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Quantitative
Conservation of Vertebrates
Electronic Companion
Michael J. Conroy
University of Georgia
Athens,
GA 30602, USA
John P. Carroll
University of Georgia
Athens, GA 30602, USA
INTRODUCTION
Our purpose in preparing this Companion
is to provide a complementary resource to our book, “Quantitative Conservation
of Vertebrates.” The material in this
Companion is provided both as a stand-alone CD accompanying our book, as well
on a website that we will maintain at the University of Georgia. If you are
using the CD, you may wish to periodically check the website, since we will
provide period updates and additions beyond the CD material.
The format here is “hypertext” meaning
that you will be able to link to locations throughout the document, as well as
to external links on the World Wide Web, simply by clinking on the colored,
underlined text. For example, this link
takes you to the website maintained for the Companion at the University of
Georgia.
Before we get into the detailed examples
that we cover in the book, we would like to be sure that all readers have at least
a basic familiarity of some simple but important tools. Readers who area already familiar with these
topics may wish to skip to the next section.
BASIC TOOLS FOR MODELING
Using spreadsheets for modeling and displaying data
Many of the examples in our Companion
depend on spreadsheet programs. A “spreadsheet” is simply
a two-dimensional form used for entering and storing numbers, text, and calculations;
often several spreadsheets are contained in the same file, which (depending on
the application) may be called a “workbook”.
We designed most of our examples based on Microsoft Excel,
but many other worksheet programs exist, including Quattro,
Lotus,
and a free web version called Google docs.
Here we give a brief tutorial on using a
spreadsheet for data entry and calculations. The examples will be based on
Microsoft Excel, so users of other program may have to modify to suit their
specific applications.
First,
we need to know some basic ‘directions’ in the spreadsheet. We will take simple data example
to illustrate. Open this file and notice
that there are two columns, labeled ‘year’ (column A) and ‘N’ (column B). In the spreadsheet, all data or other entries
are in cells, and the cells are
labeled by their row (1, 2, 3,……) and column (A, B, C, D). So for instance ‘A1’
is the label ‘year’, ‘A2’, is ‘0’, ‘B2’ is ‘100’, and so on. Go to a cell
outside the range where data are entered and type ‘=B2’ (without the quotes);
you should see displayed ‘100’. This is
saying that the whatever value occurs in cell B2 will also occur in the cell
where you typed ‘=B2’. This device
winds up being very useful for creating models, as we will see shortly.
References
like ‘A1’, ‘B2’, etc. are known as 'relative
cell references', because if you copy or move cells from one location to
another the reference goes with the copy to the new location. So for example if
you refer to 'A4' in an equation, and then copy the contents of that cell to
another location, (say 'P9') the equation will now refer to the new location.
We can see how this works with a quick example. Go to C3 and enter ‘=B3-B2’
(again, without the quotes). The cell
should display ‘100’, the difference in the values of B3 (200) and B2
(100). Now copy (click and drag) cell C3
down the page to C12. The values
displayed should now reference the differences between B3 and B2, B4 and B3, B5
and B4, etc. That is, the relative
reference is “this cell value minus the previous one”. This is often what we will want to do in
programming, as a simple example will illustrate in a minute.
Another
type of reference is an 'absolute cell
reference’, denoted by '$A$1', '$B$2' etc. Here the reference stays fixed
to the original cell location regardless of copying, etc. Again, relative cell
references handy when trying to repeat a calculation in different rows or columns,
as is common in iterative procedures like our modeling. On the other hand if
you always want the reference to stay put to the same cell, use the absolute
cell reference. This might include cases where the cell takes on a fixed value
such as parameter in a model; however, in these cases we will used named
variables. We will explain how these work shortly.
