Figure 1.

Four population abundance time series (circles), with expected values of true abundances given the other observations (short dashed lines), and bootstrapped 95% confidence intervals for true abundances (long dashed lines), estimated with restricted maximum likelihood under the Ornstein-Uhlenbeck state space model. Upper left: bobcat furbearer harvest records from Idaho, USA (parameter estimates with bootstrapped 95% confidence intervals: $\widehat{\mu }=6.79(6.61,6.97)$, $\widehat{\theta }=1.26(3.91\times {10}^{-7},20.2)$, ${\widehat{\beta }}^2=0.272(7.43\times {10}^{-3},3.94)$, ${\widehat{\tau }}^2=7.48\times {10}^{-4}(9.14\times {10}^{-10},0.0847)$). Upper right: bobcat furbearer harvest records from Maine, USA ($\widehat{\mu }=5.78(5.47,6.08)$, $\widehat{\theta }=0.877(0.0226,10.3)$, ${\widehat{\beta }}^2=0.735(0.0202,2.40)$, ${\widehat{\tau }}^2=0.00475(1.79\times {10}^{-8},0.334)$). Lower left: elk population estimates from Grand Teton National Park, Wyoming, USA ($\widehat{\mu }=7.29(7.14,7.44)$, $\widehat{\theta }=0.868(0.229,19.3)$, ${\widehat{\beta }}^2=0.0990(0.0296,1.45)$, ${\widehat{\tau }}^2=9.80\times {10}^{-9}(2.93\times {10}^{-11},1,22\times {10}^{-3})$). Lower right: grasshopper density estimates from the western mountainous region of Montana, USA ($\widehat{\mu }=1.56(1.31,1.82)$, $\widehat{\theta }=0.722(0.272,2.01)$, ${\widehat{\beta }}^2=0.347(0.160,0.752)$, ${\widehat{\tau }}^2=2.27\times {10}^{-7}(3.81\times {10}^{-8},2.27\times {10}^{-5})$).