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The effects of fire and predators on the long-term persistence of an endangered shrub, Grevillea caleyi
Biological Conservation 109 (2003) 73–83 www.elsevier.com/locate/biocon
The effects of fire and predators on the long-term persistence of an endangered shrub, Grevillea caleyi Helen M. Regana,b,*, Tony D. Auldc, David A. Keithc, Mark A. Burgmana a School of Botany, The University of Melbourne, Parkville, Victoria 3052, Australia National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, 735 State Street, Suite 300, Santa Barbara, CA 93101, USA c NSW National Parks and Wildlife Service, PO Box 1967, Hurstville, NSW 2220, Australia
b
Received 26 October 2001; received in revised form 10 February 2002; accepted 15 February 2002
Abstract Grevillea caleyi is an endangered plant species with a restricted range lying partly within Ku-ring-gai Chase and Garigal National Parks in NSW, Australia. The principle threatening processes affecting G. caleyi are habitat destruction and adverse fire regimes combined with high levels of seed predation. A stochastic, spatially explicit, individual-based model was constructed to investigate the population dynamics of small populations of the species and to determine the impact of a variety of management strategies. Results of model simulations indicate there is a high risk of population decline and local extinction in remnant sites with small populations under current management regimes. The most effective fire management strategy is to schedule fires that burn 20–100% of sub-populations every 5–15 years, in combination with reduced predation rates. When predation management strategies are employed in conjunction with a structured fire regime, then a 20–30% reduction in predation rates can improve the chance of longterm persistence substantially. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Individual-based model; Conservation management; Population dynamics; Seed predation; Fire intervals
1. Introduction Fire regimes play an important part in the survival, ecology and evolution of many plant species (Gill and Groves, 1981; Kruger, 1983; Whelan, 1995; Bond and van Wilgen, 1996). Recruitment in such species is frequently linked to fire (Tyler, 1995). This is critical in plant species in which the above-ground life-history stages are killed by fire. Such species are totally dependent upon the germination of seeds from canopy or soilstored seed banks for post-fire recovery (e.g. Banksia cuneata, Burgman and Lamont, 1992; Banksia ericifolia, Bradstock and Myerscough 1981; Acacia suaveolens, Auld, 1987). Even for species in which standing plants have some capacity to survive fire and resprout new foliage, recruitment is needed to maintain populations (Banksia goodii, Dreschler et al., 1998). Species that are less resilient to fire and more prolific in seed-production * Corresponding author. Tel.: +1-805-892-2522; fax: +1-805-8922510. E-mail address: [email protected] (H.M. Regan).
also rely on fire for seed germination (e.g. Banksia tricuspis, Lamont and van Leeuwen, 1988). The trade-off for resprouting species is their limited ability to produce seeds or seedlings. Threatened species that occur in fire-prone habitats may be particularly at risk from adverse fire regimes because of their restricted habitats in combination with a variety of other threats (Auld and Scott, 1997). Where metapopulations are fragmented in cleared landscapes, adverse fire regimes may lead to local extinctions. The aim of managing threatened species is to minimise threatening processes and to allow recovery and longterm persistence of populations in the wild. Consideration of how threatened species respond to fire will be a key component of this management in many environments. In this paper we investigate a range of management strategies for the endangered plant species, Grevillea caleyi. In particular, we investigate the impact of reducing the frequency and magnitude of key threatening processes on the population dynamics of G. caleyi, and identify the best strategy (out of those considered) for the long-term persistence of the populations.
0006-3207/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(02)00138-6
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G. caleyi (Proteaceae) is an understorey shrub of eucalypt forest in northern Sydney, Australia (Fig. 1). Its range is less than 10 km and its five populations are found on the interface between urban development and remnant bushland, some of which lies just within the boundaries of Ku-ring-gai Chase and Garigal National Parks. A recovery program is currently underway to implement research and management strategies for conservation of the species (Scott et al., 1995). It is believed that the principal threatening processes affecting G. caleyi
are habitat destruction and adverse fire regimes, combined with high levels of seed predation (Auld and Scott, 1997). The loss of emus, a suspected key seed dispersal agent, from the local landscape may also have contributed to an elevated extinction risk since European settlement. Road construction and associated rural and urban development along ridges where the species grows is estimated to have destroyed 85% of G. caleyi’s habitat (Scott et al., 1995) and led to the fragmentation of remaining clusters of plants in an urban landscape.
Fig. 1. Map of location of populations of Grevillea caleyi. Its five fragmented populations are found within the boundaries of Ku-ring-gai Chase and Garigal National Parks in northern Sydney, Australia, on the interface between urban development and remnant bushland.
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Plants of G. caleyi are killed by fire which, in turn, promotes the breaking of seed dormancy in the soil seed bank. Successful establishment of seedlings is very rare in the absence of fire, unless there has been some other disturbance, such as clearing. A very high proportion of all seeds produced are consumed, primarily by rodents and macropods, soon after their release from fruits (Auld, 1995; Auld and Denham, 1999). Populations of G. caleyi may be completely eliminated if fires occur when seed availability in the soil is low. The aims of this study are threefold: to investigate the population dynamics of the species; to predict the outcome of prescribed burning and seed-predator reduction; and to determine the optimal management strategy (in terms of probability of population persistence) from the range of options considered. In this paper, we focus on the remaining small populations as they are regarded as the most vulnerable to extinction. They also allow for detailed investigation of density-dependent processes resulting from the absence of seed dispersal and natural variation in heights. Some specific questions regarding these small populations include the following: Are current small population fragments likely to persist under a regime of prescribed and unplanned fires? How does varying fire frequency influence population persistence? Does forcing a multi-age cohort in the population through partial patch burning reduce extinction risks? How sensitive is population persistence to a reduction in seed predation? A stochastic, spatially explicit, individual-based model was developed using the available field data and the knowledge of experts. It was anticipated that spatial density-dependent processes would have important effects on the population size because seeds do not disperse far and competition for light affects the survival rates of plants (Crawley and Rees, 1996). A treatment of uncertainty and variability was incorporated into the model to ensure conservative results and consideration of the full range of possible outcomes. The model was used to investigate the dynamics of small populations of G. caleyi and to determine the risk of extinction and decline associated with various fire regimes and predation rates.
2. Material and methods 2.1. Life history and population structure Populations of G. caleyi grow as even-age cohorts. This is because all established plants die in a fire and
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seed germination of Grevillea species in this region appears to be predominantly stimulated by smokederivatives and soil-heating associated with fire (Morris, 2000). Some seeds are killed during the passage of fire and the remainder have an opportunity to germinate. The number of germinants depends on the heat and smoke outputs of the fire (Auld and Denham, 2001). For low intensity fires, the number of seeds that die via lethal soil heating and the number of seeds that have their dormancy broken are predicted to be less than that for a high intensity fire. The complex relationship this plant has with fire, due to both heat and smoke, plays an important role in its survival. The number of seeds produced by each plant is dependent on the plant’s age (Auld and Scott, 1997). Young plants grow to maturity within 3–5 years after a fire (Scott et al., 1995). One year old plants do not produce seeds, 2 year old plants rarely produce seeds while plants of at least ten years can produce around 15 seeds each annual flowering season. These seeds fall directly from the canopy and do not disperse. The seeds are quite large (they range from 1.5 cm to about 2.0 cm in length with mean seed weight from 318 to 351 mg, Auld and Denham 1999) and a substantial proportion, approximately 50–100%, are eaten by bush rats and wallabies before the remainder enter the seed bank (Auld and Denham, 1999). Immediately after a fire, seed loss to mammals can rise to 100% before beginning to decline to pre-burn levels. Seed viability (i.e. the propensity to germinate given appropriate conditions) decays exponentially with time since entering the seed bank (Auld et al., 2000). Plants can grow up to 4 m in height; however, this is dependent on competition for light from conspecific and interspecific neighbours. Plants that are shaded can grow up to approximately 2 m. Likewise, the survival coefficients are lower for plants that are shaded by other plants than for those that are not (Scott et al., 1995). The radius of the crown is generally half the height of the plant for younger plants and roughly equal to the height of the plant for older plants. Empirical studies have demonstrated that when competition for light is apparent in a population then it will consist of a few tall plants and many small ones (Obeid et al., 1967; Crawley and Rees, 1996). Known remnant patches of G. caleyi range in area from 5 m 5 m to 350 m 100 m. In 1998, of the 20 known remnant patches, there were three kinds of population structure represented: 4 year old plants and seeds (10 patches ranging from 15 plants to estimates of 2000 plants); 10 year old plants (two patches with some 200 plants each); and > 15 year old plants and seeds (seven patches including some sites with only seeds in soil, and one population with soilstored seeds and about 150 plants). Two of these long unburned patches were subsequently burnt in August 1998 and 1999, respectively.
