Birds_Med_Des_Trans_Zone_analysis_by_plot
Ron Chen
2023-04-29
## 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## [1] "Winter data excluded."
## [1] "The counts of all passing species (not resident nor breeding) were set to zero. Abreed_and_non_breed contain original data."Med-Desert Transition Zone
Factors are proximity to settlements and time. Total 5 campaigns. 5 sites with 6 plots per site.
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"
## 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).
| 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. :-2.06468 | 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.: 5.00 | 1st Qu.:2.000 | Dvir : 6 | Near:75 | 1st Qu.:-0.41891 | 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 : 7.00 | Median :4.000 | Har Amasa :29 | NA | Median : 0.07721 | 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 : 7.58 | Mean :3.987 | Lahav :31 | NA | Mean :-0.03353 | 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.: 0.22509 | 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. :19.00 | Max. :8.000 | Meitar : 6 | NA | Max. : 1.90425 | 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. Try to add them to the model to see if they have a very strong effect; otherwise remove them.
## 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 | 0.0106005 | 0.1305677 | 0.6598001 | -0.0215457 | 0.0308580 | -0.0806109 | -0.1273441 | 0.2240561 | -0.1058582 | 0.0368710 |
| year_ct | 0.0106005 | 1.0000000 | 0.0000166 | -0.0047063 | -0.4784485 | -0.4613745 | -0.4697934 | -0.4334083 | 0.3814165 | -0.4327722 | NA |
| site | 0.1305677 | 0.0000166 | 1.0000000 | 0.0035169 | -0.2288120 | -0.1363567 | -0.3069781 | -0.1032496 | 0.1542517 | -0.0901054 | 0.0447214 |
| settlements | 0.6598001 | -0.0047063 | 0.0035169 | 1.0000000 | 0.0121481 | 0.0062718 | 0.0170858 | 0.0349726 | 0.0873478 | 0.0587772 | 0.2683282 |
| td_sc | -0.0215457 | -0.4784485 | -0.2288120 | 0.0121481 | 1.0000000 | 0.9576971 | 0.9330875 | -0.0786776 | 0.0634242 | -0.0849265 | -0.1529258 |
| cos_td_rad | 0.0308580 | -0.4613745 | -0.1363567 | 0.0062718 | 0.9576971 | 1.0000000 | 0.7938914 | -0.1011147 | 0.0827235 | -0.1075303 | -0.1580054 |
| sin_td_rad | -0.0806109 | -0.4697934 | -0.3069781 | 0.0170858 | 0.9330875 | 0.7938914 | 1.0000000 | 0.0563677 | -0.0500522 | 0.0519939 | -0.0915087 |
| h_from_sunrise | -0.1273441 | -0.4334083 | -0.1032496 | 0.0349726 | -0.0786776 | -0.1011147 | 0.0563677 | 1.0000000 | -0.9216766 | 0.9965659 | 0.2604084 |
| cos_hsun | 0.2240561 | 0.3814165 | 0.1542517 | 0.0873478 | 0.0634242 | 0.0827235 | -0.0500522 | -0.9216766 | 1.0000000 | -0.8880762 | -0.2261490 |
| sin_hsun | -0.1058582 | -0.4327722 | -0.0901054 | 0.0587772 | -0.0849265 | -0.1075303 | 0.0519939 | 0.9965659 | -0.8880762 | 1.0000000 | 0.2583855 |
| monitors_name | 0.0368710 | 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 = 0.946402758279505"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) | 109.12 |
| Pseudo-R² (Cragg-Uhler) | 0.71 |
| Pseudo-R² (McFadden) | 0.21 |
| AIC | 422.28 |
| BIC | 442.19 |
| Est. | S.E. | z val. | p | |
|---|---|---|---|---|
| (Intercept) | 1.91 | 1.36 | 1.40 | 0.16 |
| settlementsNear | 0.51 | 0.33 | 1.52 | 0.13 |
| year_ct | 0.02 | 0.05 | 0.44 | 0.66 |
| cos_td_rad | -0.32 | 0.37 | -0.85 | 0.39 |
| sin_td_rad | 1.40 | 0.90 | 1.56 | 0.12 |
| cos_hsun | 0.92 | 0.91 | 1.01 | 0.31 |
| sin_hsun | -0.01 | 0.42 | -0.02 | 0.99 |
| settlementsNear:year_ct | 0.04 | 0.05 | 0.81 | 0.42 |
| Standard errors: MLE |
cosine and sine of hours from sunrise are not significant. remove them because of many NAs.
