How much gene flow is needed to avoid inbreeding depression in wild tiger populations?

Abstract

The number and size of tiger populations continue to decline owing to habitat loss, habitat fragmentation and poaching of tigers and their prey. As a result, tiger populations have become small and highly structured. Current populations have been isolated since the early 1970s or for approximately seven generations. The objective of this study is to explore how inbreeding may be affecting the persistence of remaining tiger populations and how dispersal, either natural or artificial, may reduce the potentially detrimental effect of inbreeding depression. We developed a tiger simulation model and used published levels of genetic load in mammals to simulate inbreeding depression. Following a 50 year period of population isolation, we introduced one to four dispersing male tigers per generation to explore how gene flow from nearby populations may reduce the negative impact of inbreeding depression. For the smallest populations, even four dispersing male tigers per generation did not increase population viability, and the likelihood of extinction is more than 90% within 30 years. Unless habitat connectivity is restored or animals are artificially introduced in the next 70 years, medium size wild populations are also likely to go extinct, with only four to five of the largest wild tiger populations likely to remain extant in this same period without intervention. To reduce the risk of local extinction, habitat connectivity must be pursued concurrently with efforts to increase population size (e.g. enhance habitat quality, increase habitat availability). It is critical that infrastructure development, dam construction and other similar projects are planned appropriately so that they do not erode the extent or quality of habitat for these populations so that they can truly serve as future source populations.

1. Introduction

Within the last century, the number of wild tigers has declined rapidly from an estimated 100 000 individuals in the early 1900s [1] to the most recent estimate of 3800–5180 individuals globally [2], with fewer than 1850 tigers in South Asia [3,4]. Tigers now occupy only 7.1% of their historical range [5]. Following the end of World War II, the decline of tiger habitat accelerated and, by 1965, the distribution of remaining patches of tiger habitat across Asia had become highly fragmented [6–8], resulting in small, highly structured populations [9]. Tiger dispersal patterns and recent configurations of habitat fragmentation based on Thematic Mapper data from 1972 show that the current degree of isolation of tiger habitat patches dates to the early 1970s [7,10]. Currently, all extant wild populations are estimated to consist of fewer than 100 breeding tigers that are restricted to isolated patches of suitable habitat, mostly in protected areas [7,8]. In combination with a reduction in the amount of habitat, overhunting of tiger prey has reduced carrying capacity of much of the remaining tiger habitat [3,11].

Given the current distribution of tigers into mostly small, isolated populations, the persistence of remaining populations is a function of both deterministic and stochastic factors [12]. Deterministic factors include continued habitat loss and poaching of tigers and their prey and have been prominent concerns in tiger conservation efforts [11,13,14]. However, given current estimated tiger population sizes, demographic, environmental and genetic stochasticity and the occurrence of catastrophic events are also important and need to be addressed as well [12]. How the interaction of these factors impact tiger population persistence is not well understood [15], but, in concert, they increase the likelihood of an ‘extinction vortex’ [16].

Previous models of tiger population viability analysis have focused primarily on demographic stochasticity [13]. Here, we incorporate genetic stochasticity, which includes the effect of inbreeding depression and genetic drift on population viability. In small fragmented populations, the occurrence of inbreeding, the mating of two related individuals, is inevitable [17], and it may increase a small population's risk of extinction through the expression of inbreeding depression [15,17–19]. Genetic drift is a longer term consequence that leads to increased population structure and within population loss of genetic diversity, which limits a population's ability to adapt to changing environmental conditions [20]. Inbreeding depression is generally considered to be the more immediate threat to population persistence.

The role of gene flow among small isolated populations counteracts the potentially detrimental effects of inbreeding and genetic drift [21]. Based on a number of simplifying assumptions, one migrant per generation had been considered to be a genetic rule-of-thumb sufficient to minimize the loss of genetic diversity and heterozygosity within populations, but still allow for genetic divergence among populations [22]. However, Mills & Allendorf [23] evaluated the underlying assumptions of the ‘one migrant per generation’ rule and concluded that a minimum of one and a maximum of 10 migrants per generation would be a more appropriate rule-of-thumb, with the effective number of migrants per generation being both species specific and a function of environmental conditions.

