Disclaimer
This website is a class exercise for RenR 690 at the University of Alberta. Any results and conclusions discussed here are preliminary in nature and will be more fully evaluated, using more complete data, at a future date.
Analysis Results
The results of this project are presented in two parts:
1. Analysis of spatial and environmental factors at the talus patch and haypile scales
2. Analysis of regional climate data for the study area as a whole
1. Analysis of spatial and environmental factors at the talus patch and haypile scales
2. Analysis of regional climate data for the study area as a whole
1. Analysis of Spatial and Environmental Factors
1.1 Talus Patch Scale
Talus patches represent local populations of the Pika Camp metapopulation. As mentioned previously, this study only looked at the east and west portions of the study area, since these areas had continuous data for the eleven years of the study. Three response variables were analyzed at the patch scale:
- Mean number of pikas per patch per year (MEAN_YR);
- Density of pikas per hectare (DENSITY_HA); and
- Number of years a patch is occupied from 1995 – 2005 (YRS_OCC).
The list of spatial and environmental variables and their analysis codes is shown in Table 1 on the Data page.
- Mean number of pikas per patch per year (MEAN_YR);
- Density of pikas per hectare (DENSITY_HA); and
- Number of years a patch is occupied from 1995 – 2005 (YRS_OCC).
The list of spatial and environmental variables and their analysis codes is shown in Table 1 on the Data page.
a. Ordinations
As a first step in this analysis, an indirect gradient analysis was undertaken to identify the general relationships among population and spatial/environmental factors.
To reduce complexity, three separate ordinations were undertaken: spatial measures (including slope and aspect), talus features (structure and composition of talus patches), and vegetation composition (including distance to vegetation).
The results of an indirect gradient analysis of population and spatial factors are shown in
Figure 9. Key relationships are highlighted by the solid-lined circles. In this figure, positive correlations are shown between:
· The mean number of pikas/patch/year (MEAN_YR) and the number of years of
patch occupation (YRS_OCC) with patch area (ha; AREA_HA)
and perimeter (m; PERIM) (blue circle);
· The years of occupation (YRS_OCC) and the minimum amount of connectivity
between patches (CONN_MIN) (yellow circle).
· The density of pikas per hectare (DENSITY_HA) and the maximum amount of
connectivity between patches (CONN_MAX) (purple circle).
There also appears to be a negative relationship between the mean pikas/patch/yr (MEAN_YR) and maximum connectivity (CONN_MAX).
Aspect appears to be not strongly related to any of the response variables.
To reduce complexity, three separate ordinations were undertaken: spatial measures (including slope and aspect), talus features (structure and composition of talus patches), and vegetation composition (including distance to vegetation).
The results of an indirect gradient analysis of population and spatial factors are shown in
Figure 9. Key relationships are highlighted by the solid-lined circles. In this figure, positive correlations are shown between:
· The mean number of pikas/patch/year (MEAN_YR) and the number of years of
patch occupation (YRS_OCC) with patch area (ha; AREA_HA)
and perimeter (m; PERIM) (blue circle);
· The years of occupation (YRS_OCC) and the minimum amount of connectivity
between patches (CONN_MIN) (yellow circle).
· The density of pikas per hectare (DENSITY_HA) and the maximum amount of
connectivity between patches (CONN_MAX) (purple circle).
There also appears to be a negative relationship between the mean pikas/patch/yr (MEAN_YR) and maximum connectivity (CONN_MAX).
Aspect appears to be not strongly related to any of the response variables.
Figure 9. NMDS ordination of population and spatial variables: patch scale
Figure 10 shows the results of an indirect gradient analysis of the three population variables and features of the talus (spacing of boulders (TALUSSPACE), continuity of talus (CONTIN) and % interspersion of talus and meadow (INTER)). The ordination does not show a strong relationship between population measures and any of the talus measures, although there appears to be a weak relationship between interspersion of talus and meadow with density of pikas per hectare (highlighted by the yellow circle).
Figure 10. NMDS ordination of population variables and measures of talus: patch scale
The results of an indirect gradient analysis of population variables and vegetation cover are shown in Figure 11. The following relationships are shown:
There is a positive relationship between mean number of pikas/patch/year (MEAN_YR) and number of years occupied (YRS_OCC) and cover of Dryas octopetala (DRYAS) and Cassiope tetragona (CASS), although the relationship is strongest with cover of Dryas species (green solid circle). There also appears to be a negative relationship with the amount of cover of graminoid species (green dashed line).
