User:Eli/Sea Otter Analysis
In order to make inferences on movement behaviors, we grouped the 22 observation sites into the 9 regions denoted by the different colors on the map (top right).
The coordinates of the sites and their corresponding regions are here: SeaOtterSiteTable.csv
Estimates of proportions of time spent at sites
Because the sampling efficiency was highly irregular, analysis of seasonal dynamics was performed by allocating proportions of time spent by sea otters at different sites per month pi,site,month. The proportions were estimated by counting the number of resightings, such that
where n represents the number of resightings and i refers to the individual. Thus, an animal sited three times at location A and once at location B was assumed to have split its time 75%-25%. A month was deemed a long enough period to capture multiple sightings (median number of sightings per individual per month was 2.67), but short enough to provide seasonal detail of movements without being overly biased by highly clustered sightings at single locations.
Coastal kilometer projections
Sea otters move along the coast, ranging roughly from the mouth of the Queets River (at 47.5 N, 124.35 W), wrapping around the tip of the Olympic peninsula at Cape Flattery (48.4 N, 124.7 W) back south and east to Clallam Bay (48.25 N, 124.3 W) in the Strait of Juan de Fuca. In order to quantify movements along this range, we chose to project observation onto the coastline. This reduces the dimension of the spatial data to a line and is a better approximates of actual distances traveled by the sea otters than linear displacements, many of which cross land.
Thus, ranges are presented in terms of coastline kilometer beginning at km 0 at the southernmost extent of the range (47.6 N, near the Queets River) and extending to 145.2 km at 142 E near Clallam Bay on the north coast of the peninsula, such that Cape Flattery is located at coastal km 102. The coastal data is based on the CIA World Data Bank II (available here: http://www.evl.uic.edu/pape/data/WDB/) and can be accessed via the "maps" package in R (http://www.R-project.org). The database subdivides this stretch of coastline into 242 segments of mean length 603 m (s.d. 72 m). The projections were obtained by finding the closest point on the coast to each point, usually found by identifying the perpendicular projection in the nearest coastal segment.
(Eli Note: I could illustrate this or go in more detail, but not sure if necessary)
Map of coastal kilometers
Caption: This map shows location of all sea otter resights on the Olympic Peninsula. The red line shows the extent of the coastal kilometer range.
(Eli Note: This figure is more for internal purposes. There is sure to be a better way to make it than R. Note the shift between the sea otter resight data and the actual coastline - what you explained as a Day measurement correction. In my actual analysis I did a real handwavey thing and added 0.02 degrees longitude and 0.005 latitude, just to make it fit better by eye. Not sure what better way there is to correct it, but it doesn't make a big difference in the analysis.)
Sea Otter movement plots
Sea otter movements with coastal kilometer: all data
This figure shows (again for internal use) movements of all 75 tracked sea otters along coastal kilometer against time over the entire range of observations. They are arranged in order of decreasing number of observations (from 123 observation for SO#29 to only 2 observations for SO#03 and SO#055). Darker shades indicate "summer" (from April 1 to October 1), white background indicate "winter". Red lines are males, black are females. Looking through these plots some things really stand out. (A) Almost all of them spend a lot of time at km 60-65 (Cape Alava). (B) many appear to spend somewhat more time in the Strait of JdF in winter than in summer (SO29, SO45, SO18, SO14, SO43 - quite dramatically - and many others) - but at least one (SO09) goes south (near the Hoh river) in the same period. (C) There is a lot of variability between individuals. Some hardly move at all (SO44) while others are all over the place. But most DO seem to have a few (3, 4 or 5) preferred spots. QUANTIFYING THIS STATEMENT WILL BE A GOAL OF THE "SITE-FIDELITY" INDEX.
Sea otter movements discretized according to Site and Season
This figure shows movements of all the sea otters between the discrete sites grouped in "seasonal" intervals. Seasons are defined as: Winter (January through April), Spring (March through June), Summer (July through September) and Fall (October through December). The divisions are based primarily on ease of computation, but monthly temperature and precipitation data (from: http://www-k12.atmos.washington.edu/k12/grayskies/olympics/index.html) suggest that these seasonal divisions do a decent job of separating the three coldest and three warmest months. On the other hand, to patch precipitation data, moving the divisions back one month or even more would make more sense since Nov-Dec-Jan have by far the most rain while Jun-Jul-Aug have the least.