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2.2. Individual-based model In this model the age, position, height, and radius of the crown of each plant in a rectangular patch is recorded at each time step. Eleven age classes have been assumed, including one for seeds, and 10 for standing plants (i.e. ages one to nine and 10 years and above). Plants are further categorised into two groups to model the effects of intraspecific competition: those that are below other plants; and those that are not. The former are referred to as ‘‘below’’ plants while the latter are referred to as ‘‘above’’ plants, even though all ‘‘above’’ plants may not necessarily be taller than all plants categorised as ‘‘below’’. Once an arbitrary area of the crown of a plant is shaded by another plant then it is classified as ‘‘below’’. It is assumed that all plants have circular crowns. A plant is deemed to be underneath another plant if its height is less than the adjacent plant and the centroid of its crown is underneath the adjacent plant’s crown. This simple competition model is based on that of Moore and Noble (1990), where all plants are affected by other taller plants but not by smaller plants. Competition is interrupted by recurring fires (Keith and Bradstock, 1994). The deterministic governing equations of the system are: N10þ;tþ1 ¼ Na9;t Sa9 þ Nb9;t Sb9 þ Na10þ;t Sa10þ þ Nb10þ;t Sb10þ ; Ni;tþ1 ¼ Nai1;t Sai1 þ Nbi1;t Sbi1 ; i ¼ 2; . . . ; 9; N1;tþ1 ¼ N0;t P ðrecruitment after f ire eventÞ N0;tþ1 ¼
10þ X
Ni;tþ1 fi
ð1Þ
i¼2
where Nai,t is the number of ‘‘above’’ plants of i years of age at time t years, Nbi,t is the number of ‘‘below’’ plants in age class i at time t, Sai is the survival coefficient for ‘‘above’’ plants i years of age, Sbi is the survival coefficient for ‘‘below’’ plants in age class i, P(.) is a probability function and fi is the fecundity of plants i years of age. The fecundity is made up of three components, i.e. fi=ni (1), where ni is the number of seeds produced per plant of i years of age, (=0.8) is the proportion of viable seeds from plants i years of age, and is the predation rate (i.e. 1 is the proportion of uneaten seeds). Initially, the predation rate is assigned the function 8 if TSLF 4 2 < 1:0 ¼ 0:01 TSLF þ 1:01 if 2 < TSLF 4 18 : 0:83 if TSLF > 18 ð2Þ where TSLF is the time since the last fire (linear regression from Auld and Denham, 2001). Seed predation rates and viability were estimated from empirical observations (Auld, 1995; Auld and Denham, 1999, 2001). The viability
of surviving seeds entering the seed bank m years ago is m due to the m iterations through time since they entered the seed bank. Here, only plants of ages 2 years and above have associated fecundities. At census, plants 1 year of age are too young to develop seeds (Scott et al., 1995). The number of seeds produced by a plant annually, ni, is a function of the age of the plant and was estimated from field observations combined with fire history records (Auld, unpublished). The number of seeds per plant in age class i is ( 0 if i 4 1; otherwise ni ¼ ð3Þ int 15 41 exp ði 1Þ2 =18 where int(x) is the value of x rounded to the nearest integer. Contrary to some other plant species (Samson and Werk, 1986; Rees and Brown, 1992; Klinkhamer et al., 1992), reproductive output of G. caleyi is directly dependent on age rather than size; however, there is an indirect relationship between fecundity and size due to the age dependence of plant heights, particularly in the first 10 years of development. Hence, it is assumed the competitive status of plants (that is, whether they are above or below other plants) does not affect the number of seeds produced by individuals. The function for reproductive output was constructed from data and expert opinion and is displayed in Fig. 2a. The change in height of each plant over one time step is assumed to be a function of its age. The functions determining the height (from which the change in height from year t to t+1 can be calculated) of plants below or above other plants were constructed from field observations, combined with expert opinion, as: hbelowðiÞ ¼ 2 ð2=100Þði 10Þ2 haboveðiÞ ¼ 3 ð3=100Þði 10Þ2
ð4Þ
where again, i is the age of the plants. Graphs of these functions appear in Fig. 2b. Although ‘‘above’’ plants can grow up to 4 m, the mean height of plants in age class 10+ is approximately 3 m. As a conservative assumption, a plant’s crown is assigned a radius equal to half its height and expands accordingly. The survival coefficient for a plant was assumed to depend on its age and its competitive status. Hence, for each age group two survival coefficients, Sai and Sbi, both functions of the age of the plant, were derived from field observations and censuses of tagged individuals. Eq. (5) specifies the functions and Fig. 2c displays their graphs. ( 0:99 for i 4 4; otherwise Sai ¼ 1 0:19 1 exp ði 4:5Þ2 =2:5 þ 0:01 ( 0:99 for i 4 4; otherwise Sbi ¼ 1 0:49 1 exp ði 4:5Þ2 =6 þ 0:01
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Fig. 2. (a) The number of seeds produced per plant per year as a function of the age of the plant. This does not include the reduction due to predation. (b) The relationship between height, age and competitive status for Grevillea caleyi. ‘‘Below’’ plants are those that are shaded by an arbitrarily chosen amount. ‘‘Above’’ plants are not shaded. (c) The relationship between age, survival and competitive status for G. caleyi. (d) Fire probability as a function of the time since the last fire. (e) The probability of a hot fire (given that there is a fire), as a function of the time since the last fire. If the fire occurs in the first three years after a fire then it will always be a low intensity fire.
The effects of competition were further incorporated by ensuring that the growth of a plant was halted if the edge of its crown coincided with the stem of an adjacent taller plant. Fire is incorporated into the model with the use of a probability function. The probability of a fire in year t+1 depends on the number of years since the last fire. The probability function employed in the model is: 8 TSLF 4 2 <0:005; Prfire ðTSLFÞ¼ ð0:095=3ÞTSLF 0:175=3; 2
with prescribed burning practices of the two major land management authorities in northern Sydney (New South Wales National Parks and Wildlife Service and Hornsby Shire Council unpublished; McLoughlin, 1998). When a fire occurs, all the burnt plants die and only the seeds are left in the seed bank. There are two possible types of fire in the model, depending on available fuel levels and weather: a hot (or high intensity) fire or a cool (or low intensity) fire. The probability of a hot fire is also a function of the time since the last fire, displayed in Fig. 2e, and specified as: Prhot fire ðTSLFÞ ¼ 8 TSLF 4 3 > < 0; ð0:5=25ÞðTSLF 8Þ2 þ0:5; 3 4 TSLF 4 8; > : 0:5; 8 < TSLF
ð7Þ
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The time since the last fire and fire intensity also have effects on seed survival and germination rates. If there was no fire in the previous year and a hot fire in the current year then 20% of the seeds die and 60% of the remaining seeds germinate. If there was no fire in the previous year and a cool fire the current year then 10% of the seeds die and 30% of the remaining seeds germinate. If there are fires two years in a row then the same proportion die in the second year and all the remaining seeds germinate. The number of 1 year old plants at the next census (after the fire) will then be the number of seeds that germinate. If there are fires 3 years in a row then all plants die, there are no seeds remaining in the seed bank and the species is eliminated from the patch. Environmental stochasticity is incorporated into the model by assigning a probability distribution with each of the survival and plant growth parameters Sai, Sbi, habove(i) and hbelow(i). In the case of the survival coefficients, a lognormal probability density function is associated with the survival value for each age class. Hence, Sai and Sbi are selected from the following probability distributions:
Sbi LN S"bi ; 0:1S"bi ð8Þ
Sai LN S"ai ; 0:1S"ai ;
2.3. Simulations
where S"ai and S"bi are the values taken from Eq. (5). To ensure all values lie within the bounds 0 and 1, while minimizing the effects of truncating the lognormal distribution, we adopt the strategy employed in Burgman et al. (1993) of reflecting the distribution for survival values greater than 0.5 about the point 0.5. Once the survival rates of plants in each age class have been determined, demographic stochasticity is included by selecting the number of plants that survive to the next year from a binomial distribution using the new survival rates. The survivors are chosen randomly, their positions are recorded and the height of each plant is updated. Since populations grow as even-age cohorts, a treatment of natural variation in the heights of plants is necessary to model shading and density-dependent effects. Environmental variation in the height parameters is dealt with in a similar way to the survival rates. A lognormal distribution is associated with the change in height from one age class to the next for both ‘‘above’’ and ‘‘below’’ plants as follows: $" haboveðiÞ ¼ haboveði þ 1Þ haboveðiÞ; $" hbelowðiÞ ¼ hbelowði þ 1Þ hbelowðiÞ;
$haboveðiÞ ¼ LN $" haboveðiÞ; 0:1$" haboveðiÞ ;
$hbelowðiÞ ¼ LN $" hbelowðiÞ; 0:1$" hbelowðiÞ ;
In this case the distributions are not truncated. This treatment of environmental variation in the height parameters drives competition and density dependence in the model. Each plant is compared with every other surviving plant to determine if it is above or below any other plants. The survival rates of plants are updated accordingly. The number of seeds in the seed bank is then calculated (using the updated heights of plants 2 or more years old). Demographic stochasticity is introduced in the same way as for the number of surviving plants. The number of seeds remaining after viability and predation discounts is chosen from a binomial distribution with a probability of (1). The model is initialised at t=0 by randomly assigning positions and heights to a specified number of plants in each age class in a rectangular patch of pre-assigned dimensions. The heights of plants in each age class were randomly selected from a normal distribution with a mean calculated from a similar height function to those above with a maximum height of 2.5 m, and a coefficient of variation of 0.1. The Monte Carlo method is used throughout to select random deviates from the specified probability distributions (Sobol, 1994).
