Population viability analysis the application of theory to management

The focus of population viability analysis (PVA) differs from many of the population models developed by ecologists (such as those discussed in Chapters 5, 10 and 14) because an aim of PVA is to predict extreme events (such as extinction) rather that central tendencies such as mean population sizes. Given the environmental circumstances and life history characteristics of a particular rare species, what is the chance it will go extinct in a specified period? Alternatively, how big must its population be to reduce the chance of extinction to an acceptable level? These are frequently the crunch questions in conservation management. The ideal classical approach of experimentation, which might involve setting up and monitoring for several years a number of populations of various sizes, is unavailable to those concerned with species at risk, because the situation is usually too urgent and there are inevitably too few individuals to work with. How then are we to decide what constitutes the minimum viable population (MVP)? Three approaches will be discussed in turn: (i) a search for patterns in evidence already gathered in long-term studies (Section 7.5.5.1); (ii) subjective assessment based on expert knowledge (Section 7.5.5.2); and (iii) the development of population models, both general (Section 7.5.5.3) and specific to particular species of interest (Section 7.5.5.4). All the approaches have their limitations, which we will explore by looking at particular examples. But first it should be noted that the field of PVA has largely moved away from the simple estimation of extinction probabilities and times to extinction, to focus on the comparison of likely outcomes (in terms of extinction probabilities) of alternative management strategies.

7.5.5.1 Clues from long-term studies of biogeographic patterns

Data sets such as the one displayed in Figure 7.22 are unusual because they depend on a long-term commitment trying to determine the minimum viable population ...

Figure 7.21 Percentage extinction rates as a function of habitat area for: (a) zooplankton in lakes in the northeastern USA lakes, (b) birds of the Californian Channel Islands, (c) birds on northern European islands, (d) vascular plants in southern Sweden, (e) birds on Finnish islands and (f) birds on the islands in Gatun Lake, Panama. (Data assembled by Pimm, 1991.)

X LU

10 102 Area (km2)

10 102 Area (km2)

Figure 7.21 Percentage extinction rates as a function of habitat area for: (a) zooplankton in lakes in the northeastern USA lakes, (b) birds of the Californian Channel Islands, (c) birds on northern European islands, (d) vascular plants in southern Sweden, (e) birds on Finnish islands and (f) birds on the islands in Gatun Lake, Panama. (Data assembled by Pimm, 1991.)

Area (km2)

0.25

0.25

102 104 Area (km2)

102 104 Area (km2)

Area (km2)

Area (km2)

Area (km2)

Population Viability Analysis
Figure 7.22 The percentage of populations of bighorn sheep in North America that persists over a 70-year period reduces with initial population size. (After Berger, 1990.)

to monitoring a number of populations - in this case, bighorn sheep in desert areas of North America. If we set an arbitrary definition of the necessary MVP as one that will give at least a 95% probability of persistence for 100 years, we can explore the data on the fate of bighorn populations to provide an approximate answer. Populations of fewer than 50 individuals all went extinct within 50 years whilst only 50% of populations of 51-100 sheep lasted for 50 years. Evidently, for our MVP we require more than 100 individuals; in the study, such populations demonstrated close to 100% success over the maximum period studied of 70 years.

A similar analysis of long-term records of birds on the Californian Channel Islands indicates an MVP of between 100 and 1000 pairs of birds (needed to provide a probability of persistence of between 90 and 99% for the 80 years of the study) (Table 7.6).

Studies such as these are rare and valuable. The long-term data are available because of the extraordinary interest people have in hunting (bighorn sheep) and ornithology (Californian birds). Their value for conservation, however, is limited because they deal with species that

Table 7.6 The relationship for a variety of bird species on the Californian Channel Islands between initial population size and probability of populations persisting. (After Thomas, 1990.)

Population size (pairs)

Time period (years)

Percentage persisting

1-10

80

61

10-100

80

90

100-1000

80

99

1000+

80

100

... is a risky approach are generally not at risk. It is at our peril that we use them to produce recommendations for management of endangered species. There will be a temptation to report to a manager 'if you have a population of more than 100 pairs of your bird species you are above the minimum viable threshold'. Indeed, such a statement would not be without value. But, it will only be a safe recommendation if the species of concern and the ones in the study are sufficiently similar in their vital statistics, and if the environmental regimes are similar, something that it would rarely be safe to assume.