## boundary (singular) fit: see help('isSingular')Singular fit. Check VIF of terms.
## settlements year_ct cos_td_rad sin_td_rad
## 2.932257 3.290801 2.791554 2.808034
## settlements:year_ct
## 5.025307Remove interaction of settlements X year.
## boundary (singular) fit: see help('isSingular')Still singular fit, use glm.
##
## Call:
## glm(formula = richness ~ settlements * year_ct + cos_td_rad +
## sin_td_rad + site, family = poisson, data = P.anal)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.86744 -0.70363 -0.08607 0.65863 1.99517
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.98274 0.29563 3.324 0.000887 ***
## settlementsNear 0.61552 0.10766 5.717 1.08e-08 ***
## year_ct -0.01011 0.02032 -0.498 0.618643
## cos_td_rad 0.39213 0.20505 1.912 0.055829 .
## sin_td_rad -0.49006 0.22691 -2.160 0.030796 *
## siteDvir 0.14468 0.18195 0.795 0.426516
## siteHar Amasa 0.04847 0.11397 0.425 0.670606
## siteLahav 0.17667 0.10695 1.652 0.098545 .
## siteLehavim 0.07396 0.11856 0.624 0.532723
## siteMeitar 0.13569 0.18546 0.732 0.464384
## siteMirsham 0.15749 0.10859 1.450 0.146955
## settlementsNear:year_ct 0.01881 0.02206 0.853 0.393864
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 274.96 on 149 degrees of freedom
## Residual deviance: 132.10 on 138 degrees of freedom
## AIC: 720.54
##
## Number of Fisher Scoring iterations: 4perform stepwise model selection of poisson mixed model.
## Start: AIC=720.54
## richness ~ settlements * year_ct + cos_td_rad + sin_td_rad +
## site
##
## Df Deviance AIC
## - site 6 136.28 712.71
## - settlements:year_ct 1 132.83 719.26
## <none> 132.10 720.54
## - cos_td_rad 1 135.86 722.29
## - sin_td_rad 1 136.94 723.37
##
## Step: AIC=712.71
## richness ~ settlements + year_ct + cos_td_rad + sin_td_rad +
## settlements:year_ct
##
## Df Deviance AIC
## - settlements:year_ct 1 136.98 711.42
## <none> 136.28 712.71
## - cos_td_rad 1 144.06 718.49
## - sin_td_rad 1 146.34 720.77
##
## Step: AIC=711.42
## richness ~ settlements + year_ct + cos_td_rad + sin_td_rad
##
## Df Deviance AIC
## - year_ct 1 137.00 709.43
## <none> 136.98 711.42
## - cos_td_rad 1 144.79 717.22
## - sin_td_rad 1 147.10 719.54
## - settlements 1 265.66 838.09
##
## Step: AIC=709.43
## richness ~ settlements + cos_td_rad + sin_td_rad
##
## Df Deviance AIC
## <none> 137.00 709.43
## - cos_td_rad 1 145.12 715.55
## - sin_td_rad 1 147.35 717.79
## - settlements 1 265.67 836.10settlements and time of year remain. Final model:
##
## Call:
## glm(formula = richness ~ settlements + cos_td_rad + sin_td_rad,
## family = poisson, data = P.anal)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.72380 -0.70081 -0.09132 0.67524 2.37119
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.89105 0.24034 3.707 0.000209 ***
