Woodland caribou scientific review to identify critical habitat: chapter 17

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Appendix 6.6

Non-Spatial Population Viability Analysis

Introduction

The Committee on the Status of Endangered Wildlife in Canada (COSEWIC) listed the boreal caribou ecotype as threatened in 2002 (Thomas and Gray 2002). Causes of the decline of boreal caribou populations include over-harvesting by humans and habitat alteration at the landscape scale that favours early seral stage forests and their associated prey species and predators (Environment Canada 2007). Key objectives of the national recovery strategy for boreal caribou are to prevent extirpation of local populations and to maintain or enhance habitat conditions to allow these populations to be self-sustaining (Environment Canada 2007). Concern about the long-term persistence of boreal caribou populations raises questions about the relative role of various vital rates and population size in maintaining populations of boreal caribou.

Deterministic and stochastic processes may cause populations to decline (Caughley 1994). Overharvesting, human-induced habitat loss and fragmentation, and predation are deterministic factors that may reduce population size (Diamond 1984, 1989). Once populations are small and isolated, they are vulnerable to demographic and environmental stochasticity, which may further reduce numbers and cause genetic isolation (Shaffer 1981, 1987, Lande 1988, 1993). The interaction of deterministic and stochastic factors may contribute further to endangerment, described as an extinction vortex (Gilpin and Soule1986). Stochastic factors may cause small populations to become extinct, even if habitat conditions are adequate and deterministic causes of decline are removed (Shaffer 1981). Catastrophes (such as large forest fi res) are considered to be an extreme form of environmental stochasticity that cause major reductions in populations and thus have important implications for any size of population (Lande 1993).

Habitat conditions directly affect the demographics of boreal caribou populations. Habitat alteration at the landscape scale, favouring early seral-stage forests and their associated prey species and predators, can result in declines in survival rate in boreal caribou (Wittmer et al. 2007). Reduced adult survival and recruitment increases the risk of extinction. Exploring how boreal caribou life history and vital rates infl uence population persistence in different habitat situations aids in our understanding of habitat conditions that may allow boreal caribou populations to be self-sustaining.

The Boreal Caribou Critical Habitat Science Review pursued four analytical approaches to support the critical habitat decision framework; here we report on one of these, a non-spatial population viability analysis (PVA). The objective of this work was to use non-spatial models to assess how population persistence is affected by aspects of boreal caribou life history and population structure, using the range of population vital rates and their variance that have been recorded for boreal caribou across their distribution. This work informs the Critical Habitat decision analysis by assessing population sizes required for persistence under various demographic conditions and by providing a tool to investigate the effects of altered vital rates on the population dynamics of boreal caribou.

Using a Leslie Matrix Model, we assessed the effects of variation in boreal caribou vital rates on population dynamics and persistence. Specifi cally, we explored the following questions:

1) What is the critical population size that will ensure persistence under environmental and demographic stochasticity and various combinations of adult and calf survival rates reported in the literature?

2) Of adult female survival, calf survival and their coeffi cients of variation (CV), which parameter has the greatest relative contribution to the probability of extinction?

3) How do recruitment rates affect the relative risk of extinction under various population sizes and adult female survival scenarios?

Methods

We used a two-stage, female-only Leslie matrix model with pre-calving census to model the population dynamics of boreal caribou. The model, BWCSim1.0 (Boreal Woodland Caribou Simulator; J. Tews unpubl.), was developed using Borland C++ Builder 5.0 Professional. The calculated intrinsic growth rate (lambda) was based on a deterministic projection of the stage matrix (Caswell 2001). Density dependence was incorporated as a logistic Ricker equation assuming a maximum fi nite rate of population increase (lambda) of λ =1.3. Density dependent population growth is affected when abundance reaches the carrying capacity (K); below K vital rates of the stage matrix are unchanged. Fecundity was modelled as recruitment of female calves to yearlings per adult female and calculated at t+1 as: parturition rate * sex ratio * survival rate (0 -1 yrs).