The purpose of this paper is to explore how inbreeding and dispersal may affect the local population persistence of three representative sizes of tiger populations. Our objectives are to examine: (i) the probability of extinction of representative populations of tigers owing to demographic stochasticity and inbreeding depression; (ii) the degree to which dispersal among populations may reduce inbreeding depression; (iii) the impact of delayed genetic exchange on population viability; and (iv) the implications for management actions required to reduce inbreeding depression.

2. Material and methods

To explore how inbreeding depression and dispersal may affect the long-term persistence of wild tiger populations, we developed an individually based spatially explicit population model designed specifically for tigers [13]. This model is based on the extensive dataset collected over a 30 year period in Chitwan National Park (CNP), Nepal, on a group of tigers not impacted by poaching [24–26]. The spatial structure of the model is based on breeding female territories, which we define as the minimum amount of habitat needed to provide sufficient prey and cover for a breeding female tiger and her cubs. Breeding male territories overlap one to six breeding female territories. When cubs are 2 years old, they disperse from their natal territory, and become sexually mature when they are 4 years old. Maximum lifepan is 15 years [26].

We based the spatial configuration of breeding female territories on the tiger population at CNP (figure 1). Each box in figure 1 represents a breeding female territory and the lines connecting the boxes represent connectivity (i.e. possible routes of dispersal) between the territories. This somewhat linear structure is not atypical of other tiger populations, but we did not explore other spatial patterns. To simulate a range of population sizes, we subdivided the CNP spatial structure into 12, 24 and 48 breeding female territories, which we designate as ‘small’, ‘medium’ and ‘large’ populations, respectively. These sizes are our best estimate of the range of populations that currently occur across the tiger's range. The model's large population represents the size of five of the largest remaining tiger populations (e.g. Russian Far East, Indonesia, Tenasserim on the Thailand/Burma border, Sundarbans, Nargarhole and Kerinci Seblat) [8].

Figure 1.

Female territorial structure for small, medium and large tiger populations.

Reported tiger population sizes are often based on camera trap studies that estimate the number of tigers more than 1 year old [27]. To compare our population sizes to the number of animals reported in over 35 camera trap studies, we used our simulation model to calculate that total population size, including newborn cubs 0–1 year, is approximately 1.5 times larger than populations excluding less than 1 year old animals, and the population size estimated in camera trapping studies is approximately 2.9 times greater than the number of breeding females. These ratios are critical to interpreting the results of our simulation with respect to reported population sizes for tigers.

Model parameters are derived from the CNP dataset [26] and more recent unpublished data (C. McDougal 2012 and appendix A). Tiger habitat in CNP is considered prime tiger habitat, with high prey density, dense cover and access to water. Therefore, model parameters, when compared to tiger populations living in more marginal habitats, may be overly optimistic. However, reproductive parameters reported for wild female Amur tigers in Russia are similar to those reported for the CNP population [28].

(a). Inbreeding depression

The genetic load in tiger populations is unknown. O'Grady et al. [19] conducted a meta-analysis of published studies reporting inbreeding depression in wild populations of birds and mammals and found that the weighted mean numbers of diploid lethal equivalents (LEs) for fecundity, first year survival and survival to sexual maturity are 3.94 (n = 4), 2.35 (n = 6) and 5.97 (n = 5), respectively, for a total of 12.26 LEs applied to sexual maturity. They developed a series of stochastic population simulation models for a variety of species using VORTEX [29], a generic individual-based simulation model for population viability analysis, to explore the effect of inbreeding depression on population viability. To examine the interaction of inbreeding depression and population viability in tigers, we incorporated the results of O'Grady et al.'s [19] meta-analysis into our individual-based stochastic simulation model designed specifically for tiger populations. We simulated the effect of 12 diploid LEs on population viability, with four diploid LEs affecting fecundity, two diploid LEs affecting first year survival and six diploid LEs affecting survival to sexual maturity. Because tigers reach sexual maturity at 4 years of age, we applied two diploid LEs per year for years two through to four. Inbreeding did not affect survival after 4 years of age.

