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Introduction

A growing body of literature suggests that demography-based approaches are far more effective in determining what happens to populations subjected to stressors or disturbance than short-term acute mortality estimates (e.g., LC50) (Van Straalen, Schobben & De Goede, 1989; Forbes & Calow, 1999; Sibly, 1999; Calow, Sibly & Forbes, 2001; Pastorok et al., 2002; Stark & Banks, 2003; Akçakaya, Stark & Bridges, 2008; Barnthouse, Munns & Sorensen, 2008). In particular, demography-based approaches can address issues such as sub-lethal effects, stage- or age-specific life history rates, and time-varying demographic processes far better than more static methods (Stark & Banks, 2003; Banks et al., 2008). However, the development of demographic data is costly and time-consuming. In some toxicological risk assessments, researchers have attempted to use partial life table data instead to predict population outcomes (Laskowski & Hopkin, 1996; Preston & Snell, 2001; Ducrot et al., 2010). However, it is not clear how predictions from these studies incorporating partial life tables compare with studies using complete life tables. In particular, little attention has been paid to the tradeoff between accuracy and experimental effort when comparing partial vs. full life table studies. We offer here an exploration of this issue, in which population outcomes from complete life tables are compared with those developed from partial life tables for three Daphniid species. We address the issue of whether or not partial demographic data can be used in lieu of complete demographic data without loss of accuracy in projecting population outcomes. Finally, we compare outcomes for lambda vs. other demographic parameters across all species, and assess the overall potential for using reduced datasets to generate reliable population projections.

Materials and Methods

Species tested

Three species of Daphniids were evaluated in this study; Ceriodaphnia dubia (Richard) Daphnia pulex (Leydig) and D. magna (Straus). Individuals used to develop life table data were obtained from cultures maintained at Washington State University, Puyallup Research and Extension Center. Each species was reared in reconstituted dilution water (RDW). The RDW used in this study was prepared according to a method modified from a USEPA protocol (USEPA, 2002) resulting in a RDW with pH 7.4–7.8, conductivity 260–320 µS, dissolved oxygen (DO) >8.0 mg/l, alkalinity of 60–70 mg/l and a hardness of 80–100 mg/l. Daphniids were maintained in an environmental chamber set with a photoperiod of 18 h: 6 h light: dark, 25.0 ± 0.1 °C, and 50.0 ± 0.1% relative humidity (RH).

The Daphniids were fed a solution consisting of a 1:1.5 mixture of yeast-cereal leaves-trout chow (YCT) and the algal species Pseudokirchneriella subcapitata (previously Selenastrum capricornutum) (Charles River Co., Wilmington, MA, USA).

Development of life tables

Individuals (<24 h old) at or beyond the third filial (F3) generation were transferred into glass beakers containing 25 ml RDW. Founding individuals were moved to fresh RDW every other day. Three batches (replicates) of 10 individuals of each species were used to develop life tables. Individual survival and the number of offspring produced were recorded daily throughout their life span. Offspring were removed daily. Life tables were developed at weekly intervals and at the end of each species life cycle. Beakers were held in an environmental chamber under the conditions listed above for colony maintenance.

Life tables were developed following the approach outlined in Carey (1993) and Vargas et al. (2002). The following demographic parameters were determined in this study: Net Reproductive Rate (Ro), the per generation contribution of newborn females to the next generation, Intrinsic Birth Rate (b), the per capita instantaneous rate of birth in the stable population, Intrinsic Death Rate (d), the per capita instantaneous rate of death in the stable population, Mean Generation Time (T), the time required for a newborn female to replace herself R0-fold, Doubling Time (DT), the time required for the population to increase twofold, Intrinsic Rate of Increase (rm), the rate of natural increase in a closed population, and the Finite Rate of Increase (λ), the factor by which a population increases in size from time t to time t + 1.

Statistical analysis

The data for all of the above mentioned demographic parameters were analyzed with one-way analysis of variance (ANOVA) (SAS Institute, Cary, NC, USA) to test for differences between results for the entire life table to the partial life tables , means of each demographic parameter for the partial life tables were compared to the results from the full life table using a Dunnett’s test. For each species, we compared the value of the demographic parameter of interest for each successive week to that derived from the complete life table (full life span). We thus determined the week at which the demographic parameter value was not statistically significant different (p < 0.005) from the value derived using the entire life span (complete life table), heretofore referred to as the “cutoff point.”

Results

C. dubia

The time at which net reproductive rate (Ro), birth rate (b), rm, and λ were not significantly different from the complete life table for C. dubia was four weeks (Table 1).That is, if Ro was the endpoint of interest for this species, a life table would only have to be developed for four weeks to generate the same R0 value stemming from a complete life table (nine weeks). For death rate (d) the cutoff was three weeks while the cutoff point for both generation time (T) and doubling time (DT) for C. dubia was five weeks. (Table 1).

