Interactive effects of temporal and spatial fire characteristics on the population dynamics of a fire-dependent Cypress species

Authors


Correspondence author. E-mail: susanarburitica@email.arizona.edu

Summary

  1. Current predictions about climate change and its impact on fire regimes have spurred research on how increasing fire frequencies will affect the population dynamics of fire-dependent species. There has been less consideration of changes in the spatial characteristics of fire regimes, despite recognition of the importance of spatial heterogeneity and connectivity in population dynamics.
  2. Here, we test the hypothesis that spatial heterogeneity in fire regimes may not benefit obligate seeders with canopy seed bank, due to regeneration constraints into non-burned areas. We develop a size-structured population model for a population of Tecate cypress Callitropsis forbesii (Jeps.) Little, a rare obligate seeder of conservation concern, across a complex landscape in the Santa Ana Mountains (Orange, CA, USA). Combining the population model with field measurements of stand structure and fire history, we test the roles of heterogeneity in fire regime and dispersal among patches with differing fire history on population persistence.
  3. The model predicts population persistence at fire return intervals >17 years, the approximate fire return interval at the site over the last century. However, population growth and population persistence increase when subpopulations are connected by dispersal and, within a small window of fire return intervals, when subpopulations have uncorrelated fire dynamics. Contrary to our expectations, spatial heterogeneity in fire regime increased population growth rates at intermediate (15–25 year) fire return intervals.
  4. Synthesis and applications. Conservation efforts focused on isolated populations of fire-dependent species should focus on both the temporal (fire return interval) and spatial (heterogeneity in fire occurrence) aspects of fire regimes. For one threatened Cypress species, we find that the interaction between temporal and spatial characteristics of a fire regime can increase the risks of population extinction, particularly under fire regimes characterized by more frequent, larger and more spatially homogenous fire. Species with fragmented subpopulations not well connected by dispersal also have a greater risk of extinction under these fire regimes.

Introduction

In the last decade, predictions of increasingly frequent, more severe and larger wild fires (Westerling et al. 2006) have spurred questions about how these altered fire regimes will impact plant populations. Widespread evidence has shown that fire-dependent species often persist within a specific range of fire frequencies, depending on life-history traits (e.g. Satterthwaite, Menges & Quintana-Ascencio 2002; Warton & Wardle 2003; Lamont et al. 2007; Syphard, Clarke & Franklin 2007). While less widely investigated, the heterogeneity in the fire regime – ranging from relatively homogenous fires that simultaneously burn entire populations to fires that burn portions of populations at different times and at differing intensities – can be critical to overall population persistence (e.g. Ooi, Whelan & Auld 2006; Groeneveld, Enright & Lamont 2008; Regan et al. 2010). For rare plant populations in habitats predicted to experience drastic changes in fire regimes due to climate change, understanding the effect of this heterogeneity is critical to effectively formulate conservation strategies.

It is well-established that two aspects of the fire regime – fire frequency at a given location and heterogeneity of fire events across the landscape – can influence population dynamics (Segura et al. 1998; Broncano & Retana 2004; Oliveras et al. 2009). However, few studies have investigated how both temporal and spatial aspects interact to control population growth and persistence (but see Groeneveld, Enright & Lamont 2008; Regan et al. 2010; and Noël, Machon & Robert 2013). These interactions between spatial and temporal aspects of fire regimes may be particularly relevant for fragmented populations that heavily rely on seed dispersal to persist and when spatial heterogeneity in fire events controls the availability of suitable sites for recruitment.

General disturbance theory suggests that patch connectivity, patch size and number, and spatial correlation among disturbance events regulate the overall effect of disturbance on population persistence. Patchy population configurations (e.g. variation of size and number of subpopulations across space) increase the overall probability of persistence by spreading extinction risk (Johst & Drechsler 2003); population persistence increases when populations have well-connected subpopulations that are large enough to overcome demographic stochasticity and when disturbance events do not occur in synchrony across the landscape, that is, low spatial correlation (Lande, Engen & Saether 1999; Chesson 2000; Groeneveld, Enright & Lamont 2008; Robert 2009).

