Urban Insect Biodiversity: Effects of Drought-Tolerant Plants A Negative Binomial Approach

Using count data modeling to explore how plant choices shape urban insect communities in LA’s Mediterranean climate.
Quarto
MEDS
R
Statistical Modeling
Author
Affiliation

Ixel M.

Master of Environmental Data Science Program @ The Bren School (UCSB)

Published

December 12, 2025

Background Information

Urban areas are expanding globally, yet we know little about how landscaping choices affect urban biodiversity. Cities are environmental gradients that consistently shape habitat quality and biodiversity 1. Los Angeles, a naturally arid Mediterranean climate, presents a unique opportunity to examine whether drought-tolerant landscaping supports insect diversity. Adams et al.(2020)2 sampled insects monthly at 30 sites across LA County in 2014, capturing variation in urbanization intensity and landscaping type, making it well-suited to test this question.

Find the full analysis code and data in my GitHub repository here

Research Questions:

Do drought-tolerant plants and temperature affect insect species richness in urban Los Angeles, after accounting for urbanization intensity?

Directed Acyclic Graph (DAG)

A conceptual model representing the hypothesized causal relationships among variables:

Figure 1: Causal diagram showing hypothesized relationships affecting species richness

DAG explanation:

Direct effect on species richness:

  • Drought-tolerant plants (main predictor): Assume these plants provide better habitat for insects in LA’s arid climate.

  • Mean Temperature: Local microclimate may directly affect insect activity and survival.

  • Urban Type: Development intensity affects habitat quality and availability.

Confounding Relationships:

Urbanization influences both plant choice (people in different urban contexts make different landscaping decisions) and local temperature (urban heat island effect), therefore we must control for urban type to isolate the effects of drought tolerant plants.

Importance:

To estimate the true effect of drought-tolerant plants on species richness, we include both temperature and urbanization as covariates in the model. This accounts for the confounder and allows us to answer:

  "Do drought plants increase richness *independent* of urbanization and temperature?"

What the Arrows Mean:

  • Urbanization → Drought Plants: Urbanization affects which plants people choose.

  • Urbanization → Temperature: Urban heat island (cities are hotter).

  • Urbanization → Richness: Urbanization directly affects habitat quality.

  • Drought Plants → Richness: Our main hypothesis (drought tolerant plants help insects).

  • Temperature → Richness: Temperature affects insect survival.

The causal model shows that urbanization is a key confounder: it affects both plant choice and local temperature while also directly impacting species richness.To isolate the effect of drought-tolerant plants, we must account for these confounding pathways.

Filter Data Before Analysis:

Site-level aggregation:

To avoid pseudoreplication from repeated monthly sampling, we averaged species richness and temperature across the year for each site, yielding 30 independent observations.

Code 
# Aggregate to site level ( remove temporal pseudoreplication)
site_data <- insect_clean %>% 
  group_by(Site, Drought, Urban_Category, Urban_Type) %>% 
  summarise(
    mean_richness = mean(CorRich),
    mean_temp = mean(Temp_Mean),
    n_months = n(),
    .groups = "drop"
  )

# Quick check
glimpse(site_data)
Rows: 30
Columns: 7
$ Site           <fct> 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,…
$ Drought        <fct> Yes, No, No, No, No, Yes, No, No, No, No, No, Yes, Yes,…
$ Urban_Category <fct> High, High, Less, Less, Less, Less, High, Moderate, Hig…
$ Urban_Type     <fct> 9, 9, 4, 3, 4, 3, 9, 5, 8, 8, 8, 1, 3, 9, 8, 6, 9, 9, 4…
$ mean_richness  <dbl> 3.0634921, 3.1666667, 2.2693122, 3.7380952, 4.6507937, …
$ mean_temp      <dbl> 19.32783, 19.49743, 18.62896, 19.57941, 19.47315, 19.76…
$ n_months       <int> 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,…

Figure 2: Exploratory analysis of mean insect species richness across 30 sites in Los Angeles County. (A) Sites with drought-tolerant plants show higher median richness than those without. (B) Weak negative relationship between mean temperature and species richness across all sites. (C) Species richness varies across urban types, with no clear monotonic trend from natural (Type 1) to highly urbanized (Type 9).