There is a positive relationship between the number of years occupied (YRS_OCC) and density of pikas per hectare (DENSITY_HA and distance to vegetation (m; DIST2VEG) and cover by bareground/rock (BG_ROCK) (yellow solid line). There is a negative relationship between pika density and the amount of cover by Salix (willow) species (yellow dashed line).
There is a positive relationship between mean number of pikas/patch/year (MEAN_YR) and number of years occupied (YRS_OCC) and cover of Dryas octopetala (DRYAS) and Cassiope tetragona (CASS), although the relationship is strongest with cover of Dryas species (green solid circle). There also appears to be a negative relationship with the amount of cover of graminoid species (green dashed line).
There is a positive relationship between the number of years occupied (YRS_OCC) and density of pikas per hectare (DENSITY_HA and distance to vegetation (m; DIST2VEG) and cover by bareground/rock (BG_ROCK) (yellow solid line). There is a negative relationship between pika density and the amount of cover by Salix (willow) species (yellow dashed line).
Figure 11. NMDS ordination of population variables and vegetation composition using Mahalanovis distance: patch scale
b. Multivariate regression
The multivariate regression tree in Figure 12 affirms that patch perimeter (PERIM), % cover by Dryas octopetala (DRYAS) and maximum connectivity (CONN_MAX) are key contributors to the amount of explained variance in mean number of pikas/patch/year (MEAN_YR), years of patch occupancy (YRS_OCC), and the density of pikas per hectare (DENSITY_HA).
· The first node splits at perimeters greater and less than 845 metres, which is expected
since the ordination indicates a strong, positive relationship between numbers of pikas
and patch size (area and perimeter).
· The second node splits at a connectivity value of above or below 31.5, with the density of
pikas positively associated with higher connectivity among patches.
· The third node splits at the percent cover of Dryas octopetala (above and below 20.3%),
with the mean number of pikas/patch/year and years of occupation associated with
higher % cover of Dryas.
Overall, these variables explain 74% of the variation in the response variables, although, as a constrained analysis, this result may not account for variables not included in the analysis. The cross-validation error and standard error are quite high (0.949 and 0.365, respectively) so there is not a lot of precision in this estimate, but it still provides a reasonable indication of the relationships of concern.
As shown in the table in the lower right hand corner of the figure, there are alternative factors that could contribute to the splits in the nodes, although only three splits were included in the MRT output. For Node 1 (first split), the area per ha would provide a similar result. For Node 3(second split) either measures of the continuity of talus patches provide an equivalent explanation of variance to percent cover of Dryas octopetala.
· The first node splits at perimeters greater and less than 845 metres, which is expected
since the ordination indicates a strong, positive relationship between numbers of pikas
and patch size (area and perimeter).
· The second node splits at a connectivity value of above or below 31.5, with the density of
pikas positively associated with higher connectivity among patches.
· The third node splits at the percent cover of Dryas octopetala (above and below 20.3%),
with the mean number of pikas/patch/year and years of occupation associated with
higher % cover of Dryas.
Overall, these variables explain 74% of the variation in the response variables, although, as a constrained analysis, this result may not account for variables not included in the analysis. The cross-validation error and standard error are quite high (0.949 and 0.365, respectively) so there is not a lot of precision in this estimate, but it still provides a reasonable indication of the relationships of concern.
As shown in the table in the lower right hand corner of the figure, there are alternative factors that could contribute to the splits in the nodes, although only three splits were included in the MRT output. For Node 1 (first split), the area per ha would provide a similar result. For Node 3(second split) either measures of the continuity of talus patches provide an equivalent explanation of variance to percent cover of Dryas octopetala.
Figure 12. Multivariate regression tree of population variables crossed with spatial and environmental variables
c. Linear regression of key variables
The correlation between individual response and predictor variables were tested using linear regression. As some of the datasets were strongly non-normal, as is common with ecological datasets, it was necessary to transform those data using log or square root transformation prior to undertaking the regressions (summarized in Table 4 on the Analysis page). Significant linear relationships are summarized in Figures 13 - 15.