ð9Þ
where $haboveðiÞ is the increase in height of an ‘‘above’’ plant that survives from age class i to age class i+1 etc.
Management strategies were tested in the model to investigate the effects of decreased seed predation during each annual seed-crop and various fire management regimes. The model was config. to simulate an initial population of 46 seeds and 70 four-year-old plants (total of 116 individuals) in a habitat patch 50 m by 200 m. This configuration reflected an actual population of the species. A range of initial population sizes for small populations were tested for sensitivity in the model with qualitatively the same results. The effects of fire frequency alteration were examined by running the model with deterministic fire frequencies of 5, 7, 10, 15, 20 and 30 years, as well as random unplanned fire frequency derived from the fire probability function (Fig. 2d and e). Here, unplanned fires refer to those fires that occur outside the suggested fire management schedule. Such fire events include wildfires, arson and any uncontrolled and unintentional fire that burns the patch. Mosaic fire management strategies were investigated by simulating fires in which 20, 50, 90 and 100% of the habitat patch was allowed to burn in each fire. For partial burns, the area impacted was a rectangular strip, with a randomly assigned position within the patch. The effects of reducing predation were explored by decreasing the average predation rates from the AuldDenham rates [Eq. (2)] to a mean rate of 0.8. In the first 7 years following a fire, a Normal distribution was assigned with a mean of 0.8 and a coefficient of variation of 10%, to simulate variation and uncertainty in
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predation rates while predators are trying to re-establish in the area after a fire. Predation rates were assigned a constant value thereafter (i.e. =0.8), although demographic stochasticity via Binomial distributions is still incorporated after 7 years since the last fire. This was repeated with Normal(0.7, 0.07) and Normal(0.5, 0.05) in conjunction with a selection of fire management strategies. This situation simulated what may happen, in the uncertain and variable period 7 years after a fire, if mammalian seed predator numbers (and hence, seed predation levels) are reduced and take a number of years to recover to their stable pre-fire numbers (cf. Fox and McKay, 1981). The influence of fire size on seed predation rates is considered to be minimal. Auld and Denham (2001) studied post-fire predation levels after extensive wildfires and concluded that fire size is unlikely to be important (see also Auld, 1995). As a result of urbanisation and fragmentation of habitat, seed predation is more likely to be influenced by the proximity of G. caleyi sites to areas that do not burn (i.e. potential refugia for rats and wallabies during a fire) than by the proportion of the site burned. Therefore, no further adjustments were made to predation rates in the model as a result of fire size. All selected combinations of predation, fire frequency and fire size management scenarios were simulated with unplanned fires. To investigate the impact of preventing unplanned fires from modifying the planned fire schedule, simulations that excluded the occurrence of unplanned fires were also run with the combinations of 80% mean predation rates, fire frequencies of 5, 7, 10 and 15 years and all fire sizes. For the simulations in which unplanned fires were allowed to occur in addition to a managed fire frequency, the unplanned fires burnt the entire patch. The next managed fire was then scheduled to occur 5, 7, 10, 15, 20 or 30 years, accordingly, after the unplanned fires. This resetting of the planned fire timetable reflects the current practice of field managers. The dynamics of G. caleyi populations were simulated by generating 50-year trajectories, 1000 times. In this way the combination of many stochastic events was investigated. The maximum, median and minimum population size of the 1000 replications at each time step was recorded. The risk of extinction and quasiextinction were calculated from the minimum of each 50-year trajectory.
3. Results In terms of fire frequency and predation, the baseline conditions for populations of G. caleyi are unplanned fires burning the entire patch and predation at rates specified in Eq. (2). Under these conditions, most population trajectories declined to zero (Fig. 3a). The
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Fig. 3. (a) Maximum, median and minimum for 1000 trajectories over a 50-year period for the baseline conditions of unplanned fires that burn the entire patch and the predation rates reported in Auld and Denham (2001). (b) Maximum, median and minimum for 1000 trajectories over a 50-year period when seed predation rate is reduced to a mean of 80%, in conjunction with fires that occur every 7 years (with unplanned fires) that burn 90% of the patch.
maximum population size reached across all trajectories was 208 (including seeds), however, the maximum declined to 33 individuals by year 50, and the median of all the trajectories declined to zero within 50 years. The risk of extinction for this population under this scenario is about 60%, i.e. approximately 60% of the 1000 trajectories declined to zero within the 50-year period. Simulations for the single small population under all fire management scenarios with predation rates as in Eq. (2), gave local extinction rates ranging from about 60% (for unplanned fires and for all fires sizes every 20– 30 years) to 100% (all fire sizes for a fire frequency of 5 years, Fig. 4a), and a 100% chance of decline below 50 individuals. Results indicate that random unplanned fires that burn the entire patch yield almost the lowest chance of extinction out of all the imposed fire management strategies.
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Simulations with average predation rates of 80%, in combination with managed fire frequency and fire size, indicate a marked improvement in both extinction and decline rates (Figs. 3b and 4b, however note that% decline rates are not displayed graphically throughout). When fires burn 90% of the patch every 7 years (with unplanned fires), the maximum population size increases to about 2500, the median population size does not decline below 160 individuals in the 50-year period, and the risk of extinction is reduced to about 1.5%. The results for Fig. 4a and b together indicate that planned fire management will only yield acceptable levels of extinction risk if it is carried out in conjunction with predation management. The maximum curve in Fig. 3b is characterised by peaks and troughs roughly every 7 years, interrupted by unplanned fires. Trajectories that give maximum population sizes are associated with random scenarios (out of the 1000 simulations) in which unplanned fires do not, or rarely, occur. As the time since the last fire increases, so does the seed production of new recruits, increasing the total population size until the next fire occurs. Maximum population sizes occur when environmental conditions are favourable; for instance, when natural variation in the model is such that survival rates and fecundities are higher than the mean and the sequence of fire events does not significantly
diminish the seed bank but is frequent enough to produce new recruits. All other fire management scenarios, in conjunction with an 80% predation rate, give a probability of extinction that ranges from 2 to 11% (Fig. 4b, with one exception of a 60% chance of extinction for fires that burn the entire patch every 5 years) and the chance of decline below 50 individuals ranges between 28 and 100%. The optimal fire frequency and size combinations for this predation scenario are fires that burn 50–90% of the patch every 7–15 years. Extinction and decline rates are further reduced, by an average factor of 10 and 24, respectively, if unplanned fires are prevented from occurring. When unplanned fires occur in conjunction with managed fires, the probability of extinction and decline to below 50 individuals is elevated due to the potential occurrence of three consecutive fires that eliminate the local population. Furthermore, the prevention of unplanned fires can reduce the probability of extinction to zero (for fire frequencies of 7–15 years that burn 90–100% of the patch). When average predation rates are reduced to 70%, a further improvement in extinction rates (Fig. 4c) and decline rates is achieved. The optimal fire frequency and size combinations under this predation management strategy are fires that burn 20–90% of the patch every
Fig. 4. % Chance of extinction versus fire frequency (in years) for: (a) the predation rates in Eq. (2) (Auld and Denham, 2001); (b) the predation rates reduced to an average of 80%. A fire frequency of 5 years with fire size of 100% results in a 60% chance of extinction (not shown on graph); and (c) the predation rates reduced to an average of 70%. A fire frequency of 5 years combined with a fire size of 100% results in a 24% chance of extinction (not shown on graph). For graphs (a)–(c) each curve corresponds to the proportion of patch burnt in planned fires. ‘‘unplanned’’ refers to the scenario where only random, unplanned fires occur that burn the entire patch. All scenarios allow the occurrence of unplanned fires that burn the entire patch. (d) Comparison of results of % chance of extinction versus fire size for different predation scenarios under a fire frequency of 5 years. The Auld–Denham rates [Eq. (2)] give a 100% chance of extinction for each fire size (not shown on graph).
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5–10 years, although comparable improvement is also achieved with lower fire frequencies and larger fire sizes (cf. 100% of the patch burnt every 15–30 years). A further reduction in predation rates (to a mean rate of 50%) does not gain much more improvement for a fire frequency of 5 years except when the entire patch is burnt (Fig. 4d). When unplanned fires are allowed to occur, there is an increased chance of three consecutive fires that eliminate the entire local population. This outweighs any benefits of a further 20% reduction in predation rates.
