In the limit as p goes to 0, log(p) goes to -infinity. The Shannon-Wiener terms are equal to p*log(p) and 0*(-infinity) is defined as 0, which goes along with intuition, no species would have to be zero diversity.
************************************************************* Robert Matlock Assistant Professor Department of Biology CSI/CUNY 2800 Victory Boulevard Staten Island, NY 10314 718-982-3869 Fax 718-982-3852 -----Original Message----- From: Ecological Society of America: grants, jobs, news [mailto:[email protected]] On Behalf Of Maria Van Dyke Sent: Thursday, July 16, 2009 5:39 PM To: [email protected] Subject: [ECOLOG-L] Shannon-Wiener Div Index Question - dealing with zero species per plot?? Dear ECO loggers, I have a question about utility of the Shannon-Wiener diversity index in regards to sampling units that have no species in them at a given sampling time. Normally this would get a value of zero, however with Shannon-Wiener a sampling unit that has only one individual of one species would also earn the value of zero when input into the formula -∑(1*ln1) = -∑(1*0) = 0; therefore there becomes an issue of two different species scenarios having the same values (0 for no species individuals and 0 for 1 ind of one species). For example: I am studying substrate preferences of ground nesting bees in which I created three different substrate treatment types for bees to nest in. In all, I have 20 plots that have the 3 different treatments (subplots) within each plot. I sampled all subplots of all plots 7 times throughout the bee flight season. During some rounds I would collect no bees from a subplot and therefore have no species to calculate diversity from in my data set. How do I deal with these subplots that actually had no (zero) bee species in them? I would use Simpson Diversity instead but I am interested in rare species so I thought it would not be sensitive enough. I know this is somewhat of a strange predicament b/c the data sets that Shannon-Wiener is usually applied to normally have at least one species per plot at the very least but the nature of my study forces me to deal with these true zero values. Has anyone out there had to deal with this before? I am open to any and all suggestions or varying approaches. Is there a better index to use for this analysis? I intend to use the results from diversity to calculate evenness as well. Please enlighten me Maria Van Dyke Department of Environmental Sciences University of Virginia