Figure 13 shows the regressions of two of the population variables (mean number of pikas/patch/ha and sqrt(number of years occupied)) on two measures of patch size: log (patch perimeter (m)) and log (patch area (ha)). As the graphs show, there is a strongly significant relationship between numbers of pika/patch/year and both measures of patch size (for perimeter, r2=0.79, p-0.0001; for area, r2=0.67, p=0.001). There is also a significant relationship between perimeter and number of years of patch occupation at the ą=0.05 significance level.
Figure 13 shows the regressions of two of the population variables (mean number of pikas/patch/ha and sqrt(number of years occupied)) on two measures of patch size: log (patch perimeter (m)) and log (patch area (ha)). As the graphs show, there is a strongly significant relationship between numbers of pika/patch/year and both measures of patch size (for perimeter, r2=0.79, p-0.0001; for area, r2=0.67, p=0.001). There is also a significant relationship between perimeter and number of years of patch occupation at the ą=0.05 significance level.
Figure 13. Linear regression of mean pikas/patch/yr and years of occupation on patch perimeter (m) and area (ha)
The relationship between indices of connectivity and pika population variables is shown in Figure 14. The mean number of pikas/patch/year is negatively correlated with the maximum connectivity index for a patch (r2=0.34, p=0.05) and number of years occupied is positively correlated with the minimum connectivity index for a patch (r2=0.35, p=0.04). These patterns are complementary; overall, pika populations and years of patch occupation are positively correlated with higher indices of connectivity.
Figure 14. Linear regression of population variables on indices of connectivity
Significant linear relationships between % vegetation cover and population variables are summarized in Figure 15. As indicated by the NMDS ordination, there is:
· a positive linear relationship between the % Dryas octopetala and both mean number of
pikas/patch/ year and the number of years occupied; and
· a negative relationship between the percent cover of graminoid species (grasses) and the
number of years occupied.
· a positive linear relationship between the % Dryas octopetala and both mean number of
pikas/patch/ year and the number of years occupied; and
· a negative relationship between the percent cover of graminoid species (grasses) and the
number of years occupied.
Figure 15. Linear regression of population variables on % vegetation cover
1.2 Haypile Scale
Two response variables were analyzed at the scale of individual haypiles:
- Number of years a haypile is occupied (YRS_OCC); and
- Number of years of continuous occupation (YRS_CON)
- Number of years a haypile is occupied (YRS_OCC); and
- Number of years of continuous occupation (YRS_CON)
Statistical analysis
A generalized linear model was used to assess the relationship between the number of years of haypile occupancy and multiple environmental variables. The results infer that whether or not a talus patch is level at the site of the haypile is the only factor that significantly influences haypile occupancy, among the variables tested. The final model, therefore, was reduced from fifteen environmental variables to one (Table 5). Talus levelness only reduces the AIC for the analysis from a null value of 251.21 to a final value of 248.55 and residual variation is still very high at 78.79%. These results indicate that, although the relationship between haypile occupancy and talus levelness is significant at ą = 0.05 (z=2.01; p=0.04), overall only a small amount of the total variation for years of haypile occupancy is explained by this variable.
Table 5. Results of a generalized linear model of haypile occupancy as a function of environmental variables
A_barplot of the number of years of haypile occupancy as a function of level and concave talus is shown in Figure 16. This graph shows that pikas have a preference for level talus at the site of their haypiles.
Figure 16. Barplot comparing years of haypile occupancy to talus topography
2. Analysis of Climate Factors
Population variables for the study area as a whole were assessed against a number of regional climate measures and the Pacific Decadal Oscillation (see Data). Climate variable and analysis codes are listed in Table 2 on the Data page.
a. Ordinations
The results of indirect gradient analyses to assess the relationship between regional climate measures and habitat occupancy by collared pikas are shown in Figures 17 and 18. Response variables are the total numbers of pika per year (POP_TOTAL), number of patches occupied per year (PATCH_OC) and number of local extirpation events (EXTIRP).
For ease of interpretation, climate variables were split into two groups:
· Maximum, minimum and annual seasonal temperatures (summer (sm; July - Aug); autumn
(am; Sep - Nov; winter (wt; Dec - Feb), and spring (sp; Mar - May). These values are
reported by season rather than by calendar year, so that population data for each summer
field season can be assessed against the previous year's growing season (July - August) and
subsequent autumn, winter and spring conditions.