In fire-prone ecosystems, fires can show high or low spatial correlation depending on the influence of local relative to larger-scale control of fire behaviour. When fire events are primarily controlled by local patch characteristics such as fuel load, topography, distance to ignition points (Minnich & Chou 1997; Minnich 2001; Pinol, Castellnou & Beven 2007), events will likely be smaller and more variable across space. Thus, local control of fire regime should cause high spatial and temporal heterogeneity across the landscape. Conversely, when fire events are driven by larger-scale environmental or weather conditions (Keeley & Fotheringham 2001; Moritz et al. 2004), variability of fire probabilities at a given time is decoupled from local spatial variability of fuel loads and the size and severity of fire can increase, thus decreasing heterogeneity, which limits spatial storage effects and source–sink dynamics (Kallimanis et al. 2005).

For obligate seeders with canopy seed banks, fire promotes seed dispersal and germination (i.e. that are pyroescent) and controls the availability of suitable germination sites (recently burned areas). Thus, high spatial heterogeneity in fire events might not be beneficial for the overall population, given that when patches burn at different times, seeds dispersed away from the seed bank of one patch will have a lower probability to land in a suitable, recently burned area. Thus, local seed discounting might reduce the probability of local recovery after a fire without contributing to the overall population persistence.

Negative effects of spatial heterogeneity on fire events might not be significant when species produced enough seeds to ensure local recruitment after a fire or when populations are configured in many patches, which increase the probability of dispersed seeds to land in suitable areas, as long as the scale of dispersal is larger than the scale of disturbance (Hanski 1999; Robert 2009). In fact, previous studies in fire-dependent species with population fragmented in several patches have found that heterogeneity in fire widens the range of fire frequencies under which populations of obligate seeders can persist (Groeneveld, Enright & Lamont 2008; Regan et al. 2010), but it is not clear whether this will be the case for fire-dependent species with canopy seed bank under simpler population configurations. To better understand how fire spatial heterogeneity, fire frequency and dispersal interact in controlling the population size and persistence of pyroescent obligate seeders, we focus on the simplest case of two subpopulations and hypothesize that heterogeneity in fire regime will decrease global population growth and probability of persistence.

To test this hypothesis, we develop a size-structured population model for a population of Tecate cypress Callitropsis forbesii (Jeps.) Little. We parameterize the model with field measurements, describing variation in population structure across a complex landscape in the Santa Ana Mountains (Orange, CA, USA). We evaluate long-term population growth rates, probability of population persistence and variation in population size over time under different scenarios designed to test for the effect of patchiness (populations divided or not in subpopulations), correlation of fire events among connected and not connected subpopulations, and detrimental effects of dispersal on local subpopulation dynamics.

Materials and methods

Species and Study Population

Tecate cypress is one of the 12 endangered cypress tree species that grow in California, USA. It is currently restricted to four populations within southern California and several small and scattered stands in Baja California, Mexico. After a fire, individuals are killed and population recovery is dependent on seed recruitment (Dunn 1986). Tecate cypress can reproduce at 6–7 years of age (Zedler 1977; Zedler, Gautier & Jacks 1984), but reaches peak cone production between 35 and 40 years in age (Dunn 1986). Cones require desiccation to open (Armstrong 1966), and intense heat during fire enhances this process. While there is little information about recruitment between fire events, germination and recruitment following fire is profuse, suggesting the fire-dependent nature of this species (Armstrong 1966; Dunn 1986).

We base our work on one isolated population of Tecate cypress located in the Northern extreme of the Santa Ana Mountains in southern California (N 33°51′17″, W 117°41′16″). This population is restricted to an area of c. 235·5 ha and has experienced six major fires since 1914. These six fires, in combination with strong topographic features, have created a mosaic of areas with different fire histories. The last two fires combined (in 2002 and 2006) burned the entire population, leaving individuals segregated into several large areas (87 ha total) where recruitment was profuse, and 75 isolated patches (35 ha total), mostly along ravines, with live, cone bearing adults (c. 4000 in total). We refer to these isolated patches with adult trees as refugia. The closest population is located 152 km south-west on Guatay Mountain, CA, USA.