## settlementsNear 0.69267 0.06288 11.016 < 2e-16 ***
## cos_td_rad 0.49099 0.17683 2.777 0.005494 **
## sin_td_rad -0.61983 0.19854 -3.122 0.001797 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 274.96 on 149 degrees of freedom
## Residual deviance: 137.00 on 146 degrees of freedom
## AIC: 709.43
##
## Number of Fisher Scoring iterations: 4
| Observations | 150 |
| Dependent variable | richness |
| Type | Generalized linear model |
| Family | poisson |
| Link | log |
| χ²(3) | 137.966 |
| Pseudo-R² (Cragg-Uhler) | 0.604 |
| Pseudo-R² (McFadden) | 0.164 |
| AIC | 709.428 |
| BIC | 721.470 |
| exp(Est.) | 2.5% | 97.5% | z val. | p | |
|---|---|---|---|---|---|
| (Intercept) | 2.438 | 1.522 | 3.904 | 3.707 | 0.000 |
| settlementsNear | 1.999 | 1.767 | 2.261 | 11.016 | 0.000 |
| cos_td_rad | 1.634 | 1.155 | 2.311 | 2.777 | 0.005 |
| sin_td_rad | 0.538 | 0.365 | 0.794 | -3.122 | 0.002 |
| Standard errors: MLE |
There is a statistically significant effect for proximity to settlements and time of year. 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. :-2.06468 | Min. :-0.2009 | Min. :-0.99677 | |
| 1st Qu.:1.686 | 1st Qu.:2.000 | Lehavim :30 | Near:75 | 1st Qu.:-0.41891 | 1st Qu.: 0.5142 | 1st Qu.:-0.85766 | |
| Median :2.277 | Median :4.000 | Har Amasa :29 | NA | Median : 0.07721 | Median : 0.6917 | Median :-0.72216 | |
| Mean :2.425 | Mean :3.987 | Beit Yatir:24 | NA | Mean :-0.03353 | Mean : 0.6007 | Mean :-0.69390 | |
| 3rd Qu.:2.902 | 3rd Qu.:6.000 | Mirsham :24 | NA | 3rd Qu.: 0.22509 | 3rd Qu.: 0.7383 | 3rd Qu.:-0.67444 | |
| Max. :6.325 | Max. :8.000 | Dvir : 6 | NA | Max. : 1.90425 | 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 14 (1 species with abundance of 5 and 2 species with abundance of 13, respectively). Fit fixed and mixed models.
## boundary (singular) fit: see help('isSingular')Mixed model did not converge, use glm:
##
## Call:
## glm(formula = gma ~ settlements * year_ct + cos_td_rad + sin_td_rad +
## site, family = Gamma, data = P.anal)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.62585 -0.20756 -0.03878 0.15707 0.68699
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.511507 0.103085 4.962 2.05e-06 ***
## settlementsNear -0.037200 0.030016 -1.239 0.2174
## year_ct 0.030787 0.006833 4.505 1.41e-05 ***
## cos_td_rad -0.169836 0.080077 -2.121 0.0357 *
## sin_td_rad 0.054367 0.071247 0.763 0.4467
## siteDvir 0.024033 0.052820 0.455 0.6498
## siteHar Amasa 0.017855 0.038731 0.461 0.6455
## siteLahav -0.010773 0.038383 -0.281 0.7794
## siteLehavim -0.028752 0.041712 -0.689 0.4918
## siteMeitar -0.055576 0.053538 -1.038 0.3011
## siteMirsham -0.013049 0.039936 -0.327 0.7444
## settlementsNear:year_ct -0.012041 0.007557 -1.593 0.1134
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.08981959)