To model the effect of inbreeding on survival and fecundity, we used the log-linear model developed by Morton et al. [30]:

where S is the probability of annual survival, S_o is the probability of survival of non-inbred tigers, F is the coefficient of inbreeding and B is the average number of LEs per haploid genome. The probabilities of survival of non-inbred tigers were derived from the CNP dataset collected in the 1970s–1980s and consisted of first year cub survival, second year cub survival, dispersing male survival and dispersing female survival (appendix A). We assumed that these tigers were not inbred owing to the relatively large population and relatively short period of population isolation at the time when data were collected. To estimate an individual tiger's coefficient of inbreeding, we assigned unique alleles to 100 sample loci for all founders and dispersing male tigers. We then estimated each tiger's coefficient of inbreeding as the percentage of loci in the sample genome with alleles identical by descent [31]. We assumed that the variance associated with a 100 loci sample reasonably represents the variation in inbreeding depression among individuals. Fecundity was simulated by randomly selecting a litter size from a litter size distribution based on data collected at CNP and then survival of each unborn tiger was calculated according to the log-linear model. Because the genetic load for isolated tiger populations is unknown, we also explored the population viability consequence of applying 50% of the mean number of LEs as reported by O'Grady et al. [19].

(b). Gene flow

Inbreeding increases the frequency of homozygous loci in a genome, which increases the potential expression of recessive deleterious or lethal alleles. Dispersal, the movement of individuals between isolated populations, and subsequent success in breeding may reduce the frequency of recessive homozygotes and may therefore reduce the deleterious effects of inbreeding on population viability. We simulated the effect of dispersal on population viability by introducing one or more 4 year-old dispersing male tigers per generation into a population following a 50 year period of isolation. This roughly corresponds to a period of isolation beginning in the early 1970s in CNP and the optimistic scenario of restoring connectivity between isolated populations within the next 10 years. We limited our analysis to dispersing male tigers because they typically disperse greater distances than female tigers and are more likely to disperse to a new population [10]. Because the generation interval is approximately 7 years for tigers [26], we simulated dispersal to begin at year 50 and continue in 7 year increments. We assumed that male tigers disperse from nearby populations of similar size and genetic histories so that each dispersing tiger's coefficient of inbreeding is similar to those of the population into which the tiger is dispersing. We estimated each dispersing tiger's coefficient of inbreeding as the mean coefficient of inbreeding of the population into which the tiger was dispersing so that the migrating tiger's survival rate would be similar to other tigers in the population. Each dispersing tiger was assigned a set of unique alleles at 100 loci, with a percentage of loci assigned identical alleles corresponding to the tiger's coefficient of inbreeding.

We simulated three representative sizes of tiger population with and without inbreeding depression and with and without dispersal from neighbouring populations for 300 years. We repeated each simulation for 200 replicates.

3. Results

The small population (12 breeding female territories) consisted of an average of 29 tigers over 1 year old; the medium population (24 breeding female territories) consisted of an average of 71 tigers over 1 year old and the large population (48 breeding female territories) consisted of an average of 154 tigers over 1 year old (table 1). In the absence of inbreeding depression, 15% of the small population simulations and none of the medium or large population simulations went extinct within 300 years (table 2).

Table 1.

For our simulated populations of 12, 24 and 48 breeding females, we estimate the number of tigers more than 1 year of age and total tigers ±1 s.d. so that our simulated populations can be compared to population estimates of more than 1 year old tigers widely reported in camera trap capture–recapture studies based on the methodology of Karanth & Nichols [26].

breeding females	tigers more than 1 year old	all tigers
12	29 (22–35)	40 (32–48)
24	71 (63–80)	103 (93–113)
48	154 (143–165)	225 (211–238)

Table 2.