Table 1:
C. dubia life table variables determined at weekly intervals.*
X ± SEM
Life table value Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9
Ro 12.17 ± 1.25b 50.43 ± 2.50b 103.17 ± 7.11b 153.83 ± 14.00b 199.67 ± 21.15a 228.90 ± 23.88a 237.90 ± 22.06a 239.40 ± 21.69a 239.80 ± 21.7a
Birth rate (b) 0.35 ± 0.016b 0.33 ± 0.007b 0.28 ± 0.003b 0.25 ± 0.003b 0.23 ± 0.002a 0.21 ± 0.000a 0.205 ± 0.002a 0.204 ± 0.002a 0.204 ± 0.002a
Death rate (d) −0.06 ± 0.011b −0.07 ± 0.004b −0.05 ± 0.001b −0.04 ± 0.000a −0.03 ± 0.000a −0.03 ± 0.000a −0.02 ± 0.001a −0.02 ± 0.001a −0.02 ± 0.001a
Gen. time (T) 6.11 ± 0.25b 9.78 ± 0.23b 13.99 ± 0.28b 17.50 ± 0.46b 20.70 ± 0.53b 22.98 ± 0.37a 23.88 ± 0.23a 24.06 ± 0.17a 24.12 ± 0.11a
Doubling time (DT) 1.71 ± 0.12b 1.74 ± 0.06b 2.09 ± 0.03b 2.41 ± 0.03b 2.71 ± 0.02b 2.94 ± 0.02a 3.03 ± 0.05a 3.05 ± 0.05a 3.05 ± 0.05a
rm 4.090 ± 0.027b 0.331 ± 0.007b 0.331 ± 0.004b 0.287 ± 0.004b 0.255 ± 0.002a 0.236 ± 0.001a 0.229 ± 0.004a 0.227 ± 0.004a 0.227 ± 0.004a
Lambda (λ) 1.507 ± 0.040b 1.494 ± 0.016b 1.393 ± 0.006b 1.333 ± 0.005b 1.291 ± 0.003a 1.266 ± 0.002a 1.257 ± 0.005a 1.255 ± 0.005a 1.255 ± 0.005a
DOI: 10.7717/peerj.2067/table-1

Notes:

*, Dunnett’s test.

D. pulex

The cutoff point for d was three weeks while the cutoff values for, rm and λ were four weeks. Cutoff values for Ro, b, T, and DT were five weeks (Table 2).

Table 2:
D. magna life table variables determined at weekly intervals.*
X ± SD
Life table value Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10
Ro 14.07 ± 0.78b 73.13 ± 6.21b 98.60 ± 9.37b 129.20 ± 13.58b 169.50 ± 18.65b 204.13 ± 15.07b 222.77 ± 11.81a 238.04 ± 11.76a 243.47 ± 12.33a 244.34 ± 13.58a
Birth rate (b) 0.33 ± 0.005b 0.35 ± 0.006b 0.32 ± 0.003b 0.27 ± 0.003b 0.23 ± 0.003b 0.21 ± 0.006b 0.20 ± 0.008b 0.19 ± 0.007a 0.18 ± 0.007a 0.184 ± 0.006a
Death rate (d) −0.05 ± 0.003b −0.08 ± 0.003b −0.06 ± 0.001b −0.05 ± 0.001b −0.03 ± 0.001b −0.03 ± 0.002b −0.02 ± 0.002a −0.02 ± 0.002a −0.02 ± 0.002a −0.02 ± 0.001a
Gen. time (T) 7.00 ± 0.00b 10.09 ± 0.14b 12.08 ± 0.12b 15.22 ± 0.12b 19.24 ± 0.18b 22.58 ± 0.43b 24.54 ± 0.84b 26.35 ± 0.89a 27.11 ± 0.87a 27.25 ± 0.72a
Doubling time (DT) 1.84 ± 0.04b 1.63 ± 0.04b 1.82 ± 0.02b 2.17 ± 0.03b 2.60 ± 0.03b 2.94 ± 0.10b 3.15 ± 0.14b 3.34 ± 0.14a 3.42 ± 0.14a 3.44 ± 0.12a
rm 0.378 ± 0.008b 0.425 ± 0.009b 0.380 ± 0.004b 0.319 ± 0.005b 0.267 ± 0.004b 0.236 ± 0.008b 0.220 ± 0.010b 0.208 ± 0.009a 0.203 ± 0.008a 0.202 ± 0.007a
Lambda (λ) 1.459 ± 0.012b 1.530 ± 0.014b 1.462 ± 0.006b 1.376 ± 0.006b 1.305 ± 0.005b 1.266 ± 0.010b 1.247 ± 0.010b 1.231 ± 0.011a 1.225 ± 0.010a 1.224 ± 0.009a
DOI: 10.7717/peerj.2067/table-2

Notes:

*, Dunnett’s test.