##
## Null deviance: 19.989 on 147 degrees of freedom
## Residual deviance: 11.900 on 136 degrees of freedom
## AIC: 311.7
##
## Number of Fisher Scoring iterations: 5perform stepwise model selection of Gaussian model.
## Start: AIC=311.7
## gma ~ settlements * year_ct + cos_td_rad + sin_td_rad + site
##
## Df Deviance AIC
## - site 6 12.202 303.07
## - sin_td_rad 1 11.953 310.29
## <none> 11.900 311.70
## - settlements:year_ct 1 12.128 312.25
## - cos_td_rad 1 12.326 314.45
##
## Step: AIC=303.47
## gma ~ settlements + year_ct + cos_td_rad + sin_td_rad + settlements:year_ct
##
## Df Deviance AIC
## <none> 12.202 303.47
## - sin_td_rad 1 12.428 304.05
## - settlements:year_ct 1 12.433 304.11
## - cos_td_rad 1 12.759 307.84drop sine of time of year becauese \(\Delta AIC<2\)
## Single term deletions
##
## Model:
## gma ~ settlements * year_ct + cos_td_rad
## Df Deviance AIC
## <none> 12.428 304.21
## cos_td_rad 1 12.787 306.23
## settlements:year_ct 1 12.658 304.79drop settlements:year because \(\Delta AIC<2\).
## Single term deletions
##
## Model:
## gma ~ settlements + year_ct + cos_td_rad
## Df Deviance AIC
## <none> 12.658 304.96
## settlements 1 13.785 315.47
## year_ct 1 15.943 339.43
## cos_td_rad 1 13.012 306.90drop cosine of time of year becauese \(\Delta AIC<2\).
## Single term deletions
##
## Model:
## gma ~ settlements + year_ct
## Df Deviance AIC
## <none> 13.012 307.11
## settlements 1 14.124 317.30
## year_ct 1 18.755 368.09Settlements and year remain. This is the final model:
##
## Call:
## glm(formula = gma ~ settlements + year_ct, family = Gamma, data = P.anal)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.57201 -0.24946 -0.04993 0.17284 0.62430
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.35840 0.01974 18.159 < 2e-16 ***
## settlementsNear -0.07207 0.02080 -3.465 0.000698 ***
## year_ct 0.02939 0.00374 7.857 8.11e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.09119238)
##
## Null deviance: 19.989 on 147 degrees of freedom
## Residual deviance: 13.012 on 145 degrees of freedom
## AIC: 307.11
##
## Number of Fisher Scoring iterations: 5
| Observations | 148 |
| Dependent variable | gma |
| Type | Generalized linear model |
| Family | Gamma |
| Link | inverse |
| χ²(2) | 6.977 |
| Pseudo-R² (Cragg-Uhler) | 0.387 |
| Pseudo-R² (McFadden) | 0.178 |
| AIC | 307.109 |
| BIC | 319.098 |
| Est. | S.E. | t val. | p | |
|---|---|---|---|---|
| (Intercept) | 0.358 | 0.020 | 18.159 | 0.000 |
| settlementsNear | -0.072 | 0.021 | -3.465 | 0.001 |
| year_ct | 0.029 | 0.004 | 7.857 | 0.000 |
| Standard errors: MLE |
Very significant temporal decrease in gma as well as lower gma far from settlements.
abundance
Explore data
## [1] "ABUNDANCE WITHOUT RARE SPECIES"
| abundance | year_ct | site | settlements | td_sc | cos_td_rad | sin_td_rad | |
|---|---|---|---|---|---|---|---|
| Min. : 3.00 | Min. :0.000 | Lahav :31 | Far :75 | Min. :-2.06468 | Min. :-0.2009 | Min. :-0.99677 | |
| 1st Qu.: 9.00 | 1st Qu.:2.000 | Lehavim :30 | Near:75 | 1st Qu.:-0.41891 | 1st Qu.: 0.5142 | 1st Qu.:-0.85766 | |
| Median : 17.00 | Median :4.000 | Har Amasa :29 | NA | Median : 0.07721 | Median : 0.6917 | Median :-0.72216 | |
| Mean : 23.77 | Mean :3.987 | Beit Yatir:24 | NA | Mean :-0.03353 | Mean : 0.6007 | Mean :-0.69390 | |
| 3rd Qu.: 32.75 | 3rd Qu.:6.000 | Mirsham :24 | NA | 3rd Qu.: 0.22509 | 3rd Qu.: 0.7383 | 3rd Qu.:-0.67444 | |
| Max. :113.00 | Max. :8.000 | Dvir : 6 | NA | Max. : 1.90425 | Max. : 1.0000 | Max. : 0.01721 | |
| NA | NA | (Other) : 6 | NA | NA | NA | NA |
Outlier with total abundance >100. 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> -0.3091928 -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 14 113 4.830157Exclude point with abundance of 113 (Lehavim Near 4 from 2012). Nearest total abundance is 80.
