ECS 111 Homework Problems January 2018 1) Choose a region (state, province, part of a country or country) and discuss their carrying capacity relative to Lester Brown’s three factors. Include the constraint in terms of the current populations and future population trends. 2) Describe the various ways that water is used as an ecosystem service. How do these uses impact ecosystem function? Provide examples. 3) Discuss examples of soil loss and their causes. How can these be tied to population transitions in human civilizations? 4) What is meant by population transition? Briefly describe the recent changes in human populations and the driving factors involved. Historically what other transitions have occurred? Is this a constant process or have there been periods with larger changes? What has the role of technology played in different population transitions? 5) If births (b) are influenced by population density (N) such that b = bo - N, and deaths (d) by d = do + N rewrite the equation for population change dN/dt = (b=d) N as a logistic equation dN/dt = r N (1 – N/K). What are the r and K terms in terms of b and d? 6) The current turmoil in the Middle East is causing sharp transitions in populations and a great deal of environmental damage. Summarize the recent history of these events and the social economic problems behind them. Include an explicit discussion of demographics of the situation. 7) The western United States is currently experiencing a prolonged drought. It is especially severe in California.Write a short essay focusing in on one aspect of the situation. For example, one might discuss the impact this is having on a particular food such as almonds or a commodity such as cotton. Another topic might be wild fires. ECS 111 Spring 2018 Dr. Olson Writing Tips for Homework: Homework and rewrites of test questions will be graded primarily based on the scientific and analytical content of the work. This includes an adequate use of citations to appropriate literature, use of appropriate analytical tools including proper introduction and explanation of equations and calculations used to consider the problems, a concise discussion of the conclusions of the work. Homework assignments are considered part of your own work and therefore should not include material copied from other sources. To do so is plagiarism and will be grounds for disciplinary action. Below the basic formats expected and some guidelines for layout of assignments are outlined. References: Appropriate references are typically considered to stem from juried (reviewed) literature. This means that the work should have been reviewed and published in scientific or engineering journals. Citing textbooks is allowed when documenting well known techniques and or solutions to specific mathematical problems. In general, it is not appropriate to quote a text book when the object is to refer to a specific piece of work in the juried literature. Instead it ...

1. ECS 111 Homework Problems January
2018
1) Choose a region (state, province, part of a country or
country) and discuss their carrying capacity relative to Lester
Brown’s three factors. Include the constraint in terms of the
current populations and future population trends.
2) Describe the various ways that water is used as an ecosystem
service. How do these uses impact ecosystem function? Provide
examples.
3) Discuss examples of soil loss and their causes. How can
these be tied to population transitions in human civilizations?
4) What is meant by population transition? Briefly describe the
recent changes in human populations and the driving factors
involved. Historically what other transitions have occurred? Is
this a constant process or have there been periods with larger
changes? What has the role of technology played in different
population transitions?
5) If births (b) are influenced by population density (N) such
that b = bo - N, and deaths (d) by d = do + N rewrite the
equation for population change
dN/dt = (b=d) N
as a logistic equation
dN/dt = r N (1 – N/K).
What are the r and K terms in terms of b and d?
6) The current turmoil in the Middle East is causing sharp
transitions in populations and a great deal of environmental
damage. Summarize the recent history of these events and the
social economic problems behind them. Include an explicit
discussion of demographics of the situation.

2. 7) The western United States is currently experiencing a
prolonged drought. It is especially severe in California.Write a
short essay focusing in on one aspect of the situation. For
example, one might discuss the impact this is having on a
particular food such as almonds or a commodity such as cotton.
Another topic might be wild fires.
ECS 111 Spring 2018
Dr. Olson
Writing Tips for Homework:
Homework and rewrites of test questions will be graded
primarily based on the scientific and analytical content of the
work. This includes an adequate use of citations to appropriate
literature, use of appropriate analytical tools including proper
introduction and explanation of equations and calculations used
to consider the problems, a concise discussion of the
conclusions of the work. Homework assignments are considered
part of your own work and therefore should not include material
copied from other sources. To do so is plagiarism and will be
grounds for disciplinary action. Below the basic formats
expected and some guidelines for layout of assignments are
outlined.
References: Appropriate references are typically considered to
stem from juried (reviewed) literature. This means that the work
should have been reviewed and published in scientific or
engineering journals. Citing textbooks is allowed when
documenting well known techniques and or solutions to specific
mathematical problems. In general, it is not appropriate to quote
a text book when the object is to refer to a specific piece of
work in the juried literature. Instead it the original work should
be cited. A text may be cited when it provides an overview of
an entire field. The discussion should still quote the individual
works that are pertinent to the discussion in the homework. A
final note on textbooks is that they are usually out of date,

