Acanthonyx petiverii " H. Milne Edwards 1834

Improvement in Survivorship: The Key for Population Recovery? María Florencia Grandi1,*, Silvana L. Dans1,2, and Enrique A. Crespo1,2 1Laboratorio de Mamíferos Marinos, Centro Nacional Patagónico-CONICET, Bvd. Brown 2915, 9120 Puerto Madryn, Chubut, Argentina 2Universidad Nacional de la Patagonia San Juan Bosco, Bvd. Brown 3051, 9120 Puerto Madryn, Chubut, Argentina. E-mail: [email protected], [email protected] (Received May 15, 2014; Accepted October 13, 2015) María Florencia Grandi, Silvana L. Dans, and Enrique A. Crespo (2016) In northern Patagonia, commercial harvesting of South American sea lions, Otaria flavescens, from 1920 to 1960, decimated its population abundance. Population recovery was not immediate after hunting ceased in 1962. The population was stable until 1989, and since then has grown at an annual rate of increase of 5.7%. Along with this growth there was an increase of the juvenile fraction and changes in the social composition of colonies, which could be related to changes in some population vital rates. The aim of this study was to analyze changes in the survivorship pattern of Otaria flavescens through time. The ultimate goal was to contribute to a better understanding of changes that could have operated on the ecosystem after the decline and recovery of one of the main marine top-predators in the southern South Atlantic Ocean. The comparisons of survivorship curves of males and females, obtained from the life tables of two periods with different population trends: 1981-1987 (stationary) and 2000-2008 (recovering), showed that there were differences in survivorship between sexes, where recent female age-specific survival was higher than that of males at any age. The comparison of survivorship between periods showed differences in both sexes. Both juveniles and adults, both male and female, from the recent period showed higher survival than those of the 1980’s decade. This improvement in survivorship could be one of the essential factors that drove population recovery in the last decades. Here we discuss the possible hypotheses of which factors could have changed in the ecosystem to favour juvenile and adult survivorship, such as an increase in the availability of food recourses, a decrease of exogenous mortality causes, or a combination of both factors. Key words: Life table, Otaria flavescens, South American sea lion, Survivorship, Population recovery, Northern Patagonia. *Correspondence: Tel: +054-280-4883184 int. 1272. Fax: +054-280-4883543. E-mail: [email protected] BACKGROUND Most natural populations experience fluctuations in their abundance through time. These fluctuations could be due to the intrinsic characteristics of a species (i.e. life history traits), or because of the influence of external factors (such as prey availability, competition, exploitation, habitat degradation, disease, etc.). Understanding the factors and mechanisms causing these fluctuations is a key subject in ecological studies, especially for the conservation of populations that have suffered dramatic declines. Ageand sex-specific survival and reproductive rates are essential for understanding the dynamics of animal populations. However, these vital rates are rarely available for long-lived mammals because the longterm data sets and large sample sizes required for these analyses are difficult to obtain from wildlife populations (Eberhardt 1985). South American sea lions (Otaria flavescens) are distributed along the South American coast from Torres (29.33°S; 49.71°W), southern Brazil, on the Atlantic Ocean (Rosas et al. 1994) to Zorritos (4°S), northern Peru on the Pacific Ocean (Cappozzo and Perrin 2009). This species was one of the seals most exploited along the South American coast, and populations were decimated Zoological Studies 55: 9 (2016) doi:10.6620/ZS.2016.55-09 1 during the early 20th century (Crespo and Pedraza 1991; Páez 2006). This dramatic decline leads to the present great dissimilarities in abundance and population trends observed throughout their range (Crespo et al. 2012). Populations from Uruguay and austral Chile (XII