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Testing the r' method of estimating per capita growth rate in Aedes albopictus Matthew Chmielewski, Camilo Khatchikian and Todd Livdahl Department of Biology, Clark University, Worcester MA Abstract Results The per capita rate of change was found to be an accurate Discussion We used laboratory populations of the Asian Tiger Mosquito -1 0.15 predictor of trends in instantaneous growth rate when r was Given the ability of r’ to correctly predict trends in r, this study Aedes albopictus to compare Livdahl and Sugihara’s (1984) method Per capita rate of change (r) d regressed on r′ (F2,28 = 9.14, p<0.01, Figure 1). Despite an further supports the use of r’ as a method of predicting population of projecting population growth rate (r') with the derived population accurate correlation, r’ tended to overpredict r. Analysis of growth rates. The lack of accuracy in the values of r’ relative to r growth rate (r) generated using life table methods. Additionally, we tested r’ for possible density effects by raising populations of three 0.1 covariance among density groups failed to show a significant can be further diagnosed by studying the r’ equation itself. In order interaction between r′ and density (ANCOVA, F2,24=0.72, p=0.50), to determine why the r′ values were not accurate, it is important to different larval densities. r’ was found to be a significant predictor of indicating that the predictive capacity of r′ was robust to differences look at the equation for r′ in terms of numerator (Ro) and trends in r, although accuracy was low. Additionally, r’ was not found to be susceptible to density effects, supporting the robustness of this in larval density conditions. Further support for the robustness of r′ denominator () driving the overall value of r′ . 0.05 as a predictor is indicated by no significant departure from the The conjunction of an overestimate of Ro (Figure 3)and method regardless of the level of larval competition. overall model for any of the density groups after the interaction term underestimate of t (Figure 4) is the driving factor in the inflation of r′ had been removed (ANCOVA, F2,26=0.27, p=0.76). relative to r. The overprediction of Ro most likely has to do with the 0 Regressions of r and r′ on density (n) were both significant (r: assumption that a given female will have a reproductive output that Introduction 0 0.05 0.1 0.15 F2,28=7.02, p=0.01; r′: F2,28=166.45, p<0.01, Figure 2). Once can be predicted by her size. The amount of variation in egg laying Livdahl and Sugihara’s1 method of projecting population growth regressed, the predicted values of the maximum per capita rate of based on size may be large enough in this population to cause the rate (r’), -0.05 increase (r: 0.056; r’: 0.11) and carrying capacity (r: 21.35; r’: 34.74) overprediction. were found to be quite variable, indicating that r’ is prone to The underestimation of t may stem from the same issue, but 1 Estimated per capita rate of producing inflated values in these populations statistics. it may also come from the assumed value of D, the time lag ln N0 A x f (w x ) change (r') d-1 The net reproductive rate (Ro) generated using the r’ method between emergence and the beginning of oviposition. The tended towards overpredicting r-derived Ro (Figure 3). Alternately, r’ r' x  assumed value of D may be too low, although it is more likely that D xA f (w ) x x Figure 1: r (derived population growth rate) regressed on r′ tended to underpredict the cohort generation time () when compared with r (Figure 4). is not constant with every population. Because of the consistency of prediction across densities, it is tempting to suggest a simple D x (projected population growth rate (y = 0.8831x - 0.0389, R2 = corrective calibration of r’ to adjust for the overestimation. We do A f (w ) x x 0.246, F2,28 = 9.14, p<0.01). The diagonal line through the not advocate this because of the likely difference between survival x origin represents the ideal correlation (1:1) between r and r′. and reproductive rates under field and laboratory conditions. As Those values below this line represent an overestimate of r by survival in laboratory conditions seems likely to exceed field allows for a less time consuming and less resource intensive method, r′, and those values above the line represent an underestimate. survival, and blood meal access in field conditions