Probabilities of population extinction as a function of population size, degree of inbreeding, average number of LEs and dispersal beginning at year 50. (LE, lethal equivalents; F, coefficient of inbreeding with no LEs or dispersers.)

years	F	no LE (%)	six LEs dispersers per generation					12 LEs dispersers per generation
			0 (%)	1 (%)	2 (%)	3 (%)	4 (%)	0 (%)	1 (%)	2 (%)	3 (%)	4 (%)
(a) small population—12 breeding females
50	0.24	2	25	30	23	21	21	77	67	73	75	75
100	0.47	5	100	78	62	51	43	100	97	93	94	92
150	0.62	7	100	90	74	55	50	100	100	99	95	92
200	0.73	11	100	95	83	66	56	100	100	100	97	93
250	0.81	12	100	98	89	72	60	100	100	100	98	95
300	0.86	15	100	100	91	79	67	100	100	100	99	96
(b) medium population—24 breeding females
50	0.12	0	0	0	0	0		1	0	0	0
100	0.22	0	4	2	0	0		82	31	10	8
150	0.32	0	65	11	0	1		100	74	29	16
200	0.40	0	100	24	0	1		100	93	43	20
250	0.47	0	100	35	1	1		100	97	58	24
300	0.54	0	100	49	2	1		100	98	64	31
(c) large population—48 breeding females
50	0.09	0	0	0	0			0	0	0	0
100	0.15	0	0	0	0			3	1	0	0
150	0.20	0	0	0	0			93	29	5	2
200	0.24	0	9	0	0			100	77	25	5
250	0.28	0	71	1	0			100	93	45	10
300	0.32	0	99	6	0			100	100	64	19

(a). Inbreeding depression

When we applied two levels of genetic load to the three representative population sizes (table 2), we discovered a threshold effect consistent with Frankham [32], where the probability of population extinction increased rapidly over a relatively short interval of time (see the electronic supplementary material). With 12 diploid LEs, the threshold for the small, medium and large populations occurred after approximately 30, 70 and 100 years, respectively, and with six LEs, the threshold occurred after 30, 100 and 190 years (figure 2). Even with the lower level of genetic load, the extinction threshold still occurred in 30 years for small populations.

Figure 2.

Probability of extinction for ‘small’, ‘medium’ and ‘large’ tiger populations with 12 (red line) and six (black line) diploid LEs and no dispersal.

The slopes of the extinction curves for populations with the higher level of genetic load are steeper than the slopes associated with lower levels of genetic load, indicating that there is less time to respond with management actions between the beginning of the extinction threshold and 100% probability of extinction for greater genetic loads. For example, the extinction threshold for small populations begins after 30 years for both six and 12 LEs, but reaches 100% extinction in 40 additional years with 12 LEs and 70 additional years with six LEs (table 2 and figure 2).

(b). Gene flow

Gene flow (dispersal and successful breeding) between isolated populations may be able to ameliorate the potentially detrimental effects of inbreeding [21]. It is important to note that our individually based model simulates different rates of dispersal and not gene flow. One successful breeding tiger will usually require more than one successful disperser reaching a population. Only approximately 60% of dispersers succeed in establishing breeding territories. For small populations with 12 LEs, the probability of population extinction is in the 70–80% range after 50 years of isolation, which is alarming because many wild populations of tigers have been isolated for approximately 40 years. If tiger managers wait another 10 years to establish programmes to naturally or artificially foster dispersal, our results will be of limited value in preventing extinctions. Initiating exchange among small populations with 12 LEs after a 50 year period of isolation lowers the probability of extinction in the next 50 years from 100 to 97% with one dispersing male tiger per generation, 93% with two dispersing male tigers per generation and no further reduction with three to four dispersing male tigers per generation (figure 3 and table 2a). For small populations with six LEs, however, dispersal is more beneficial, decreasing the probability of extinction from 100 to 78% with one dispersing male tiger per generation, 62% with two dispersing male tigers per generation, 51% with three dispersing male tigers per generation and 43% with four dispersing male tigers per generation.

Figure 3.

Probability of extinction for small (red line) and medium (black line) populations with and without inbreeding depression 12 diploid LEs and with 0–3 dispersing male tigers per generation (mpg).

The impact of dispersal is more effective in reducing the extinction probability in medium and large populations with both 12 and six LEs (table 2b,c). For example, the beginning of the extinction threshold for the large population with 12 LEs occurs after 100 years, with 100% probability of population extinction after 180 years (figure 2). Dispersal beginning after a 50 year period of isolation reduces the probability of population extinction within the following 100 years from 93 to 29% with one dispersing male tiger per generation, 5% with two dispersing male tigers per generation and 2% with three dispersing male tigers per generation (table 2c and figure 3).

