Search

The author comments on the recovery of the population of grizzly bear in the modern landscape.

In this study, we develop spatial autoregressive ( SAR) models relating grizzly bear body length to environmental predictor variables in the Alberta Rocky Mountains. We examine the ability of several different spatial neighborhoods to model spatial dependence and compare the estimated parameters and residuals from a standard linear regression model ( LRM) with those from three types of SAR models: error, lag, and Durbin. Further, we examine variable selection in the presence of negative dependence by repeating the modeling process using a SAR model. Two findings are that significant negative spatial dependence was present in the residuals of the LRM and that the choice of spatial neighborhood greatly affects the ability to detect spatial dependence. The incorporation of appropriate spatial weights into SAR models improves the fit and increases the significance of the parameter estimates vis-à-vis the linear model. The results of this study indicate that negative dependence may not have as severe negative effects on variable selection and parameter estimation as positive dependence. An examination of spatial dependence in regression modeling appears to be an important means of exploring the appropriateness of a sampling framework, predictor variables, and model form. En este estudio desarrollamos modelos espaciales autorregresivos (SAR) que vinculan la longitud del cuerpo de osos grizzli con variables predictivas ambientales en las montañas rocosas de Alberta, Canadá. Examinamos la capacidad de varias vecindades espaciales para modelar la dependencia espacial y la comparación de los parámetros estimados, así como los residuos de un modelo de regresión lineal estándar (LRM) versus tres tipos de modelos SAR: error, retraso ( lag) y Durbin. Además, se examina la selección de variables en la presencia de dependencia negativa mediante la repetición del proceso de modelado con un modelo de SAR. El estudio concluye que: 1) existe dependencia espacial negativa significativa en los residuos de la LRM y; 2) la selección de la vecindad espacial afecta en gran medida la capacidad de detectar la dependencia espacial. La incorporación de ponderaciones espaciales correspondientes a los modelos SAR mejora el ajuste y aumenta la importancia de los parámetros estimados versus el modelo lineal. Los resultados de este estudio indican que la dependencia negativa puede no tener los graves efectos negativos en la selección de variables y la estimación de parámetros si se comparan dichos efectos con = la dependencia positiva. Los autores recomiendan un examen de la dependencia espacial en modelos de regresión como medio importante para explorar la conveniencia de un marco de muestreo, de variables de predicción, y de la forma del modelo. 本文构建了阿尔伯达省落基山脉地区的灰熊体态大小与环境预测变量之间的空间自回归模型（SAR），检验了几种以不同空间邻域矩阵拟合变量的空间相关性，并比较了标准回归模型(LRM)与几种不同类型的SAR模型（空间残差模型、空间滞后模型和空间杜宾模型）的估计参数和残差大小。进而利用一种SAR模型重复模拟过程，进一步测试变量选择对负相关性存在的影响。研究表明，显著的空间负相关存在于LRM的残差中，且空间邻域权重的选择很大程度上影响模型空间相关性的探测能力。将适当的空间权重引入SAR模型中可提高拟合精度，增加相对于线性模型参数估计的显著性。研究结果表明，负相关性在变量选择和参数估计上严重负影响的程度不如正相关性强。回归模型中空间相关性检验似乎是采样结构、预测变量和模型形式适用性分析的一个重要途径。 [ABSTRACT FROM AUTHOR]

Background: Individual body growth is controlled in large part by the spatial and temporal heterogeneity of, and competition for, resources. Grizzly bears (Ursus arctos L.) are an excellent species for studying the effects of resource heterogeneity and maternal effects (i.e. silver spoon) on life history traits such as body size because their habitats are highly variable in space and time. Here, we evaluated influences on body size of grizzly bears in Alberta, Canada by testing six factors that accounted for spatial and temporal heterogeneity in environments during maternal, natal and 'capture' (recent) environments. After accounting for intrinsic biological factors (age, sex), we examined how body size, measured in mass, length and body condition, was influenced by: (a) population density; (b) regional habitat productivity; (c) inter-annual variability in productivity (including silver spoon effects); (d) local habitat quality; (e) human footprint (disturbances); and (f) landscape change. Results: We found sex and age explained the most variance in body mass, condition and length (R2 from 0.48-0.64). Inter-annual variability in climate the year before and of birth (silver spoon effects) had detectable effects on the three-body size metrics (R2 from 0.04-0.07); both maternal (year before birth) and natal (year of birth) effects of precipitation and temperature were related with body size. Local heterogeneity in habitat quality also explained variance in body mass and condition (R2 from 0.01-0.08), while annual rate of landscape change explained additional variance in body length (R2 of 0.03). Human footprint and population density had no observed effect on body size. Conclusions: These results illustrated that body size patterns of grizzly bears, while largely affected by basic biological characteristics (age and sex), were also influenced by regional environmental gradients the year before, and of, the individual's birth thus illustrating silver spoon effects. The magnitude of the silver spoon effects was on par with the influence of contemporary regional habitat productivity, which showed that both temporal and spatial influences explain in part body size patterns in grizzly bears. Because smaller bears were found in colder and less-productive environments, we hypothesize that warming global temperatures may positively affect body mass of interior bears. [ABSTRACT FROM AUTHOR]