D. magna

For D. magna, the cutoff times for Ro and d were six weeks while the cutoff times for b, T, DT, rm, and λ were seven weeks (Table 3).

Table 3:
D. pulex life table variables determined at weekly intervals.*
X ± SD
Life table value Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9
Ro 8.70 ± 1.04b 69.80 ± 7.60b 122.83 ± 15.95b 169.43 ± 19.00b 201.60 ± 18.28b 223.50 ± 13.87a 231.40 ± 9.43a 234.93 ± 5.30a 237.43 ± 2.66a
Birth rate (b) 0.31 ± 0.013b 0.33 ± 0.005b 0.30 ± 0.004b 0.26 ± 0.004b 0.24 ± 0.006b 0.23 ± 0.008a 0.22 ± 0.011a 0.22 ± 0.014a 0.22 ± 0.017a
Death rate (d) −0.03 ± 0.009a −0.07 ± 0.003b −0.05 ± 0.002b −0.04 ± 0.003b −0.03 ± 0.003a −0.03 ± 0.004a −0.03 ± 0.005a −0.03 ± 0.006a −0.03 ± 0.007a
Gen. time (T) 6.27 ± 0.04b 10.54 ± 0.07b 13.79 ± 0.26b 16.78 ± 0.01b 19.12 ± 0.32b 21.03 ± 0.75a 21.86 ± 1.22a 22.33 ± 1.75a 22.70 ± 2.14a
Doubling time (DT) 2.02 ± 0.13b 1.72 ± 0.04b 1.99 ± 0.03b 2.23 ± 0.05b 2.50 ± 0.08b 2.70 ± 0.13a 2.75 ± 0.18a 2.83 ± 0.23a 2.88 ± 0.28a
rm 0.344 ± 0.021b 0.402 ± 0.00ba 0.349 ± 0.006b 0.306 ± 0.007b 0.277 ± 0.009a 0.257 ± 0.012a 0.250 ± 0.016a 0.246 ± 0.020a 0.242 ± 0.023a
Lambda (λ) 1.411 ± 0.030b 1.495 ± 0.013b 1.417 ± 0.009b 1.357 ± 0.009b 1.320 ± 0.012a 1.294 ± 0.016a 1.284 ± 0.020a 1.278± 0.026a 1.275 ± 0.03a
DOI: 10.7717/peerj.2067/table-3

Notes:

*, Dunnett’s test.

Discussion

A number of studies have shown that incorporating demographic data into population models has the potential to improve population projections, an approach that has been widely used in conservation and ecological risk assessment (Forbes & Calow, 2002; Stark & Banks, 2003; Stark, Vargas & Banks, 2007; Forbes, Calow & Sibly, 2008; Hommen et al., 2010; Forbes et al., 2011; Mills et al., in press). However, demographic data are expensive to develop, and it is not clear how much data is needed to generate sufficiently accurate population endpoints. Past studies have empirically demonstrated that partial life tables may yield accurate population projections (Van Straalen, Schobben & De Goede, 1989; Oli & Zinner, 2001), but none to our knowledge have attempted to quantify the cutoff point beyond which adding more life history data does not improve accuracy. To this end, in this study we sought to determine the minimum amount of time a life table needs to be developed to get a measurement of species demographic parameters that is not statistically different from data developed over the entire life span of an organism. Our results suggest that if we were only interested in population growth rate (λ), commonly used in population studies, then partial life tables can be used without sacrificing accuracy. However, the cutoff times varied among the species we evaluated, with four weeks of data collection (instead of nine weeks) sufficient for C. dubia and D. pulex, but seven weeks (instead of ten weeks) necessary for D. magna. Notably, these cutoff times differed not only in real time, but also in terms of the proportion of the life span of each species. That is, accurate estimates of λ were generated from data collected for 70–80% of the lifespan of D. magna, whereas it took only 44% of the lifespan of C. dubia and D. pulix to generate accurate estimates for λ. Furthermore, there were no clear patterns discernible in differences among the other demographic parameters measured for the three species. For instance, accurate estimates of the death rate (d) were generated earlier than accurate estimates of λ. Taken together, the variable responses among parameters and among species suggests that simple predictions relating longevity or life history ecology patterns to the amount of data we need to accurately characterize population projections may not be forthcoming.

We compared the values of λ in the current study, as this parameter is mostly commonly used as a population endpoint in disciplines such as conservation science and ecotoxicology. However, it is important to note that an underlying assumption of the calculation of λ in life tables is that the population undergoes continuous exponential growth. This assumption may yield misleading population predictions in cases of density-dependence or time-varying per capita reproduction (e.g., Banks et al., 2008). More attention might be profitably paid to such contingencies; here the use of more sophisticated mathematical models may elucidate differences in life history that are driving differences in population outcomes.