In general, dispersal tends to flatten the slopes of population extinction curves and to diminish the threshold effect in the medium and large populations, but has little or no effect on the slopes of the extinction curves for small populations (figure 3).

4. Discussion

(a). Current structure of tiger populations

Until recently, tigers occupied most forest and grassland habitat of Asia [33]. In a relatively short period of time, from the late nineteenth century to the 1960s, tigers declined dramatically in both number and range owing to widespread habitat destruction, hunting and prey depletion. In 1972, the declining number of tigers and degree of habitat fragmentation evoked worldwide alarm and tiger range countries established a system of protected areas to conserve remaining tiger populations. More recently, the World Wildlife Fund shifted to a broader conservation approach that defines landscapes within ecoregions [34,35]. Landscape conservation emphasizes connectivity and a metapopulation approach to tiger conservation [36,37] to ensure genetic exchange among tiger populations.

Sanderson et al. [5] identified 76 tiger conservation landscapes (TCLs). Based on area alone, they estimated that 16 TCLs (21%) have sufficient habitat to support 100+ more than 1 year old tigers, roughly equivalent to our ‘large’ populations; 15–20% of TCLs have sufficient habitat to potentially support 50–100 tigers, roughly equivalent to our ‘medium’ populations and 55–59% TCLs are small or indeterminant in size. Populations in these small TCLs may already be in the early stages of the inbreeding extinction threshold. Our simulations indicate that efforts to improve connectivity between these small isolated populations will only reduce the risk of local extinction if these efforts occur concurrently with work to increase the size or carrying capacity of existing tiger habitat.

Walston et al. [8], based on expert opinion, estimated the size of existing tiger populations and classified 42 as potential tiger source populations. Of these 42 source populations, only four are equivalent to our large population and eight are equivalent to our medium population. The remaining 30 source populations fall within the small population category. Given the difficulty in recovering potentially inbred ‘small’-sized populations, it might be more reasonable to consider that only the 12 medium and large populations be given status as source populations. Even the eight ‘medium’-sized populations are questionable source populations because they may require immediate conservation efforts to reduce the potential threat posed by inbreeding depression. Given that these medium-sized populations have been isolated already for 50 years, they will potentially reach a serious threat of extinction within the next 25 years (three to four generations). For the four ‘large’ tiger populations, our results indicate that no immediate threat of extinction exists owing to inbreeding depression within the next 100 years (14–15 generations), provided that efforts to reduce poaching of tigers and their prey through increased patrolling and participatory conservation strategies are successful. But, despite this optimistic scenario, governments must also be proactive in preventing further fragmentation of these ‘large’ populations from infrastructure development projects [37].

(b). Management recommendations

Recent genetic data demonstrating an increase in tiger population structure in India indicate that establishing and/or enhancing connectivity through habitat restoration or genetic exchange needs to be one of the primary conservation objectives in tiger landscapes [38]. To achieve the goal of enhancing movement of tigers between populations, a primary objective should be to restore habitat to facilitate natural dispersal throughout the landscape. Where natural dispersal is not immediately feasible due to isolating features in the landscape, genetic and demographic rescue through translocation among wild populations are increasingly being considered as an alternative [39,40]. However, our simulation experiments indicate that the beneficial effects of connectivity is limited for small populations. Given these results, managers need to first determine an acceptable level of risk within a specific time frame and then take appropriate action to enlarge these populations using one or more of the following actions: (i) increase the land base for individual tiger populations; (ii) improve the habitat quality to increase tiger carrying capacity; (iii) increase connectivity among neighbouring populations; and (iv) supplement tiger populations where the land and prey base still exist, but tiger numbers are low, as has been effective for the Florida panther [41].

The Terai Arc Landscape (TAL) project on the border of Nepal and India [42,43] is a good example of where active management would greatly improve the genetic viability of tiger populations. Although densely populated by humans, the TAL contains five tiger populations centered on CNP, Bardia Wildlife Reserve, Dudwa Tiger Reserve, Sukla Phanta Wildlife Reserve and Corbett/Sonanadi Tiger Reserve, with nine other protected areas that serve as potential links between these core populations. Community forestry, driven by rural people managing forests for both sustainable resource use and for ecological services, is improving habitat quality outside many of these reserves [44], creating areas that are likely to increase habitat connectivity. Elsewhere across the tigers range, it may be possible to increase population size in the core protected areas by reversing a trend of prey depletion and thus increasing tiger carrying capacity [11,45].

