Probing activity with the signal equal to the number of successes.

<p>Green values indicate no probing activity, blue values represent fewer restrictions with the adaptive strategy, yellow/red values indicate more restrictions with the active strategy.</p

Individual site joint state/signal probability matrix.

<p><i>p_c</i> probability that an empty site is occupied (colonized) next year.</p><p><i>p_n</i> probability that a site is re-occupied next year if fledging is not successful.</p><p><i>p_s</i> probability that a site is re-occupied next year if fledging is successful.</p><p><i>p_u</i>(<i>h</i>) probability that fledging is successful if access to the site is unrestricted.</p><p><i>p_r</i>(<i>h</i>) probability that fledging is successful if access to the site is restricted.</p><p><i>p_u</i> and <i>p_r</i> depend on the size of the arctic hare population <i>h</i>, which is assumed known at the time restriction decisions are made.</p

Single site state transition when if <i>p_n</i> = <i>p_s</i>.

<p>Single site state transition when if <i>p_n</i>  =  <i>p_s</i>.</p

Time paths of expected beliefs when <i>p_u</i> is known.

<p>The three subplots represent cases for each of the three possible disturbance effect models. Each plot shows time paths of expected beliefs over 100 years. Line color is associated with the belief in a specific disturbance effect: blue – no disturbance, green –moderate disturbance, red – strong disturbance. Line type represents the signal used for updating beliefs: solid – full information, dash/dot – number of successes only, dashed – no signal.</p

Enumeration of States and Signals with 2 Sites.

<p>The tabled values represent the number of sites in each category. The number of unrestricted and successful sites, <i>Y</i>₁, is the sum of columns 2 and 4 (SE and SO). The number of occupied sites next period, <i>S</i>⁺, is the sum of columns 3 and 4 (NO and SO).</p><p>NE: either restricted or not successful/empty next period.</p><p>SE: unrestricted, successful/empty next period.</p><p>NO: either restricted or not successful/occupied next period.</p><p>SO: unrestricted, successful/occupied next period.</p

Time paths of expected beliefs when <i>p_r</i> is known.

<p>The three subplots represent cases for each of the three possible disturbance effect models. Each plot shows time paths of expected beliefs over 100 years. Line color is associated with the belief in a specific disturbance effect: blue – no disturbance, green –moderate disturbance, red – strong disturbance. Line type represents the signal used for updating beliefs: solid – full information, dash/dot – number of successes only, dashed – no signal.</p

Probing activity using information optimally.

<p>Differences in the number of restrictions between the active management strategy (shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0102434#pone-0102434-g002" target="_blank">Figure 2</a>) and the passive management strategy. Green values indicate no probing activity, blue values represent fewer restrictions with the active strategy, yellow/red values indicate more restrictions with the active strategy.</p

Joint state/signal probability matrix for 1 and 2 sites.

<p> = (i, j): i sites are occupied & j sites are restricted  = (i, j): i unrestricted sites have successful fledging & j sites are occupied next year.</p

Time paths of expected beliefs when both <i>p_u</i> and <i>p_r</i> are uncertain.

<p>The three subplots represent cases for each of the three possible disturbance effect models. Each plot shows time paths of expected beliefs over 100 years. Line color is associated with the belief in a specific disturbance effect: blue – no disturbance, green –moderate disturbance, red – strong disturbance. Line type represents the signal used for updating beliefs: solid – full information, dash/dot – number of successes only, dashed – no signal.</p

Parameter values of alternative models and assumptions.

<p></p><p> pc = 0.2315, pn = 0.9427, ps = 0.9573.</p><p>The hare level is treated as constant and set to its mean value (<i>h</i> = 9.4).</p