PHI>1, hence choose negative binomial. Fit fixed and mixed models. Choose mixed model if possible, otherwise choose a model with fixed-effects only.
## boundary (singular) fit: see help('isSingular')Mixed model is singular. check variance inflation factor:
## settlements year_ct cos_td_rad sin_td_rad
## 2.742010 2.760979 2.701299 2.683580
## settlements:year_ct
## 4.304603none of the terms seem to have an extreme inflation factor (>5). Use glm.
##
## Call:
## glm.nb(formula = abundance ~ settlements * year_ct + cos_td_rad +
## sin_td_rad + site, data = P.anal, init.theta = 5.037571108,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6469 -0.9017 -0.0167 0.4426 2.1611
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.81324 0.38426 4.719 2.37e-06 ***
## settlementsNear 0.82583 0.13942 5.923 3.16e-09 ***
## year_ct -0.11835 0.02578 -4.591 4.41e-06 ***
## cos_td_rad 0.92561 0.27720 3.339 0.00084 ***
## sin_td_rad -0.81311 0.29399 -2.766 0.00568 **
## siteDvir -0.10833 0.24057 -0.450 0.65249
## siteHar Amasa -0.23185 0.15220 -1.523 0.12769
## siteLahav -0.01785 0.14855 -0.120 0.90433
## siteLehavim 0.03900 0.16242 0.240 0.81023
## siteMeitar -0.02033 0.25500 -0.080 0.93646
## siteMirsham 0.09152 0.15086 0.607 0.54409
## settlementsNear:year_ct 0.06823 0.02947 2.315 0.02061 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(5.0376) family taken to be 1)
##
## Null deviance: 373.50 on 149 degrees of freedom
## Residual deviance: 148.24 on 138 degrees of freedom
## AIC: 1115.6
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 5.038
## Std. Err.: 0.712
##
## 2 x log-likelihood: -1089.641
Perform stepwise model selection of mixed model.
## Start: AIC=1113.64
## abundance ~ settlements * year_ct + cos_td_rad + sin_td_rad +
## site
##
## Df Deviance AIC
## - site 6 153.68 1107.1
## <none> 148.24 1113.6
## - settlements:year_ct 1 153.88 1117.3
## - sin_td_rad 1 155.45 1118.8
## - cos_td_rad 1 158.96 1122.4
##
## Step: AIC=1107
## abundance ~ settlements + year_ct + cos_td_rad + sin_td_rad +
## settlements:year_ct
##
## Df Deviance AIC
## <none> 149.22 1107.0
## - settlements:year_ct 1 154.70 1110.5
## - sin_td_rad 1 164.30 1120.1
## - cos_td_rad 1 169.57 1125.4The final model:
##
## Call:
## glm.nb(formula = abundance ~ settlements + year_ct + cos_td_rad +
## sin_td_rad + settlements:year_ct, data = P.anal, init.theta = 4.852344004,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.60195 -0.89967 -0.07725 0.59045 2.29614
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.49528 0.33359 4.482 7.38e-06 ***