Field Data Collection

Between March and June 2009, we carried out a census and mapped the entire Santa Ana population of Tecate cypress. We sampled recently burned areas using a stratified sampling, and within each stratum, we counted Tecate cypress seedlings and skeletons (adults that had died in the 2002 or 2006 fires) along two randomly located transects of 100 × 1 m, running perpendicular to the main slope. Skeletons were a good proxy to estimate effective population sizes prior the 2002 or 2006 fires. In strata with high densities of seedlings and skeletons (7 of 12 strata, densities of 1·6–3·5 seedlings m−2), we also counted and classified all seedlings and skeletons by size [using height and diameter at breast height (m)-DBH] along two additional 100 × 1 m transects running parallel to the main slope, for a total of 38 transects. Within each of the 41 areas that did not burn in the 2002 or 2006 fires (refugia), we measured all individuals and counted cones using a subsample of at least five trees.

Size-Structured Demographic Model

We model the whole Tecate cypress population using a size-structured matrix model (Fig. 1) with seven size classes based on a combination of total height and basal diameter (Table S1 in Supporting Information). We used our field data and an extensive literature review to estimate transition probabilities among classes using stage duration methods (Caswell 2001; Table 1). To capture the reported decline in seed viability and germination as population ages without fire (Appendix S1 in Supporting Information), we used negative exponential functions that depend on the time since last fire. We applied density-dependent mortality to all size classes, except seeds; this regulation relies on a stage-specific, time-decreasing carrying capacity function. We evaluated Tecate cypress population by estimating the long-term population growth rate, the importance of transient population dynamics, parameter elasticities and the stable-state population structure based on an initial stage vector that describes the stage composition of the largest refugium found during our census (a 23 ha area with c. 2000 individuals that has not burnt for at least 28 years). We evaluated the effect of density-dependent mortality by comparing populations with and without the density-dependent mortality term and the time-dependent seed survival and germination rates. We will refer to these models (both with and without density-dependent mortality) as deterministic.

Table 1. Summary of stage-specific parameters used to estimate population transitions
ClassAverage height (m)Average age (years)Stage durationCensused live individualsCensused dead individualsSurvivalσiγiAverage conesProportion of adultsPer capita average conePer capita annual seed production
  1. Individuals in the census were grouped into size classes according to predefined diameter and height classes (Table S3 in Supporting Information). Stage duration (Ti) was estimated from age differences between class-specific average age derived from age vs. height data based on tree-core sections (Table S1 in Supporting Information). Annual probability of growth to the next class (σi) was estimated as 1/Ti, we used the number of dead individuals detected during our 2009 census to estimate annual survival probabilities per class (γi), and calculated stage transitions for the base line projection matrix using σi and γI. Per capita seed production was estimated using total count of cones per class, number of adults per class, age since first reproduction (7; Armstrong 1966 and Dunn 1986), average number of seeds per cone (89 SD = 22·3; De Gouvenain & Ansary 2006), and 2 years for cone production.

Seedling0·30014·37914·3791836420·9770·0700·998    
Immature0·80023·3088·93023811100·9540·1120·995    
Young adult1·90031·1847·875291100·9660·1270·9963·8130·8963·4176·288
Adult 12·90035·0333·850350840·7600·2600·93121·3261·00021·32633·853
Adult 26·10041·8036·770361540·8500·1480·97682·3771·00082·377105·329
Adult 37·30043·4381·635126140·8890·6120·930238·1451·000238·145290·834
Adult 410·00046·3032·865100·9900·3490·996535·0001·000535·000605·736
Figure 1.

Life cycle diagram and flow diagram of an annual projection for the Santa Ana population of Tecate cypress. In (a) circles indicate different life stages; solid black arrows represent the probability that an individual grows from one stage to the other during a year (gij in matrix A); solid grey arrows indicate the probability that an individual survives and stays in the same stage (aii). Dashed arrows indicate annual per capita seed production (ri1). Dotted arrows indicate the transitions in the post-fire matrix as no other class survives a fire. In (b) solid lines represent changes in population structure; dashed lines represent effects of factors controlling those changes. Probability of fire is given by a Weibull probability distribution depending on the number of years since last fire. We projected the population over 500 years and ran 1000 iterations.

In a stochastic version of the model with density-dependent mortality (Fig. 1), we used hazard functions based on Weibull probability distributions to describe the probability of a fire event at any given year as a function of the number of years after the last fire (Moritz 2003). Fire effects are incorporated by killing all individuals after a fire (except seeds) using a fire-dependent survival vector (Appendix S1 in Supporting Information) and by increasing seed germination right after a fire, which captures the recruitment surge observed in obligate seeders.

