNear         year_ct      sin_td_rad        siteDvir 
##     -0.69748361     -3.03354620     -0.08288128     -0.66822779    -18.62332362 
##   siteHar Amasa       siteLahav     siteLehavim      siteMeitar     siteMirsham 
##     -0.57479278     -1.57156237     -0.52007543    -18.94831464     -0.81731126
## [1] 0.56880471 0.02738488
## [1] 1977.076
## [1] 19.77076
## [1] 20.77076

Session information

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value
##  version  R version 4.2.3 (2023-03-15 ucrt)
##  os       Windows 10 x64 (build 22631)
##  system   x86_64, mingw32
##  ui       RTerm
##  language (EN)
##  collate  Hebrew_Israel.utf8
##  ctype    Hebrew_Israel.utf8
##  tz       Asia/Jerusalem
##  date     2024-04-10
##  pandoc   3.1.1 @ C:/Program Files/RStudio/resources/app/bin/quarto/bin/tools/ (via rmarkdown)
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  package      * version    date (UTC) lib source
##  abind          1.4-7      2017-09-03 [1] R-Forge (R 4.2.3)
##  backports      1.4.1      2021-12-13 [1] CRAN (R 4.2.0)
##  betareg        3.2-0      2021-02-09 [1] R-Forge (R 4.2.3)
##  boot           1.3-28.1   2022-11-22 [1] CRAN (R 4.2.3)
##  broom          1.0.4      2023-03-11 [1] CRAN (R 4.2.3)
##  bslib          0.4.2      2022-12-16 [1] CRAN (R 4.2.3)
##  cachem         1.0.7      2023-02-24 [1] CRAN (R 4.2.3)
##  Cairo        * 1.6-0      2022-07-05 [1] CRAN (R 4.2.2)
##  callr          3.7.3      2022-11-02 [1] CRAN (R 4.2.3)
##  car          * 3.1-2      2023-03-30 [1] CRAN (R 4.2.3)
##  carData      * 3.0-5      2022-01-06 [1] CRAN (R 4.2.3)
##  cellranger     1.1.0      2016-07-27 [1] CRAN (R 4.2.3)
##  cli            3.6.1      2023-03-23 [1] CRAN (R 4.2.3)
##  cluster        2.1.4      2022-08-22 [1] CRAN (R 4.2.3)
##  coda           0.19-4     2020-09-30 [1] CRAN (R 4.2.3)
##  codetools      0.2-19     2023-02-01 [1] CRAN (R 4.2.2)
##  colorspace     2.1-1      2023-03-08 [1] R-Forge (R 4.2.2)
##  crayon         1.5.2      2022-09-29 [1] CRAN (R 4.2.3)
##  data.table   * 1.14.8     2023-02-17 [1] CRAN (R 4.2.3)
##  devtools     * 2.4.5      2022-10-11 [1] CRAN (R 4.2.3)
##  digest         0.6.31     2022-12-11 [1] CRAN (R 4.2.3)
##  doParallel     1.0.17     2022-02-07 [1] CRAN (R 4.2.3)
##  dplyr        * 1.1.1      2023-03-22 [1] CRAN (R 4.2.3)
##  ecoCopula    * 1.0.2      2022-03-02 [1] CRAN (R 4.2.3)
##  ellipsis       0.3.2      2021-04-29 [1] CRAN (R 4.2.3)
##  emmeans      * 1.8.6      2023-05-11 [1] CRAN (R 4.2.3)
##  estimability   1.4.1      2022-08-05 [1] CRAN (R 4.2.1)
##  evaluate       0.20       2023-01-17 [1] CRAN (R 4.2.3)
##  extrafont    * 0.19       2023-01-18 [1] CRAN (R 4.2.2)
##  extrafontdb    1.0        2012-06-11 [1] CRAN (R 4.2.0)
##  fansi          1.0.4      2023-01-22 [1] CRAN (R 4.2.3)
##  farver         2.1.1      2022-07-06 [1] CRAN (R 4.2.3)
##  fastmap        1.1.1      2023-02-24 [1] CRAN (R 4.2.3)
##  flexmix        2.3-19     2023-03-16 [1] CRAN (R 4.2.3)
##  foreach        1.5.2      2022-02-02 [1] CRAN (R 4.2.3)
##  