S 3
Results of logistic regression analyses. These are presented for 1) lakes (space) and 2) seasons (time). Lakes and seasons are treated as categorical variables. The response variable is rarity status with the model asking the probability of detecting whether a species is ‘rare locally’ based on its occurrence (in space or time) and its body size (log wet weight in g). In each case we examine four different definitions of ‘rare locally’ using information on the species in six other habitats in the reserve. These are a) present in at least two other habitats; b) present in at least 3 other habitats; c) present in at least 2 other habitats or at least 0.5% relative abundance when present anywhere; d) present in at least 2 other habitats or at least 1% relative abundance when present anywhere. (See ESM 2 for more details). A graph of the predicted probabilities (with 95% confidence limits) is presented in each case. This was created using ggplot2 following http://www.ats.ucla.edu/stat/r/dae/logit.htm.
1. LAKES

present in at least 2 other habitats
Deviance Residuals:
Min 1Q Median 3Q Max
1.9285 0.9036 0.6989 0.9530 1.7507
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 1.37917 0.38728 3.561 0.000369 ***
log10size 0.86555 0.35038 2.470 0.013500 *
lakes2 0.05968 0.50039 0.119 0.905056
lakes3 0.25545 0.79585 0.321 0.748228
lakes4 1.13752 0.52774 2.155 0.031127 *
lakes5 1.52289 0.54121 2.814 0.004896 **
Figure a. Probability of being regionally rare in relation to log_{10} body size, and lake number, when rare locally is defined as being present in two other habitat types.

present in at least 3 other habitats
Deviance Residuals:
Min 1Q Median 3Q Max
1.6249 0.7664 0.6075 0.9972 2.0443
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 2.1121 0.4536 4.656 <0.0001 ***
log10size 0.9225 0.3673 2.511 0.01202 *
lakes2 0.2058 0.5654 0.364 0.71587
lakes3 0.1771 0.9008 0.197 0.84415
lakes4 0.4694 0.5823 0.806 0.42014
lakes5 1.4734 0.5384 2.736 0.00621 **
Figure b. Probability of being regionally rare in relation to log_{10} body size, and lake number, when rare locally is defined as being present in three other habitat types.

present in at least 2 other habitats or at least 0.5% relative abundance when present anywhere
Deviance Residuals:
Min 1Q Median 3Q Max
1.9811 0.9767 0.5972 1.0842 1.5786
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 0.9549 0.3684 2.592 0.00953 **
log10size 0.4981 0.3440 1.448 0.14768
lakes2 0.5475 0.4743 1.154 0.24839
lakes3 0.2108 0.7438 0.283 0.77688
lakes4 1.3877 0.5363 2.587 0.00967 **
lakes5 1.8759 0.5791 3.239 0.00120 **
Figure c. Probability of being regionally rare in relation to log_{10} body size, and lake number, when rare locally is defined as being present in at least two other habitat types or at least 0.5% of total abundance when present.

present in at least 2 other habitats or at least 1% relative abundance when present anywhere
Deviance Residuals:
Min 1Q Median 3Q Max
1.8885 0.9361 0.8014 0.9793 1.5861
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 0.97408 0.36818 2.646 0.00815 **
log10size 0.52551 0.34258 1.534 0.12503
lakes2 0.05396 0.48937 0.110 0.91220
lakes3 0.20086 0.74456 0.270 0.78734
lakes4 1.38611 0.53675 2.582 0.00981 **
lakes5 1.63433 0.55247 2.958 0.00309 **
Figure d. Probability of being regionally rare in relation to log_{10} body size, and lake number, when rare locally is defined as being present in at least two other habitat types or at least 1% of total abundance when present.
2. SEASONS
a) present in at least 2 other habitats
Deviance Residuals:
Min 1Q Median 3Q Max
1.9322 0.8791 0.6936 0.9662 1.7669
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 1.3968 0.3831 3.646 0.000266 ***
log10size 0.8981 0.3483 2.578 0.009926 **
seasons2 0.1555 0.4863 0.320 0.749207
seasons3 1.1740 0.5662 2.074 0.038119 *
seasons4 1.4909 0.4930 3.024 0.002495 **
Figure a. Probability of being regionally rare in relation to log_{10} body size, and season number, when rare locally is defined as being present in at least two other habitat types.
b) present in at least 3 other habitats
Deviance Residuals:
Min 1Q Median 3Q Max
1.5600 0.7483 0.5678 1.0134 2.0713
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 2.1666 0.4503 4.811 <0.0001 ***
log10size 0.9561 0.3627 2.636 0.00839 **
seasons2 0.1571 0.5720 0.275 0.78357
seasons3 0.9665 0.5870 1.646 0.09966 .
seasons4 1.3238 0.5000 2.648 0.00810 **
Figure b. Probability of being regionally rare in relation to log_{10} body size, and season number, when rare locally is defined as being present in at least three other habitat types.

present in at least 2 other habitats or at least 0.5% relative abundance when present anywhere
Deviance Residuals:
Min 1Q Median 3Q Max
1.948 1.002 0.593 1.045 1.526
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 0.80056 0.35602 2.249 0.02453 *
log10size 0.57940 0.33887 1.710 0.08731 .
seasons2 0.03185 0.45528 0.070 0.94423
seasons3 1.07981 0.56577 1.909 0.05632 .
seasons4 1.49990 0.50857 2.949 0.00319 **
Figure c. Probability of being regionally rare in relation to log_{10} body size, and season number, when rare locally is defined as being present in at least two other habitat types or at least 0.5% of total abundance when present.

present in at least 2 other habitats or at least 1% relative abundance when present anywhere
Deviance Residuals:
Min 1Q Median 3Q Max
1.9502 0.9500 0.7793 1.0848 1.6061
Coefficients:
Estimate Std. Error z value Pr(>z)
(Intercept) 0.9438 0.3617 2.610 0.00907 **
log10size 0.5850 0.3390 1.725 0.08444 .
seasons2 0.1716 0.4672 0.367 0.71339
seasons3 0.9775 0.5525 1.769 0.07688 .
seasons4 1.6387 0.5105 3.210 0.00133 **
Figure d. Probability of being regionally rare in relation to log_{10} body size, and season number, when rare locally is defined as being present in at least two other habitat types or at least 1% of total abundance when present.
1. Wickham H. 2009 ggplot2: elegant graphics for data analysis. New York, Springer.
S 4
Distribution of body size (log_{10} wet weight)