To investigate the sensitivity of Tecate cypress populations to different fire regimes, we simulated population trajectories over 500 years with different fire probability distributions using the model described above (Fig. 1). We evaluated population trajectories by calculating year-to-year growth rates and estimating probability of persistence (the proportion of iterations that did not go extinct) after 500 years. Finally, we estimated the proportion of years Tecate cypress populations spent at suboptimal sizes, which was assumed to be any density below the stable population size obtained from the deterministic model with density dependence (83 individuals). Populations below this threshold are vulnerable to local extinction, as the number of reproductively active individuals (effective population size) might not be enough to guarantee self-replacement in the absence of immigration. Model details are included in Appendix S1 in Supporting Information. We will refer to this first stochastic model as Model 1.

Incorporation of Spatial Heterogeneity: Four Model Variations

To evaluate the sensitivity of the population to spatial heterogeneity in fire regime, we compared population persistence among three variations of Model 1 that split the larger population into two equally sized subpopulations while maintaining the same population size. The first variation (Model 2) depicts a scenario with spatial heterogeneity; the probability of a fire occurring at each subpopulation was independently determined and analyses only included iterations with a weak correlation between fire events at both subpopulations (correlation coefficients were <0·5). The second variation depicts low spatial heterogeneity (Model 3); analyses were performed with iterations that showed a high correlation in fire events (correlation coefficient >0·5). To explore the impact of immigration among subpopulations (Model 4), we used Model 2 but with a constant unidirectional dispersal rate of the seed from one subpopulation (source) to the other (sink). Given that we obtained similar results with different dispersal rates [with FRI between 10 and 500 years, λ = (1·017; 1·207) for source populations loosing between 10% and 90% of seeds to sink populations]; we will only present results for simulations using 50% dispersal rates. For each model, 45 simulations were conducted with different combinations of hazard functions. Results are presented in terms of the fire return intervals (FRI) in each simulation, independent of the hazard function.

For each of the four models, we evaluated the long-term population growth rate, probability of persistence and time with suboptimal densities. We assessed the effect of fragmentation by comparing Models 1 (unstructured population) and 2 (two subpopulations) across fire return intervals. The effect of spatial heterogeneity was quantified by comparing Models 2 and 3, and the overall effect of dispersal was assessed by comparing Models 2 and 4. We tested for a negative impact of dispersal at the subpopulation level (local seed discounting) by comparing source and sink subpopulations that experienced the same local FRI but came from different simulations. All simulations were conducted in Octave 3.2.3 (2009), and the script for Model 4, which is the most complex model, is provided in Appendix S2 in Supporting Information.

Results

The Tecate cypress population in the Santa Ana Mountains is dominated by seedlings and plants <30 years old. Less than 16% of the individuals are adults, and these individuals are confined to refugia along ravines (Table 1 and Table S2 in Supporting Information). Survival probabilities were lowest for adults, while growth estimates were highest for these same size classes. Seed production increased with size, and we did not detect a decline in cone production with size as suggested in other studies using age-based estimations (Dunn 1986; Markovchick-Nicholls 2007).

Model 1: Homogenous Fire, Single Population

Without density-dependent mortality, in the absence of fire, and with constant life-history transitions (Table S3 in Supporting Information where a11 = 0·1 and g12 = 0·003), the studied population has a slightly positive annual growth rate (λ = 1·06). Transient dynamics are short (damping ratio = 1·11), with the population rapidly reaching a stable size structure dominated by seeds (99%) and few adults (<0·6%). Population growth rate showed little sensitivity to changes in recruitment probabilities [λ = (1·05–1·25) when recruitment ranged from 0·1% to 10%] and λ dropped below 1 only when recruitment was lower than 0·05%. Survival of seedlings, immature and young adults is the most influential transition, with elasticities being 0·228, 0·253 and 0·150, respectively (Table S5 in Supporting Information).

