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Ecological and anthropogenic covariates ... - GANGAPEDIA

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the effects of <strong>covariates</strong> measured at the site as well spatial continuity across sampling<br />

units or spatial adjacency.<br />

We used Bayesian spatial count regression models for analyzing the effects of two<br />

ecological <strong>covariates</strong> <strong>and</strong> spatial adjacency on habitat-use (encounter-rates). While<br />

frequentist methods treat model parameters as unknown constants, Bayesian analysis<br />

consider them as r<strong>and</strong>om variables (Ellison 1996). The Poisson distribution is the<br />

most natural choice for modeling count data, such as gharial abundance per site.<br />

Although the Poisson model is generally used for abundance, animals may not be<br />

distributed completely r<strong>and</strong>omly in space, <strong>and</strong> as there are a large number of<br />

unoccupied sites (zeros) as well as clusters of animals at other sites.<br />

For site (i), gharial count [i] ~ Intercept + slope * basking site [i] + spatial effect<br />

term[i]<br />

Or gharial count [i] ~ Intercept + slope * depth [i] + spatial effect term[i]<br />

Here, gharial count (site-specific count) is assumed to come from a Zero-inflated<br />

Poisson or Negative Binomial distribution (negative binomial distribution can be used<br />

for clumped data). Intercept <strong>and</strong> slope follow uninformative or flat prior normal<br />

distributions with zero mean <strong>and</strong> low precision (high variance). The zeroes of the<br />

dataset are separately treated as Bernoulli outcomes with a probability p0 for the<br />

proportion of zeroes in the data. The remaining counts are treated as following a<br />

Poisson distribution, with overall mean of counts equal to 1 – prob(zero count) * site-<br />

specific count.<br />

<strong>Ecological</strong> datasets tend to contain a large proportion of zero values (Clarke & Green<br />

1988), <strong>and</strong> such data do not readily fit st<strong>and</strong>ard distributions (e.g. normal, Poisson,<br />

binomial, negative-binomial <strong>and</strong> beta). These are referred to as ‘zero inflated’<br />

20

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