Optimal number of surveys (contours) when maximizing the expected probability of detection as a function of the budget to fixed-cost ratio <i>B</i>/<i>c</i> ( = <i>B</i>′/<i>c</i>′) and the coefficient of variation θ.

<p>The figures compare the exact solution with <i>c</i>′ = 0.5 (a) and approximate solution (b). For the approximate solution, dashed-line A corresponds to <i>Litoria pearsoniana</i> (θ = 2.45), dashed-line B corresponds <i>Atriplex semibaccata</i> (θ = 0.91) and dashed-line C corresponds <i>Lomandra longifolia</i> (θ = 0.87). Note that exact solution depends on the value of <i>B</i>, not just the ratio <i>B</i>/<i>c</i>, hence lines indicating the optimal number of surveys for the case studies are not shown on (a).</p

Expected probability of detection (a) as a function of the scaled budget <i>B</i>′, with <i>c</i>′ = 0.5, when detection rate is assumed to be variable (solid line, θ = 1.5) compared to when it is assumed to be constant (dashed line).

<p>Likelihood that the failed-detection probability <i>Q</i> is less than the prescribed value <i>Qc</i> (b) as a function of the scaled budget <i>B</i>′, with θ = 1.5 and <i>c</i>′ = 0.5, when detection rate is assumed to be variable (solid lines) compared to when it is assumed to be constant (dashed line).</p

Summary of key results.

<p>Summary of key results.</p

Optimal number of surveys for <i>Litoria pearsoniana</i> when the objective is to maximize the expected probability of detection (a &amp; b), and maximize the probability of satisfying a prescribed detection rate of 95% (c &amp; d).

<p>Abundance = 1 (µ = 0.67) in (a) &amp; (d), and abundance  = 3 (µ = 2.2) in (b) &amp; (d). The shaded area is the region such that the expected probability of failed detection is no more than 0.01 probability units away from the optimum. The correlation coefficient <i>r</i> = 0.3, fixed cost <i>c</i> = 1 hour and survey season length <i>T</i> = 90 days.</p

Optimal number of surveys (contours) when maximizing the probability of achieving a prescribed detection rate as a function of the scaled budget <i>B</i>′ and the prescribed detection rate <i>Qc</i> for the exact solution, with θ = 1.5 and <i>c</i>′ = 0.5

<p>Optimal number of surveys (contours) when maximizing the probability of achieving a prescribed detection rate as a function of the scaled budget <i>B</i>′ and the prescribed detection rate <i>Qc</i> for the exact solution, with θ = 1.5 and <i>c</i>′ = 0.5, (a) and the approximate solution, with <i>c</i>′ = 0.5 (b).</p

Predicted versus observed optimal number of quadrats to search when: the objective is to maximize the expected probability of detection for <i>Atriplex semibaccata</i> (a) and <i>Lomandra longifolia</i> (b); the objective is to satisfy a required probabil

<p>Multiple values are indicated by the bolder points; three values at the point (1,1) for <i>Atriplex</i> (c), and two values at point (1,2) for <i>Lomandra</i> (d). Search budget <i>B</i> is 5,10 and 15 minutes; travel time between quadrats <i>c</i> is 0.25, 0.5 and 1 minute. The diagonal line represents perfect correspondence.</p

Leaf and flower colour difference.

<p>Pairwise Euclidean distance in CIE 1976 (L*a*b*) space was calculated and an nMDS generated for a) yellow-orange flowers and b) leaves (the leaf nMDS used data from the two highest quality cameras only: the Nikon D300 and Sony NEX-5n).</p

Flower colour difference between species in the field and two invasive species.

<p>Pairwise mean flower colour difference (measured as the Earth Mover’s Distance) was calculated between individual yellow-orange flowers of different species and mean colour of individuals of <i>H</i>. <i>aurantiacum</i> (light bars) and <i>H</i>. <i>praealtum</i> (dark bars). 95% confidence intervals are shown.</p

Variation in leaf colour measured by different cameras.

<p>Leaf colour is shown in <i>a*</i>-<i>b*</i> space for five species calculated from images taken with five different digital cameras.</p

Change in abundance and richness of non-native and native species after nutrient treatments for sites included in the study

This file contains data on the change in abundance and richness of non-native and native species after nutrient enrichment (1-3 years) use for analyses. The change in abundance data was derived at the plot level. Metadata can be found in the ReadMe file