## settlementsNear 0.81387 0.14127 5.761 8.35e-09 ***
## year_ct -0.11512 0.02361 -4.875 1.09e-06 ***
## cos_td_rad 1.12586 0.24894 4.523 6.11e-06 ***
## sin_td_rad -1.05028 0.26643 -3.942 8.08e-05 ***
## settlementsNear:year_ct 0.06830 0.02980 2.292 0.0219 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(4.8523) family taken to be 1)
##
## Null deviance: 362.58 on 149 degrees of freedom
## Residual deviance: 149.22 on 144 degrees of freedom
## AIC: 1109
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 4.852
## Std. Err.: 0.683
##
## 2 x log-likelihood: -1095.005
Interpretation of abundance model:
## Error in glm.control(...) :
## unused argument (family = list("Negative Binomial(4.8523)", "log", function (mu)
## log(mu), function (eta)
## pmax(exp(eta), .Machine$double.eps), function (mu)
## mu + mu^2/.Theta, function (y, mu, wt)
## 2 * wt * (y * log(pmax(1, y)/mu) - (y + .Theta) * log((y + .Theta)/(mu + .Theta))), function (y, n, mu, wt, dev)
## {
## term <- (y + .Theta) * log(mu + .Theta) - y * log(mu) + lgamma(y + 1) - .Theta * log(.Theta) + lgamma(.Theta) - lgamma(.Theta + y)
## 2 * sum(term * wt)
## }, function (eta)
## pmax(exp(eta), .Machine$double.eps), expression({
## if (any(y < 0)) stop("negative values not allowed for the negative binomial family")
## n <- rep(1, nobs)
## mustart <- y + (y == 0)/6
## }), function (mu)
## all(mu > 0), function (eta)
## TRUE, function (object, nsim)
## {
## ftd <- fitted(object)
## rnegbin(nsim * length(ftd), ftd, .Theta)
## }))| Observations | 150 |
| Dependent variable | abundance |
| Type | Generalized linear model |
| Family | Negative Binomial(4.8523) |
| Link | log |
| χ²(NA) | NA |
| Pseudo-R² (Cragg-Uhler) | NA |
| Pseudo-R² (McFadden) | NA |
| AIC | 1109.005 |
| BIC | 1130.079 |
| Est. | S.E. | z val. | p | |
|---|---|---|---|---|
| (Intercept) | 1.495 | 0.334 | 4.482 | 0.000 |
| settlementsNear | 0.814 | 0.141 | 5.761 | 0.000 |
| year_ct | -0.115 | 0.024 | -4.875 | 0.000 |
| cos_td_rad | 1.126 | 0.249 | 4.523 | 0.000 |
| sin_td_rad | -1.050 | 0.266 | -3.942 | 0.000 |
| settlementsNear:year_ct | 0.068 | 0.030 | 2.292 | 0.022 |
| Standard errors: MLE |
community analysis using package MVabund
## nb po
## 196.9227 253.6069## [1] "POISSON"
## [1] "NEGATIVE BINOMIAL"
negative binomial model is better than poisson according to residuals and AIC comparison.