Formula        1.2-6      2023-02-25 [1] R-Forge (R 4.2.2)
##  fs             1.6.1      2023-02-06 [1] CRAN (R 4.2.3)
##  generics       0.1.3      2022-07-05 [1] CRAN (R 4.2.3)
##  ggnewscale   * 0.4.9      2023-05-25 [1] CRAN (R 4.2.3)
##  ggplot2      * 3.5.0      2024-02-23 [1] CRAN (R 4.2.3)
##  ggrepel      * 0.9.3      2023-02-03 [1] CRAN (R 4.2.3)
##  glm2           1.2.1      2018-08-11 [1] CRAN (R 4.2.0)
##  glue           1.6.2      2022-02-24 [1] CRAN (R 4.2.3)
##  gtable         0.3.3      2023-03-21 [1] CRAN (R 4.2.3)
##  highr          0.10       2022-12-22 [1] CRAN (R 4.2.3)
##  htmltools      0.5.5      2023-03-23 [1] CRAN (R 4.2.3)
##  htmlwidgets    1.6.2      2023-03-17 [1] CRAN (R 4.2.3)
##  httpuv         1.6.9      2023-02-14 [1] CRAN (R 4.2.3)
##  interactions * 1.1.5      2021-07-02 [1] CRAN (R 4.2.3)
##  iterators      1.0.14     2022-02-05 [1] CRAN (R 4.2.3)
##  jquerylib      0.1.4      2021-04-26 [1] CRAN (R 4.2.3)
##  jsonlite       1.8.4      2022-12-06 [1] CRAN (R 4.2.3)
##  jtools       * 2.2.1      2022-12-02 [1] CRAN (R 4.2.3)
##  kableExtra   * 1.4.0      2024-01-24 [1] CRAN (R 4.2.3)
##  knitr          1.42       2023-01-25 [1] CRAN (R 4.2.3)
##  labeling       0.4.2      2020-10-20 [1] CRAN (R 4.2.0)
##  later          1.3.0      2021-08-18 [1] CRAN (R 4.2.3)
##  lattice      * 0.21-8     2023-04-05 [1] CRAN (R 4.2.3)
##  lifecycle      1.0.3      2022-10-07 [1] CRAN (R 4.2.3)
##  lme4         * 1.1-32     2023-03-14 [1] CRAN (R 4.2.3)
##  lmtest         0.9-40     2022-03-21 [1] CRAN (R 4.2.3)
##  lubridate    * 1.9.2      2023-02-10 [1] CRAN (R 4.2.3)
##  magrittr       2.0.3      2022-03-30 [1] CRAN (R 4.2.3)
##  MASS         * 7.3-58.3   2023-03-07 [1] CRAN (R 4.2.3)
##  Matrix       * 1.5-5      2023-04-05 [1] R-Forge (R 4.2.3)
##  memoise        2.0.1      2021-11-26 [1] CRAN (R 4.2.3)
##  mgcv           1.8-42     2023-03-02 [1] CRAN (R 4.2.3)
##  mime           0.12       2021-09-28 [1] CRAN (R 4.2.0)
##  miniUI         0.1.1.1    2018-05-18 [1] CRAN (R 4.2.3)
##  minqa          1.2.5      2022-10-19 [1] CRAN (R 4.2.3)
##  modeltools     0.2-23     2020-03-05 [1] CRAN (R 4.2.0)
##  multcomp       1.4-23     2023-03-09 [1] CRAN (R 4.2.3)
##  munsell        0.5.0      2018-06-12 [1] CRAN (R 4.2.3)
##  mvabund      * 4.2.1      2022-02-16 [1] CRAN (R 4.2.3)
##  mvtnorm        1.2-0      2023-04-05 [1] R-Forge (R 4.2.3)
##  nlme           3.1-162    2023-01-31 [1] CRAN (R 4.2.3)
##  nloptr         2.0.3      2022-05-26 [1] CRAN (R 4.2.3)
##  nnet           7.3-18     2022-09-28 [1] CRAN (R 4.2.3)
##  numDeriv       2022.9-1   2022-09-27 [1] R-Forge (R 4.2.1)
##  ordinal        2022.11-16 2022-11-16 [1] CRAN (R 4.2.3)
##  pander         0.6.5      2022-03-18 [1] CRAN (R 4.2.3)
##  pbkrtest       0.5.2      2023-01-19 [1] CRAN (R 4.2.3)
##  permute      * 0.9-7      2022-01-27 [1] CRAN (R 4.2.3)
##  pillar         1.9.0      2023-03-22 [1] CRAN (R 4.2.3)
##  pkgbuild       1.4.2.9000 2023-07-11 [1] Github (r-lib/pkgbuild@7048654)
##  pkgconfig      2.0.3      