4. Discussion The model highlights just how difficult it is to maintain small populations of G. caleyi in a fire-prone habitat. The only circumstances in which a small population has a reasonable chance of not being lost completely is if there is an imposed reduction in predation rates and fire events are managed at regular intervals. The optimal fire management strategy depends on the extent to which seed predation is reduced. For scenarios where predation rates are reduced to 80% the optimal strategy is fires that are managed to occur every 7–15 years, burning 90–100% of the patch each time (in the absence of unplanned fires), or burning between 50 and 100% of the patch (when unplanned fires are allowed to occur and the planned fire regime is consequently modified). When predation rates are reduced to 70%, the optimal fire management strategies are fires every 5–10 years, burning 20–90% of the patch each time. Comparable improvement under this predation scenario is achieved with lower fire frequencies and larger fire sizes (100% of the patch burnt every 15–30 years). These results suggest that effective control of seed predation would confer greater viability of small G. caleyi populations in the face of frequent patchy fires, a regime otherwise associated with very high risks of extinction. It is not surprising that the long-term persistence of small populations increases when predation decreases from the rates in Eq. (2) to means of 80 and 70%. It is surprising, however, that a further decrease in seed predation, from a mean of 70 to 50%, does not have a comparable impact on population persistence. This indicates that no important benefit is gained from the extra effort involved in reducing predation rates below a mean of 70%. Predation management alone does not give the best chances of long-term persistence of small populations. The results presented here indicate that when seed predation is reduced by at least 20% (i.e. when predation rates are reduced to 80% or lower), small populations in remnant patches have the best chance of persistence when survival of mature plants and seed germination occur simultaneously, i.e. when the population
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has plants from a wider range of age classes. The only way to achieve this is to plan fires that burn part of the patch at regular intervals. In reality, fires that burn part of the patch may be difficult to implement for small populations without further detrimental site disturbance. It may, however, be a more practical option for larger sites. These results indicate that multi-age cohorts have a better chance of long-term persistence than even-age cohorts. This has favourable implications for the entire population of G. caleyi because remnant sub-populations span a range of age classes. Furthermore, we expect that the bulk of the results obtained from the model for small sub-populations could be relevant for large populations. For instance, it is expected that a reduction in seed predation would benefit all sub-populations regardless of their size. We also expect that an interval fire regime in the absence of wild fires would be of benefit for the long-term persistence of larger populations, however, the optimal fire regime might not necessarily be the same for populations of all sizes. A meta-population model for all sub-populations of G. caleyi is currently being developed to test these strategies. These results highlight the need to plan strategically for the risk of unplanned fires, either through attempting to manage their exclusion when fire frequency is likely to be high or by permitting their passage when a fire is desirable. There will always be a chance of extinction when unplanned fires are allowed to occur, regardless of the size of the population or the fire management strategy employed. This is because a population is eliminated if fires that burn the entire patch occur in three consecutive years or in years close enough together to prevent maturation of seedlings. The results presented here also highlight the critical need for maintaining accurate fire history records for remnant G. caleyi sites. The method used to model density-dependent processes induces a higher rate of population decline and extinction than would be seen if such processes were absent from the model. The result is that many small plants become shaded by a few tall ones. This is the case regardless of population sizes or patch dimensions, because seeds do not disperse. As a result, recruits from seeds produced by the same plant will occur within close proximity to each other. Many recruits become stunted as heights and crown widths increase and shade adjacent plants. While the rate of seed production is not affected by density-dependent processes, the survival rates, on average, are reduced for shaded plants over 4 years of age. This may not have measurable impacts on large populations of G. caleyi because the high rate of seed production of these large cohorts outweighs any increased mortality due to shading. However, it can affect the long-term persistence of small populations where the seed production of a few plants may not be
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high enough to counteract the increased mortality due to shading. This is especially pertinent for scenarios with high predation rates. The type of density-dependent processes modelled here are usually absent from plant population models but we believe they are necessary to avoid underestimating decline and extinction rates of small populations. Explicit treatment of natural variation in growth parameters needs to be a key component in modelling the effects of competition and density dependence for any plant species that occurs in even-age cohorts. We believe that the approach we have taken here to explicitly represent density dependence and response to fire events is relevant to many plant species in fire-prone habitats (e.g. Californian chapparal, Franklin et al., 2001; Yellowstone lodgepole pine, Nyland, 1998; fynbos communities in South Africa, Privett et al., 2001), particularly where adverse fire regimes pose a threat to populations. Our model does not examine the effects of habitat destruction due to development, which is one of the major threatening processes affecting the species. It is often argued that small populations are expendable in the face of development proposals, so long as the larger populations remain. The contribution that each small population makes to the viability of the whole species depends on how independent the fire regimes are for different populations. If fire regimes are less than perfectly correlated, then the maintenance of small populations could contribute to a reduced extinction risk for the whole species, even if there is negligible dispersal between populations. The level of fragmentation of G. caleyi habitat and other landscape features mean that its populations are unlikely to be exposed to perfectly correlated fire regimes. Indeed, a large fire in 1994 burnt most of the largest remnant populations, but left several small population fragments unburned. Further modeling to examine the interaction between asynchrony of fires across multiple populations would yield valuable insight into the contribution of small patches to overall viability of the species. Furthermore, if the remnant patches are genetically distinct and can persist as such in small populations (as appears to be the case, T. Llorens personal communication) then all sites need to be protected in order to protect the full range of genetic diversity in the species. The results presented here for existing levels of seed predation support findings of Bradstock et al. (1996), that extinction risk is minimised at intermediate fire frequencies and large fire sizes. Their findings were based on a model with a very different structure (spatial automata with rule-based functions and no competition or predation), a larger implicit spatial scale (tens to hundreds of hectares cf. one hectare) and a species with somewhat different life-history characteristics (a serotinous obligate-seeding Banksia cf. obligate-seeding Grevillea with persistent soil seed bank). Given these
differences the finding would seem to be a reasonable generalization. The results are also consistent with the intermediate disturbance hypothesis for fire frequency (Connell, 1978), but not for fire size. The results of the model employed in this study indicate that a seed predation management strategy is imperative if there are to be maximal benefits gained from fire management for the persistence of small populations. This result suggests that further research may be best directed towards improving understanding and development of mechanisms that limit seed predation, or at least determining if observed seed predation levels from the larger remnant populations also apply in small remnant patches (Auld and Denham, 1999, 2001). This may lead eventually to new management options, using strategies that are currently not available to us. Given that probabilities of persistence for G. caleyi increase with a reduction in seed predation in conjunction with regular fires, it is important to know how the populations of seed predators respond to fire and whether or not the urban fragmentation of the habitat influences these seed predator responses. If seed predation rates depend on distances to human populations (for instance), then plant populations furthest from human populations are most likely to persist. Knowledge of this kind may serve to establish priorities for the protection and rehabilitation of habitat for this endangered plant.
Acknowledgements This project was supported, in part, by an Environment Australia grant to MAB to develop stochastic population models for Australian plants. The authors wish to thank A. Rawlinson and H.R. Akc¸akaya for valuable comments on the manuscript and the model. Part of this work was conducted by HMR while a Postdoctoral Associate at the National Center for Ecological Analysis and Synthesis, a Center funded by NSF (Grant #DEB-0072909), the University of California, and the Santa Barbara campus.
References Auld, T.D., 1987. Population dynamics of the shrub Acacia suaveolens (Sm.) Wild. Survivorship throughout the life cycle: a synthesis. Australian Journal of Ecology 12, 139–151. Auld, T.D., 1995. Burning grevilleas, ants, rats and wallabies. CALMScience Supplement 4, 159–164. Auld, T.D., Denham, A.J., 1999. The role of ants and mammals in dispersal and post-dispersal seed predation of the shrubs Grevillea (Proteaceae). Plant Ecology 144, 201–213. Auld, T.D., Denham, A.J., 2001. The impact of seed predation by mammals on post-fire seed accumulation in the endangered Grevillea caleyi (Proteaceae). Biological Conservation 97, 377–385.
H.M. Regan et al. / Biological Conservation 109 (2003) 73–83 Auld, T.D., Keith, D.A., Bradstock, R.A., 2000. Patterns in longevity of soil seedbanks in fire-prone communities of southeastern Australia. Australian Journal of Botany 48, 539–548. Auld, T.D., Scott, J., 1997. Conservation of endangered plants in urban fire-prone habitats. In: Proceedings: Fire Effects on Rare and Endangered Species and Habitats Conference, Coeur D’Alene, Idaho, USA. International Association of Wildland Fire, USA, pp. 163–171. Bond, W.J., van Wilgen, B.W., 1996. Fire and Plants. Chapman and Hall, London. Bradstock, R.A., Bedward, M., Scott, J., Keith, D.A., 1996. Simulation of the effect of spatial and temporal variation in fire regimes on the population viability of a Banksia species. Conservation Biology 10, 776–784. Bradstock, R.A., Myerscough, P., 1981. Fire effects on seed release and the emergence and establishment of seedlings in Banksia ericifolia L.f. Australian Journal of Botany 29, 521–532. Burgman, M.A., Ferson, S., Akc¸akaya, H.R., 1993. Risk Assessment in Conservation Biology. Chapman and Hall, London. Burgman, M.A., Lamont, B.B., 1992. A stochastic model for the viability of Banksia cuneata populations: environmental, demographic and genetic effects. Journal of Applied Ecology 29, 719–727. Connell, J.H., 1978. Diversity in tropical rainforests and coral reefs. Science 199, 1302–1310. Crawley, M.J., Rees, M., 1996. The balance of plant populations. In: Floyd, R.B., Sheppard, A.W., de Barro, P.J. (Eds.), Frontiers of Population Ecology. CSIRO Publishing, Melbourne, pp. 191– 212. Dreschler, M., Lamont, B.B., Burgman, M.A., Akc¸akaya, H.R., Witkowski, E.T.F., Supriyadi, X., 1998. Modelling the persistence of an apparently immortal Banksia species after fire and land clearing. Biological Conservation 88, 246–259. Fox, B.J., McKay, G.M., 1981. Small mammal responses to pyric successional changes in eucalypt forest. Australian Journal of Ecology 6, 29–41. Franklin, J., Syphard, A.D., Mladenoff, D.J., He, H.S., Simons, D.K., Martin, R.P., Deutschman, D., O’Leary, J.F., 2001. Simulating the effects of different fire regimes on plant functional groups in Southern California. Ecological Modelling 142, 261–283. Gill, A.M., Groves, R.H., 1981. Fire regimes in heathlands and their plant-ecological effects. In: Specht, R.L. (Ed.), Ecosystems of the World. 9B. Heathlands and Related Shrublands. Elsevier Scientific, Amsterdam, pp. 61–84.