We used stage-specifi c (calf, yearling, and adult) demographic data for boreal caribou available from published literature to populate the model (Table 1). We calculated the mean, minimum, and maximum values for female calf and female adult survival and corresponding coeffi cients of variation (CV; Table 1). From each study, we calculated each individual CVs using one of three approaches: 1) for studies that reported SE or 95% confi dence intervals (CI) that were symmetrical around the estimate, we calculated CV as SE/Parameter Estimate; 2) for studies reporting 95% CI that had been calculated using bootstrapping or other techniques (making the back-calculation of CVs impossible), we divided the CI by 4 to obtain a rough estimate of SE and then calculated the CV as above; or 3) for studies that reported a CI that was asymmetrical or its upper bound was truncated to 1 (e.g., survival rates), we determined the difference between the mean and the upper or lower CI bounds, whichever had the highest value. We then estimated the CI as equal to twice that value and then calculated the corresponding CV.

A number of additional parameters were necessary to run the models (Table 2). We assumed that: adults represented 70% of the population, females represented 61% of adults, yearlings were14% of the population, and calves were 16% of the population, and female adults and yearlings comprised 50% of the population 1, based on the means of values reported in the literature (Table 1). We set the proportion of calves that were female produced each year at 0.50 (Gustine et al. 2006) and, in the absence of published data for the proportion of female 1 Adults in population = Total population (100%) – Yearlings (14%) - Calves (16%) = 70%; Adult females = 70% * 61% = 42.7% of population; Yearling females = 50% sex ratio * 14% = 7% of Population; Adult females + yearling females = 42.7% + 7% = 49.7 or ≈ 50% of population. yearlings, we also set this value at 0.50. The model generated a stable age distribution for the initial population (Ni) based on survival rates and Ni. We estimated that yearling females and adult females represented ~50% of population . Given that BWCSim1.0 predicts female abundance only (e.g., adults + yearlings), we doubled female abundance values predicted by the model to obtain total population sizes (including males, see footnote Table 1 for calculation). For all results, we reported total population size.

We set parturition rate for adults (>2 yrs old) at 0.76 based on the mean of values reported in the literature (Table 1). Caribou typically have their fi rst calf at age 3, but earlier reproduction (as early as 2 yrs.) has been reported (Bergerud 1980). Consequently, we set the yearling parturition rate at 0. Although variations of parturition rate and calf sex ratio were not reported in the literature, we assigned a CV of 0.10 to both parameters under the assumption that they do vary.

We modelled simulated populations over 100 years, with 500 replicates. Carrying capacity was set at three times the initial female abundance (3Ni) to coincide with the widely accepted belief that boreal caribou populations occur at densities typically well below the carrying capacity of their habitat, likely because predation limits many North American caribou populations to levels below the density that food availability could sustain (Seip 1991, Bergerud 1996). BWCSim1.0 incorporates demographic stochasticity by using a random number generator to ascribe annual values for vital rates within the range of variation around mean values reported in the literature, thus simulating the variation in vital rates among individuals. Environmental stochasticity is simulated through the model replicates (e.g., generation of multiple Leslie matrices), which incorporate a range of survival and fecundity estimates derived from variation in vital rates.

BWCSim1.0 models the population demographics of single populations, whereby no immigration or emigration occurs between populations. Environmental catastrophes were not included in the model and there was neither maximum age nor maximum breeding age. To buffer against overly optimistic estimates of population persistence due to limitations of the model, we report quasi-extinction risk (risk of population dropping below 10 females) for critical population size assessment. For all other analysis, we reported predictions of extinction risk. The IUCN criterion for classifying species as Vulnerable (equivalent to COSEWIC’s Threatened category) is a risk of extinction ≥10% over 100 yrs (SSC 2001). We therefore set the threshold of acceptable risk of extinction at <10% over 100 yrs.

Appendix 6.6 - Table 1. Mean, minimum, and maximum population parameter values for boreal caribou across Canada.