When density-dependent regulation, variability in recruitment (dependent on time since last fire) and seed viability were included in the model, long-term annual population growth rate dropped below 1 (λ = 0·99, SD = 0·02). After 500 years, the pseudo-equilibrium distribution was dominated by seeds (97%), and the population without considering seeds consisted of about 83 individuals predominantly in the first two reproductive classes (of the overall population without seeds, 31% were young adults and 34% stage 1 adults); seedlings (0%), juveniles (4%) and the largest adults (14%, 16% and 0% for adults 2–4) represented <34%. The strong density-dependent regulation on recruitment made the population even more insensitive to changes in recruitment transitions [λ = (0·9919–0·9928) when recruitment ranged from 0·1% to 10%]. With the stochastic model, long-term population trajectories of Tecate cypress were significantly higher and had more variable annual growth rates than the deterministic model (with time-varying parameters but no stochasticity). The stochastic long-term, interannual population growth, λs, ranged from 1·01 (SD = 0·008; for large FRI) to 1·26 (SD = 0·0251; for intermediate FRI). Independently of the FRI, λs strongly decreased during the first years due to density dependence, then increased as established adults reproduced and then fluctuated around a mean until the end of the simulation (Fig. S1 in Supporting Information). Average annual population growth rate increased when fire return intervals increased from 4 to 14 years (λs increased from 1·14 SD = 0·18 to 1·26 SD = 0·0251), but it was more variable (from SD 0·18 to 0·008) due to a larger extinction probability at low FRI. With larger FRI, λs progressively decreased (to a minimum λs = 1·01 SD = 0·008, Fig. 2). Positive population growth rates and high persistence probabilities occurred when fire return intervals were between 17 and 89 years; with FRI <17 years, the population showed a low probability of persistence and spent a larger proportion of years at suboptimal population sizes (Fig. 2). Increasing recruitment after fire slightly increased total population growth rate [λs > 1 when recruitment was higher than 0·3%, and λs = (1·04–1·16) when recruitment ranged from 0·4% to 90% at a 22 year FRI]; we use a post-fire recruitment rate of 10% in the subsequent model comparisons.

Figure 2.

Population-level metrics using size-structured model with stochastic fire events (Model 1). Annual population growth rate (left; solid circles, ±SE), probability of persistence (right; black line) and proportion of years at suboptimal size (right; grey dashed line) for Tecate cypress population experiencing different fire return intervals. Each point represents population trajectory simulated for 500 years and 1000 iterations. Probability of persistence is estimated as the number of iterations where the population went extinct. Proportion of time at suboptimal population sizes refers to the number of years with population sizes lower than the stable population size in a deterministic model (see 'Materials and methods' section). Fire return intervals were estimated as the average number of fires observed during each simulation divided by the average number of years the population persisted.

Model 2: Subpopulations, Weakly Correlated Fire Regimes

In populations divided into two subpopulations (structured population) with weakly correlated fires, λs decreased compared with unstructured populations (Model 1) by 8% to 14%. Annual population growth rates decreased by 0·16 (SD = 0·22) to 0·14 (SD = 0·03) depending on fire frequency (Fig 3a). With short FRI (<9 years), structured populations tended to grow faster and marginally outperformed intact populations at intermediate FRIs (13–35 years; > 0·05). Similarly, probability of persistence was higher in structured populations when FRI was <14 years; persistence was between 0·04 and 0·16 using Model 1 and between 0·12 and 0·90 with Model 2 (Fig. 4a). Structured populations tended to spend less time at suboptimal densities (Fig. 4b), particularly under shorter fire return intervals.

Figure 3.

Difference in annual population growth rates among models depicting a single population with one fire regime (Model 1) or as two subpopulations experiencing heterogeneous (weakly correlated with one another) or homogenous (strongly correlated with one another) fire regimes (Models 2 and 3, respectively). (a) Differences between Models 1 and 2; positive values indicate greater population growth for single unstructured populations. (b) In populations structured into two subpopulations, differences between population growth rates in spatially heterogeneous (weakly correlated) fire regimes (Model 2) and homogenous (strongly correlated) fire regimes (Model 3); positive values indicate higher growth rates under heterogeneous fire regimes. *In both graphs indicate values significantly different from zero (t-test, α = 0·05). Each point in the graph represents population trajectory simulated for 500 years and 1000 iterations. Fire return intervals are estimated as the average number of fires observed during each simulation.

Figure 4.