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Keith, D.A., Bradstock, R.A., 1994. Fire and competition in Australian heath: a conceptual model and field investigations. Journal of Vegetation Science 5, 347–354. Klinkhamer, P.G.L., Meelis, E., de Jong, T.J., Weiner, J., 1992. On the analysis of size-dependent reproductive output in plants. Functional Ecology 6, 308–316. Kruger, F.J., 1983. Plant community dynamics and diversity in relation to fire. Mediterranean-type ecosystems. In: Kruger, F.J., Mitchell, D.T., Jarvis, J.U.M. (Eds.), The Role of Nutrients. Ecological Studies 43. Springer-Verlag, Berlin, pp. 446–472. Lamont, B.B., van Leeuwen, S.J., 1988. Seed production and mortality in a rare Banksia species. Journal of Applied Ecology 25, 551–559. McLoughlin, L.C., 1998. Season of burning in the Sydney region: the historical records compared with recent prescribed burning. Australian Journal of Ecology 23, 393–404. Moore, A.D., Noble, I.R., 1990. An individualistic model of vegetation stand dynamics. Journal of Environmental Management 31, 61–81. Morris, E.C., 2000. Germination response of seven east Australian Grevillea species (Proteaceae) to smoke, heat exposure and scarification. Australian Journal of Botany 48, 179–189. Nyland, R.D., 1998. Patterns of lodgepole pine regeneration following the 1988 Yellowstone fires. Forest Ecology and Management 111, 23–33. Obeid, M., Machin, D., Harper, J.L., 1967. Influence of density on plant to plant variation in fiber flax, Linum usitatissimum. Crop Science 7, 471–473. Privett, S.D.J., Cowling, R.M., Taylor, H.C., 2001. Thirty years of change in the fynbos vegetation of the Cape of Good Hope Nature Reserve, South Africa. Bothalia 31, 99–115. Rees, M., Brown, V.K., 1992. Interactions between invertebrate herbivores and plant competition. Journal of Ecology 80, 353–360. Samson, D.A., Werk, K.S., 1986. Size-dependent effects in the analysis of reproductive effort in plants. The American Naturalist 127, 667–680. Scott, J., Marshall, A., Auld, T.D., 1995. Conservation Research Statement and Recovery Plan for Grevillea caleyi. Australian Nature Conservation Agency, Canberra. Sobol, I.M., 1994. A Primer for the Monte Carlo Method. CRC Press, Boca Raton, FL. Tyler, C.M., 1995. Factors contributing to postfire seedling establishment in chaparral: direct and indirect effects of fire. Journal of Ecology 83, 1009–1020. Whelan, R.J., 1995. The Ecology of Fire. Cambridge University Press, Cambridge.
The effects of fire and predators on the long-term persistence of an endangered shrub, Grevillea caleyi Helen M. Regana,b,*, Tony D. Auldc, David A. Keithc, Mark A. Burgmana a School of Botany, The University of Melbourne, Parkville, Victoria 3052, Australia National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, 735 State Street, Suite 300, Santa Barbara, CA 93101, USA c NSW National Parks and Wildlife Service, PO Box 1967, Hurstville, NSW 2220, Australia
b
Received 26 October 2001; received in revised form 10 February 2002; accepted 15 February 2002
Abstract Grevillea caleyi is an endangered plant species with a restricted range lying partly within Ku-ring-gai Chase and Garigal National Parks in NSW, Australia. The principle threatening processes affecting G. caleyi are habitat destruction and adverse fire regimes combined with high levels of seed predation. A stochastic, spatially explicit, individual-based model was constructed to investigate the population dynamics of small populations of the species and to determine the impact of a variety of management strategies. Results of model simulations indicate there is a high risk of population decline and local extinction in remnant sites with small populations under current management regimes. The most effective fire management strategy is to schedule fires that burn 20–100% of sub-populations every 5–15 years, in combination with reduced predation rates. When predation management strategies are employed in conjunction with a structured fire regime, then a 20–30% reduction in predation rates can improve the chance of longterm persistence substantially. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Individual-based model; Conservation management; Population dynamics; Seed predation; Fire intervals
1. Introduction Fire regimes play an important part in the survival, ecology and evolution of many plant species (Gill and Groves, 1981; Kruger, 1983; Whelan, 1995; Bond and van Wilgen, 1996). Recruitment in such species is frequently linked to fire (Tyler, 1995). This is critical in plant species in which the above-ground life-history stages are killed by fire. Such species are totally dependent upon the germination of seeds from canopy or soilstored seed banks for post-fire recovery (e.g. Banksia cuneata, Burgman and Lamont, 1992; Banksia ericifolia, Bradstock and Myerscough 1981; Acacia suaveolens, Auld, 1987). Even for species in which standing plants have some capacity to survive fire and resprout new foliage, recruitment is needed to maintain populations (Banksia goodii, Dreschler et al., 1998). Species that are less resilient to fire and more prolific in seed-production * Corresponding author. Tel.: +1-805-892-2522; fax: +1-805-8922510. E-mail address: [email protected] (H.M. Regan).
also rely on fire for seed germination (e.g. Banksia tricuspis, Lamont and van Leeuwen, 1988). The trade-off for resprouting species is their limited ability to produce seeds or seedlings. Threatened species that occur in fire-prone habitats may be particularly at risk from adverse fire regimes because of their restricted habitats in combination with a variety of other threats (Auld and Scott, 1997). Where metapopulations are fragmented in cleared landscapes, adverse fire regimes may lead to local extinctions. The aim of managing threatened species is to minimise threatening processes and to allow recovery and longterm persistence of populations in the wild. Consideration of how threatened species respond to fire will be a key component of this management in many environments. In this paper we investigate a range of management strategies for the endangered plant species, Grevillea caleyi. In particular, we investigate the impact of reducing the frequency and magnitude of key threatening processes on the population dynamics of G. caleyi, and identify the best strategy (out of those considered) for the long-term persistence of the populations.
0006-3207/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(02)00138-6
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G. caleyi (Proteaceae) is an understorey shrub of eucalypt forest in northern Sydney, Australia (Fig. 1). Its range is less than 10 km and its five populations are found on the interface between urban development and remnant bushland, some of which lies just within the boundaries of Ku-ring-gai Chase and Garigal National Parks. A recovery program is currently underway to implement research and management strategies for conservation of the species (Scott et al., 1995). It is believed that the principal threatening processes affecting G. caleyi
are habitat destruction and adverse fire regimes, combined with high levels of seed predation (Auld and Scott, 1997). The loss of emus, a suspected key seed dispersal agent, from the local landscape may also have contributed to an elevated extinction risk since European settlement. Road construction and associated rural and urban development along ridges where the species grows is estimated to have destroyed 85% of G. caleyi’s habitat (Scott et al., 1995) and led to the fragmentation of remaining clusters of plants in an urban landscape.
Fig. 1. Map of location of populations of Grevillea caleyi. Its five fragmented populations are found within the boundaries of Ku-ring-gai Chase and Garigal National Parks in northern Sydney, Australia, on the interface between urban development and remnant bushland.
H.M. Regan et al. / Biological Conservation 109 (2003) 73–83
Plants of G. caleyi are killed by fire which, in turn, promotes the breaking of seed dormancy in the soil seed bank. Successful establishment of seedlings is very rare in the absence of fire, unless there has been some other disturbance, such as clearing. A very high proportion of all seeds produced are consumed, primarily by rodents and macropods, soon after their release from fruits (Auld, 1995; Auld and Denham, 1999). Populations of G. caleyi may be completely eliminated if fires occur when seed availability in the soil is low. The aims of this study are threefold: to investigate the population dynamics of the species; to predict the outcome of prescribed burning and seed-predator reduction; and to determine the optimal management strategy (in terms of probability of population persistence) from the range of options considered. In this paper, we focus on the remaining small populations as they are regarded as the most vulnerable to extinction. They also allow for detailed investigation of density-dependent processes resulting from the absence of seed dispersal and natural variation in heights. Some specific questions regarding these small populations include the following: Are current small population fragments likely to persist under a regime of prescribed and unplanned fires? How does varying fire frequency influence population persistence? Does forcing a multi-age cohort in the population through partial patch burning reduce extinction risks? How sensitive is population persistence to a reduction in seed predation? A stochastic, spatially explicit, individual-based model was developed using the available field data and the knowledge of experts. It was anticipated that spatial density-dependent processes would have important effects on the population size because seeds do not disperse far and competition for light affects the survival rates of plants (Crawley and Rees, 1996). A treatment of uncertainty and variability was incorporated into the model to ensure conservative results and consideration of the full range of possible outcomes. The model was used to investigate the dynamics of small populations of G. caleyi and to determine the risk of extinction and decline associated with various fire regimes and predation rates.