3. therefore the newest juried literature is the place to start on
homework.
When providing a reader with a reference list a good “rule of
thumb” is to quote the most up to date references on the topic, a
few of the major contributions on the issues, and the original
work on the problem. Be explicit in discussing the role of each
of the works cited in framing the conclusions in your paper.
This is very important in documenting what you have added to
our understanding of the problem with your own analysis. In
other words carefully documenting what you have added.
Citations should appear in the text. While modern word
processing has made it easy to use footnotes, you should use the
authors’ names and the date for their work in the text. Single
authors should appear as Smith (2001) if you are discussing the
work outright in the sentence. If the citation is just to provide a
source for further research by the reader, the citation usually
appears at the end of the discussion as (Smith, 2001). In
general, in scientific papers page numbers are not given in the
text. For two authors, both are provided, i.e. Smith and Jones
(2008). For three or more authors make use of the Latin et al.,
i.e. Jones et al. (2010). Again these should be worked into the
narrative when you are actually discussing a work or placed in
parenthesis if you are just supplying references for the reader to
go to for further information.
The reference section of your work should provide the reader all
the information needed to find the work. In science the common
widely used style is that of the American Chemical Society.
There are a number of other formats also. Typically one must
conform to a specific style of reference to comply with specific
journals for publication. The important issue is to be consistent
with a specific style. In the literature there are various
templates for references. Any will be accepted for homework as
long as they are consistently followed. Here are a set of
examples:
Haywood, A.M., P. J. Valdes, and B. W. Sellwood. 2000.
Global scale paleoclimate reconstruction of the middle Pliocene

4. climate using the UKMO GCM: Initial results. Global and
Planet. Change, 25, 239-256.
Fiedler, P. C. and L. P. Talley 2006. Hydrography of the eastern
tropical Pacific: A review. Prog. Oceanogr., 69, 143-180.
Mullen KM, Peters EC, Harvell CD 2004. Coral resistance to
disease. In: Rosenberg E, Loya Y (eds) Coral Health and
Disease. Springer, New York, pp 377-399
Greenspan, H. P. 1969. The Theory of Rotating Fluids.
Cambridge Uni. Press., London, 328 pp.
Darwin, C. 1890. Coral Reefs, Volcanic Islands, South
American Geology. Bettany ed., Ward, Lock and Co. G. T.
London, pgs 312-318.
Note here the first two are juried articles. The journal titles area
abbreviated and the citations includes the volume number and
page numbers for the articles. Author lists include all of the
authors and their initials. The Mullen article is in a book and
therefore includes the editors in the citations (eds). The last two
are also books, but involve single authors who are responsible
for the publication and therefore there is not mention of an
editor. The Greenspan book just lists the total number of pages.
The Darwin citation involves a long book without an index.
Therefore the page numbers for the specific quotation are given.
The books also list the publisher and the city where they were
published. This is particularly important for the Darwin quote
since his writings are voluminous and this is not an easy book
to find.
Using the Internet and the Library: The Internet is a very
powerful tool, that along with word processing, makes it far
easier to complete academic work than in the past. That said, it
is very easy to be lead astray by bogus information found on it.
The ephemeral nature of material on line and the tendency for
old information to hang on for years, make the Internet a
problematic in terms of proper referencing. This is an issue that
has seen considerable debate within the scientific publishing
community. In general, sources from the juried literature should
be used as much as possible. There are some data sets, however,

5. that can only be accessed through the Internet. These should be
fully documented including the agency source and the date of
the product, plus the date when it was retrieved. This should
allow a reader sometime in the future to find the data. The two
important dates also allow checks on data recalls and
modifications over time to data bases.
In terms of other uses of the Internet, a good way to start on a
project is to “surf the web.” While this may not provide the
reference material that is required in the final product, it does
do a good job of opening up information on problems. Sources
such as Wickipedia are fine for getting basic definitions. Most
of their offerings also contain useful references to get start with
the literature. Google and other search engines are also useful.
In general it is better to use Google Scholar. Services such as
the Web of Science and Web of Knowledge are also good places
to start. Most University libraries are equipped to facilitate the
development of references for a project. In particular, there is
access to most of the juried literature through E-Journals. The
library also has excellent citation services and topic search
capabilities. The citation indices are particularly useful in
chasing down references on a topic by just checking on authors
that have cited a work you have already found.
Writing Essays and Homework problems: In general in
scientific writing it is typical to use third person as
demonstrated in this manual. The present tense should also be
used for everything that exists in the present. These include data
sets, manuscripts themselves, and the work of authors even if
they are deceased. Actions or events that are clearly in the past
should be described using past tense. This being said, some
authors are more comfortable using personal tenses with “I
have…” or “We.” If the student insists on using first person,
the usage should be consistent, i.e. do not switch back and forth
between tenses.
All work should be carefully organized with clear introductions
stating the purpose of the essay or focus of the problem.
Paragraphs should be laid out in a logical order. Typically in