2019-09-22 [1] CRAN (R 4.2.3)
##  pkgload        1.3.2      2022-11-16 [1] CRAN (R 4.2.3)
##  prettyunits    1.1.1      2020-01-24 [1] CRAN (R 4.2.3)
##  processx       3.8.0      2022-10-26 [1] CRAN (R 4.2.3)
##  profvis        0.3.7      2020-11-02 [1] CRAN (R 4.2.3)
##  promises       1.2.0.1    2021-02-11 [1] CRAN (R 4.2.3)
##  ps             1.7.4      2023-04-02 [1] CRAN (R 4.2.3)
##  purrr          1.0.1      2023-01-10 [1] CRAN (R 4.2.3)
##  R6             2.5.1      2021-08-19 [1] CRAN (R 4.2.3)
##  RColorBrewer   1.1-3      2022-04-03 [1] CRAN (R 4.2.0)
##  Rcpp           1.0.10     2023-01-22 [1] CRAN (R 4.2.3)
##  readxl       * 1.4.2      2023-02-09 [1] CRAN (R 4.2.3)
##  remotes        2.4.2      2021-11-30 [1] CRAN (R 4.2.3)
##  rlang        * 1.1.0      2023-03-14 [1] CRAN (R 4.2.3)
##  rmarkdown      2.21       2023-03-26 [1] CRAN (R 4.2.3)
##  rstudioapi     0.14       2022-08-22 [1] CRAN (R 4.2.3)
##  Rttf2pt1       1.3.12     2023-01-22 [1] CRAN (R 4.2.2)
##  sandwich       3.1-0      2023-04-04 [1] R-Forge (R 4.2.3)
##  sass           0.4.5      2023-01-24 [1] CRAN (R 4.2.3)
##  scales         1.3.0      2023-11-28 [1] CRAN (R 4.2.3)
##  sessioninfo    1.2.2      2021-12-06 [1] CRAN (R 4.2.3)
##  shiny          1.7.4      2022-12-15 [1] CRAN (R 4.2.3)
##  solartime    * 0.0.2      2021-04-22 [1] CRAN (R 4.2.3)
##  statmod        1.5.0      2023-01-06 [1] CRAN (R 4.2.3)
##  stringi        1.7.12     2023-01-11 [1] CRAN (R 4.2.2)
##  stringr        1.5.0      2022-12-02 [1] CRAN (R 4.2.3)
##  survival       3.5-5      2023-03-12 [1] CRAN (R 4.2.3)
##  svglite        2.1.1      2023-01-10 [1] CRAN (R 4.2.3)
##  systemfonts    1.0.4      2022-02-11 [1] CRAN (R 4.2.3)
##  TH.data        1.1-2      2022-11-07 [1] R-Forge (R 4.2.3)
##  tibble         3.2.1      2023-03-20 [1] CRAN (R 4.2.3)
##  tidyr          1.3.0      2023-01-24 [1] CRAN (R 4.2.3)
##  tidyselect     1.2.0      2022-10-10 [1] CRAN (R 4.2.3)
##  timechange     0.2.0      2023-01-11 [1] CRAN (R 4.2.3)
##  tweedie        2.3.5      2022-08-17 [1] CRAN (R 4.2.3)
##  ucminf         1.1-4.1    2022-09-29 [1] CRAN (R 4.2.1)
##  urlchecker     1.0.1      2021-11-30 [1] CRAN (R 4.2.3)
##  usethis      * 2.1.6      2022-05-25 [1] CRAN (R 4.2.3)
##  utf8           1.2.3      2023-01-31 [1] CRAN (R 4.2.3)
##  vctrs          0.6.1      2023-03-22 [1] CRAN (R 4.2.3)
##  vegan        * 2.6-4      2022-10-11 [1] CRAN (R 4.2.3)
##  viridisLite    0.4.1      2022-08-22 [1] CRAN (R 4.2.3)
##  withr          2.5.0      2022-03-03 [1] CRAN (R 4.2.3)
##  xfun           0.38       2023-03-24 [1] CRAN (R 4.2.3)
##  xml2           1.3.3      2021-11-30 [1] CRAN (R 4.2.3)
##  xtable         1.8-6      2020-06-19 [1] R-Forge (R 4.2.3)
##  yaml           2.3.7      2023-01-23 [1] CRAN (R 4.2.3)
##  zoo            1.8-11     2022-09-17 [1] CRAN (R 4.2.3)
## 
##  [1] C:/Users/Ron Chen/AppData/Local/R/win-library/4.2.3
##  [2] C:/Program Files/R/R-4.2.3/library
## 
## ──────────────────────────────────────────────────────────────────────────────