## nb po nb1
## 196.9227 253.6069 191.3415The 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> 7845.0
## cos_td_rad 41 7860.7
## sin_td_rad 41 7888.3
## site 246 8073.8
## settlements:year_ct 41 7837.8drop interaction of settlements with year.
## Single term deletions
##
## Model:
## spp_no_rare ~ settlements + year_ct + cos_td_rad + sin_td_rad +
## site
## Df AIC
## <none> 7837.8
## settlements 41 8763.2
## year_ct 41 7854.6
## cos_td_rad 41 7853.2
## sin_td_rad 41 7884.2
## site 246 8051.7final model includes settlements, year, sampling time of year and site.
##
## Coefficients: (2 not defined because of singularities)
## wald value Pr(>wald)
## (Intercept) NaN 0.001 ***
## settlementsNear NaN 0.001 ***
## year_ct NaN 0.001 ***
## cos_td_rad NaN 0.001 ***
## sin_td_rad NaN 0.001 ***
## siteAderet NaN 0.001 ***
## siteBeit Yatir NaN 0.001 ***
## siteDvir NaN 0.001 ***
## siteHar Amasa NaN 0.001 ***
## siteLahav NaN 0.001 ***
## siteLehavim NaN 0.001 ***
## siteMeitar NaN 0.001 ***
## siteMirsham NaN 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Test statistic: NaN, 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 + cos_td_rad + sin_td_rad + site
##
## Multivariate test:
## Res.Df Df.diff Dev Pr(>Dev)
## (Intercept) 149
## settlements 148 1 823.4 0.001 ***
## year_ct 147 1 131.9 0.001 ***
## cos_td_rad 146 1 77.4 0.003 **
## sin_td_rad 145 1 147.9 0.002 **
## site 139 8 705.3 0.001 ***
## ---
## 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 0.001 2.828 0.681
## year_ct 19.477 0.003 1.321 0.999
## cos_td_rad 1.296 1.000 0.96 1.000
## sin_td_rad 1.647 0.994 2.553 0.981
## site 19.206 0.195 8.707 0.955
## Anthus.similis Apus.apus Apus.melba
## Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 22.266 0.001 7.183 0.119 0.526 0.977
## year_ct 0.023 1.000 0.214 1.000 0.339 1.000
## cos_td_rad 0.25 1.000 0.569 1.000 1.075 1.000
## sin_td_rad 0.127 1.000 6.432 0.579 8.356 0.292
## site 7.763 0.955 3.725 0.999 16.079 0.425
## Apus.pallidus Bubulcus.ibis Burhinus.oedicnemus
## Dev Pr(>Dev) Dev Pr(>Dev) Dev
## (Intercept)
## settlements 0.628 0.977 0.692 0.977 0
## year_ct 2.015 0.985 0.082 1.000 0.071
## cos_td_rad 4.193 0.810 0.041 1.000 2.905
## sin_td_rad 13.679 0.035 5.666 0.677 0.04
## site 13.342 0.637 9.626 0.949 6.807
## Cecropis.daurica Chloris.chloris
## Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 0.977 32.021 0.001 46.076 0.001
## year_ct 1.000 0.056 1.000 1.089 0.999
## cos_td_rad 0.957 0.392 1.000 1.852 0.991
## sin_td_rad 1.000 2.531 0.981 0.108 1.000
## site 0.959 25.448 0.046 17.316 0.314
## Cinnyris.osea Columba.livia Corvus.cornix
## Dev Pr(>Dev) Dev Pr(>Dev) Dev
## (Intercept)
## settlements 41.406 0.001 53 0.001 50.914
## year_ct 8.852 0.129 0.485 1.000 1.249
## cos_td_rad 2.182 0.987 5.339 0.638 0.092
## sin_td_rad 4.529 0.820 3.444 0.943 1.206
## site 18.567 0.227 13.558 0.637 35.867
## Corvus.monedula Curruca.conspicillata
## Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 0.001 9.184 0.052 57.418 0.001
## year_ct 0.999 1.44 0.996 4.035 0.785
## cos_td_rad 1.000 4.401 0.788 2.186 0.987
## sin_td_rad 0.998 2.638 0.980 0.063 1.000
## site 0.005 37.938 0.004 3.439 0.999
## Curruca.melanocephala Delichon.urbicum
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 5.2 0.340 3.584 0.589
## year_ct 3.848 0.807 4.47 0.731
## cos_td_rad 6.546 0.444 0.019 1.000
## sin_td_rad 3.425 0.943 3.626 0.943
## site 45.442 0.003 8.947 0.955
## Emberiza.calandra Emberiza.hortulana
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 0.961 0.958 8.751 0.057