7.5.5.2 Subjective expert assessment

Information that may be relevant to a conservation crisis exists not only in the scientific literature but also in the minds of experts. By bringing experts together in conservation workshops, well-informed decisions can be reached (we have already considered an example of this approach in the selection of overwintering reserves for monarch butterflies - Section 7.2.3). To illustrate the strengths and weaknesses of the approach when estimating extinction probability, we take as our example the results of a workshop concerning the Sumatran rhinoceros (Dicerorhinus sumatrensis).

The species persists only in small, isolated subpopulations in an increasingly fragmented habitat in Sabah (East Malaysia), Indonesia and West Malaysia, and perhaps also in Thailand and Burma. Unprotected habitat is threatened by timber harvest, human resettlement and hydroelectric development. There are only a few designated reserves, which are themselves subject to exploitation, and only two individuals were held in captivity at the time of the workshop.

The vulnerability of the Sumatran rhinoceros, the way this vulnerability varies with different management options and the most appropriate management option given various criteria-were assessed by a technique known as decision analysis. A decision tree is shown in Figure 7.23, based on the estimated probabilities of the species becoming extinct within a 30-year period (equivalent to approximately two rhinoceros generations). The tree was constructed in the following way. The two squares are decision points: the first distinguishes between intervention on the rhinoceros' behalf and nonintervention (status quo); the second distinguishes the various management options. For each option, the line branches at a small circle. The branches represent alternative scenarios that might occur, and the numbers on each branch indicate the probabilities estimated for the alternative scenarios. Thus, for the status quo option, there was estimated to be a

Intervention

0.1 Epidemic

Status quo

«

0.9 No epidemic

0.2 Increased support

Control poaching

0.3 No change

«

0.5 Decreased support

0.6 Timber harvest

0.85

New reserve

0.4 Protected

New reserve

0.4 Protected

0.1 Dam

Expand reserve

0.2 Timber harvest

0.7 Protected

0.2 Disease

Fencing

0.8 No disease

0.1 Success

Translocation

0.9 Failure

0.8 Success

Captive breeding

0.2 Failure

0.45

0.85

0.45

0.37

0.95

0.95

0.19 3.69 m in the minds of experts: decision analysis the case of the Sumatran rhinoceros

Figure 7.23 Decision tree for management of the Sumatran rhinoceros. ■, decision points; •, random events. Probabilities of random events are estimated for a 30-year period; pE, probability of species extinction within 30 years; E(pE), expected value of pE for each alternative. Costs are present values of 30-year costs discounted at 4% per year; m, million. (After Maguire et al., 1987.)

probability of 0.1 that a disease epidemic will occur in the next 30 years, and hence, a probability of 0.9 that no epidemic will occur.

If there is an epidemic, the probability of extinction (pE) is estimated to be 0.95 (i.e. 95% probability of extinction in 30 years), whereas with no epidemic the pE is 0.85. The overall estimate of species extinction for an option, E(pE), is then given by:

E(pE) = probability of first option X pE for first option +

probability of second option X pE for second option, which, in the case of the status quo option, is:

The values of pE and E(pE) for the intervention options are calculated in a similar way. The final column in Figure 7.23 then lists the estimated costs of the various options.

We will consider here two of the evaluating interventionist management options management options in a little more detail. The first is to fence an area in an existing or new reserve, and to manage the resulting high density of rhinoceroses with supplemental feeding and veterinary care. Disease here is a major risk: the probability of an epidemic was estimated to be higher than in the status quo option (0.2 as opposed to 0.1) because the density would be higher. Moreover, the pE if there was an epidemic was considered to be higher (0.95), because animals would be transferred from isolated subpopulations to the fenced area. On the other hand, if fencing were successful, the pE was expected to fall to 0.45, giving an overall E(pE) of 0.55. The fenced area would cost around US$60,000 to establish and $18,000 per year to maintain, giving a 30-year total of $0.60 million.

For the establishment of a captive breeding program, animals would have to be captured from the wild, increasing the pE if the program failed to an expected 0.95. However, the pE would clearly drop to 0 if the program succeeded (in terms of the continued persistence of the population in captivity). The cost, though, would be high, since it would involve the development of facilities and techniques in Malaysia and Indonesia (around $2.06 million) and the extension of those that already exist in the USA and Great Britain ($1.63 million). The probability of success was estimated to be 0.8. The overall E(pE) is therefore 0.19.