The sites are color-coded going South to North along the y-axis. The height of the rectangles represents the proportional number of times an animal was resighted at a given site during the "season", such that if all observations were at one site (e.g. SO29 in winter and spring of 1995) the boxes are all of full height, whereas if the animal was observed in multiple locations (e.g. SO29 in summer of 1996), the box-heights are accordingly allocated to each site.
(Eli Note: I can make any stylistic or formatting changes desired on any of these box-plots. Let me know. Also, any all plots can be made into .png, .bmp, .jpg format or other. Pdf's usually look best. )
Male-Female range comparisons
Caption: Ranges of male (red tones) and female (green tones) sea otter aggregated ranges. Coastal kilometers are on the y-axis. The pale plots in the background represent the pooled male/female comparison. The darker plots in the foreground represent the age groups (Adult, Sub-adult and Pup). Areas of boxes are proportional to the sample sizes.
Range against Year and Season
Two boxplots showing ranges against (A) year and (B) season. The top plot shows the increasing and gradually northward shifting range of the sea-otters since 1992. The second compares the summer (defined as April 1 to October 1) and winter distribution (rest of year). The summer distribution is fairly compactly distributed around Cape Alava (coastal kilometer mean = 62.95, sd = 14.1) compared to the slightly more northerly and more widely distributed winter distribution (mean = 71.4, sd = 20.6). The differences are highly significant (Mann-Whitney's p-value < 2.2e-16).
Analysis of Site Usage
Preferred sites of all 75 tagged animals were identified from discretized, site-based, seasonal observations. Over 60% of all females (n=52) prefer Cape Alava to all sites, whereas males were about evenly split between Cape Alava, the Straight of Juan de Fuca and the Cedar Creek Area (26, 26 and 30% respectively, n=23).
We were looking for a way to quantify the site-fidelity of individual sea otters. I chose to use the Shannon Index, which is a commonly used index of diversity, used most commonly for species in a community (Krebs 1989). The index is defined as:
where S is the number of sites and pi is the proportion of time spent at each site for each animal. The proportions were taken from the methodology described above: using a site and seasonal discretization and counting within a season the number of resights at different locations. A value of 0 indicates total homogeneity, i.e. an animal is only observed at a single site. The maximum value of the index is ln(S), representing an equal proportion of time spent at all sites. In this case, Hmax = ln(9) = 2.197.
The results are in this table: IndividualShannonIndexTable.csv
The values range from 0 (for 5 animals, some of which were resighted as many as 10-12 times) to over 1.7 (SO14 and SO48, resighted 32 and 65 times respectively). There is no significant difference in the Shannon index between sexes (unbalanced t-test, p-value 0.12). Surprisingly, it is the females that have the slightly higher mean value (1.02 vs. 0.84). This, despite the fact that both males and females were resighted about the same amount of times on average (median: 30.5 and 29 resights per animal). In general, the Shannon index appears fairly robust to number of resights. This is clear in the following plot:
Shannon index values are presented for all animals: females are boxes while males are circles and the colors represent each animals preferred location. There are no significant patterns anywhere in the plot.
Monthly Movements of Males and Females
Ok, this is pretty much my favorite, most informative plot yet (except for the awful "fuscia" representing the straits of Juan de Fuca!). It shows normalized, estimated frequencies of different site use intensity throughout the year by sex.
The basic stories are: females do love Alava, but mostly in March-April and October. The rest of the year, they shift throughout the range, especially in summer where there are almost as likely to be seen at Sand Point and south as at Cape Alava and north. Males really like the Straits of Juan de Fuca, especially in December-April (during which time there are significant numbers of females up there as well), and then start scattering along the Pacific coast until they practically empty SJdF in August and September (perhaps to look for females?) I think discussing this plot tells more than any more fancy quantitative comparison or model can contribute, and it is my (professional!) opinion that we are reaching the limits of what can be extracted out of the data.
- Modify plots it necessary
- R Development Core Team (2006). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
- For the Shannon Index, Wikipedia suggests:
- Krebs, Charles (1989) Ecological Methodology. Harper Collins, New York,
- but I'm not familiar with this source.