Fig. 2 Diagram illustrating the way temperature dependence was modeled

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Fig. 2 Diagram illustrating the way temperature dependence was modeled Fig. 2 Diagram illustrating the way temperature dependence was modeled. (Top row) Typical stage-structured model, where transition probabilities are temperature independent. (Middle row) Two stages might be modeled in physiological age units (eggs, 7 DD; and instar 1, 6 DD), where temperature T<sub>1</sub> is 2 degrees above MTD and temperature T<sub>2</sub> is 4 degrees above MTD. (Bottom row) Effect of temperature on the transition matrix (see explanation in text). From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 1 General structure of the transition matrix A Fig. 1 General structure of the transition matrix A. The upper left submatrix is the temperature-dependent component of the model. The structure of each submatrix is explained in detail in the text. From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 3 (A) Average daily temperature between 1990 and 2003 for three sites at the east side of Mauna Loa, Hawaii. Four different seasons are separated by vertical dashed lines. (B) Mean monthly rainfall (1990–2003) at the same stations. (C) Relationship between temperature (°C) and population growth rate for a constant daily temperature regime. Log-log linear regression: intercept, −276.08; slope, 104.07; R<sup>2</sup> = 0.998. (D) Relationship between temperature (°C) and population growth rate for the seasonal temperature regime. Log-log linear regression: intercept, −280.5; slope, 104.5; R<sup>2</sup> = 0.999. (E) Relationship between elevation and mean annual temperature for stations on the east side of the Big Island of Hawaii. Linear regression: intercept, 23.06; slope, −0.00571; R<sup>2</sup> = 0.978. The vertical dash line shows the maximum elevation at which the population can grow. (F) Relationship between temperature and the population growth rate (λ) during four different seasons within a year (each number is a season). Log-log linear regression for summer: intercept, −68.6691; slope, 26.56; R<sup>2</sup> = 0.998. From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 4 (A) Survival of immatures as a function of the number of previous consecutive “dry” days (below a threshold ϕ) at different sensitivities to drought (ω). (B) Density dependent survival (D) for immatures as a function of the number of individuals in the cavity. Solid curves show the low (L) density-dependent scenario, and broken curves the high (H) density-dependent scenario. Curves are shown for each of three physiological ages i: 31 (instar 1), 131 (instar 3), and 179 (pupae). From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 5 Digital elevation map of the Island of Hawaii showing the maximum elevation at which mosquitoes can persist on an annual basis (white line) and during the summer period (dark line). From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 6 Population projections of mosquitoes at three different elevations under low- and high-density dependence (high elevation, 1,580 m; middle elevation, 1,200 m; and low elevation, 11 m). Projections were started in 1988 to allow for transient dynamics with 10 individuals in each physiological age and adult age class. The parameters used where ϕ = 5 and ω = 0.1 for all elevations. From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 7 Isoclines of population growth (left column) as a function of threshold daily rain and sensitivity to drought for an extreme dry year (1995, broken lines) and an extreme wet year (1990, solid lines) at three elevations (same as Fig. 6). The dots in each graph represent a particular combination of parameters used to run population projections (right column). A week where an extreme rainfall event occurred is shown as a vertical dotted line. All simulations were run under low-density dependence, started with 10 individuals in each class and run for two previous years to allow for transient dynamics. From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Fig. 8 Comparison of number of adult Cx Fig. 8 Comparison of number of adult Cx. quinquefasciatus per 100 trap nights (open circles and lines) with model fits (solid lines) at each of three different elevations: C.J. Ralph (1,800 m), Crater rim (1,200 m), and Bryson's (280 m). Time is measured as the number of days since 1 January 2002. Dotted vertical line indicates the end of 2002. At the highest elevation, the model predicts no mosquitoes, so no climatic stations were used for the fit. Best fit parameters and R<sup>2</sup>: middle elevation, ϕ = 5, ω = 0.342, R<sup>2</sup> = 0.75; and low elevation, ω = 6, ω = 0.716, r<sup>2</sup> = 0.41. From: Modeling the Population Dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an Elevational Gradient in Hawaii J Med Entomol. 2004;41(6):1157-1170. doi:10.1603/0022-2585-41.6.1157 J Med Entomol | © 2004 Entomological Society of AmericaThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com