Where do these various probability values come from? The answer is from a combination of data, the educated use of data, educated guesswork and experience with related species. Which would be the best management option? The answer depends on what criteria are used in the judgement of 'best'. Suppose we wanted simply to minimize the chances of extinction, irrespective of cost. The proposal for best option would then be captive breeding. In practice, though, costs are most unlikely to be ignored. We would then need to identify an option with an acceptably low E(pE) but with an acceptable cost.

The subjective expert assessment approach has much to commend it. It makes use of available data, knowledge and experience in a situation when a decision is needed and time for further research is unavailable. Moreover, it explores the various options in a systematic manner and does not duck the regrettable but inevitable truth that unlimited resources will not be available.

However, it also runs a risk. In the absence of all necessary data, the recom- ... and weaknesses mended best option may simply be wrong. With the benefit of hindsight (and in all probability some rhinoceros experts who were not part of the workshop would have suggested this alternative outcome), we can now report that about $2.5 million have been spent catching Sumatran rhinoceroses; three died during capture, six died postcapture, and of the 21 rhinoceroses now in captivity only one has given birth and she was pregnant when captured (data of N. Leader-Williams reported in Caughley, 1994). Leader-Williams suggests that $2.5 million could have been used effectively to protect 700 km2 of prime rhinoceros habitat for nearly two decades. This could in theory hold a population of 70 Sumatran rhinoceroses which, with a rate of increase of 0.06 per individual per year (shown by other rhinoceros species given adequate protection), might give birth to 90 calves during that period.

7.5.5.3 A general mathematical model of population persistence time a general modeling approach ...

At its simplest, the likely persistence time of a population, T, can be expected to be influenced by its size, N, its intrinsic rate of increase, r, and the variance in r resulting from variation in environmental conditions through time, V. Demographic uncertainty is only expected to be influential in very small populations; persistence time increases from a low level with population size when numbers are tiny, but approaches infinity at a relatively small population (dashed curve in Figure 7.24).

Various researchers have manipulated the mathematics of population growth, allowing for uncertainty in the expression of the intrinsic rate of increase, to provide an explicit estimate, T, of mean time to extinction as a function of carrying capacity, K (briefly reviewed by Caughley, 1994). Making a number of approximations (e.g. that demographic uncertainty is inconsequential, and that r is constant except if the population is at the carrying capacity when r is zero), Lande (1993) has produced one of the more accessible equations:

Demographic

stochasticity

Environmental stochasticity

and disasters

r > Ve

i i i i i i / / /

Environmental stochasticity

t/y

and disasters

/// i/f

r < Ve

Population size

Figure 7.24 Relationships between population persistence time and population size, both on arbitrary scales, when the population is subject to demographic uncertainty or to environmental uncertainty/disasters. (After Lande, 1993.)

where:

c = 2r/V - 1, r is the intrinsic rate of increase and V is the variance in r resulting from variation in environmental conditions through time.

This equation is the basis for the solid curves in Figure 7.24, which indicate that mean time to extinction is higher for larger maximum population sizes (K), for greater intrinsic rates of population growth and when environmental influences on the expression of r are smaller. In contrast to earlier claims that random disasters pose a greater threat than smaller environmental variation, it turns out that what really matters is the relationship between the mean and variance ofr (Lande, 1993; Caughley, 1994). The relationship between persistence time and population size curves sharply upwards (i.e. is influential only for small or intermediate population sizes) if the mean rate of increase is greater than the variance, whereas if the variance is greater than the mean the relationship is convex - so that, even at large population sizes, environmental uncertainty still has an influence on likely persistence time. This all makes intuitive good sense but can it be put to practical use?

In their study of the Tana River ... put to the test crested mangabey (Cercocebus galeritus galeritus) in Kenya, Kinnaird and O'Brien (1991) used a similar equation to estimate the population size (K) needed to provide a 95% probability of persistence for 100 years. This endangered primate is confined to the floodplain forest of a single river where it declined in numbers from 1200

to 700 between 1973 and 1988 despite the creation of a reserve. Its naturally patchy habitat has become progressively more fragmented through agricultural expansion. The model parameters, estimated on the basis of some real population data, were taken to be r = 0.11 and V = 0.20. The latter was particularly uncertain because only a few years' data were available. Substituting in the model yielded a MVP of 8000. Using the standard rule of thumb described earlier, that to avoid genetic problems an effective population size of 500 individuals is needed, an actual population of about 5000 individuals was indicated. Given the available habitat it was concluded that the mangabeys could not attain a population size of 5000-8000. Moreover, Kinnaird and O'Brien think it unlikely that this naturally rare and restricted species ever has. Either the data were deficient (e.g. environmental variation in r may be smaller than estimated if they are able to undergo dietary shifts in response to habitat change) or the model is too general to be much use in specific cases. The latter is likely to be true. However, this is not to deny the value of ecologists continuing to search for generalizations about processes underlying the problems facing conservation managers.

