Appendix A: Insect Production Values for Lentic Waterbodies from the Literature
Site name / Location / InsectProduction
(g C·m−2·y−1) / Source
Texas pond / Texas, USA / 4.6 / (Benson and others 1980)
tundra pond J / Alaska, USA / 3.1 / (Hobbie 1980)
tundra pond D / Alaska, USA / 1.0 / (Hobbie 1980)
tundra pond B / Alaska, USA / 0.7 / (Hobbie 1980)
Crampton Lake / Michigan, USA / 1.9 / (Babler and others 2008)
Alderfen Broad / UK / 1.2 / (Mason 1977)
Upton Broad / UK / 5.1 / (Mason 1977)
Lake Manitoba / Manitoba, Canada / 1.5 / (Tudorancea and others 1979)
Lake Ontario,
Bay of Quinte / Ontario, Canada / 1.6 / (Johnson and Brinkhurst 1971)
Lake Ontario / Canada-USA / 0.2 / (Johnson and Brinkhurst 1971)
Eglwys Nunydd Res. / UK / 9.9 / (Potter and Learner 1974)
Ovre Heimdalsvatn / Norway / 0.4 / (Larsson and others 1978)
Mirror Lake / New Hampshire, USA / 3.3 / (Strayer and Likens 1986)
Port-Biehl / France / 1.0 / (Laville 1975)
Char / Northwest Territories, Canada / 0.2 / (Welch Jr 1973; Welch 1976)
Lake Myvatn / Iceland / 18.1 / (Jónasson and others 1990; Lindegaard and Mæhl 1992; Lindegaard 1994)
Hjarbaek Fjord / Denmark / 23.6 / (Lindegaard 1994)
Thingvallavatn / Iceland / 1.1 / (Jónasson and others 1990)
Esrom / Denmark / 14.3 / (Jónasson and others 1990)
Werowrap / Australia / 31.2 / (Paterson and Walker 1974)
Lake 95 / Greenland / 0.5 / (Lindegaard and Mæhl 1992)
Lake Zelenetzkoye / USSR / 0.2 / (Winberg 1972)
Red / USSR / 2.1 / (Andronikova and others 1972)
Naroch / USSR / 0.9 / (Winberg 1972)
Myastro / USSR / 0.4 / (Winberg 1972)
Batorin / USSR / 1.5 / (Winberg 1972)
Memphremagog / Canada–USA / 1.4 / (Dermott and others 1977)
Erie / Canada–USA / 1.0 / (Johannsson and others 2000)
Appendix B: Insect Production Values (g C·m−2·y−1) for Lotic Waterbodies from the Literature
Site name / Location / Production Insects(g C·m−2·y−1) / Source
Oconee / USA (GA) / 19.6 / (Nelson and Scott 1962)
Satilla / USA (GA) / 9.9 / (Benke 1984)
Satilla / USA (GA) / 8.4 / (Benke 1984)
Satilla / USA (GA) / 30.5 / (Benke 1984)
Factory Brook / USA (MA) / 2.1 / (Neves 1979)
Fort / USA (MA) / 1.6 / (Fisher 1977)
Shane Creek / USA (MI) / 0.5 / (Entrekin and others 2007)
St Marys / USA (MI) / 5.9 / (Duffy and others 1987)
State Creek / USA (MI) / 1.3 / (Entrekin and others 2007)
Walton Creek / USA (MI) / 0.6 / (Entrekin and others 2007)
North Branch / USA (MN) / 5.2 / (Krueger and Waters 1983)
CIII / USA (NC) / 6.6 / (Lugthart and Wallace 1992)
CIV / USA (NC) / 5.4 / (Lugthart and Wallace 1992)
CIV / USA (NC) / 2.1 / (Lugthart and Wallace 1992)
Convict / USA (NC) / 2.1 / (Leland and others 1986)
CV / USA (NC) / 4.5 / (Lugthart and Wallace 1992)
Upper Ball / USA (NC) / 3.7 / (Huryn and Wallace 1987)
Bear Brook / USA (NH) / 1.9 / (Fisher and Likens 1973)
Douglas / USA (WA) / 10.9 / (Gaines and others 1992)
Rattlesnake / USA (WA) / 7.7 / (Gaines and others 1992)
Snively / USA (WA) / 6.6 / (Gaines and others 1992)
Rold Kilde / Denmark / 1.4 / (Mothiversen and Thorup 1987)
Estaragne / France / 2.9 / (Lavandier and Décamps 1984)
Pioverna / Italy / 0.5 / (Buffagni and Comin 2000)
Takami / Japan / 30.2 / (Gose 1975)
Hinau / New Zealand / 3.9 / (Hopkins 1976)
Hinau / New Zealand / 15.3 / (Hopkins 1976)
Hinau / New Zealand / 34.6 / (Hopkins 1976)
Horokiwi / New Zealand / 16.8 / (Hopkins 1976)
Horokiwi / New Zealand / 9.2 / (Hopkins 1976)
Horokiwi / New Zealand / 19.6 / (Hopkins 1976)
Ekso / Norway / 0.7 / (Baekken and others 1984)
Ekso / Norway / 0.4 / (Baekken and others 1984)
Ekso / Norway / 0.3 / (Baekken and others 1984)
Ekso / Norway / 0.5 / (Baekken and others 1984)
Ekso / Norway / 0.9 / (Baekken and others 1984)
