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Managing more than the mean: using quantile regression to identify factors related to large elk groups

View Article: PubMed Central - PubMed

ABSTRACT

Animal group size distributions are often right‐skewed, whereby most groups are small, but most individuals occur in larger groups that may also disproportionately affect ecology and policy. In this case, examining covariates associated with upper quantiles of the group size distribution could facilitate better understanding and management of large animal groups.

We studied wintering elk groups in Wyoming, where group sizes span several orders of magnitude, and issues of disease, predation and property damage are affected by larger group sizes. We used quantile regression to evaluate relationships between the group size distribution and variables of land use, habitat, elk density and wolf abundance to identify conditions important to larger elk groups.

We recorded 1263 groups ranging from 1 to 1952 elk and found that across all quantiles of group size, group sizes were larger in open habitat and on private land, but the largest effect occurred between irrigated and non‐irrigated land [e.g. the 90th quantile group size increased by 135 elk (95% CI = 42, 227) on irrigation].

Only upper quantile group sizes were positively related to broad‐scale measures of elk density and wolf abundance. For wolf abundance, this effect was greater on elk groups found in open habitats and private land than those in closed habitats or public land. If we had limited our analysis to mean or median group sizes, we would not have detected these effects.

Synthesis and applications. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management.

Synthesis and applications. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management.

No MeSH data available.


Estimated coefficients from model 1 for each quantile of interest. Panel a shows the estimated group size for each quantile on public land, at average values of the other covariates. In panels b and c, coefficients describe the estimated change in group size between private and public land and between management closures and public land, respectively, at average values of the other covariates. In panels d–f, coefficients describe the estimated rate of change in group size for every unit change in the explanatory variable, while holding all other variables constant. Shaded area indicates bootstrapped 95% confidence intervals.
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jpe12514-fig-0002: Estimated coefficients from model 1 for each quantile of interest. Panel a shows the estimated group size for each quantile on public land, at average values of the other covariates. In panels b and c, coefficients describe the estimated change in group size between private and public land and between management closures and public land, respectively, at average values of the other covariates. In panels d–f, coefficients describe the estimated rate of change in group size for every unit change in the explanatory variable, while holding all other variables constant. Shaded area indicates bootstrapped 95% confidence intervals.

Mentions: As expected, most quantile group sizes from models 1 and 2 were larger on private land and management closures (than on public land), larger on irrigated land (than on non‐irrigated), positively related to habitat openness, and negatively related to habitat diversity, slope of the landscape and winter severity, while holding other covariates fixed (Figs 2 and 3). Coefficient estimates for distance to road were near zero for all quantile group sizes, but uncertainty was high at upper quantiles (Fig. S3). Uncertainty was high at upper quantiles for other variables as well (Figs 2 and 3), but this was expected due to the larger sampling variation in the tails of the group size distributions (Cade & Noon 2003). Differences between irrigated and non‐irrigated land caused the largest effect on group size (while holding winter severity and winter elk density constant). For this model, median and 0·90 quantile group sizes were estimated to be larger on irrigated land by 61 elk (95% CI = 6, 116) and 135 elk (95% CI = 42, 227), respectively.


Managing more than the mean: using quantile regression to identify factors related to large elk groups
Estimated coefficients from model 1 for each quantile of interest. Panel a shows the estimated group size for each quantile on public land, at average values of the other covariates. In panels b and c, coefficients describe the estimated change in group size between private and public land and between management closures and public land, respectively, at average values of the other covariates. In panels d–f, coefficients describe the estimated rate of change in group size for every unit change in the explanatory variable, while holding all other variables constant. Shaded area indicates bootstrapped 95% confidence intervals.
© Copyright Policy - creativeCommonsBy-nc-nd
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5016784&req=5

jpe12514-fig-0002: Estimated coefficients from model 1 for each quantile of interest. Panel a shows the estimated group size for each quantile on public land, at average values of the other covariates. In panels b and c, coefficients describe the estimated change in group size between private and public land and between management closures and public land, respectively, at average values of the other covariates. In panels d–f, coefficients describe the estimated rate of change in group size for every unit change in the explanatory variable, while holding all other variables constant. Shaded area indicates bootstrapped 95% confidence intervals.
Mentions: As expected, most quantile group sizes from models 1 and 2 were larger on private land and management closures (than on public land), larger on irrigated land (than on non‐irrigated), positively related to habitat openness, and negatively related to habitat diversity, slope of the landscape and winter severity, while holding other covariates fixed (Figs 2 and 3). Coefficient estimates for distance to road were near zero for all quantile group sizes, but uncertainty was high at upper quantiles (Fig. S3). Uncertainty was high at upper quantiles for other variables as well (Figs 2 and 3), but this was expected due to the larger sampling variation in the tails of the group size distributions (Cade & Noon 2003). Differences between irrigated and non‐irrigated land caused the largest effect on group size (while holding winter severity and winter elk density constant). For this model, median and 0·90 quantile group sizes were estimated to be larger on irrigated land by 61 elk (95% CI = 6, 116) and 135 elk (95% CI = 42, 227), respectively.

View Article: PubMed Central - PubMed

ABSTRACT

Animal group size distributions are often right‐skewed, whereby most groups are small, but most individuals occur in larger groups that may also disproportionately affect ecology and policy. In this case, examining covariates associated with upper quantiles of the group size distribution could facilitate better understanding and management of large animal groups.

We studied wintering elk groups in Wyoming, where group sizes span several orders of magnitude, and issues of disease, predation and property damage are affected by larger group sizes. We used quantile regression to evaluate relationships between the group size distribution and variables of land use, habitat, elk density and wolf abundance to identify conditions important to larger elk groups.

We recorded 1263 groups ranging from 1 to 1952 elk and found that across all quantiles of group size, group sizes were larger in open habitat and on private land, but the largest effect occurred between irrigated and non‐irrigated land [e.g. the 90th quantile group size increased by 135 elk (95% CI = 42, 227) on irrigation].

Only upper quantile group sizes were positively related to broad‐scale measures of elk density and wolf abundance. For wolf abundance, this effect was greater on elk groups found in open habitats and private land than those in closed habitats or public land. If we had limited our analysis to mean or median group sizes, we would not have detected these effects.

Synthesis and applications. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management.

Synthesis and applications. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management.

No MeSH data available.