Region) are decreasing (Venegas et al. 2001; Páez 2006), while those from central and southern Chile (V-IX and X-XI Regions, respectively) are stable (Oliva et al. 2008; Sepúlveda et al. 2011). Populations from the Malvinas (Falkland) Islands, Peru and northern Chile are slowly recovering (Thompson et al. 2005; Bartheld et al. 2008; Crespo et al. 2012), and those of Patagonia (Argentina) are steadily recovering (Reyes et al. 1999; Dans et al. 2004; Schiavini et al. 2004; Grandi et al. 2015). In Argentina, harvesting operations occurred between 1920 and 1960, mostly on northern Patagonia and Tierra del Fuego stocks, while stocks from central and southern Patagonia remained almost unexploited (Godoy 1963; Crespo 1988; Crespo and Pedraza 1991; Grandi et al. 2015). However, both exploited and unexploited stocks showed similar trajectories (reduction in abundance and posterior recovery), suggesting a strong interconnection in the Patagonian region (Reyes et al. 1999; Dans et al. 2004; Grandi et al. 2015). The population of South American sea lions in northern Patagonia (Fig. 1) has been monitored almost continuously since 1972, resulting in a data set that comprises 40 years of census data. Based on historical data, it is known that the population declined from an estimated 137,500 individuals in 1938 (Godoy 1963) to 18,396 in 1946 (Carrara 1952). It has been estimated that the population reached its lowest numbers (~ 5000 individuals) in the 1960s (Koen-Alonso and Yodzis 2005; Grandi 2010). Although hunting ceased in 1962, signs of population recovery were not detected until 1990 (Crespo and Pedraza 1991). Fortunately, the northern Patagonian stock is recovering and at present is growing at an annual rate of increase of 5.7% (Dans et al. 2004; Grandi 2010). As a result of the population recovery, the Fig. 1. Detailed study area with the current distribution of Otaria flavescens colonies at northern Patagonia N page 2 of 17Zoological Studies 55: 9 (2016) social composition and spatial distribution of certain northern Patagonian colonies changed through time (Crespo 1988; Dans et al. 2004; Grandi et al. 2008). The process of this change began with the establishment of juveniles of both sexes in new and small breeding areas near larger rookeries or within haul-out sites, followed by the arrival of adult males, subadult males, or both. This process yields mixed-composition colonies with higher rates of pup production in comparison to the dense established breeding sites. Consequently, new areas were colonized and colonies turned from haul-outs to rookeries (Crespo 1988; Dans et al. 2004; Grandi et al. 2008). It was hypothesized that all these changes that accompanied the population recovery could be related directly or indirectly to changes of vital rates through time, such as age specific survivorship and/or fecundity (Dans et al. 2004; Grandi et al. 2008). This could be supported by a positive rate of increase of pups in all colonies (Dans et al. 2004; Grandi et al. 2008), higher rates of pup production in new sites (Grandi et al. 2008), and an increase in the juvenile fraction of the population since among non-pups, juveniles were the age-class that had the highest intrinsic rate of increase in recent times (Dans et al. 2004). Age-specific survival (or mortality) rates are one of the most useful demographic parameters used to interpret and understand animal population dynamics, because they enable estimations of how natural mortality affects different age classes and the intensity of those interactions (Caughley 1977). Accurate estimates of ageand sexspecific survival rates are essential to develop population models to be used in conservation and management (Caswell 2001). In practice, accurate measurements of age-specific survival are difficult to obtain in the field because they require longterm longitudinal monitoring of known-aged individuals (Lebreton et al. 1992). Traditionally, two approaches have been used to estimate agespecific demographic rates. The first approach includes long-term mark-recapture studies, which does not require assumptions about the dynamics of the population, but