Ok,
go to the next spreadsheet showing
logarithmic growth data, and look in column 'A'. Keep your eye on the equation
box (after the '=' sign). In the top row, nothing is happening: just labels for
time and abundance. Go down to A2. This just contains the first time period,
which is zero. In A3 things are more interesting: '=A2+1'. This expression
tells the program (yes, it's a program) to 'take the contents of cell A2 and
add 1'. This repeats all the way down the column to time 21 (we could have kept
going but my mouse finger ran out). Now, this is sort of a model, but a trivial
one: we are just counting by ones. We could have typed all these numbers in by
hand, but by copying cell A3 to the other cells, we saved ourselves the work.
We used some of the time saved to continue to work on the novel we are writing.
Now go to column B. Notice in cell B2 that '=n_0' appears in the equation box,
but '100' appears in the cell. How did this happen? Check out columns G and H.
Here we used named variables.
What we did was go to H2 and H3, go to the menu toolbar and hit 'insert', then 'name' , and then the names that appear in column G (these are both labeled as 'parameters' even though n_0 is really an initial condition, not a parameter). Now whenever we use 'r_max' or 'n_0' in an equation, the equation will pick up the values in H2 and H3, which are 0.1 and 100 now, but could be anything we change them to. Pretty slick, huh? Now let’s see how we used this. Go to B3. The equation box says 'B2*(1+r_max)' This will take our previous value of B2 (100) and multiply it by (1+r_max)=1.10. The result is 110, printed in B3. In B4 we have 'B3*(1+r_max)', etc. Note that this is exactly the same process as expressed in
equation
(1), that is
N(t+1) = (1 + r ) N(t)
is
just coded as
Bn+1=Bn*(1+r_max)
where n is the row number (corresponding to time).
Many
mathematical operations and functions are built into the typical spreadsheet
program. Math operators in Excel in include addition (+), subtraction (-),
multiplication (*), division (/), and exponentiation (^). Functions include natural logarithm (ln), base
10 logarithm (log), exponential function (exp), and square root, to name a few.
So for instance
=exp(B7/B6)+ln(A8/A9)*A10
would yield 182.51 given values in our first spreadsheet.
The second example in the same spreadsheet on exponetial growth illustrates another very typical and desirable feature of spreadsheets: the ease with which basic graphics can be produced. In this example a line graph plotting N versus time (e.g., years) can be built very easily by highlighting the two columns containing data, and then selecting the “chart wizard” and “line”. A bit of editing provides axis labels and other features. We will often display model results graphically, since graphs provide a very quick summary of how models are behaving (e.g., changing over time).
Accessing software via the WWW
Spreadsheet programs (or in some cases,
simple calculations by hand or on a desk calculator) suffice for many of the
examples in the book. However, many problems involve sufficient volumes of
data, complexity of models, or both, so that such simple approaches are no
longer practicable (or even possible). Fortunately, a large suite of software
is available for solving quantitative ecological problems, and many of the most
important analysis packages are freely available over the World
Wide Web,
often accompanied by excellent online documentation.
DETAILED EXERCISES COVERED
IN THE BOOK EXAMPLES
PART I. BASIC CONCEPTS IN SCIENTIFIC INVESTIGATIONS FOR CONSERVATION
Models of population dynamics (Chapter 3)
Applying population models to conservation (Chapter 4)
Basics of study design and analysis (Chapter 5)
PART II. CONSERVATION STUDIES AND MONITORING PROGRAMS
Occupancy/presence-absence (Chapter 7)
Sample counts for abundance estimation (Chapter 8).
Distance sampling for estimating density and abundance (Chapter 9)
Mark-recapture and removal for abundance estimation (Chapter 10)
Estimation of survival from radiotelemetry, nesting success and age distribution (Chapter 11)
Analysis of habitat (Chapter 13)
Species richness and other community parameters (Chapter 14)
PART III. INTEGRATING MODELING AND MONITORING FOR CONSERVATION
Elements of conservation decision modeling (Chapter 15)
Accounting for uncertainty in conservation decisions (Chapter 16)
Learning and
adaptive management (Chapter 17)
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