2. Material and methods 2.1. Life history and population structure Populations of G. caleyi grow as even-age cohorts. This is because all established plants die in a fire and
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seed germination of Grevillea species in this region appears to be predominantly stimulated by smokederivatives and soil-heating associated with fire (Morris, 2000). Some seeds are killed during the passage of fire and the remainder have an opportunity to germinate. The number of germinants depends on the heat and smoke outputs of the fire (Auld and Denham, 2001). For low intensity fires, the number of seeds that die via lethal soil heating and the number of seeds that have their dormancy broken are predicted to be less than that for a high intensity fire. The complex relationship this plant has with fire, due to both heat and smoke, plays an important role in its survival. The number of seeds produced by each plant is dependent on the plant’s age (Auld and Scott, 1997). Young plants grow to maturity within 3–5 years after a fire (Scott et al., 1995). One year old plants do not produce seeds, 2 year old plants rarely produce seeds while plants of at least ten years can produce around 15 seeds each annual flowering season. These seeds fall directly from the canopy and do not disperse. The seeds are quite large (they range from 1.5 cm to about 2.0 cm in length with mean seed weight from 318 to 351 mg, Auld and Denham 1999) and a substantial proportion, approximately 50–100%, are eaten by bush rats and wallabies before the remainder enter the seed bank (Auld and Denham, 1999). Immediately after a fire, seed loss to mammals can rise to 100% before beginning to decline to pre-burn levels. Seed viability (i.e. the propensity to germinate given appropriate conditions) decays exponentially with time since entering the seed bank (Auld et al., 2000). Plants can grow up to 4 m in height; however, this is dependent on competition for light from conspecific and interspecific neighbours. Plants that are shaded can grow up to approximately 2 m. Likewise, the survival coefficients are lower for plants that are shaded by other plants than for those that are not (Scott et al., 1995). The radius of the crown is generally half the height of the plant for younger plants and roughly equal to the height of the plant for older plants. Empirical studies have demonstrated that when competition for light is apparent in a population then it will consist of a few tall plants and many small ones (Obeid et al., 1967; Crawley and Rees, 1996). Known remnant patches of G. caleyi range in area from 5 m 5 m to 350 m 100 m. In 1998, of the 20 known remnant patches, there were three kinds of population structure represented: 4 year old plants and seeds (10 patches ranging from 15 plants to estimates of 2000 plants); 10 year old plants (two patches with some 200 plants each); and > 15 year old plants and seeds (seven patches including some sites with only seeds in soil, and one population with soilstored seeds and about 150 plants). Two of these long unburned patches were subsequently burnt in August 1998 and 1999, respectively.
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2.2. Individual-based model In this model the age, position, height, and radius of the crown of each plant in a rectangular patch is recorded at each time step. Eleven age classes have been assumed, including one for seeds, and 10 for standing plants (i.e. ages one to nine and 10 years and above). Plants are further categorised into two groups to model the effects of intraspecific competition: those that are below other plants; and those that are not. The former are referred to as ‘‘below’’ plants while the latter are referred to as ‘‘above’’ plants, even though all ‘‘above’’ plants may not necessarily be taller than all plants categorised as ‘‘below’’. Once an arbitrary area of the crown of a plant is shaded by another plant then it is classified as ‘‘below’’. It is assumed that all plants have circular crowns. A plant is deemed to be underneath another plant if its height is less than the adjacent plant and the centroid of its crown is underneath the adjacent plant’s crown. This simple competition model is based on that of Moore and Noble (1990), where all plants are affected by other taller plants but not by smaller plants. Competition is interrupted by recurring fires (Keith and Bradstock, 1994). The deterministic governing equations of the system are: N10þ;tþ1 ¼ Na9;t Sa9 þ Nb9;t Sb9 þ Na10þ;t Sa10þ þ Nb10þ;t Sb10þ ; Ni;tþ1 ¼ Nai1;t Sai1 þ Nbi1;t Sbi1 ; i ¼ 2; . . . ; 9; N1;tþ1 ¼ N0;t P ðrecruitment after f ire eventÞ N0;tþ1 ¼
10þ X
Ni;tþ1 fi
ð1Þ
i¼2
where Nai,t is the number of ‘‘above’’ plants of i years of age at time t years, Nbi,t is the number of ‘‘below’’ plants in age class i at time t, Sai is the survival coefficient for ‘‘above’’ plants i years of age, Sbi is the survival coefficient for ‘‘below’’ plants in age class i, P(.) is a probability function and fi is the fecundity of plants i years of age. The fecundity is made up of three components, i.e. fi=ni (1), where ni is the number of seeds produced per plant of i years of age, (=0.8) is the proportion of viable seeds from plants i years of age, and is the predation rate (i.e. 1 is the proportion of uneaten seeds). Initially, the predation rate is assigned the function 8 if TSLF 4 2 < 1:0 ¼ 0:01 TSLF þ 1:01 if 2 < TSLF 4 18 : 0:83 if TSLF > 18 ð2Þ where TSLF is the time since the last fire (linear regression from Auld and Denham, 2001). Seed predation rates and viability were estimated from empirical observations (Auld, 1995; Auld and Denham, 1999, 2001). The viability
of surviving seeds entering the seed bank m years ago is m due to the m iterations through time since they entered the seed bank. Here, only plants of ages 2 years and above have associated fecundities. At census, plants 1 year of age are too young to develop seeds (Scott et al., 1995). The number of seeds produced by a plant annually, ni, is a function of the age of the plant and was estimated from field observations combined with fire history records (Auld, unpublished). The number of seeds per plant in age class i is ( 0 if i 4 1; otherwise ni ¼ ð3Þ int 15 41 exp ði 1Þ2 =18 where int(x) is the value of x rounded to the nearest integer. Contrary to some other plant species (Samson and Werk, 1986; Rees and Brown, 1992; Klinkhamer et al., 1992), reproductive output of G. caleyi is directly dependent on age rather than size; however, there is an indirect relationship between fecundity and size due to the age dependence of plant heights, particularly in the first 10 years of development. Hence, it is assumed the competitive status of plants (that is, whether they are above or below other plants) does not affect the number of seeds produced by individuals. The function for reproductive output was constructed from data and expert opinion and is displayed in Fig. 2a. The change in height of each plant over one time step is assumed to be a function of its age. The functions determining the height (from which the change in height from year t to t+1 can be calculated) of plants below or above other plants were constructed from field observations, combined with expert opinion, as: hbelowðiÞ ¼ 2 ð2=100Þði 10Þ2 haboveðiÞ ¼ 3 ð3=100Þði 10Þ2
ð4Þ
where again, i is the age of the plants. Graphs of these functions appear in Fig. 2b. Although ‘‘above’’ plants can grow up to 4 m, the mean height of plants in age class 10+ is approximately 3 m. As a conservative assumption, a plant’s crown is assigned a radius equal to half its height and expands accordingly. The survival coefficient for a plant was assumed to depend on its age and its competitive status. Hence, for each age group two survival coefficients, Sai and Sbi, both functions of the age of the plant, were derived from field observations and censuses of tagged individuals. Eq. (5) specifies the functions and Fig. 2c displays their graphs. ( 0:99 for i 4 4; otherwise Sai ¼ 1 0:19 1 exp ði 4:5Þ2 =2:5 þ 0:01 ( 0:99 for i 4 4; otherwise Sbi ¼ 1 0:49 1 exp ði 4:5Þ2 =6 þ 0:01
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Fig. 2. (a) The number of seeds produced per plant per year as a function of the age of the plant. This does not include the reduction due to predation. (b) The relationship between height, age and competitive status for Grevillea caleyi. ‘‘Below’’ plants are those that are shaded by an arbitrarily chosen amount. ‘‘Above’’ plants are not shaded. (c) The relationship between age, survival and competitive status for G. caleyi. (d) Fire probability as a function of the time since the last fire. (e) The probability of a hot fire (given that there is a fire), as a function of the time since the last fire. If the fire occurs in the first three years after a fire then it will always be a low intensity fire.
