566 P. Adamski and A. M. C´miel
where r is population growth rate and Kis habitat- determined population carrying capacity. Model parameters were estimated fromresults obtained during the design phase of the project and fromdata gathered during 1991–2019 using the methods and assumptions described below.
Estimation of model parameters
Carrying capacity and regime shift The estimated carrying capacity (K) of the study area before the project’s inception was based on host plant abundance only (Witkowski et al., 1992). In the Pieniny National Park, 10,200 stonecrop Sedum maximum L. plants were recorded, 6,600 of which were growing in habitats potentially suitable for the Apollo. Assuming that five stonecrop plants are sufficient for the development of one Apollo imago, the study area’s carrying capacity was estimated to be c. 1,320 individuals (Witkowski et al., 1992). Although this estimate did not take into account caterpillar mortality or variability in stonecrop plant size and its local spatial distribution, it is nevertheless the most appropriate in this case. Infor- mation on population abundance available in the liter- ature and unpublished materials (Chrostowski, undated; Żukowski, 1959; Witkowski et al., 1997) is qualitative (e.g. presence/absence at particular sites) or, at most, categorical (e.g. ‘single specimens’, ‘abundant’). Wetherefore estimated carrying capacity from the abundances attained by the restored population, assuming that the successful reintro- duction of a population should enable it to reach the local carrying capacity. However, if over-supplementation has occurred, local habitats may be overexploited, with a sub- sequent reduction in their carrying capacity (Adamski & Witkowski, 2007). As estimated population abundance fluc- tuates annually, we used regime shift analysis to distinguish between random fluctuations and directional processes. Hitherto applied mainly in climate analysis, regime shift analysis determines the level around which individual measurements fluctuate randomly, and also detects regime shifts, defined as rapid reorganization of processes from one relatively stable state to another (Rodionov & Overland, 2005). Regime shifts in the recovered abundance of the Apollo butterfly were analysed using Rodionov’s(2004) algorithm implemented in Sequential Regime Shift Detection Software 3.2 (Bering Climate, 2006). The difference between the mean values of neighbouring regimes was assessed using aStudent’s two-tailed t test with unequal variance, at P = 0.05. The regimemeans wereweighted with Huber’s weight func- tion with the parameter = 1. The cut-off length parameter was set at 6.
Population growth rate In both classical (Ricker, 1958) and modern approaches the population growth rate (r) is related to the average life-history traits in a given population, such
as fecundity and developmental mortality (Caswell, 1978), which are mediated by environmental factors determining the carrying capacity. However, studies of wild population dynamics yield only the net population growth, and it is therefore difficult to separate the influence of carrying ca- pacity from other factors affecting population abundance. We therefore used the maximum growth rate recorded dur- ing the recovery process. For the years when the population was supplemented with captive-reared individuals (1992– 2001 and 2004), the introduced individuals were included in the calculation in a manner analogous to the calculation of the reintroduction effectiveness coefficient proposed by Adamski & Witkowski (2007), using the following formula:
r =
Wt − Wt−1 +Ct−1 Wt−1 +Ct−1
() (2) where r is population growth rate,Wt is the estimated wild
population in year t,Wt−1 is the estimated wild population in year t–1, and Ct−1 is number of captive-reared individuals introduced into the population in year t–1.
Modelled scenarios Because of the shifting level of popula- tion abundance during the restoration process, two variants of the model were run: (1) assuming a constant habitat car- rying capacity (K1) throughout the process, and (2) assum- ing that over-supplementation during 2003–2005 reduced the carrying capacity from (K1)to (K2). In addition, each set of parameters was separately modelled in two versions: (1) with, and (2) without the inclusion of the captive-bred individuals. As a result, six theoretical population growth scenarios were modelled: Scenario 1 (WO K1): not including captive-reared individuals (wild only); carrying capacity K1 constant; Scenario 2 (WO+ shift): not including captive- reared individuals; carrying capacity reduced from K1 to K2; Scenario 3 (WO K2): not including captive-reared individuals; carrying capacity K2 constant; Scenario 4 (CI K1): including captive-reared individuals (captive- reared included); carrying capacity K1 constant; Scenario 5 (CI + shift): including captive-reared individuals; carrying capacity reduced from K1 to K2; Scenario 6 (CI K2): including captive-reared individuals; carrying capacity K2 constant.
Results
Estimation of model parameters The annual estimated population abundances, the numbers of captive-reared indi- viduals released into the wild and the growth rate are listed in Table 1. Based on these data, the estimated growth rate used in themodelswas r = 0.6. Regime shift analysis showed there were two periods when the estimated population abundance changed: a rapid increase during 1996–1997, and a decrease during 2003–2004 (Fig. 2). Before the
Oryx, 2022, 56(4), 564–571 © The Author(s), 2022. Published by Cambridge University Press on behalf of Fauna & Flora International doi:10.1017/S0030605321000296
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