The difficulty with genetic and demographic management of tiger populations is that many tiger reserve managers in Asia lack the background in risk assessment and calculating extinction probabilities. The relatively new field of quantitative conservation planning is addressing these technical issues, but communication between academics and tiger reserve managers is limited [46]. There is a strong need to create a structure that links technical experts directly to tiger reserve managers to address tiger conservation as well as a broad range of conservation issues.

The genetic load in remaining tiger populations is unknown and is expected to vary among populations. Given strong evidence of inbreeding depression in many mammal and bird species [18,47,48], there is no reason to believe that tigers are less susceptible to inbreeding depression than other mammalian species. Therefore, it is wise to apply a precautionary approach regarding the potential effect of inbreeding depression on the future viability of this already highly endangered species.

5. Conclusion

We explored the effect of inbreeding depression on the viability of tiger populations using parameters derived from a meta-analysis of published data and found a real threat exists to the continued persistence of all but the largest remaining wild tiger populations, even at 50% of the reported levels of inbreeding depression. We were conservative in our approach in that our simulated small and medium-sized populations may have been larger than many of the current wild tiger populations that we sought to simulate, and we may have therefore underestimated the true impact of inbreeding depression on tiger population viability. Second, we did not apply inbreeding depression to adult survival. The detrimental effect of inbreeding on morphological and physiological traits that decrease a tiger's ability to survive and reproduce are more likely to occur under stressful conditions and will almost certainly affect adult tigers, especially under fluctuating environmental conditions [49–51]. Third, we used demographic and spatial parameters from the tiger population in CNP, which were collected in prime tiger habitat before the onset of widespread poaching. Because many remaining wild tiger populations persist in marginal habitat at best, the demographic parameters of litter size and survival in CNP may be higher than elsewhere. Although we assume that the spatial arrangement of the CNP population is representative of many of the remaining tiger populations, alternative spatial arrangements may affect a population's viability, either positively or negatively. Finally, we did not consider environmental stochasticity and the effects of catastrophic events (e.g. fires, floods, disease) that further increase the risk of extinction. For these reasons, we believe that we underestimated the threats of extinction.

Although the tiger is a resilient species [52], inbreeding has the potential to depress many aspects of tiger biology and therefore increase risk of population extinction. Inaction regarding the potential effects of inbreeding depression and dispersal on remaining tiger populations will dismiss the precautionary principle for a species that is rapidly declining for multiple known and unknown reasons [53].

Appendix A. Model parameters used to simulate tiger population dynamics.

annual survival
resident male	0.825
resident female	0.95
dispersing male	0.70
dispersing female	0.70
first year cub	0.80
second year cub	0.80
whole litter	0.70
annual fecundity
probability that 3 year old resident female breeds:	0.90
probability that 4+ year old resident female breeds:	1.00
maximum litter size:	5
litter size distribution	no. cubs	probability
	0	0.00
	1	0.00
	2	0.23
	3	0.58
	4	0.17
	5	0.02
inbreeding depression: average number of LEs per diploid genome
	6 LEs	12 LEs
applied at birth	2	4
applied year 1 through to 4	1	2
annual dispersal
maximum territorial changes per tiger	20
probability that a dispersing male challenges a resident male	1.00
probability of infanticide following successful challenge	1.00
probability that the dispersing male dies during challenge	0.25
probability that the resident male dies during challenge	0.60
probability that dispersing male successfully challenges resident male for territory as a function of age
age of resident male	age of dispersing male
	4	5	6
3	1.00	1.00	1.00
4	0.50	0.55	0.65
5	0.45	0.50	0.55
6	0.40	0.45	0.50
7	0.35	0.40	0.45
8	0.40	0.45	0.50
9	0.45	0.50	0.55
10	0.50	0.55	0.60
11	0.70	0.75	0.80
12	1.00	1.00	1.00
13	1.00	1.00	1.00
14	1.00	1.00	1.00
15	1.00	1.00	1.00