Negative binomial regression model for monitoring rare species data: A case study at Ngorongoro conservation Area-Tanzania

Introduction

The conservation of rare species is a fundamental aspect of biodiversity management, especially in ecologically significant regions such as Tanzania's Ngorongoro Conservation Area. Rare species often exhibit vulnerability to environmental changes, necessitating robust methods to monitor their population dynamics. Traditional models like Poisson regression have been widely used to analyse count data; however, their assumption of equidispersion often fails in ecological contexts where overdispersion is common. In such cases, the Negative Binomial Regression Model (NBRM) provides a more suitable alternative by effectively handling overdispersed count data, yielding more reliable predictions (Hilbe, 2011; Warton & Hui, 2011) [3,7] . Habitat quality plays a vital role in determining species abundance, as it encompasses critical factors such as food availability, shelter, and absence of pollutants. Quantifying habitat quality through indices like the Habitat Quality Index (HQI) has proven to be an effective approach in ecological studies. Recent research underscores a positive relationship between HQI and species abundance, emphasizing the importance of habitat restoration and management in conservation efforts (Zhang & Ma, 2021; Lasway et al., 2022) [6, 5] . On the other hand, habitat fragmentation remains a significant threat to biodiversity conservation. Fragmentation disrupts continuous habitats, isolates populations, and hampers genetic exchange, often leading to reduced species abundance. Studies have shown that increased habitat fragmentation correlates negatively with species abundance, highlighting the necessity for strategies to mitigate its ecological impacts (Haddad et al., 2015; Fahrig, 2003) [2,1] . In Tanzania, integrating scientific approaches with community-based conservation has been pivotal. For instance, Kidegesho (2016) highlights the need for balancing conservation objectives with local livelihoods, particularly in regions facing human-wildlife conflicts. Such integrated efforts are crucial for maintaining the ecological integrity of areas like Ngorongoro, which host rare and endangered species.

This study utilizes the Negative Binomial Regression Model to evaluate the effects of habitat quality and habitat fragmentation on the abundance of rare species. By integrating continuous measures of habitat quality and fragmentation, this research aims to provide insights into the factors influencing rare species populations, thus offering practical guidance for conservation strategies in the Ngorongoro Conservation Area and similar ecosystems.

Literature Review

Monitoring rare species is a critical aspect of biodiversity conservation, particularly in regions with unique ecosystems. Rare species often exhibit sensitivity to environmental changes, necessitating robust statistical approaches for population monitoring. Traditional methods, such as Poisson regression, are limited by their assumption of equidispersion, where the mean equals the variance. Negative Binomial Regression has been widely recognized as a superior alternative in cases of overdispersion, as it allows for more accurate modelling of ecological count data (Hilbe, 2011; Brooks et al., 2019) [3,8] . Habitat quality is a fundamental determinant of species abundance. Measures like the Habitat Quality Index (HQI) provide valuable insights into environmental conditions, including resource availability and ecological integrity. Recent studies have established a positive correlation between habitat quality and species abundance, underscoring the importance of habitat preservation in conservation planning (Zhang & Ma, 2021; Thompson et al., 2022) [6,9] . This relationship highlights the need for targeted interventions to improve habitat conditions. Conversely, habitat fragmentation remains one of the most significant threats to biodiversity. Fragmentation isolates populations, disrupts migration corridors, and reduces genetic diversity, ultimately leading to population declines. Several studies have demonstrated the negative impact of fragmentation on species abundance, emphasizing the importance of mitigating fragmentation through sustainable land-use practices (Fahrig, 2003; Haddad et al., 2015) [1,2] . These findings are critical for informing policy and conservation efforts. In Tanzania, the integration of local knowledge with scientific approaches has proven effective in addressing conservation challenges.

Kideghesho (2016) [4] highlights the need for community involvement in mitigating human-wildlife conflicts and fostering conservation-friendly practices. This review underscores the importance of applying advanced statistical tools, such as Negative Binomial Regression, to assess the impact of habitat quality and fragmentation on rare species. By integrating these insights, conservation strategies can be better tailored to address the specific needs of vulnerable populations.