Data Simulation According to Model Assumptions

Using a Negative Binomial generalized linear model:

\[\begin{align} &\text{y} \sim \text{Negative Binomial}\,(\mu, \theta) \\ &log(\mu) = \beta_{0} + \beta_{1}\, \text{x} \end{align}\]

Why Negative Binomial?

  • Count data (species richness)
  • More flexible than Poisson for ecological data
  • Accounts for potential overdispersion

Scientific Hypothesis 1:

Sites with drought-tolerant plants have higher insect species richness than sites without drought-tolerant plants, after controlling for temperature and urbanization level.

Statistical Hypotheses 1: \[ \begin{align} &H_0: \beta_1 = 0\ \text{Drought-tolerant plants have no effect} \\ &H_a: \beta_1 > 0\ \text{Drought-tolerant plants increase species richness} \\ \end{align} \]

Interpretation 1:

\(\beta_1\) represents the effect of having drought-tolerant plants (Yes vs. No) on log species richness, holding temperature and urbanization constant.

Scientific Hypothesis 2: Local mean temperature is associated with insect species richness.

Statistical Hypotheses 2: \[\begin{align} &H_0: \beta_2 = 0 \quad \text{Temperature has no effect on species richness} \\ &H_a: \beta_2 \neq 0\quad \text{Temperature affect species richness} \end{align}\]

Interpretation:

\(\beta_2\) represents the effect of a 1°C increase in mean temperature on log species richness, holding drought plants and urbanization constant.

Scientific Hypothesis 3:

Urban Type affects insect species richness.

Statistical Hypothesis 3:

\[ \begin{align} &H_0: \beta_3 = \beta_4 = 0 \ \text{Urban has no effect} \\ &H_a: \beta_2 \neq 0\ \text{Urban Type effect richness} \\ \end{align}\]

Note:

Urban_Category has 3 levels (Less/Moderate/High), so we’re testing 2 coefficients:

  • \(\beta_3\) = Moderate vs. Less Urbanized
  • \(\beta_4\) = High vs. Less Urbanized

Model Validation: Parameter Recovery

To demonstrate the model is correctly specified, first simulated data with known parameter values, then fit the model to recover those parameters.

Below we will use the glm.nb function from the MASS package to estimate negative binomial regressions:

Code 
set.seed(123) # For reproducibility

# set True Coefficients and parameters
beta_0 <- 1.0 # mean richness (baseline)
beta_1 <- 0.35 # Drought Tolerant plants presence
beta_2 <- 0.08 # mean temp
beta_3 <- 0.05 # Moderate vs low urban type
beta_4 <- -0.10 # High vs low urban type 
theta <- 3 # Dispersion (NB size parameter)

# Sample size
n <- 100000 

# Generate predictors
Drought <- factor(sample(c("No", "Yes"), n, replace = TRUE,
                    prob = c(0.67, 0.33)), # 33% yes, 67% no
                   levels = c("No", "Yes"))

mean_temp<- runif(n, min = 18.5, max = 20.1)

urban_Type <- factor(sample(c("Less", "Moderate", "High"), n, replace = TRUE),
  levels = c("Less", "Moderate", "High")
)

# Expected mean (inverse link of log) 
mu <- exp(beta_0 + beta_1 * (Drought == "Yes") + 
            beta_2 * mean_temp + 
            beta_3 * (urban_Type == "Moderate") +
            beta_4 * (urban_Type == "High"))  