¹Coeffi cient of Variation

Appendix 6.6 - Table 2. Model parameters used for the non-spatial boreal caribou PVA

¹ Edmonds 1988; 2 Bergerud 1971; 3 Courtois et al. 2007; 4 Courtois et al. 2005; 5 Ferguson et al. 1988; 6 Fuller and Keith 1981; 7 Gustine et al. 2006; 8 Mahoney and Virgl 2003; 9 McLoughlin et al. 2003; 10 Schaefer et al. 1999; 11 Smith 2004; 12 Sorenson et al. (2008); 13 Stuart Smith et al. 1997; 14 Vors 2006; 15 Rettie and Messier 1998; 16 Culling et al. (no date)

Critical Population Size Assessment

We modelled a combination of calf survival (S calf) and adult female survival (Sad ) rates to assess the population size required to reduce the probability of quasi-extinction to <0.10 over 100 years. The values we used for low (L), medium (M), and high (H) survival and CV for calves and adult females, which were compiled from the mean and minimum and maximum of mean published values (Table 1). We assessed the following four combinations of vital rates:

i) Low Scalf , high CV of Scalf , mean Sad , and mean CV of Sad(LHMM);

ii) Mean Scalf , high CV of Scalf , mean Sadand mean CV of Sad(MHMM);

iii) Mean Scalf ; High CV of Scalf; Mean Sad , High CV of Sad(MHMH);

iv) Low Scalf , high CV of Scalf , high Sadand mean CV of Sad(LHHM);

v) 75th percentile of S calf, CV of Scalf, S ad, and CV of S ad (75th percentile; Table 3).

We did not model a combination of high S calf and low S ad because we assumed this was unlikely to be observed in natural populations.

For each scenario, we increased initial female abundance until the risk of quasi-extinction was <10%. The risk of quasi-extinction was calculated as the average number of years, over 500 replicates, for which abundance was equal to less than 10 female caribou over 100 yrs.).

Appendix 6.6 - Table 3. Scenario parameter values to assess population size thresholds of boreal caribou, based on calf and adult female survival (S) and variation (CV = coeffi cient of variation).

Population Trajectory Models

We modelled population trajectories using data from the only studies that reported both calf and adult female survival for four populations of boreal caribou (Table 1), including two study periods for a population in Labrador (for which vital rates differed substantially), for a total of fi ve models (Table 4). We used mean survival rates and CVs of survival rates and population sizes reported in the studies. For the three studies that did not report variation in survival estimates, we used CVs compiled in Table 1 for the missing values. We assigned the Max CV (as reported in Table 1) to the missing Scalf CVs because because the corresponding Scalf rates for the missing values were below the overall mean of 0.38 and low survival estimates are associated with higher inter-annual variation and (Table 1). We used the mid-CV of 8% reported in Table 1 for the missing Sad CV because the corresponding Sad value was equal to the overall mean Sad compiled in Table 1. All studies reported estimates of population size. We used 50% of these estimates as the initial female abundance to be modelled; given that we calculated female adults and yearlings represented ~50% of the total population. We used values reported in Table 2 for parturition, proportion of yearlings in population and calf sex ratio.

Appendix 6.6 - Table 4. Parameter estimates used to model populations of boreal caribou.

* Initial female abundances (Ni) were set to 50% of population estimates reported in the studies.
** Data in italics denotes values assigned from range of mean values in Table 1.

Sensitivity Analysis

We conducted sensitivity analyses to determine the relative importance of adult female survival (Sad ), calf survival (Scalf ), and their coeffi cients of variation (S ad CV and S calf CV) to risk of extinction, by modeling the range of mean values for each parameter that we compiled from the literature (Table 1). We varied one parameter at a time, while keeping the other parameters at mean values (Table 5). We then calculated the percent risk of extinction for each scenario as the average number of times the population reached 0 in 100 yrs over 500 replications. We ran models with three initial female abundances (Ni) at 100, 200 and 400 individuals to investigate the potential effect of population size on extinction risk.

Appendix 6.6 – Table 5. Scenario parameter values to assess the relative importance of population parameters to risk of extinction for boreal caribou.

Recruitment Analysis

We modelled the effect of recruitment on risk of extinction under a variety of female survival rates (0.80, 0.84, 0.88) and initial female abundances of 200, 400, 600, and 800 (corresponding to population sizes of 400, 800, 1200 and1600 caribou; Table 5). We calculated corresponding calf survival rates from mean recruitment values taken from the National Meta-analysis of Boreal Caribou Demography and Range Disturbance (Table 6; see also Appendix 4.5). Given an assumed parturition rate of 0.76, calf survival was calculated as:

S calf = (mean recruitment / 0.76) / 100

 Appendix 6.6 - Table 6. Recruitment of boreal caribou and corresponding calf survival values

1 Calf survival calculated as S calf = Recruitment/Parturition. Parturition rate assumed to be 0.76.