has a number of assumptions about the probability of individual capture and tag loss (e.g. Boyd et al. 1995; Beauplet et al. 2006; Pendleton et al. 2006; Hernández-Camacho et al. 2008; Pistorius et al. 2004, 2008; McMahon and White 2009). On the other hand these studies are extremely costly in terms of effort and money. The second approach corresponds to the generation of life tables, and provides indirect estimates from age frequency distributions of a sample, but this requires some assumptions about population dynamics (i.e. random sampling, age structure stability, Caughley 1977). Even so, life tables provide a useful summary to describe mortality patterns operating on a population. The ageand sex-specific survival rates they describe can also be an essential tool for evaluating the status of a population, and are very effective in the conservation area when they are associated with models that assess the susceptibility of different age classes to anthropogenic factors (e.g. Crouse et al. 1987; Doak et al. 1994; Winship and Trites 2006). Moreover, life tables can be used for the design of conservation and management strategies, mainly because there is evidence that variations in juvenile and adult survival rates of pinnipeds have an important effect on the rate of population increase (York 1994; Holmes and York 2003; Pendleton et al. 2006). There are a small number of published examples of life tables for marine mammals in general (Barlow and Boveng 1991), but only a few have been developed for sea lions (York 1994; Hernández-Camacho 2001; McIntosh 2007). When considering South American sea lions, Crespo (1988) developed vertical life tables for the northern Patagonian stock from the period 19811987, when the population was stationary. These data, together with the present knowledge about this population provide a unique opportunity to understand its recovery process. The aim of this study was to analyze changes in the survivorship pattern of Otaria flavescens through time. To do this we compare survivorship curves of males and females obtained from life tables from two periods of different population trend: 1981-1987 (stationary) and 2000-2008 (recovering). The ultimate goal was to contribute to a better understanding of how the ecosystem could have reorganized after the decline and recovery of one of the main marine top-predators in the Atlantic Ocean. MATERIALS AND METHODS Collection of specimens and age estimation The study area includes sea lion colonies that conform the northern Patagonia population (Fig. 1). During the period 2000-2008 the coastline of the study area as well as sea lion colonies were surveyed seasonally, looking for dead animals. All accessible sites were walked (322 km) and the page 3 of 17Zoological Studies 55: 9 (2016) effort was equally distributed both spatial (both provinces) and temporally (all seasons in each year). Skulls of sea lions were collected, and then cleaned by dermestid beetles, boiled to eliminate the remaining fat and flesh, washed with water and soap, and finally stored dry. All specimens were deposited in the scientific collection of Marine Mammals at CENPAT (Puerto Madryn, Argentina). Individual ages were estimated by two methods: a) for pups (i.e. newborns to individuals of less than 1 year), ages were estimated according to the teeth eruption schedule defined by E. A. Crespo (1988: 76-79). He established four age-classes for pups: category A (0 to 1.5 months); B (from 1.5 to 5 months); C (from 5 to 8 months); and D (from 8 to 12 months) (see description in Fig. 2); b) for individuals of one or more years old, age was estimated from counts of incremental growth layers of tooth sections (Crespo et al. 1994). The tooth preparation and age reading techniques used were described by Crespo (1988) and are also detailed in Grandi et al. (2010). Frequency distribution of age at death The sample collected represents the age distribution at death. However it may be biased from the true distribution due to several factors. Therefore, age frequencies were corrected by three adjustments previous to the construction of life tables. a) Adjustment of