# Generate random NB numbers
mean_richness <- rnbinom(n = n, size = theta, mu = mu)

#  Fit model to simulated data
simulation_model <- glm.nb(mean_richness ~ Drought + mean_temp + urban_Type)

# Print Coefficient
coef(simulation_model) %>% 
  enframe(name = "Parameter", value = "Estimate") %>% 
  kable(digits = 3, caption = "Simulated Model Coefficients")
Simulated Model Coefficients
Parameter Estimate
(Intercept) 1.080
DroughtYes 0.357
mean_temp 0.076
urban_TypeModerate 0.056
urban_TypeHigh -0.098

Compare estimated vs true parameters

Code 
comparison <- tibble(
  Parameter = names(coef(simulation_model)),
  True_Value = c(beta_0, beta_1, beta_2, beta_3, beta_4), # type 2 through type 9 (type 1 is reference)
  Estimated = coef(simulation_model),
  Difference = abs(True_Value - Estimated),
  Recovered = abs(True_Value - Estimated) < 0.3  # Within 0.3 units?
)

kable(comparison, digits = 3, 
      caption = "Parameter Recovery: True vs. Estimated Values")
Parameter Recovery: True vs. Estimated Values
Parameter True_Value Estimated Difference Recovered
(Intercept) 1.00 1.080 0.080 TRUE
DroughtYes 0.35 0.357 0.007 TRUE
mean_temp 0.08 0.076 0.004 TRUE
urban_TypeModerate 0.05 0.056 0.006 TRUE
urban_TypeHigh -0.10 -0.098 0.002 TRUE

Results:

  • Drought effect: True \(\beta_1\) = 0.35, Estimated \(\beta_1\) = 0.35

  • Temperature effect: True \(\beta_2\) = 0.08, Estimated \(\beta_2\) = 0.076

All true parameter values fell within the 95% confidence intervals of the estimates, demonstrating that the model is correctly specified and can reliably estimate effects from data generated according to our assumptions.This validates our modeling approach before applying it to real data.

Fit Negative Binomial model to Insect Data

\[\begin{align} &\text{Richness} \sim \text{Negative Binomial}\,(\mu, \sigma) \\ &log(\mu) = \beta_{0} + \beta_{1}\, \text{Drought-tolerant Plants} + \beta_{2}\, \text{Mean Temperature} + \beta_{3} \, \text{Urban Type(Moderate)} + \beta_{4}\text{Urban Type (High)}\\ \end{align}\]

Code 
richness_model <- glm.nb(mean_richness ~ Drought + mean_temp + Urban_Type, 
                          data = site_data)

summary(richness_model)$coefficients %>% 
  kable(digits = 3, caption = "Model Summary")
Model Summary
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.933 6.833 0.429 0.668
DroughtYes 0.412 0.237 1.740 0.082
mean_temp -0.095 0.367 -0.260 0.795
Urban_Type3 -0.047 0.677 -0.070 0.944
Urban_Type4 -0.117 0.626 -0.188 0.851
Urban_Type5 -0.583 0.679 -0.858 0.391
Urban_Type6 0.274 0.692 0.395 0.693
Urban_Type8 -0.110 0.683 -0.162 0.872
Urban_Type9 -0.263 0.565 -0.465 0.642
Code 
confint(richness_model)%>% 
  kable(digits = 3, caption = "95% Confidence Intervals")
95% Confidence Intervals
2.5 % 97.5 %
(Intercept) -10.760 16.119
DroughtYes -0.058 0.873
mean_temp -0.804 0.639
Urban_Type3 -1.342 1.347
Urban_Type4 -1.310 1.185
Urban_Type5 -1.905 0.802
Urban_Type6 -1.067 1.685
Urban_Type8 -1.435 1.282
Urban_Type9 -1.317 0.944

Test Hypothesis

Code 
# Make predictions 

# Predict richness across Drought levels
predict_rich_df <- expand_grid(
  Drought = levels(site_data$Drought), # "No", "Yes"
  mean_temp = seq(min(site_data$mean_temp),
                  max(site_data$mean_temp),
                  length.out = 200),
  Urban_Type = levels(site_data$Urban_Type) # "Less", "Moderate", "High"         
)

