University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Wildlife Damage Management, Internet Center Bird Control Seminars Proceedings for November 1976 EXAMINATION OF REDWINGED BLACKBIRD NESTLING GROWTH RATES USING THE LOGISTIC MODEL: A CASE FOR r AND k SELECTION? M. I. Dyer Natural Resource Ecology Laboratory, Fort Collins, Colorado Z. Abramsky Natural Resource Ecology Laboratory, Fort Collins, Colorado Follow this and additional works at: https://digitalcommons.unl.edu/icwdmbirdcontrol Part of the Environmental Sciences Commons Dyer, M. I. and Abramsky, Z., "EXAMINATION OF REDWINGED BLACKBIRD NESTLING GROWTH RATES USING THE LOGISTIC MODEL: A CASE FOR r AND k SELECTION?" (1976). Bird Control Seminars Proceedings. 62. https://digitalcommons.unl.edu/icwdmbirdcontrol/62 This Article is brought to you for free and open access by the Wildlife Damage Management, Internet Center for at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Bird Control Seminars Proceedings by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 121 EXAMINATION OF REDWINGED BLACKBIRD NESTLING GROWTH RATES USING THE LOGISTIC MODEL: A CASE FOR r AND k SELECTION? M.I. Dyer and Z. Abramsky 1 Natural Resource Ecology Laboratory Fort Collins, Colorado One of the few processes of an avian population t hat presents the opportunity to col - lect sensitive information about the performance of that population is growth rates of young throughout the brooding period. Growth rate data are sensitive to many conditions of the breeding cycle: proximate influences, such as food availability and weather (Fran - cis, et al., in prep.), and ultimate factors, such as species -specific characteristics, (Ricklefs, 1968). Additionally, the measurements themselves can be obtained with precision. The ability to make such detai led observations is extremely useful and is not always pos - sible for other population parameters, such as determining life table data. Ricklefs (1967) gave considerable attention to this subject and elaborated techniques for making compari - sons of growth rates of young of various bird species. From these, he and others (Fretwell and Bowen, 1974) have gone on to make several predictions about the status of various species and their populations in nature (Ricklefs, 1968, 1972, 1976). Two parameters emerged from Ricklefs' work that are quite important for examining these processes: (1) the rate of growth ( g)2 of the young throughout the nesting period and (2) fledging weight ( w) of the individual. Ricklefs (1967) presented three different curves which are us eful to fit nestling growth data: the logistic, Gompertz, and von Bertalanffy equations. To determine the growth function parameters, Ricklefs (1967) described a four -step graphical method of fitting the logistic equation to empirical weight data. Initial ly the asymptote of the growth curve is estimated; then the the growth data are recalculated as percentages of the estimated asymptote. For the third a conversion factor [= ¼ log (w/1 -w) where w = percentage of the asymptote for each data point, see Rickle fs, 1967] is calculated and plotted as a function of time. In the final step the relationship resulting from step 3 is checked: if it follows a straight line, the growth rate ( g) is calculated directly from the slope ( g = 4 x the slope). However, if the es timated growth rate ( g) does not follow a straight line, a new asymptote is determined and steps 1 -4 are reiterated (see Ricklefs, 1967). We were interested in investigating the hypotheses about intraspecific variability put forward by Ricklefs (1968) and in further determining the growth performances of the two major "populations" or "ecological races" (Mayr, 1963) of the Redwinged Blackbird ( Agelaius phoeniceus ), viz. marshland or wetland inhabitants and upland inhabitants. There have been reports about the possibilities of their distinctness (Dyer, 1964, 1968; Robertson, 1972, 1973a, b; Hesse and Lustick, 1972; Stone, 1973), and we wanted to test whether vital differ - ences exist in growth rates of young in the nest between the two biotopes. Such differe nces, if existent, especially in adjacent regions, would indicate major differences in ecological associations in upland and wetland biotopes and perhaps genetic differences between the two populations. METHODS Testing of Logistic Models Using Ricklefs' data (1967) we employed his suggested iterative method, but with dif - fering estimates of the asymptote (30.0, 30.5, and 31.3) (Table 1). We then computed values of g to determine if the growth rates were dependent upon the initial estimates of asymptotes. Further, if N is the total number of days in the record, Ricklefs 1 method uses day N -3 (=14) for the basic calculations. To see if the final outcome was sensitive to this choice, we compared these results to the outcome using N -1, N -2, …, N- 5. The growth rates obtained from these manipulations were tested for differences by a t -test (Table 2). The second method we considered is a straightforward, nonlinear least squares (NLLS) fit for the logistic. We obtained F and R 2 values for testing the significance of model parameters. The R 2 is an estimate of one minus the correlation ratio (Wilks, 1962:86) and is not a linear correlation coefficient. In general, R 2 depends on the particular sequence of times b y, …, b n; it is not comparable between data sets if the times of observation are not comparable. 