first-year mortality Among pups, it is more likely to find dead newborn pups (0 to 1.5 months of life) because they do not swim and are more probable to die on the beach, than pups of other age-classes. Thus the number of individuals younger than one year in the sample was corrected by considering data on pup mortality estimated in other sources and the number of pups born in one year in the whole population. First-year mortality of pups (q0) - defined as the proportion of newborn that die before their first birthday (Caughley 1977) - was estimated in two steps. First, mortality from 0 to 1.5 months, that is the mortality of pups from age-class category A (MA), was estimated from available information in the literature (Campagna et al. 1992; Soto et al. 2004; Svendsen 2005; Svendsen et al. 2012). Fourteen different mortality estimates were available, which were averaged. Then, the mortality of the categories B, C and D were estimated as a proportion of the estimated mortality in category A (i.e. relative mortality for each category, MRi), as follows: MRi = × MA 'A 'i where 'i is the expected number of dead pups in age-class category i, 'A is the expected number of dead pups in age-class category A, and MA is the mortality of pups from age-class category A (Crespo 1988). The expected number of dead pups corresponds to the observed number in the sample when the sex ratio did not differ from 1:1. In the case that the sex ratio was different, the expected number of dead pups was estimated from the observed ratio. Fig. 2. Lateral view of the teeth eruption schedule of O. flavescens pups (extracted from Crespo 1988). Category A: milk and permanent teeth present (mi: milk incisor; mpct: milk postcanine teeth; mct: milk canine teet; pi: permanent incisor h) and the permanent canine teeth (pct) inside the alveolus; Category B: mct, pi and permanent postcanine teeth (ppct) present; Category C: mct are lost and pct remain inside the alveolus; Category D: pct erupt through the gum and become visible. page 4 of 17Zoological Studies 55: 9 (2016) The expected number of female and male dead pups in the population were then reconstructed applying the relative mortality for each category (MRi) to a cohort of 10940 individuals (that correspond to the mean pups born in the study area in the period 2005-2008; Grandi 2010). Subsequently, first-year mortality (q0) was estimated for each sex as the ratio between the sum of the expected number of dead pups in each category i and the size of the cohort considered. b) Adjustment for known rate of population growth The frequency distribution of deaths (f’x) from age-class x = 1 to the last age-class were adjusted for population growth by multiplying by the correction factor erx (Caughley 1977), where r is the exponential growth rate estimated from censuses from the period 1982-2007 (r = 0.0581 from Grandi 2010). Second, this adjusted frequency distribution (F’x) was smoothed by a log-polynomial regression (Caughley 1977). c) Adjustment of pup frequency It is more probable to find dead pups than dead animals of other age classes. Thus after applying the previous adjustments, the frequency for the age-class 0 (F’0) was adjusted. This was first calculated for females by iterations of the F’0 values until q0 was equal to the estimates calculated in the first step, using the Solver function in Microsoft Excel (Microsoft Corp.). Then r values were estimated from the resolution of the Lotka’s equation (Σlxe-rxmx = 1, Caughley 1977). The fit was repeated considering the mean, minimum and maximum values of q0 until obtaining a value of r that was inside the CI of the exponential growth rate estimated from censuses (0.055 ≥ r ≤ 0.061, Grandi 2010). Age-specific fecundity rates (mx, Table 2) were considered as 1/2 of age-specific pregnancy rates (bx) calculated in previous studies from the examination of reproductive tracts, mammary glands and the presence and development of corpora lutea and corpora albicantia in the ovaries, n = 76 (Grandi 2010; Grandi et al. 2010). Considering that the average age at sexual maturity for female South American sea lions was estimated at 4.8 ± 