is likely to be when compared to traditional life table (r) calculations, of much more difficult, the lengthy period of reproduction observed in 40 understanding population growth. Due to the accessibility of this this study may not be approached by field populations. As such, a method, a number of studies have gone on to employ r’ as a measure major source of error in r’ estimates could be reduced, and the Value of Ro derived using life table (r) 0.12 35 Per capita rate of change (r) d -1 of population success. Despite the ease of use, it has been unclear predictive ability of r’ could actually be improved under field whether or not r’ might be sensitive to density effects. 0.1 conditions. We aimed to examine the applicability of r’ in predicting r in the 30 0.08 Asian Tiger Mosquito Aedes albopictus. In particular we were interested in how well population growth rates generated using r’ 0.06 25 methods methods reflect changes in population growth derived via life table 0.04 20 methods in the presence of multiple larval densities. 0.02 15 0 120 0 5 10 15 -0.02 10 Value of τ derived from life table (r) -0.04 Methods 5 100 -0.06 F1 generation Aedes albopictus eggs (adult collection in Bermuda) were hatched and the larvae subsequently sorted into 0 0 5 10 15 20 25 30 35 40 80 three different densities (low=5, medium=10, and high=15 individuals 30 mL-1), with ten replicates each. Adults were kept in 20 x 20 x 20 0.12 Value of Ro using r' methods methods cm mesh cages and given the opportunity to blood feed every two d. 60 On feeding days, egg-trap liners were removed so that eggs could be 0.1 Per capita rate of change (r') d-1 counted. Additionally, dead females were removed and wing lengths were measured. 0.08 Figure 3: The net reproductive value (R0) derived from the life table 40 Age-specific survival fractions (lx) and fecundity values (mx) t 0.06 study regressed on the net reproductive value (R0) estimated from the were constructed in order to iteratively find the derived population r′ calculations (y = 0.2016x + 8.184, R2 = 0.0103, F2,28=0.34, p=0.57). growth rate (r) using the Lotka-Euler equation2: 0.04 Any values below the 45 degree x=y line represent an overestimation 20 1 l x mx e rx  of R0 by the r′ calculation. Any values above the line represent 0.02 underestimates. x 0 A projected population growth rate (eqn. ) was derived for References 0 20 40 60 80 100 120 t 0 each replicate, and was regressed against the derived population 1. Livdahl, T.P. and Sugihara, G. (1984) Non-linear interactions of Value of τ estimated using r' methods 0 5 10 15 growth rate. An analysis of covariance was conducted to observe populations and the importance of estimating per capita rates of possible density effects that might change the predictive capability of r’ Larval density (individuals 30mL-1) change. Journal of Animal Ecology 53: 573-580. in various density regimes. These two growth rate measures were 2. Lotka, A. J. 1907. Studies on the mode of growth of material Figure 4: The net cohort generation time (t) derived from the life table then regressed on larval density, allowing for a measure of potential Figure 2: r and r’ regressed by larval density (r: y = -0.0026x + 0.0555, aggregates. American Journal of Science 24:199-216. study regressed on the cohort generation time (t) estimated from the r′ carrying capacity (K) and maximum growth rate (rmax) of the study R2 = 0.2005, F2,28=7.02, p=0.01; r’: y= -0.0031x+0.1077, R2 = 0.856, calculations (y = 0.6912x + 50.739, R2 = 0.1056, F2,28=2.64, p=0.12). species. F2,28=166.45, p<0.01). The y intercept predicts rmax (r 0.056; r’ 0.11), Any values below the 45 degree x=y line represent an overestimation The net reproductive value (Ro) and cohort generation time () Acknowledgments of t by the r′ calculation. Values above the line represent the maximum per capita rate of increase one could expect these for both methods of generating population growth rate were compared We thank the Department of Biology, Clark University, the National populations to exhibit. The x intercept predicts K (r 21.35; r’: 34.74), the underestimates with one another to determine where variation in the prediction of r by Institutes of Health (R15 AI062712-01) and the Keck Foundation for carrying capacity for this species under similar environmental r’ might be generated. supporting this project. conditions.
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