7.5.5.4 Simulation models: population viability analysis (PVA)

Simulation models provide an alternative, more specific way of gauging viability. Usually, these encapsulate survivorships and reproductive rates in age-structured populations. Random variations in these elements or in K can be employed to represent the impact of environmental variation, including that of disasters of specified frequency and intensity. Density dependence can be introduced where required, as can population harvesting or supplementation. In the more sophisticated models, every individual is treated separately in terms of the probability, with its imposed uncertainty, that it will survive or produce a certain number of offspring in the current time period. The program is run many times, each giving a different population trajectory because of the random elements involved. The outputs, for each set of model parameters used, include estimates of population size each year and the probability of extinction during the modeled period (the proportion of simulated populations that go extinct).

Koalas (Phascolarctos cinereus) are regarded as near-threatened nationally, with populations in different parts of Australia varying from secure to vulnerable or extinct. The primary aim of the national management strategy is to retain viable populations throughout their natural range (ANZECC, 1998). Penn et al. (2000) used a widely available demographic forecasting tool, known as VORTEX (Lacey, 1993), to model two populations in Queensland, one thought to be declining (at Oakey), the other secure (at Springsure). Koala breeding commences at 2 years in species-specific approach: simulation modeling the case of the koala bear: identifying populations at particular risk

Variable

Oakey

Springsure

Maximum age

12

12

Sex ratio (proportion male)

0.575

0.533

Litter size of 0 (%)

57.00 (± 17.85)

31.00 (± 15.61)

Litter size of 1 (%)

43.00 (± 17.85)

69.00 (± 15.61)

Female mortality at age 0

32.50 (± 3.25)

30.00 (± 3.00)

Female mortality at age 1

17.27 (± 1.73)

15.94 (± 1.59)

Adult female mortality

9.17 (± 0.92)

8.47 (± 0.85)

Male mortality at age 0

20.00 (± 2.00)

20.00 (± 2.00)

Male mortality at age 1

22.96 (± 2.30)

22.96 (± 2.30)

Male mortality at age 2

22.96 (± 2.30)

22.96 (± 2.30)

Adult male mortality

26.36 (± 2.64)

26.36 (± 2.64)

Probability of catastrophe

0.05

0.05

Multiplier, for reproduction

0.55

0.55

Multiplier for survival

0.63

0.63

% males in breeding pool

50

50

Initial population size

46

20

Carrying capacity, K

70 (± 7)

60 (± 6)

Table 7.7 Values used as inputs for simulations of koala populations at Oakey (declining) and Springsure (secure), Australia. Values in brackets are standard deviations due to environmental variation; the model procedure involves the selection of values at random from the range. Catastrophes are assumed to occur with a certain probability; in years when the model selects a catastrophe, reproduction and survival are reduced by the multipliers shown. (After Penn et al., 2000.)

Table 7.7 Values used as inputs for simulations of koala populations at Oakey (declining) and Springsure (secure), Australia. Values in brackets are standard deviations due to environmental variation; the model procedure involves the selection of values at random from the range. Catastrophes are assumed to occur with a certain probability; in years when the model selects a catastrophe, reproduction and survival are reduced by the multipliers shown. (After Penn et al., 2000.)

females and 3 years in males. The other demographic values used in the two PVAs were derived from extensive knowledge of the two populations and are shown in Table 7.7. Note how the Oakey population had somewhat higher female mortality and fewer females producing young each year. The Oakey population was modeled from 1971 and the Springsure population from 1976 (when the first estimates of density were available) and the model trajectories were indeed declining and stable, respectively. Over the modeled period (Figure 7.25), the probability of extinction of the Oakey population was 0.380 (i.e. 380 out of 1000 iterations went extinct) while that for Springsure was 0.063. Managers concerned with critically endangered species do not usually have the luxury of monitoring populations to check the accuracy of their predictions. In contrast, Penn et al. (2000) were able to compare the predictions of their PVAs with real population trajectories, because the koala populations have been continuously monitored since the 1970s (Figure 7.25). The predicted trajectories were close to the actual population trends, particularly for the Oakey population, and this gives added confidence to the modeling approach.