0.5 years old (Grandi et al. 2010), fecundity rates were applied to mature age-classes (x = 4 and older). Survival estimates for the period 2000-2008 Survival (lx) is defined as the probability at birth of surviving to the age x (Caughley 1977). Here lx was estimated, for male and female South American sea lions, constructing life tables from age distribution at death considering natural mortality factors (Caughley 1977; Krebs 1999) and applying the former adjustments. Life table calculations were based on the assumptions that the probability of finding a carcass was independent of the age and sex of South American sea lions from northern Patagonia, reproductive and mortality rates remained constant throughout the study period and there was no emigration or immigration or they were balanced (Caughley 1977; Rabinobich 1980; Krebs 1985). Survival estimates for the period 1981-1987 Crespo (1988) developed several life tables using stranded sea lions collected from northern Patagonia between 1981 and 1987 (n = 140; females = 57, males = 83). Eighteen models of life table were constructed considering different adjustments of the age frequency distribution at death and three ages of development of sexual maturity. Each life table was projected to obtain population growth rates (Crespo 1988). Here we select, from those eighteen life tables, the mean survivorship values (lx) of those models (3 for females and 2 for males) that correspond to a stationary population trajectory during the period 1981-1987 (Crespo 1988), as representative of the mortality pattern of male and female South American sea lions from that period. Comparison of survivorship curves Survivorship values obtained from all life tables were adjusted by Siler’s competing risk model (Siler 1979). Siler’s curve was designed to fit three general stages of life -a juvenile stage with increasing survival, an adult stage with stable survival, and a late stage with decreasing survival. So this model considers the total risk of mortality at a given age x as the product of three competing risks: l(x) = lj(x) × lc(x) × ls(x), an exponentially decreasing risk due to juvenile mortality factors lj(x) = exp[(-a1/b1)] × {1 - exp(-b1 × x/Ω)}, a constant risk experience by all age classes lc(x) = exp(-a2 × x/Ω)), and an exponentially increasing risk due mortality factors associated with senescence ls(x) = exp[(a3/ b3) × {1 - exp(b3 × x/Ω)}]. page 5 of 17Zoological Studies 55: 9 (2016) To be able to compare survivorship patterns from different periods age was re-expressed as a fraction of longevity, Ω (Barlow and Boveng 1991), defining this parameter as the 99th percentile of the age distribution of the sample. The transformation of age as a fraction of longevity proved to be less dependent on sample size than is a definition based on the maximum age observed (Barlow and Boveng 1991). The five parameters of the survivorship model (a1, a2, a3, b1 and b3) are constants that allow considerable flexibility in the shape of this function and were fit using a maximum likelihood approach. The likelihood function L is given by: L(Y/Θ) = Π w i=0 p(li) where each li is an observation of the variable Y, p is the probability density function, and Θ is the vector of parameters (Hilborn and Mangel 1997). A likelihood ratio test (LRT) was used to compare the full model where all parameters could vary with models that constrained some of them to test the following hypothesis: H01: survivorship curves have a similar constant risk of mortality experience by all age classes (i.e. a2 = a2’). H02: survivorship curves have a similar risk of juvenile mortality (i.e. a1 = a1’; b1 = b1’). H03: survivorship curves have a similar risk of senescent mortality (i.e. a3 = a3’; b3 = b3’) H04: survivorship curves have similar risks of mortality (i.e. a1 = a1’; b1 = b1’; a2 = a2’; a3 = a3’; b3 = b3’) where Θ and Θ ’ are parameters of each different data sets used to test each hypothesis (i.e. females vs. males, recent vs. past, etc.). Survivorship models of male and female sea lions within and between periods were compared by LRT, considering α = 0.15 to increase test power due to