1 Present address: Department of Ecology and Evolutionary Biology, The University of Arizona, Tucson, Arizona 85721. 2 We prefer g to k (used by Ricklefs) because it avoids confusion between the constant proportio nal to rate of growth in individuals and K used by MacArthur and Wilson (1967) for population growth conditions, all within the context of the logistic model. 122 Data on which logistic model was applied . The data on Redwings, which were used ini - tially to examine the performance of the two methods for estimating the logistic model, stemmed form several published reports and from Dyer (unpubl. data from Ontario, Canada) and Francis, et al. (unpubl. data of northern Ohio) (see Tables 3 and 4). As far as w e know, all values were obtained from field programs where marked nestlings were weighed to the nearest 0.1 g on daily or on alternate -day schedules. Even though we had detailed original data from which to compute the logistic equation, we chose to uniform ly use means of each day class throughout the nesting period so that those data reported in various literature sources could be utilized. For this report, we compare several examples of growth rate for males and females from Redwing marsh or wetland and up land habitats. RESULTS Comparison of Ricklefs’ Method and Nonlinear Least Squares Method We encountered difficulties with Ricklefs' method of computing the logistic values that gave us concern. When we computed the growth rate using his method and his da ta with three different asymptotes (30.0, 30.5, and the largest weight, 31.3), the resultant growth rates were significantly different (Table 1). This points out that Ricklefs' technique is sensi - tive to the first estimate of the asymptote and thus, biase d. Furthermore, when we corrected the asymptotes (the conversion factors do not fall on a straight line; see Ricklefs, 1967) using his method (based on the adjustment of days N -2, …, N -5) for each asymptote, we obtained significantly different values (Tabl e 2). This test also points out that Ricklefs' method is subjective, and the resultant growth rates are dependent upon (1) the first estimate of the asymptote and (2) if correction of the asymptote is needed, on the day from which the first asymptote estim ate was made, (to correct the asymptote (N - (N -i) = i, where N = days used for full growth period and i = day chosen for correction). Exceptions were classes N-2 for asymptotes 30.0 vs 30.5 (NS); 30.0 vs 31.3, 31.3 vs 30.5 (p < 0.1); and N -3 asymp - totes 31.3 vs 30.5 (NS). In order to see if correcting the asymptote according to day N -2 always yields consistent growth rate estimates or is just a coincidence, we examined several sets of Redwing growth data. In these cases the growth rates, which we obtained after correcting the asymptote according to day N -2, also were significantly different (p < 0.05). In this respect we feel we have demonstrated a considerable amount of sensitivity in the method which is dependent upon several starting assumptions. This sensitivity is mainly due to the initial estimate of the asymptote and is easily a place where one can go wrong in attempting to compute growth rates with consistency. To avoid these difficulties, we adopted a more objective method, viz. the NLLS method. By minimizing the sum of the squared deviaton of the fitted curve from the data, this technique finds the best estimates for growth rate and asymptote for any logistic growth data. The goodness of fit, as measured by R 2, for the blackbird data we have is n ever below 0.962 (Tables 3 and 4). Growth Characteristics of Redwinged Blackbird Nestlings The growth rates and asymptotic weights at the end of the nestling phase are given in Table 3 and Fig. 1 for 10 sets of Redwing data from wetland biotopes and 7 set s from upland biotopes. A comparison of growth rates of nestlings in these two biotopes using students' t-test show both the growth rates and asymptotic weights to be significantly different (p < 0.01, 15 df) (Table 3, Fig. 1). There are no demonstrable di fferences in g between males and females (p > 0.1, 27 df), but there are quite obviously major differences between the asymptotes for estimates of fledging weights (p < 0.01, 27 df) (Table 4, Fig.