The predictive accuracy of VORTEX and other simulation modeling tools was also found to be high for 21 long-term animal data sets by Brook et al. (2000). How can such modeling be put to management use? Local governments in New South Wales are obliged both to prepare comprehensive koala management plans and to ensure that developers survey for potential koala habitat when a building application affects an area greater than 1 ha. Penn et al. (2000) argue that PVA modeling can be used to determine whether any effort made to protect habitat is likely to be rewarded by a viable population.

Overall numbers of African elephants (Loxodonta africana) are in decline and few populations are expected to survive over the next few decades outside high-security areas, mainly because of habitat loss and poaching for ivory. For their simulation models Armbruster and Lande (1992) chose to represent the elephant population in twelve 5-year age classes through discrete 5-year time steps. Values for age-specific survivorship and density-dependent reproductive rates were derived from a thorough data set from Tsavo National Park in Kenya, because its semiarid nature has the general characteristics of land planned for game reserves now, and in the future. Environmental stoch-asticity, perhaps most appropriately viewed as disasters, was modeled as drought events affecting sex- and age-specific survivorship - again realistic data from Tsavo were used, based on a mild drought cycle of approximately 10 years superimposed on a more severe 50-year drought and an even more severe 250-year drought cycle. Table 7.8 gives the survivorship of females under 'normal' conditions and the three drought conditions. The relationship between habitat area and the probability of extinction was examined in 1000-year simulations with and without a culling regime. At least 1000 replicates were performed for each model with many more (up to 30,000) to attain acceptable statistical confidence in the smaller extinction probabilities associated with larger habitat areas. Extinctions were taken to have occurred when no individuals remained or when only a single sex was represented.

The results imply that an area of 1300 km2 (500 sq. miles) is required to yield a 99% probability of persistence for 1000 years (Figure 7.26). This conservative outcome was chosen because of the case of the African elephant -necessary size of reserves?

Figure 7.25 Observed koala population trends (♦) compared with trajectories (a ± 1 SD) predicted by 1000 iterations of VORTEX at (a) Oakey and (b) Springsure, USA. (After Penn et al., 2000.)

Figure 7.25 Observed koala population trends (♦) compared with trajectories (a ± 1 SD) predicted by 1000 iterations of VORTEX at (a) Oakey and (b) Springsure, USA. (After Penn et al., 2000.)

Springsure Koala Reserve

Table 7.8 Survivorship for 12 elephant age classes in normal years (occur in 47% of 5-year periods), and in years with 10-year droughts (41% of 5-year periods), 50-year and 250-year droughts (10 and 2% of 5-year periods, respectively). (After Armbruster & Lande, 1992.)

Female survivorship

Age class (years) Normal years 10-year droughts 50-year droughts 250-year droughts

0-5

0.500

0.477

0.250

0.01

5-10

0.887

0.877

0.639

0.15

10-15

0.884

0.884

0.789

0.20

15-20

0.898

0.898

0.819

0.20

20-25

0.905

0.905

0.728

0.20

25-30

0.883

0.883

0.464

0.10

30-35

0.881

0.881

0.475

0.10

35-40

0.875

0.875

0.138

0.05

40-45

0.857

0.857

0.405

0.10

45-50

0.625

0.625

0.086

0.01

50-55

0.400

0.400

0.016

0.01

55-60

0.000

0.000

0.000

O.OO1

Pva Loxodonta

4OO BOO Time (years)

O.OO1

4OO BOO Time (years)

1000

Figure 7.26 Cumulative probability of elephant population extinction over 1000 years for six habitat areas (without culling). (After Armbruster & Lande, 1992.)

the difficulty of reestablishing viable populations in isolated areas where extinctions have occurred and because of the elephant's long generation time (about 31 years). In fact, the authors recommend to managers an even more conservative minimum area of 2600 km2 (1000 sq. miles) for reserves. The data are least reliable for survivorship in the youngest age class and for the long-term drought regime, and a 'sensitivity analysis' shows extinction probability to be particularly sensitive to slight variations in these parameters. Of the parks and game reserves in Central and Southern Africa, only 35% are larger than 2600 km2.