6. scientific and engineering papers this will involve an
introduction, a methods section, a results section and a
discussion and/or conclusion. For mathematics incorporated into
papers see the following sections. There is also a discussion on
the use of graphs and charts below.
Writing Mathematics: Many of the problems for homework in
the class involve mathematical calculations or can be done far
more easily using some mathematics. There are two reasons to
include math in a text; the fist is to streamline the discussion in
a concise manner, the second is to explicitly demonstrate a
calculation or provide a derivation or proof. To demonstrate the
use of math to shorten and concisely define concepts consider
the following discussion of what is known as a structured
population problem.
Consider the population of some entity, ,T, G), where the
variables that define are the position in space, and time (t),
and a set of three functions involving the other populations that
the ith population interacts with, , environmental variables, T,
and a state variable containing information, G. Note that
typically these latter variables are also functions of space and
time. These for example could be the temperature field, while
G might denote population genotypes for organisms or design
templates for built structures such as bridges. This use of an
equation with the symbol, , designate that is a function of a set
of state variables that can be used to define it in the
independent variables of space and time and the interacting
variables representing its properties and that of its
surroundings. Note that writing out this relation takes far less
space than trying to express the relationships in words. While it
is important to define the variables involved when the equation
is introduced, it is not necessary to reintroduce the definitions
as the problem is discussed further in a text or homework.
This definition of a function and it’s variables also allows direct
access to calculus to derive an equation for . This is
accomplished by expanding the total derivative of
+ .

7. This is an example of expanding the total derivative in terms of
all of the partial differentials that provide responses between
state variables. This is one of the fundamental concepts in
multi-variable calculus.
The second use for math is to carry out computations. There
will be many homework problems set up to allow the student to
practice solving problems. There are also some homework sets
that as the student to derive equations for various situations.
Here a simple example is given. Assume that we are interested
in a simple entity say the total population of a species or the
concentration of a radioactive isotope given as N. The species
population might be given in terms of numbers in total or
numbers per area or volume of habitat. Isotopes can be given in
actual concentrations say μg/ or in some mass or molar
fraction. If these are not variable in space, on environmental
variables such as T, other species, or G-factors, the total
derivative can be completed with respect to time to yield
where here a sink term has been added to indicate mortality or
decay when This is simple to integrate for find a solution for N
in the case where the initial value for N(0) The solution is then
N(t) = .
In many of the problems assigned in class students will not want
to make use of a word processor and can just write them out
with pen or pencil. These should still be laid out carefully with
sentences for discussion of assumptions and variable
definitions. The steps taken in solving the problems should be
explained so that the reader can understand the mathematics that
was carried out. It is important to define the units of all of the
variables introduced. This makes it easier to check the solutions
and make conclusions concerning the computation.
Acknowledgements: This is a good time to start using
acknowledgements in your work. These are typically found at
the end of an article just before the references. In a journal
article this is where collaborators who are not coauthors are
thanked for their contributions. In homework this is also the

8. appropriate place to acknowledge information that you gained
from a lecture, since the lectures are not part of the open
literature that a reader could find in a library or online.
Choosing and Displaying Figures: Like mathematics the careful
use of figures whether they are simple schematics that are
drawn by the author, graphs done from either data or an
equation, or figures taken from other literature, can greatly
simplify and shorten a manuscript. In particular, if a geographic
area is discussed in the text it is common practice to include a
chart showing the area and the particular features or locations
discussed. Students today have many means of producing charts
through resources such as Google Maps or ARC-GIS software.
The former is available free online. The UM library and the
computer labs in MSC and engineering have programs for the
latter. Below is a discussion of choosing figures and the layout
of figure captions.
Fig. 1. Plots comparing the nutricline () in the North Atlantic to
that in the North Pacific. Data are from GEOSECS North
Atlantic stations 26 and 26 and North Pacific GEOSEC station
213. Both oceans have lower surface concentrations than can be
measured using the methods available in 1972. The North
Atlantic, however, has higher concentrations than the North
Pacific beween70 and 200m. Below this the North Pacific has
higher levels at depth exceeding the Atlantic by a factor of two
by 500 m. The water column maximum values for the two
locations are also included on the plot.
Here the data are from the GEOSEC data sets that are available
on line. They were plotted on graph paper by the author. Note
that symbols differentiate the two oceans both in terms color
and shape, read circles versus blue squares. The figure caption
includes all of the material that is needed to understand the
graphs. The axes and units are given in the graphic itself. The
material in the caption should not just repeat the discussion in
the text. The same is true in reverse, i.e. put the full description
of the graph in the caption, not in the text.

9. The second figure, Fig. 2, is taken from a publication by Walsh
(1983) and was redone to combine two of that author’s figures
into a single panel. This was republished in The Sea Vol. 12 by
the author (Olson, 2001). Since the figure was redone by the
author it was not necessary to obtain permission from the
previous publisher, although the work of Walsh (1983) was
quoted in the figure caption and in the discussion surrounding
the figure in the Olson (2001) text. . Figures used straight from
other publications can be used in homework with proper
attribution as to source.