Materials and Methods

Data Type and Sources This study utilized ecological and environmental datasets to assess the relationship between species abundance, habitat quality, and habitat fragmentation in the Ngorongoro Conservation Area, Tanzania. The data were structured to include both response and explanatory variables relevant to the study objectives. The response variable for this study was 'species abundance' derived from field research conducted in collaboration with local conservation authorities and research institutions. These surveys recorded the count of individuals within targeted rare species populations across various ecological zones within the conservation area. Data collection followed standardized protocols to ensure consistency, including transect walks and camera trapping methods, where applicable. For independent variables, two primary data sources were used:

Habitat Quality Index (HQI): The HQI was quantified using geospatial data, ecological indicators, and field-based assessments. Satellite imagery and remote sensing data, sourced from platforms such as Landsat and Sentinel, were processed to evaluate land cover, vegetation density, and other environmental attributes.

Habitat Fragmentation: Data on habitat fragmentation were obtained from land use and land cover maps, derived from high-resolution satellite imagery. A continuous measure of the degree of habitat fragmentation, derived from metrics like patch size, edge density, and connectivity. Values range from 0.5 to 5.0.

Variable Definitions and Measurements

Control Variables Latitude

The geographical latitude of each sampling site, measured in decimal degrees.

Longitude

The geographical longitude of each sampling site, measured in decimal degrees.

Source: Author's construction STATA version 17

Negative Binomial Regression Model

The Negative Binomial Regression Model (NBRM) is one of the common statistical models used for count data and used when data displays overdispersion (i.e., the variance is greater than the mean). In contrast to Poisson regression model that postulates Equi dispersion. The NBRM introduces an extra parameter to deal with overdispersion, making it more robust for modeling ecological and biological data. The NBRM can be expressed as:

Here: 𝑌 𝑖: The count response variable (e.g., species abundance). 𝜇 𝑖: The expected value of 𝑌 𝑖 , which is a function of the predictors. 𝜃: The dispersion parameter that controls the degree of overdispersion. The mean and variance of the negative binomial distribution are:

This linear predictor is obtained from Negative Binomial probability mass function The negative binomial distribution describes the probability of observing 𝑦 𝑖 counts for a given mean (Mi) and dispersion parameter (θ):

Diagnostic test for Negative Binomial Regression Model Overdispersion

The mean should be less than the variance of the count data. This is an important assumption because the negative binomial distribution models this overdispersion, while the Poisson assumes that mean and variance are equal. we evaluate the overdispersion assumption by evaluating the mean and variance of our dependent variable (Species Abundance). As demonstrated by Species Abundance descriptive statistics, the dependent variable (Species richness) is variable across 100 sampled sites. The average is 4.94 (SD 2.38), showing moderate dispersion in number of individual species. Fully recorded abundance minimum = 0; Fully recorded abundance maximum = 11, reflecting the absence of species to high counts at sites. The median is 5, meaning that 50% of the sites had an abundance of 5 or fewer species. Similarly, the 25th and 75th percentiles are 3 and 6, respectively, indicating that 50% of the sites contain considerably more species abundances than this. These statistics help in forming a basic understanding of the data distribution and supporting the appropriate characterization of all the factors influencing the species abundance via Negative Binomial Regression Model.

Descriptive Statistics for Independent and Control Variables

Source: Author's construction STATA version 17

The correlation matrix indicates the level of linear relationship between the independent variables of Habitat Quality Index and Habitat Fragmentation. We should get a low correlation value to have less multicollinearity, meaning both variables independently contributing to the model. This indicates both variables are suited in either of two areas. The table shows the AIC value, which is a measure of the quality of a model, where lower values indicate a model that fits and is parsimonious than alternatives (models with lower AIC values are preferred). The deviance value is a measure of the difference between the observed value, and a predicted value, the smaller the number the better the fit to the data. The above-mentioned metrics are the pointers that indicate the Negative binomial regression model is the apt model to be used and also it does so as the model performs as well with these metrics. Intercept: The intercept is the expected log species abundance when all other independent variables are zero. A notable intercept represents a minimum threshold of species abundance without influential factors from habitat quality and fragmentation. Habitat Quality Index (X1) The coefficient for Habitat Quality Index represents the log change in species abundance attributed to a one-unit increase in habitat quality. A positive and substantial coefficient supports that better habitat quality explained higher species abundance. Habitat Fragmentation (X2): The coefficient for Habitat Fragmentation represents the log change in species abundance corresponding to a one-unit increase in fragmentation A negative and significant. The negative coefficient indicates that allowing more fragmentation leads to lower levels of species abundance. This outcome is presented in the data on 'Negative Binomial Regression Model': the relationship between species abundance (dependent variable) and the predictors, Habitat Quality index and Habitat Fragmentation. The model indicates that increased habitat quality leads to higher species abundance, and, conversely, that more fragmentation can be negatively correlated with species abundance. Goodness-of-fit statistics (e.g., AIC, deviance) reveal satisfactory fitting of the model to data, considering an overdispersion typical of ecological counts.