Many aspects of the life history of plants present particular challenges for simulation modeling, including seed dormancy, highly periodic recruitment and clonal growth (Menges, 2000). However, as with endangered animals, different management scenarios can be usefully simulated in PVAs. The royal catchfly, Silene regia, is a long-lived iteroparous prairie perennial whose range has shrunk dramatically. Menges and Dolan (1998) collected demographic data for up to 7 years from 16 midwestern USA populations (adult population sizes of 45-1302) subject to different management regimes. The species has high survivorship, slow growth, frequent flowering and nondormant seeds, but very episodic recruitment (most populations in most years fail to produce seedlings). Matrices, such as that illustrated in Table 7.9, were produced for individual populations and years. Multiple simulations were then run for every matrix to determine the finite rate of increase (X; see Section 4.7) and the probability of extinction in 1000 years. Figure 7.27 shows the median finite rate of increase for the 16 populations, grouped into cases where particular management regimes were in place, for years when recruitment of seedlings occurred and for years when it did not. All sites where X was greater than 1.35 when recruitment took place were managed by burning and some by mowing as well; none of these were predicted to go extinct during the modeled period. On the other hand, populations with no management, or whose management did not include fire, had lower values for X and all except two had predicted extinction probabilities (over 1000 years) of from 10 to 100%. The obvious management recommendation is to use prescribed burning to provide opportunities for seedling recruitment. Low establishment rates of seedlings in the field may be due to frugivory by rodents or ants and/or competition for light with established vegetation (Menges & Dolan, 1998) - burnt the case of the royal catchfly: management of an endangered plant

Table 7.9 An example of a projection matrix for a particular Silene regia population from 1990 to 1991, assuming recruitment. Numbers represent the proportion changing from the stage in the column to the stage in the row (bold values represent plants remaining in the same stage). 'Alive undefined' represents individuals with no size or flowering data, usually as a result of mowing or herbivory. Numbers in the top row are seedlings produced by flowering plants. The finite rate of increase X for this population is 1.67. The site is managed by prescribed burning. (After Menges & Dolan, 1998.)

Table 7.9 An example of a projection matrix for a particular Silene regia population from 1990 to 1991, assuming recruitment. Numbers represent the proportion changing from the stage in the column to the stage in the row (bold values represent plants remaining in the same stage). 'Alive undefined' represents individuals with no size or flowering data, usually as a result of mowing or herbivory. Numbers in the top row are seedlings produced by flowering plants. The finite rate of increase X for this population is 1.67. The site is managed by prescribed burning. (After Menges & Dolan, 1998.)

Seedling

Vegetative

Small flowering

Medium flowering

Large flowering

Alive undefined

Seedling

-

-

5.32

12.l4

3O.88

-

Vegetative

0.308

o.111

O

O

O

0

Small flowering

O

0.566

o.5o6

0.131

0.161

0.361

Medium flowering

O

0.111

0.210

o.6o8

0.161

0.300

Large flowering

O

O

0.012

O.O39

o.667

0.161

Alive undefined

O

O.222

O.198

O.196

O

o.133

Figure 7.27 Median finite rates of increase of Silene regia populations as a function of management regime, for years with seedling recruitment (•) and without (v). Unburned management regimes include just mowing, herbicide use or no management.

areas probably reduce one or both of these negative effects. While management regime was by far the best predictor of persistence, it is of interest that populations with higher genetic diversity also had higher median values for X.

In an ideal world, a PVA would enable us to produce a specific and reliable recommendation for an endangered species of the population size, or reserve area, that would permit persistence for a given period with a given level of probability. But this is rarely achievable because the biological data are hardly ever good enough. The modelers know this and it is important that conservation managers also appreciate it. Within the inevitable constraints of lack of knowledge and lack of time and opportunity to gather data, the model building exercise is no more nor less than a rationalization of the problem and quantification of ideas. Moreover, even though such models produce quantitative outputs, common sense tells us to trust the results only in a qualitative fashion. Nevertheless, the examples above show how, on the basis of ecological theory discussed in Chapters 4-6, we can construct models that allow us to make the very best use of available data and may well give us the confidence to make a choice between various possible management options and to identify the relative importance of factors that put a population at risk (Reed et al., 2003). The sorts of management interventions that may then be recommended include translocation of individuals to augment target populations, creating larger reserves, raising the carrying capacity by artificial feeding, restricting dispersal by fencing, fostering of young (or cross-fostering of young by related species), reducing mortality by controlling predators or poachers, or through vaccination and, of course, habitat preservation.

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