## year_ct 0.711 1.000 3.297 0.884
## cos_td_rad 0 1.000 0.284 1.000
## sin_td_rad 2.395 0.983 13.624 0.035
## site 25.485 0.046 7.204 0.959
## Falco.naumanni Falco.tinnunculus
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 0.312 0.977 1.443 0.902
## year_ct 1.693 0.994 0.071 1.000
## cos_td_rad 0.184 1.000 0.099 1.000
## sin_td_rad 0.669 1.000 0.571 1.000
## site 21.251 0.141 4.163 0.999
## Galerida.cristata Garrulus.glandarius
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 37.532 0.001 27.928 0.001
## year_ct 16.713 0.009 6.706 0.334
## cos_td_rad 1.991 0.991 0.526 1.000
## sin_td_rad 0.015 1.000 0.033 1.000
## site 36.052 0.005 11.095 0.860
## Hirundo.rustica Lanius.senator Merops.apiaster
## Dev Pr(>Dev) Dev Pr(>Dev) Dev
## (Intercept)
## settlements 0.06 0.977 7.661 0.099 0.2
## year_ct 8.685 0.135 2.843 0.935 0.624
## cos_td_rad 5.478 0.622 3.773 0.856 0.004
## sin_td_rad 17.355 0.007 0.389 1.000 1.825
## site 12.336 0.751 2.956 0.999 8.767
## Oenanthe.hispanica.melanoleuca Parus.major
## Pr(>Dev) Dev Pr(>Dev) Dev
## (Intercept)
## settlements 0.977 2.775 0.687 22.544
## year_ct 1.000 0.302 1.000 0.071
## cos_td_rad 1.000 3.944 0.840 0.032
## sin_td_rad 0.994 0.579 1.000 1.946
## site 0.955 27.468 0.028 23.277
## Passer.domesticus Petronia.petronia
## Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 0.001 34.617 0.001 8.64 0.070
## year_ct 1.000 12.018 0.040 0.35 1.000
## cos_td_rad 1.000 0.013 1.000 3.376 0.906
## sin_td_rad 0.994 9.288 0.209 0.823 1.000
## site 0.080 20.032 0.182 16.089 0.425
## Prinia.gracilis Pycnonotus.xanthopygos
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 3.78 0.574 24.463 0.001
## year_ct 1.108 0.999 4.364 0.733
## cos_td_rad 4.335 0.798 0.676 1.000
## sin_td_rad 0.113 1.000 0.087 1.000
## site 19.33 0.195 22.526 0.093
## Scotocerca.inquieta Serinus.serinus
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 13.177 0.007 10.117 0.034
## year_ct 1.287 0.999 0.404 1.000
## cos_td_rad 2.778 0.966 0.268 1.000
## sin_td_rad 0.615 1.000 0.144 1.000
## site 20.024 0.182 26.547 0.034
## Spilopelia.senegalensis Streptopelia.decaocto
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 68.189 0.001 81.258 0.001
## year_ct 10.358 0.056 0.33 1.000
## cos_td_rad 0.371 1.000 0.698 1.000
## sin_td_rad 12.268 0.060 0.187 1.000
## site 14.283 0.555 9.068 0.955
## Streptopelia.turtur Sylvia.atricapilla
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 17.901 0.001 11.678 0.015
## year_ct 5.018 0.628 1.625 0.994
## cos_td_rad 6.524 0.444 2.209 0.987
## sin_td_rad 0.72 1.000 16.725 0.009
## site 25.303 0.046 16.367 0.394
## Turdus.merula Upupa.epops Vanellus.spinosus
## Dev Pr(>Dev) Dev Pr(>Dev) Dev
## (Intercept)
## settlements 41.91 0.001 0.355 0.977 16.373
## year_ct 3.432 0.880 0.506 1.000 0.33
## cos_td_rad 4.273 0.800 0.095 1.000 1.133
## sin_td_rad 1.973 0.994 5.103 0.746 0.404
## site 15.664 0.431 4.256 0.999 23.939
##
## Pr(>Dev)
## (Intercept)
## settlements 0.003
## year_ct 1.000
## cos_td_rad 1.000
## sin_td_rad 1.000
## site 0.068
## Arguments:
## Test statistics calculated assuming uncorrelated response (for faster computation)
## P-value calculated using 999 iterations via PIT-trap resampling.All factors (settlements, year, time of year and site) have a statistically significant effect on community composition.
## 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.## [[1]]
##
## [[2]]
##
## [[3]]
## [[1]]
##
## [[2]]
##
## [[3]]
Significant negative temporal effect on house sparrow and positive effect on common myna. Significant effect of settlement proximity: synanthrope / invasive species near settlements, endangered and / or batha specialists far from settlements.