Appendix C: Model Assumptions and Sensitivity analysis
There are a number of assumptions, potential sources of error, and caveats which we address below. First, our analysis does not include most wetland habitats. We only considered waterbodies that are classified as ‘lentic’ (lakes, ponds and reservoirs) or ‘lotic’, relying on the available hydrography datasets for Wisconsin (WDNR 2011). Wetlands cover approximately 15% of the state of Wisconsin (WDNR 1998). Although some wetlands produce aquatic insects (Batzer and Wissinger 1996), the term ‘wetland’ encompasses a remarkably diverse range of habitat types, making them difficult to incorporate into this analysis. Our analysis only includes habitats classified as lotic or lentic, as such, it may be a conservative estimate of total aquatic insect emergence Wisconsin.
Second, estimates of waterbody area are important in this model, because area was the primary factor determining aquatic insect inputs from water to land. Shapefiles for lentic waterbodies were taken from the highest resolution hydrography datasets available for Wisconsin (WDNR, 2011). This data set is incredibly detailed, and includes a total of 87,400 lentic waterbodies, with a median surface area of 0.18 hectares. Because lakes larger than the median make up 99.1% of the total surface area of these features (excluding the Great Lakes), we are confident that this data set approximates actual lentic waterbody surface area for this landscape. Stream width for small lotic systems that were not included as shapefiles in the hydrography datasets was estimated from an empirical model. Although the model had high predictive power for estimating stream width (RMSE = 37%), our estimates of surface area of individual lotic features are less precise than those of lentic features. However, because our analysis of statewide and watershed-scale emergence patterns are based on summing estimates from hundreds or thousands of features, aggregate errors in emergence due to errors in surface area estimates are likely to be minimal.
Third, the modeling approach distributes all aquatic insect emergence to the surrounding land. We did not adjust for the fraction of insect emergence that falls back to water, how much it varies, and whether it varies with lake/stream attributes. As such, our estimates reflect potential aquatic insect inputs to land - the realized inputs would fall below this level since some fraction of emergent insects return back to the water. Jackson and Fisher (1986) in their study of a productive Sonoran desert (USA) stream found that about 3% of emergent aquatic insects return to water. We know of no comparable estimates for lentic systems. Thus, we opted for the simplest approach of not attempting to adjust for this unknown effect that would undoubtedly reduce aquatic insect inputs to land, though we expect that it will be a small fraction of total emergence.
Finally, our analysis distributes emergent aquatic insects within a 100 m buffer zone surrounding lakes and streams. Though our assumption of a 100 m buffer zone is empirically based (Gratton and Vander Zanden 2009) this value is an estimate. Like many of our assumptions, the penetration of emergent aquatic insects to land is likely to vary depending on species composition, environmental conditions, and landscape context. Related to this, we did not apply a distance decay function to distribute insect emergence within riparian zones because our focus was on aggregate landscape patterns, rather than fine-scale patterns within buffers. How emergent aquatic insects are spread within the buffer zone is not relevant at the broad spatial scales considered in this study.