The effects of competition were further incorporated by ensuring that the growth of a plant was halted if the edge of its crown coincided with the stem of an adjacent taller plant. Fire is incorporated into the model with the use of a probability function. The probability of a fire in year t+1 depends on the number of years since the last fire. The probability function employed in the model is: 8 TSLF 4 2 <0:005; Prfire ðTSLFÞ¼ ð0:095=3ÞTSLF 0:175=3; 2
with prescribed burning practices of the two major land management authorities in northern Sydney (New South Wales National Parks and Wildlife Service and Hornsby Shire Council unpublished; McLoughlin, 1998). When a fire occurs, all the burnt plants die and only the seeds are left in the seed bank. There are two possible types of fire in the model, depending on available fuel levels and weather: a hot (or high intensity) fire or a cool (or low intensity) fire. The probability of a hot fire is also a function of the time since the last fire, displayed in Fig. 2e, and specified as: Prhot fire ðTSLFÞ ¼ 8 TSLF 4 3 > < 0; ð0:5=25ÞðTSLF 8Þ2 þ0:5; 3 4 TSLF 4 8; > : 0:5; 8 < TSLF
ð7Þ
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The time since the last fire and fire intensity also have effects on seed survival and germination rates. If there was no fire in the previous year and a hot fire in the current year then 20% of the seeds die and 60% of the remaining seeds germinate. If there was no fire in the previous year and a cool fire the current year then 10% of the seeds die and 30% of the remaining seeds germinate. If there are fires two years in a row then the same proportion die in the second year and all the remaining seeds germinate. The number of 1 year old plants at the next census (after the fire) will then be the number of seeds that germinate. If there are fires 3 years in a row then all plants die, there are no seeds remaining in the seed bank and the species is eliminated from the patch. Environmental stochasticity is incorporated into the model by assigning a probability distribution with each of the survival and plant growth parameters Sai, Sbi, habove(i) and hbelow(i). In the case of the survival coefficients, a lognormal probability density function is associated with the survival value for each age class. Hence, Sai and Sbi are selected from the following probability distributions:
Sbi LN S"bi ; 0:1S"bi ð8Þ
Sai LN S"ai ; 0:1S"ai ;
2.3. Simulations
where S"ai and S"bi are the values taken from Eq. (5). To ensure all values lie within the bounds 0 and 1, while minimizing the effects of truncating the lognormal distribution, we adopt the strategy employed in Burgman et al. (1993) of reflecting the distribution for survival values greater than 0.5 about the point 0.5. Once the survival rates of plants in each age class have been determined, demographic stochasticity is included by selecting the number of plants that survive to the next year from a binomial distribution using the new survival rates. The survivors are chosen randomly, their positions are recorded and the height of each plant is updated. Since populations grow as even-age cohorts, a treatment of natural variation in the heights of plants is necessary to model shading and density-dependent effects. Environmental variation in the height parameters is dealt with in a similar way to the survival rates. A lognormal distribution is associated with the change in height from one age class to the next for both ‘‘above’’ and ‘‘below’’ plants as follows: $" haboveðiÞ ¼ haboveði þ 1Þ haboveðiÞ; $" hbelowðiÞ ¼ hbelowði þ 1Þ hbelowðiÞ;
$haboveðiÞ ¼ LN $" haboveðiÞ; 0:1$" haboveðiÞ ;
$hbelowðiÞ ¼ LN $" hbelowðiÞ; 0:1$" hbelowðiÞ ;
In this case the distributions are not truncated. This treatment of environmental variation in the height parameters drives competition and density dependence in the model. Each plant is compared with every other surviving plant to determine if it is above or below any other plants. The survival rates of plants are updated accordingly. The number of seeds in the seed bank is then calculated (using the updated heights of plants 2 or more years old). Demographic stochasticity is introduced in the same way as for the number of surviving plants. The number of seeds remaining after viability and predation discounts is chosen from a binomial distribution with a probability of (1). The model is initialised at t=0 by randomly assigning positions and heights to a specified number of plants in each age class in a rectangular patch of pre-assigned dimensions. The heights of plants in each age class were randomly selected from a normal distribution with a mean calculated from a similar height function to those above with a maximum height of 2.5 m, and a coefficient of variation of 0.1. The Monte Carlo method is used throughout to select random deviates from the specified probability distributions (Sobol, 1994).
ð9Þ
where $haboveðiÞ is the increase in height of an ‘‘above’’ plant that survives from age class i to age class i+1 etc.
Management strategies were tested in the model to investigate the effects of decreased seed predation during each annual seed-crop and various fire management regimes. The model was config. to simulate an initial population of 46 seeds and 70 four-year-old plants (total of 116 individuals) in a habitat patch 50 m by 200 m. This configuration reflected an actual population of the species. A range of initial population sizes for small populations were tested for sensitivity in the model with qualitatively the same results. The effects of fire frequency alteration were examined by running the model with deterministic fire frequencies of 5, 7, 10, 15, 20 and 30 years, as well as random unplanned fire frequency derived from the fire probability function (Fig. 2d and e). Here, unplanned fires refer to those fires that occur outside the suggested fire management schedule. Such fire events include wildfires, arson and any uncontrolled and unintentional fire that burns the patch. Mosaic fire management strategies were investigated by simulating fires in which 20, 50, 90 and 100% of the habitat patch was allowed to burn in each fire. For partial burns, the area impacted was a rectangular strip, with a randomly assigned position within the patch. The effects of reducing predation were explored by decreasing the average predation rates from the AuldDenham rates [Eq. (2)] to a mean rate of 0.8. In the first 7 years following a fire, a Normal distribution was assigned with a mean of 0.8 and a coefficient of variation of 10%, to simulate variation and uncertainty in
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predation rates while predators are trying to re-establish in the area after a fire. Predation rates were assigned a constant value thereafter (i.e. =0.8), although demographic stochasticity via Binomial distributions is still incorporated after 7 years since the last fire. This was repeated with Normal(0.7, 0.07) and Normal(0.5, 0.05) in conjunction with a selection of fire management strategies. This situation simulated what may happen, in the uncertain and variable period 7 years after a fire, if mammalian seed predator numbers (and hence, seed predation levels) are reduced and take a number of years to recover to their stable pre-fire numbers (cf. Fox and McKay, 1981). The influence of fire size on seed predation rates is considered to be minimal. Auld and Denham (2001) studied post-fire predation levels after extensive wildfires and concluded that fire size is unlikely to be important (see also Auld, 1995). As a result of urbanisation and fragmentation of habitat, seed predation is more likely to be influenced by the proximity of G. caleyi sites to areas that do not burn (i.e. potential refugia for rats and wallabies during a fire) than by the proportion of the site burned. Therefore, no further adjustments were made to predation rates in the model as a result of fire size. All selected combinations of predation, fire frequency and fire size management scenarios were simulated with unplanned fires. To investigate the impact of preventing unplanned fires from modifying the planned fire schedule, simulations that excluded the occurrence of unplanned fires were also run with the combinations of 80% mean predation rates, fire frequencies of 5, 7, 10 and 15 years and all fire sizes. For the simulations in which unplanned fires were allowed to occur in addition to a managed fire frequency, the unplanned fires burnt the entire patch. The next managed fire was then scheduled to occur 5, 7, 10, 15, 20 or 30 years, accordingly, after the unplanned fires. This resetting of the planned fire timetable reflects the current practice of field managers. The dynamics of G. caleyi populations were simulated by generating 50-year trajectories, 1000 times. In this way the combination of many stochastic events was investigated. The maximum, median and minimum population size of the 1000 replications at each time step was recorded. The risk of extinction and quasiextinction were calculated from the minimum of each 50-year trajectory.
3. Results In terms of fire frequency and predation, the baseline conditions for populations of G. caleyi are unplanned fires burning the entire patch and predation at rates specified in Eq. (2). Under these conditions, most population trajectories declined to zero (Fig. 3a). The
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Fig. 3. (a) Maximum, median and minimum for 1000 trajectories over a 50-year period for the baseline conditions of unplanned fires that burn the entire patch and the predation rates reported in Auld and Denham (2001). (b) Maximum, median and minimum for 1000 trajectories over a 50-year period when seed predation rate is reduced to a mean of 80%, in conjunction with fires that occur every 7 years (with unplanned fires) that burn 90% of the patch.
maximum population size reached across all trajectories was 208 (including seeds), however, the maximum declined to 33 individuals by year 50, and the median of all the trajectories declined to zero within 50 years. The risk of extinction for this population under this scenario is about 60%, i.e. approximately 60% of the 1000 trajectories declined to zero within the 50-year period. Simulations for the single small population under all fire management scenarios with predation rates as in Eq. (2), gave local extinction rates ranging from about 60% (for unplanned fires and for all fires sizes every 20– 30 years) to 100% (all fire sizes for a fire frequency of 5 years, Fig. 4a), and a 100% chance of decline below 50 individuals. Results indicate that random unplanned fires that burn the entire patch yield almost the lowest chance of extinction out of all the imposed fire management strategies.
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Simulations with average predation rates of 80%, in combination with managed fire frequency and fire size, indicate a marked improvement in both extinction and decline rates (Figs. 3b and 4b, however note that% decline rates are not displayed graphically throughout). When fires burn 90% of the patch every 7 years (with unplanned fires), the maximum population size increases to about 2500, the median population size does not decline below 160 individuals in the 50-year period, and the risk of extinction is reduced to about 1.5%. The results for Fig. 4a and b together indicate that planned fire management will only yield acceptable levels of extinction risk if it is carried out in conjunction with predation management. The maximum curve in Fig. 3b is characterised by peaks and troughs roughly every 7 years, interrupted by unplanned fires. Trajectories that give maximum population sizes are associated with random scenarios (out of the 1000 simulations) in which unplanned fires do not, or rarely, occur. As the time since the last fire increases, so does the seed production of new recruits, increasing the total population size until the next fire occurs. Maximum population sizes occur when environmental conditions are favourable; for instance, when natural variation in the model is such that survival rates and fecundities are higher than the mean and the sequence of fire events does not significantly
diminish the seed bank but is frequent enough to produce new recruits. All other fire management scenarios, in conjunction with an 80% predation rate, give a probability of extinction that ranges from 2 to 11% (Fig. 4b, with one exception of a 60% chance of extinction for fires that burn the entire patch every 5 years) and the chance of decline below 50 individuals ranges between 28 and 100%. The optimal fire frequency and size combinations for this predation scenario are fires that burn 50–90% of the patch every 7–15 years. Extinction and decline rates are further reduced, by an average factor of 10 and 24, respectively, if unplanned fires are prevented from occurring. When unplanned fires occur in conjunction with managed fires, the probability of extinction and decline to below 50 individuals is elevated due to the potential occurrence of three consecutive fires that eliminate the local population. Furthermore, the prevention of unplanned fires can reduce the probability of extinction to zero (for fire frequencies of 7–15 years that burn 90–100% of the patch). When average predation rates are reduced to 70%, a further improvement in extinction rates (Fig. 4c) and decline rates is achieved. The optimal fire frequency and size combinations under this predation management strategy are fires that burn 20–90% of the patch every
Fig. 4. % Chance of extinction versus fire frequency (in years) for: (a) the predation rates in Eq. (2) (Auld and Denham, 2001); (b) the predation rates reduced to an average of 80%. A fire frequency of 5 years with fire size of 100% results in a 60% chance of extinction (not shown on graph); and (c) the predation rates reduced to an average of 70%. A fire frequency of 5 years combined with a fire size of 100% results in a 24% chance of extinction (not shown on graph). For graphs (a)–(c) each curve corresponds to the proportion of patch burnt in planned fires. ‘‘unplanned’’ refers to the scenario where only random, unplanned fires occur that burn the entire patch. All scenarios allow the occurrence of unplanned fires that burn the entire patch. (d) Comparison of results of % chance of extinction versus fire size for different predation scenarios under a fire frequency of 5 years. The Auld–Denham rates [Eq. (2)] give a 100% chance of extinction for each fire size (not shown on graph).