small sample size (Buckland et al. 2001). RESULTS Age frequency distribution of deaths A total of 424 dead sea lions were found from 2000 to 2008. Of these, 210 were female and 214 male (Fig. 3). Ages ranged from newborn pups to 19 year-old males and 22 year-old females. This sample showed a pronounced mode in the ageclass 0, a high frequency of juveniles of age-class 1 and 2, and an increase of frequency of adult ageclasses (> 6 years) for both males and females. We consider juvenile South American sea lions, Fig. 3. Age-frequency distribution of female (n = 210) and male (n = 214) South American sea lions from northern Patagonia collected between 2000-2008. page 6 of 17Zoological Studies 55: 9 (2016) both females and males, from age 1 to 4 (Grandi et al. 2010). Ages were estimated with an error of -0.084 ± 0.79 years (mean ± SD), and there were no differences among readers (Kruskal-Wallis test, H2,724 = 0.778; p = 0.677). The age-class frequency distribution of the pups collected is shown in figure 4. There were significant differences between sex ratio only in the age-class category B (G = 7.883; d.f. = 1; p = 0.0049), with male pups being more represented than female pups. Mortality estimation of the first year Mean mortality of pups from age-class category A was 0.0585 ± 0.0428 (mean ± SD; n = 14). The relative mortality proportions for the rest of the categories were calculated using the former estimate (Table 1). Considering a cohort of 5470 individuals born per sex in the area (Grandi 2010), and equal sex ratio at birth (Lewis and Ximénez 1983; Crespo 1988), females had a lower mortality rate than males for the first year (Table 1). The strong difference found between male and female age-class B mortality (Fig. 4) explains the resultant disparity in mortality of the first year. Life tables From the resolution of Lotka’s equation, the female pup mortality estimation (q0) that best fitted into the CI of the observed population exponential growth rate was the maximum value obtained. Therefore life tables were calculated considering q0 = 0.29 for females and q0 = 0.39 for males (Table 1). Tables 2 and 3 show age frequency in the sample, the adjusted age frequency and parameter values of life tables for female and male South American sea lions. Comparison of survivorship curves The maximum likelihood fit of the full Siler model to the age-frequency distribution for male and female sea lions is shown in Figure 5. The parameter values which resulted in the best fit are given in table 4. Comparison between present male and female survivorship risks showed that there was significant difference in juvenile mortality factors (H02: LRT = 42.103; d.f. = 2; p < 0.001), in senescent mortality factors (H03: LRT = 35.357; d.f. = 2; p < 0.001) and in all mortality factors together Table 1. Relative mortality estimated, and expected frequency of death by age class category and sex calculated from a cohort of 5470 per sex. Pup mortality estimate (q0) from the total. Minimum and maximum values are in brackets Age-class category Females Males MRif’iMRif’i A0.0585 (0.0157-0.1013) 320 (86-554) 0.0585 (0.0157-0.1013) 320 (86-554) B 0.1304 713 0.2307 1262 C 0.0251 137 0.0251 137 D 0.0351 192 0.0351 192 Total 1363 (1129-1597) 1911 (1677-2145) q0 0.25 (0.21-0.29) 0.35 (0.31-0.39) Fig. 4. Age-frequency distribution of female (n = 70) and male (n = 109) pups by age-class category from northern Patagonia collected between 2000-2008. page 7 of 17Zoological Studies 55: 9 (2016) Table 2. Life table for female South American sea lions based on stranded animals from 2000 to 2008 (n = 214) Age Sample frequency Corrected frequency Smoothed frequency Fecundity rate Life table xf’xf’xerx F’xmxdxlxqxpx 0 70 70 119 0 0.290 1.000 0.290 0.710 1 16 17 35 0 0.085 0.710 0.120 0.880 2 15 17 22 0 0.054 0.625 0.086 0.914 3 5 6 14 0 0.034 0.571 0.060 0.940 4 5 6 8 0.099 0.020 0.537 0.036 0.964 5 5 7 5 0.171 0.012 0.517 0.024 0.976 6 4 6 3 0.248 0.007 0.505 0.014 0.986 7 4 6 2 0.323 0.005 0.498 0.010 0.990 8 7 11 3 0.389 0.007 0.493 0.015 0.985 9 3 5 5 0.441 0.012 0.486 0.025 0.975 10 10 18 8 0.470 0.020 0.473 0.041 0.959 11 4 8 12 