Probability of persistence (a) and proportion of years at suboptimal sizes (b) for Tecate cypress populations when modelled as one unstructured population (Model 1), as a structured population (two subpopulations) with spatially heterogenous (uncorrelated) fire regimes (Model 2) or as a structured population with homogenous (correlated) fire regimes (Model 3). Influence of dispersal on probability of persistence (c) and proportion of years at suboptimal sizes (d), comparing Model 2 (no dispersal between subpopulations) with Model 4 (allowing 50% of seeds to disperse from one subpopulation to the other, under spatially heterogeneous (weakly correlated) fire regimes). Probability of persistence is estimated as the number of iterations that did not go extinct (of 1000 iterations). Proportion of time at suboptimal population sizes refers to the number of generations with population sizes lower than 83 established plants, the stable population size in the deterministic model.

Model 3: Subpopulations, Strongly Correlated Fire Regimes

The effect of spatial heterogeneity in fire regimes on population growth rate depended on FRI. Populations with strongly correlated fires (Model 3) performed significantly worse at intermediate FRI (17–24 years; t-test against 0, < 0·005, Fig. 3b) compared with populations where subpopulations experience weakly correlated fires (Model 2); at this range of FRIs, simulations with Model 3 had between 6·7% and 8·9% lower annual growth rates than subpopulations with more weakly correlated fires. For FRI >35 years, we did not detect differences between our models.

Although fire correlation did not affect the proportion of time at suboptimal sizes, it did significantly reduce persistence probabilities at any FRI (< 0·006 for all FRI comparisons; Fig. 4a).

Model 4: Subpopulations, Weakly Correlated Fire Regimes, Dispersal

Structured populations connected through dispersal had similar λs compared with unconnected populations, irrespective of fire return intervals. Connectivity through dispersal among subpopulations increased probability of persistence only when populations experienced fire return intervals between 6 and 12 years (Fig. 4c), although connected populations remained longer at suboptimal population sizes (Fig. 4d).

Performance did not differ between source and sink subpopulations when both types of subpopulations experienced the same FRI (Fig. 5a). Sink subpopulations tended to grow faster and persist more frequently than source subpopulations only when the fire return interval was low (FRI <14 years). Population persistence probabilities also increased when dispersal to a sink subpopulations occurred from a source subpopulation that experienced a higher FRI (Fig. 5a–b; t-test against zero < 0·05, Fig. 5b).

Figure 5.

Difference in annual population between source and sink subpopulations for the model with subpopulations connected through dispersal (Model 4). Each point represents mean differences between a source experiencing a given FRI and sink population that experienced the same FRI but from a different simulation. Negative values indicate that under that sink subpopulations perform better. Results are grouped in three series depending on whether focal sink, sink subpopulations have lower, higher or the same FRI than the source subpopulation.

Discussion

Fire is an intrinsically heterogeneous process due to the spatial variability in fuel loads and topography (Minnich 2001; Moritz 2003; Wells et al. 2004; Keeley & Zedler 2009). When pyroescent obligate seeders like Tecate cypress experience homogenous fire regimes, the whole population is reset to seedling stage and population persistence depends on fire frequency. On the other hand, when fire is spatially heterogeneous across the landscape, fire causes populations to have asynchronous dynamics. In this study, we tease apart the temporal effect of fire on structural population changes and the effect of spatial heterogeneity among fires on population persistence. Using Tecate cypress as a focal species, we tested the hypothesis that spatial heterogeneity in fire regimes, particularly at high fire frequencies, can negatively affect population growth of fire-dependent species.

Our initial stochastic model confirmed the tight control that fire return interval exerts on population dynamics of obligate seeders with canopy seed bank, especially at lower fire return intervals. Populations had the highest growth rates when the fire frequency was short enough to avoid the negative effects of density-dependent mortality but long enough to reach self-replacing seed bank sizes and reproductive success (for Tecate cypress, at FRI >17 years). Our population was especially sensitive to changes in FRI around the current empirical value (average FRI = 17, considering major fires in the last 92 years) and within the range reported for Southern California (30–50 years, Wells et al. 2004). We detected that without dispersal, fragmentation will have strong negative impacts on Tecate cypress persistence by reducing population growth rates in 14% under FRI that will otherwise support growing populations (between 14 and 35 years). Impact of fragmentation will probably be higher when fragmentation also includes habitat losses (e.g. loss of suitable areas for germination to more competitive, invasive grasses: Keeley, Baer-Keeley & Fotheringham 2005). Thus, our results highlight the vulnerability to frequent fires of Tecate cypress and other obligate seeders with canopy seed bank, despite life-history traits that favour their post-fire population recovery.