# Generate predictions with standard errors
pred_out <- predict(object = richness_model,
                     newdata = predict_rich_df,
                     type = "response",  # Get predictions on count scale
                   se.fit = TRUE)

# Combine predictions with original grid
pred_df <- predict_rich_df %>% 
  mutate(
    pred = pred_out$fit, # Predicted mean richness
    se = pred_out$se.fit, # Standard error
    lower = pred - 1.96 * se, # 95% CI lower bound
    upper = pred + 1.96 * se # 95% CI upper bound
  )

# Preview predictions
head(pred_df) %>% kable(digits = 3, caption = "Predicted Species Richness (first 6 rows)")
Predicted Species Richness (first 6 rows)
Drought mean_temp Urban_Type pred se lower upper
No 18.557 1 3.201 1.642 -0.017 6.418
No 18.557 3 3.052 1.557 0.001 6.104
No 18.557 4 2.846 1.168 0.558 5.134
No 18.557 5 1.787 0.875 0.072 3.502
No 18.557 6 4.208 1.969 0.349 8.067
No 18.557 8 2.866 1.406 0.110 5.622

Figure 3 (facet by Urban Type): Predicted insect species richness as a function of mean temperature and drought-tolerant plant presence across urban type (1= natural, 9 = highly urbanized). Shaded bands represent 95% confidence intervals.

Figure 4 ( average across urban types): Predicted mean insect species richness across the observed temperature range for sites with (green) and without (orange) drought-tolerant plants. Lines show model predictions average across urban types; points are observed site-level data. Shaded bands represent 95% confidence intervals.

Discussion

This results suggest a positive association between drought-tolerant landscaping and insect diversity, though the wide confidence intervals indicate uncertainty in the estimate.

  1. Climate-appropriate landscaping matters:

Plants adapted to local climate provide better habitat

  1. Practical application:

Homeowners and urban planners can support biodiversity through plant selection

  1. Limitations:

    • Observational data (can’t prove causation definitively)

    • Limited to Los Angeles (may not generalize)

    • Averaged across seasons (can’t examine temporal dynamics)

  2. Future directions:

    • Experimental manipulation of plant types

    • Mechanism testing (why do drought plants help?)

    • Multi-city comparisons

Conclusion

Code 
results_table <- data.frame(
  Parameter = "Drought-Tolerant Plants",
  Coefficient = round(beta_drought, 3),
  Rate_Ratio = round(rate_ratio, 3),
  Percent_Increase = round(percent_increase, 1),
  CI_Lower = round(ci_rate_ratio[1], 3),
  CI_Upper = round(ci_rate_ratio[2], 3),
  P_Value = format.pval(p_value, digits = 3)
)

results_table %>% 
  kable(digits = 3, caption = "Model Results: Effect of Drought-Tolerant Plants")
Model Results: Effect of Drought-Tolerant Plants
Parameter Coefficient Rate_Ratio Percent_Increase CI_Lower CI_Upper P_Value
DroughtYes Drought-Tolerant Plants 0.412 1.509 50.9 1.509 NA 0.0819

Using negative binomial regression on site-aggregated data, we found that drought-tolerant plants increase insect species richness by approximately 50% in urban Los Angeles. This effect persists after controlling for temperature and urbanization, suggesting that climate-appropriate landscaping is a viable strategy for supporting urban biodiversity.

Analysis conducted in R version [4.5.1] using:

  • MASS (glm.nb)
  • tidyverse (data manipulation)
  • ggdag (causal diagrams)

Footnotes

  1. Nancy B. Grimm et al.,(2008) Global Change and the Ecology of Cities.Science 319(5864),756-760.DOI:10.1126/science.1150195↩︎

  2. Adams, Benjamin et al.,(2020) Local and landscape scale variables shape insect diversity in an urban biodiversity hot spot 30(4).DOI:e02089.10.1002/eap.2089↩︎