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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


  1. 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 log10 body size, and lake number, when rare locally is defined as being present in two other habitat types.



  1. 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 log10 body size, and lake number, when rare locally is defined as being present in three other habitat types.


  1. 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 log10 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.

  1. 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 log10 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 log10 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 log10 body size, and season number, when rare locally is defined as being present in at least three other habitat types.


  1. 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 log10 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.


  1. 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 log10 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 (log10 wet weight)





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