Estimating production and emergence - An important aspect of the model involves assigning insect production values to individual waterbodies. For lakes, we estimated per unit area production from Secchi depth using eq. 1 for the 8,602 lakes for which Secchi was available, and we applied the geometric mean for the remaining lakes. The alternative approach would have been to apply the geometric mean production value to all lakes. Comparison of these two approaches revealed a near 1:1 correlation between the two deposition estimates, both when comparing individual lakes (Depbuffer; Figure A1, A) and when aggregating at the watershed scale (Deptotal-watershed; Figure A1, B). Total statewide emergence, Estate, using the Secchi method was 5.4x109 gC·y−1, whereas simply applying the geometric mean gave an estimate that was 9% higher (5.8x109 gC·y−1), and the contribution of lakes to total emergence increased from 79% to 81%. This difference occurs primarily because the two approaches give different estimates for Lake Superior and Lake Michigan. For these two exceptionally clear lakes (Secchi depths of 20 m and 12 m, respectively), the Secchi model estimates total insect production to be 0.3×109 gC·y−1 (per unit area production: 0.58 gC·m−2·y−1) for Superior and 0.8×109 gC·y−1 (per unit area production: 0.82 gC·m−2·y−1) for Michigan. In contrast, use of the geometric mean assigns much higher per unit area insect production (2.07 gC·m−2·y−1) to these lakes. Due to their large surface areas, this has a significant effect on the individual, overall (watershed), and statewide calculations (Figure A1). For these reasons, the Secchi model provides a better overall estimate.
We also examined the effect of incorporating model uncertainty into estimates of insect production (P). For lentic systems, where Secchi depth was available, the predicted value of P was perturbed using estimates of uncertainty of P from the regression model output. Specifically, we randomly selected values from the distribution of model residuals, and added them to the estimated P. In the absence of Secchi estimates, values were randomly drawn from a kernel density distribution of insect production (log transformed, obtained from the literature, Appendix 1). The probability density function was estimated using density function in R (R Development Core Team 2013), with Gaussian smoothing and bandwidth nrd0, which is 0.9 times the minimum of the standard deviation and the interquartile range divided by 1.34 times the sample size to the negative one-fifth power (Silverman 1986). For lotic systems, values of P from the regression model were perturbed randomly in accordance with the observed model error (RMSE). Using these ‘error-adjusted’ values of P, Depbuffer and Deptotal-watershed were calculated for lotic and lentic systems. We compared Depbuffer and Deptotal-watershed calculated from ‘base’ and ‘error-adjusted’ insect production values. The procedure was repeated 100 times to obtain distributions of insect deposition based on P values that include model uncertainty.
There was little overall difference between ‘base’ and ‘error-adjusted’ estimates of deposition for either lentic or lotic systems, though for individual ecosystems (Depbuffer), a comparison of base and error-adjusted estimates generated substantial scatter (Figure A2, Figure A3). Statewide, error-adjusted emergence ranged from 10% lower to 20% higher for lentic systems, and from 5% lower to 1% higher for lotic systems. Overall, error adjustment had little impact on the relative contributions of lotic and lentic systems to statewide emergence. Our general findings are robust to efforts to adjust insect production estimates for the error in regression model predictions.
Figure A1. A comparison of lentic aquatic insect deposition calculated using two methods: insect production values estimated from Secchi depth where possible (y-axis), and calculated using the geometric mean of insect production values for all lentic waterbodies (x-axis). A) Comparison for individual lakes (Depbuffer), B) Comparison of results aggregated at the watershed scale (Deptotal-watershed). 1:1 lines are shown.
Figure A2. Comparing aquatic insect inputs to land (gC·m−2·y−1) for lentic systems estimated in two ways: ‘base’ estimates from our Secchi-based regression model (x-axis), and the error-adjusted estimate from our Secchi-based regression model (y-axis). Comparison for A) individual lentic waterbodies (Depbuffer) and B) results aggregated at the watershed scale (Deptotal-watershed). 1:1 lines are shown.
Figure A3. Comparing aquatic insect inputs to land (gC·m−2·y−1) for lotic systems estimated in two ways: ‘base’ model predictions from our regression model (x-axis), and ‘error-adjusted’ model prediction from our regression model (y-axis). A) Comparison for individual waterbodies (Depbuffer), B) comparison of results aggregated at watershed scale (Deptotal-watershed). 1:1 lines are shown.
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