0.470 0.029 0.454 0.065 0.935 12 14 28 16 0.433 0.039 0.425 0.092 0.908 13 9 19 20 0.354 0.049 0.385 0.127 0.873 14 7 16 22 0.177 0.054 0.337 0.159 0.841 15 10 24 23 0.177 0.056 0.283 0.198 0.802 16 3 8 23 0.177 0.056 0.227 0.247 0.753 17 8 21 20 0.177 0.049 0.171 0.286 0.714 18 4 11 17 0.177 0.041 0.122 0.340 0.660 19 5 15 13 0.177 0.032 0.081 0.394 0.606 20 4 13 9 0.177 0.022 0.049 0.450 0.550 21 1 3 5 0.177 0.012 0.027 0.455 0.545 22 1 4 6 0.000 0.015 0.015 1.000 0.000 Table 3. Life table for male South American sea lions from 2000 to 2008 (n = 210) Age Sample frequency Corrected frequency Smoothed frequency Life table xf’xf’xerx F’xdxlxqxpx 0 109 109 104 0.390 1.000 0.390 0.610 1 18 19 21 0.079 0.610 0.130 0.870 2 8 9 12 0.045 0.531 0.085 0.915 3 6 7 7 0.026 0.486 0.054 0.946 4 4 5 5 0.019 0.459 0.041 0.959 5 5 7 5 0.019 0.441 0.043 0.957 6 7 10 5 0.019 0.422 0.045 0.955 7 4 6 8 0.030 0.403 0.075 0.925 8 7 11 9 0.034 0.373 0.091 0.909 9 8 13 12 0.045 0.339 0.133 0.867 10 7 13 12 0.045 0.294 0.154 0.846 11 8 15 13 0.049 0.249 0.197 0.803 12 4 8 12 0.045 0.200 0.226 0.774 13 5 11 11 0.041 0.154 0.268 0.732 14 1 2 9 0.034 0.113 0.300 0.700 15 5 12 7 0.026 0.079 0.333 0.667 16 2 5 4 0.015 0.053 0.286 0.714 17 1 3 4 0.015 0.038 0.400 0.600 18 0 0 2 0.008 0.023 0.333 0.667 19 1 3 4 0.015 0.015 1.000 0.000 page 8 of 17Zoological Studies 55: 9 (2016) (H04: LRT = 151.012; d.f. = 5; p < 0.001) (Table 4). Additionally there was no significant difference in constant risk of mortality experienced by all age classes (H01: LRT = 0.248; d.f. = 1; p = 0.618) (Table 4). Females had higher survival (lx and px) in juvenile and adult age classes than males (Fig. 5; Tables 2 and 3). When we compared each sex separated in two time periods (2000-2008 vs. 1981-1987); the pattern was similar to the later (Tables 5 and 6). There was no significant difference in female constant risk of mortality experienced by all age classes (H01: LRT = 1.159; d.f. = 1; p = 0.282). However, there was significant difference in female juvenile mortality factors (H02: LRT = 17.478; d.f. = 2; p < 0.001), in female senescent mortality factors (H03: LRT = 24.551; d.f. = 2; p < 0.001), and in all mortality factors together (H04: LRT = 148.061; d.f. = 5; p < 0.001). These could indicate Table 4. Likelihood estimates of the survivorship models (full and constrained) adjusted to the data for males and females from 2000-2008 Sex Model Siler parameters a1a2a3b1b3 Female full 8.905 -0.651 0.155 11.212 4.454 H01 8.905 -0.720 0.170 10.987 4.356 H02 10.249 -0.567 0.164 13.856 4.349 H03 9.138 -0.690 0.211 11.877 3.997 H04 10.742 -0.845 0.371 13.507 3.330 Male full 12.543 -1.150 0.820 15.830 2.337 H01 12.684 -0.720 0.580 16.896 2.663 H02 10.249 -0.226 0.288 13.856 3.417 H03 11.942 -0.225 0.211 15.757 3.997 H04 10.742 -0.845 0.371 13.507 3.330 Fig. 5. Survivorship curves for male (black) and female (grey) sea lions from 2000-2008. Parameter values for the full model are given in table 4. Age is expressed as proportion of longevity, Ω. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0.2 0.4 0.6 0.8 1 1.2 Age (proportion of longevity) Females Males Survivorship (l x ) Table 5. Likelihood estimates of the survivorship models (full and constrained) adjusted to the data for females from different periods Period Model Siler parameters a1a2a3b1b3 2000-2008 full 8.908 -0.651 0.155 11.212 4.457 H01 8.920 -0.541 0.132 11.611 4.632 H02 9.818 0.432 0.013 19.503 7.177 H03 10.266 0.527 0.009 20.977 7.368 H04 19.732 -17.453 17.988 47.196 0.169 1981-1987 full 25.640 1.347 0.198 85.048 3.108 H01 27.776 -0.541 1.789 84.404 1.004 H02 9.818 -35.167 35.508 19.503 0.115 H03 24.764 1.711 0.009 86.288 7.368 H04 19.732 -17.453 17.988 47.196 0.169 page 9 of 17Zoological Studies 55: 9 (2016) Radzilani PM. 2007. Median pupping date, pup mortality and sex ratio of fur seals at Marion Island. S Afr J Wildl Res 37:1-8. Holmes EE, York AE. 2003. Using age structure to detect impacts on threatened populations: a case study with Steller sea lions. Conserv Biol 17(6):1794-1806. Holmes EE, Fritz LW, York AE, Sweeney K. 2007. 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