GEOG 566

         Advanced spatial statistics and GIScience

June 5, 2018

Comparing SnowModel output to metrics of Dall Sheep recruitment.

Filed under: 2018,Exercise/Tutorial 3 2018 @ 4:16 pm

Question asked

Is Dall Sheep recruitment more influenced by near-summer snow conditions or do early snow season conditions also play a role?

A typical metric for assessing sheep recruitment, i.e. the number of young animals available to ‘recruit’ into the population, is the lamb to ewe ratio (hereafter referred to as lamb:ewe). In the case of Dall sheep, demographic surveys take place most frequently in the summer months of June and July, after their lambing months of April and May. In this question I will examine the prevailing theory that a cause of Dall sheep population decline are spring snow storms causing high lamb mortality by comparing summer lamb:ewe ratios to aggregated monthly and seasonal snow data derived from a spatially explicit snow evolution model run at daily timesteps.

Data / Tool / Approach used

Snow Data

The snow data for this analysis is derived from SnowModel, a spatially explicit snow evolution model, and consists of daily mean snow depth, total snowfall, mean air temperature, and forageable area (the percentage area under snow depth and density thresholds that allow Dall sheep to graze) aggregated into monthly and seasonal means and totals.

Sheep Data

Sheep data used here is from annual surveys completed by Alaska Department of Fish and Game, Bureau of Land Management, US Fish and Wildlife Service and National Park Service in 6 different Dall Sheep ranges – see blogpost 2. Survey methods include distance sampling, stratified random sampling, and minimum count methods either from a ground location or fixed wing aircraft.

Approach used and steps followed

At this initial stage a simplistic approach was employed to test the research question by counting the occurrence of observations by month and season that confirm the following conditions.

  1. High month/season snowfall andlow lamb:ewe ratios
  2. Low month/season air temperature andlow lamb:ewe ratios
  3. High month/season snow depth andlow lamb:ewe ratios
  4. Low month/season forageable area and low lamb:ewe ratios

The basis of these statements are the assumptions that increased snowfall and snow depth, or lower air temperatures and forageable area, produce conditions where greater energy expenditure is required for survival. Dall sheep are in calorific deficit during the snow season so benign conditions mean that ewes reach the lambing period in better condition and are potentially then more able to provide for their lambs, increasing the observed lamb:ewe ratio. An alternative or complementary idea is that conditions during and after lambing are more important as lambs require a narrower range of conditions than adult sheep to survive.

To test these conditions the snow data and lamb:ewe ratios were converted into anomalies and coded as being strongly/weakly positive or negative based on whether they were outside or within one standard deviation and the direction of their sign. The above conditions were then assessed based on this coded data via the plotting of heatmaps and tallying occurrences (see results below).

This approach is not complex but does begin to examine which time-scales and time periods of the snow season are important for Dall sheep, insight that can later be used in more complex predictive models.

The analysis took place using R and the biggest hurdle was the being able to pass column names as arguments into functions. This was overcome by learning the use of ‘enquo()’, tilde ‘~’, and the nuances of standard versus lazy evaluation that govern whether to include an underscore (e.g. aes_()) after function calls in dplyr pipes. See further, and better described, info!

Brief description of results obtained

In the following section I will present graphs from the Wrangell St Elias primarily, analysis was also conducted in the five other domains but in the interest of brevity I am limiting the number of figures.

Above average snowfall and below average lamb:ewe ratios by month


The heatmap, top left, shows in blue the months where the condition is met (the x axis is the same as the bar chart beneath). The dark grey bars correspond to years where a sheep survey took place (yaxis, 15 out of 37). On the right panel, the scatter diagram shows the lamb:ewe anomaly for each year.

From fig. 1 we can see that 9 of the 15 years of sheep surveys had a lamb:ewe ratio below the mean. Of these nine years the most common months that had higher than average snowfall were October and November, with 6 each. By contrast, the months believed to be important to lamb survival (Apr, May, June) only have 4 recorded instances of above average snowfall. Each year with below average lamb:ewe ratios had at least 4 months of higher than average snowfall (excluding August, which comes after the survey). 50 out of the 99 months (9 years with below average lamb:ewe ratios, excluding August) have above average snowfall.

Below average air temperature and below average lamb:ewe ratios by month


Fig. 2 by contrast shows air temperature by month. Here we see that May has the greatest number of months where the condition is met (n = 6). However, October to November, have the same number of instances as Mar, June and July. 48 out of 99 months agree with the condition.

Above average snow depth and below average lamb:ewe ratios by month


Mean snow depth, fig. 3, shows 4 to 5 instances per month meet the condition from October to June for years with low lamb:ewe ratios. 45 out of 99 months agree with the condition.

Below average forageable area and below average lamb:ewe ratios by month


The autumn months of September to November are comparatively low in instances where the condition is met (n = 4 to 5) for below average forageable area next to December through May where at least 6 out of 9 years show the condition met. February the condition is recorded 8 times. 66 of 99 possible months agree with the condition.

By season


When considering the conditions by season, both autumn and spring snowfall meet the condition 6 years out of 9. Above average snowfall is seen in 19 out 36 possible seasons in low lamb:ewe ration years. Summer air temperature meets the condition 6 times, winter and spring 5 times each, autumn just twice. 19 out of 36 possible seasons snow lower than average air temperature. Snow depth by season is not seen to meet the condition more than 5 times for any season (winter and summer) and 17 out of 36 seasons meet the condition. Forageable area meets the conditions 23 out of 36 seasons, winter with the highest count of 7 out of 9 years met.

Conclusions / Critique of method

This method was a simplistic approach to examine which variable and when could have an effect on Dall sheep summer recruitment. Both by month and by season, below average forageable area had the most recorded instances of being seen alongside low average lamb:ewe ratios, 66 out of 99 possible months, 23 out of 36 seasons. Snow depth did not appear as important as either snowfall or air temperature in monthly or seasonal comparisons.

A critique of this method is that it doesn’t capture instances where the opposite of the condition occurs, e.g. high lamb:ewe ratios and high forageable area. It also doesn’t test the significance of any relationships and is suspect to potential anomalies affecting a limited sample size and its mean in the lamb:ewe ratios. The same tests presented above but with conditions that described instances of a snow variable and lamb:ewe ratios outside of one standard deviation did not produce any meaningful patterns, with occurrences being isolated to single months or seasons, if at all. Despite these limitations this approach does however give insight towards exploring the variables using more complex regression methods.

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