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5–10 years, although comparable improvement is also achieved with lower fire frequencies and larger fire sizes (cf. 100% of the patch burnt every 15–30 years). A further reduction in predation rates (to a mean rate of 50%) does not gain much more improvement for a fire frequency of 5 years except when the entire patch is burnt (Fig. 4d). When unplanned fires are allowed to occur, there is an increased chance of three consecutive fires that eliminate the entire local population. This outweighs any benefits of a further 20% reduction in predation rates.
4. Discussion The model highlights just how difficult it is to maintain small populations of G. caleyi in a fire-prone habitat. The only circumstances in which a small population has a reasonable chance of not being lost completely is if there is an imposed reduction in predation rates and fire events are managed at regular intervals. The optimal fire management strategy depends on the extent to which seed predation is reduced. For scenarios where predation rates are reduced to 80% the optimal strategy is fires that are managed to occur every 7–15 years, burning 90–100% of the patch each time (in the absence of unplanned fires), or burning between 50 and 100% of the patch (when unplanned fires are allowed to occur and the planned fire regime is consequently modified). When predation rates are reduced to 70%, the optimal fire management strategies are fires every 5–10 years, burning 20–90% of the patch each time. Comparable improvement under this predation scenario is achieved with lower fire frequencies and larger fire sizes (100% of the patch burnt every 15–30 years). These results suggest that effective control of seed predation would confer greater viability of small G. caleyi populations in the face of frequent patchy fires, a regime otherwise associated with very high risks of extinction. It is not surprising that the long-term persistence of small populations increases when predation decreases from the rates in Eq. (2) to means of 80 and 70%. It is surprising, however, that a further decrease in seed predation, from a mean of 70 to 50%, does not have a comparable impact on population persistence. This indicates that no important benefit is gained from the extra effort involved in reducing predation rates below a mean of 70%. Predation management alone does not give the best chances of long-term persistence of small populations. The results presented here indicate that when seed predation is reduced by at least 20% (i.e. when predation rates are reduced to 80% or lower), small populations in remnant patches have the best chance of persistence when survival of mature plants and seed germination occur simultaneously, i.e. when the population
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has plants from a wider range of age classes. The only way to achieve this is to plan fires that burn part of the patch at regular intervals. In reality, fires that burn part of the patch may be difficult to implement for small populations without further detrimental site disturbance. It may, however, be a more practical option for larger sites. These results indicate that multi-age cohorts have a better chance of long-term persistence than even-age cohorts. This has favourable implications for the entire population of G. caleyi because remnant sub-populations span a range of age classes. Furthermore, we expect that the bulk of the results obtained from the model for small sub-populations could be relevant for large populations. For instance, it is expected that a reduction in seed predation would benefit all sub-populations regardless of their size. We also expect that an interval fire regime in the absence of wild fires would be of benefit for the long-term persistence of larger populations, however, the optimal fire regime might not necessarily be the same for populations of all sizes. A meta-population model for all sub-populations of G. caleyi is currently being developed to test these strategies. These results highlight the need to plan strategically for the risk of unplanned fires, either through attempting to manage their exclusion when fire frequency is likely to be high or by permitting their passage when a fire is desirable. There will always be a chance of extinction when unplanned fires are allowed to occur, regardless of the size of the population or the fire management strategy employed. This is because a population is eliminated if fires that burn the entire patch occur in three consecutive years or in years close enough together to prevent maturation of seedlings. The results presented here also highlight the critical need for maintaining accurate fire history records for remnant G. caleyi sites. The method used to model density-dependent processes induces a higher rate of population decline and extinction than would be seen if such processes were absent from the model. The result is that many small plants become shaded by a few tall ones. This is the case regardless of population sizes or patch dimensions, because seeds do not disperse. As a result, recruits from seeds produced by the same plant will occur within close proximity to each other. Many recruits become stunted as heights and crown widths increase and shade adjacent plants. While the rate of seed production is not affected by density-dependent processes, the survival rates, on average, are reduced for shaded plants over 4 years of age. This may not have measurable impacts on large populations of G. caleyi because the high rate of seed production of these large cohorts outweighs any increased mortality due to shading. However, it can affect the long-term persistence of small populations where the seed production of a few plants may not be
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high enough to counteract the increased mortality due to shading. This is especially pertinent for scenarios with high predation rates. The type of density-dependent processes modelled here are usually absent from plant population models but we believe they are necessary to avoid underestimating decline and extinction rates of small populations. Explicit treatment of natural variation in growth parameters needs to be a key component in modelling the effects of competition and density dependence for any plant species that occurs in even-age cohorts. We believe that the approach we have taken here to explicitly represent density dependence and response to fire events is relevant to many plant species in fire-prone habitats (e.g. Californian chapparal, Franklin et al., 2001; Yellowstone lodgepole pine, Nyland, 1998; fynbos communities in South Africa, Privett et al., 2001), particularly where adverse fire regimes pose a threat to populations. Our model does not examine the effects of habitat destruction due to development, which is one of the major threatening processes affecting the species. It is often argued that small populations are expendable in the face of development proposals, so long as the larger populations remain. The contribution that each small population makes to the viability of the whole species depends on how independent the fire regimes are for different populations. If fire regimes are less than perfectly correlated, then the maintenance of small populations could contribute to a reduced extinction risk for the whole species, even if there is negligible dispersal between populations. The level of fragmentation of G. caleyi habitat and other landscape features mean that its populations are unlikely to be exposed to perfectly correlated fire regimes. Indeed, a large fire in 1994 burnt most of the largest remnant populations, but left several small population fragments unburned. Further modeling to examine the interaction between asynchrony of fires across multiple populations would yield valuable insight into the contribution of small patches to overall viability of the species. Furthermore, if the remnant patches are genetically distinct and can persist as such in small populations (as appears to be the case, T. Llorens personal communication) then all sites need to be protected in order to protect the full range of genetic diversity in the species. The results presented here for existing levels of seed predation support findings of Bradstock et al. (1996), that extinction risk is minimised at intermediate fire frequencies and large fire sizes. Their findings were based on a model with a very different structure (spatial automata with rule-based functions and no competition or predation), a larger implicit spatial scale (tens to hundreds of hectares cf. one hectare) and a species with somewhat different life-history characteristics (a serotinous obligate-seeding Banksia cf. obligate-seeding Grevillea with persistent soil seed bank). Given these
differences the finding would seem to be a reasonable generalization. The results are also consistent with the intermediate disturbance hypothesis for fire frequency (Connell, 1978), but not for fire size. The results of the model employed in this study indicate that a seed predation management strategy is imperative if there are to be maximal benefits gained from fire management for the persistence of small populations. This result suggests that further research may be best directed towards improving understanding and development of mechanisms that limit seed predation, or at least determining if observed seed predation levels from the larger remnant populations also apply in small remnant patches (Auld and Denham, 1999, 2001). This may lead eventually to new management options, using strategies that are currently not available to us. Given that probabilities of persistence for G. caleyi increase with a reduction in seed predation in conjunction with regular fires, it is important to know how the populations of seed predators respond to fire and whether or not the urban fragmentation of the habitat influences these seed predator responses. If seed predation rates depend on distances to human populations (for instance), then plant populations furthest from human populations are most likely to persist. Knowledge of this kind may serve to establish priorities for the protection and rehabilitation of habitat for this endangered plant.
Acknowledgements This project was supported, in part, by an Environment Australia grant to MAB to develop stochastic population models for Australian plants. The authors wish to thank A. Rawlinson and H.R. Akc¸akaya for valuable comments on the manuscript and the model. Part of this work was conducted by HMR while a Postdoctoral Associate at the National Center for Ecological Analysis and Synthesis, a Center funded by NSF (Grant #DEB-0072909), the University of California, and the Santa Barbara campus.
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