· Other climate variables including precipitation (seasonal averages, precipitation as snow
(PAS), mean summer precipitation (MSP), length of growing season (frost-free period (FFP),
Pacific Decadal Oscillation (PDO) as a surrogate for first date of snow melt).
Figures 17 and 18 show the outputs of indirect gradient analysis of seasonal temperatures in relation to variables associated with habitat occupancy. There is a striking result for winter and summer temperatures (Figure 17), where winter temperatures (maximum, minimum and average) all correlate with the number of local extirpations (EXTIRP) and temperatures for the previous summer correlate with total number of pikas (POP_TOTAL) and the number of patches occupied (PATCH_OC). There is no real relationship evident between spring and autumn temperatures and habitat occupancy (Figure 18), with the exception of a correlation between minimum spring temperature and the number of local extirpations.
The results of the ordination in Figure 19 indicates that the amount of snow in a year (precipitation as snow (PAS) and winter precipitation (PPT_wt)) and, to some extent, the amount of precipitation in the spring (PPT_sp) all correlate with the number of local extirpations, while the length of growing season, as indicated by the number of frost-free days (NFFD) and Pacific Decadal Oscillation (PDO) correlates with the number of pikas/year and number of patches occupied.
For ease of interpretation, climate variables were split into two groups:
· Maximum, minimum and annual seasonal temperatures (summer (sm; July - Aug); autumn
(am; Sep - Nov; winter (wt; Dec - Feb), and spring (sp; Mar - May). These values are
reported by season rather than by calendar year, so that population data for each summer
field season can be assessed against the previous year's growing season (July - August) and
subsequent autumn, winter and spring conditions.
· Other climate variables including precipitation (seasonal averages, precipitation as snow
(PAS), mean summer precipitation (MSP), length of growing season (frost-free period (FFP),
Pacific Decadal Oscillation (PDO) as a surrogate for first date of snow melt).
Figures 17 and 18 show the outputs of indirect gradient analysis of seasonal temperatures in relation to variables associated with habitat occupancy. There is a striking result for winter and summer temperatures (Figure 17), where winter temperatures (maximum, minimum and average) all correlate with the number of local extirpations (EXTIRP) and temperatures for the previous summer correlate with total number of pikas (POP_TOTAL) and the number of patches occupied (PATCH_OC). There is no real relationship evident between spring and autumn temperatures and habitat occupancy (Figure 18), with the exception of a correlation between minimum spring temperature and the number of local extirpations.
The results of the ordination in Figure 19 indicates that the amount of snow in a year (precipitation as snow (PAS) and winter precipitation (PPT_wt)) and, to some extent, the amount of precipitation in the spring (PPT_sp) all correlate with the number of local extirpations, while the length of growing season, as indicated by the number of frost-free days (NFFD) and Pacific Decadal Oscillation (PDO) correlates with the number of pikas/year and number of patches occupied.
Figure 17. Indirect gradient analysis of habitat occupancy as a function of summer and winter temperatures (°C)
Figure 18. Indirect gradient analysis of habitat occupancy as a function of spring and autumn temperatures
Figure 19. Indirect gradient analysis of habitat occupancy as a function of precipitation and snow-free season
b. Multivariate Regression
The multivariate regression tree (MRT) of habitat occupancy variables as a function of climate factors (Figure 20) shows that average winter temperature is the main factor influencing population numbers, numbers of patches occupied and number of local extirpations. Average winter temperatures lower than -15.1 °C positively influence population numbers and patch occupancy and negatively influence number of patch extirpations. Warmer winter temperatures have the opposite effect. The second key climate influence is spring precipitation. Precipitation levels less than 56.5 mm negatively influence pika numbers and positively influence the number of patch extirpations. Although this analysis explains over 70% of the variability in response variables, the cross validation and standard errors are quite high at 0.845 and 0.330, respectively. One of the limitations of MRT is that it can only work with the variables it is given, so there may be other key sources of variability that are not identified in this analysis.
b. Multivariate regression
Figure 20. Multivariate regression tree showing the relationship between habitat occupancy and climate variables