Model Goodness-of-Fit Results

Results for Link Function

Discussion of the findings Intercept

The intercept represents the expected log count of species abundance (the response variable), when all predictor variables equal zero, in the Negative Binomial Regression Model. This is because in this study the intercept is statistically significant, showing that the species abundance has a baseline value despite the effects of habitat quality and fragmentation. Essentially, this is the absence of influence of the predictors, and with this, we can understand how magnitude of change in the predictors influence species abundance.

Habitat Quality Index (X1):

The coefficient for Habitat Quality Index is positive and statistically significant, indicating that a higher habitat quality is correlated with greater abundance of species. Five of the 12 articles represent classic studies of responses by birds and butterflies to habitat quality, a quality that is widely recognized as essential to the protection of biodiversity. Mortelliti et al. Such as the study of (2010), which showed that in fragmented landscapes, the quality of patches plays a critical role in determining the dynamics of distribution and abundance of various species. This increase could be due to more suitable resources and environmental conditions for species survival and reproduction.

Habitat Fragmentation (X2)

These results show a statistically significant negative coefficient for Habitat Fragmentation implying that with an increase in habitat fragmentation, we will be getting a drop in the species abundance. This result aligns with research emphasizing the negative impact of habitat fragmentation on biodiversity. Habitat Fragmentation Reduction of species abundance and diversity at a landscape level can be caused by habitat fragmentation that is the outcome of anthropic actions or natural processes; Fahrig (2003) [1] highlighted that an habitat fragmentation cannot permit viable populations to ensure in less patches of smaller size. Fragmentation may alter movement patterns, restrict access to resources, and make species more susceptible to risks from external sources, all of which are detrimental to species abundance.

Model Fit and Implications

With a low Akaike Information Criterion (AIC) and deviance among the goodness-of-fit metrics, the model shows a strong fit to the data, thereby reinforcing the model's suitability for analysing over dispersed count data, as is common in ecology studies. This justifies and affirms the applicability of the Negative Binomial Regression Model in modelling the associations between habitat variables and species abundance. The results highlight the importance of maintaining high quality habitats and avoiding fragmentation to sustain species abundance.

Conclusion

This study reveals how much habitat conditions promote species abundance in the Ngorongoro Conservation Area. Higher habitat quality, which involves better ecological resources and fewer disruptions, contributes greatly to more species in an area, while habitat fragmentation reduces species abundance through its negative ecosystem impacts. Compared to other models, the Negative Binomial Regression Model was appropriate and could effectively solve the problem of overdispersion, which yielded true observations of species and predictors. The findings underscore the role of habitat integrity and connectivity in supporting biodiversity. Overall, this study emphasizes the ecological dynamics that influence species populations, providing a basis from which targeted conservation strategies and long-term management of biodiversity can be guided.

Recommendations

In response to the aforementioned threats habitat restoration and management effectively improving vegetation cover, protecting essential resources, and reducing anthropogenic degradation should be prioritized when convening conservation initiatives. Habitat fragmentation can be minimized by developing ecological corridors and implementing sustainable land-use practices that support habitat connectivity and resilience. Long term biodiversity monitoring programs should be established to monitor trends in abundance of species and health of species habitats, allowing adaptive management approaches. Communities must educate themselves and become engaged in local efforts regarding conservation so key stakeholders are supportive of conservation priorities, which policymakers can support by implementing additional land-use regulations and economic incentives to protect natural habitats. These strategies remain generic and they could be refined by expanding research to other regions or by incorporating climate variables.

Area for further Studies

Further studies should be done in advanced statistical techniques to further refine the analysis of species abundance in relation to habitat variables. For applying statistical methods like Bayesian hierarchical models that could provide a robust framework for including spatial and temporal variability, accounting for uncertainty in parameter estimates. Furthermore, integrating Generalized Additive Models (GAMs) might allow for non-linear relationships between habitat predictors and species abundance, unveiling complex ecological dynamics.

References

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