In other fire-dependent species, spatial heterogeneity in fire regime ameliorates the effects of fragmentation by spreading the risk of local extirpation in any given fire event and promotes source–sink dynamics (Groeneveld, Enright & Lamont 2008; Regan et al. 2010). Although we hypothesized that in pyroescent obligate seeders, spatial heterogeneity in fire regime might rather be detrimental for the overall population, we detected that within a small window of FRI (e.g. 15 years), weakly correlated fires had a small but significant positive effect by spreading the risk of global extinction. In contrast to our expectations, source subpopulations showed no demographic costs of losing seeds in unsuitable patches, given that Tecate cypress required only a small percentage of its seed bank to ensure post-fire recovery. With FRI below this window, lower growth rates reduce the ability of populations to reach stand-replacing seed bank sizes and increase the risk of demographic stochasticity (Lande, Engen & Saether 1999); in our case, population size (from local recruitment or immigration) was never old enough to guarantee recovery after a fire.

When fire regimes are spatially homogenous, synchrony among subpopulations can decrease population persistence (Lande, Engen & Saether 1999; Vuilleumier et al. 2007; Regan et al. 2010) as the benefits of spreading the risk among subpopulations depend on fewer and more distant subpopulations (Johst & Drechsler 2003; Kallimanis et al. 2005; Vuilleumier et al. 2007; Robert 2009) and dispersal might buffer effects of disturbance, as long as scale of dispersal is greater than the scale of disturbance (Hanski 1999; Williams, ReVelle & Levin 2005; Vuilleumier et al. 2007; Robert 2009). Particularly for fire-dependent species and populations divided into several patches, dispersal will improve global population probability of persistence, given that seeds that are dispersed after a fire should have a higher probability to land in a suitable patch (Groeneveld, Enright & Lamont 2008), simply because the probability of having suitable patches increases. On the other hand, for pyroescent obligate seeders, lack of synchrony might reduce the probability of seeds dispersed after a fire to land suitable, recently burned areas. Despite this potential limitation, we found that life-history characteristics of Tecate cypress will allow for some rescue effects under uncorrelated fired, especially when at least one subpopulation experiences larger FRI. Moreover, given that Tecate cypress seed bank sizes were always large enough to ensure local recovery after a fire, spatially homogenous fires had a net negative effect, given that it reduced growth rates of structured populations by up to 9%. In fact, when fire regimes were spatially homogenous, population persistence declined, irrespectively of FRI. Thus, our model (with only two subpopulations) identified a positive effect of dispersal that is independent of the potential numerical effect of increasing the number of subpopulations. It remains to be seen whether this positive effects of dispersal is also effective under more complex population configuration (patches of different sizes or under habitat loss after a fire) or when the scale of fires is higher than the scale of dispersal.

Large-scale fires that burn entire populations are common in fire-prone environments. Our results build on previous studies that highlight the risks of current trends in fire regimes (Groeneveld, Enright & Lamont 2008; Regan et al. 2010; Noël, Machon & Robert 2013). We find that different population characteristics will impact the chances of Tecate cypress (and similar pyroescent obligate seeders) to persist under more severe and frequent fires. Fragmentation – irrespective of habitat loss – will favour population persistence following more frequent fires as long as there is some spatial heterogeneity in fire events. Lack of heterogeneity has the strongest negative effects on growth and persistence on a wide range of FRI. Connectivity between subpopulations is pivotal to buffer negative effects of more severe frequent fires. Thus, establishing new patches of a species at risk will not be enough to prevent extinction without the assurance that patches are in spatially distinct areas with different fire probabilities and that these patches are fully connected through dispersal.

Management solutions should emphasize reducing spatial homogeneity in fire regimes to avoid the negative impact of entire populations being burned. Spatially uncorrelated fire regimes may be very hard to ensure, particularly under the forecast of more severe fire events initiated by region-wide weather events (e.g. annual Santa Ana wind conditions with winds reaching up to 90 km h−1). Spatial heterogeneity in the fire regimes of subpopulations may also be difficult to ensure alongside the need for connectivity among these subpopulations. Thus, our results suggest prioritization of those areas with low fire probabilities, as these will more likely escape more severe fires. In the case of Tecate cypress, population persistence may only be due to current refugia that have escaped the last fires. Alternatively, expanding the current spatial extent of the population (Robert 2009) may be another way to ensure that subpopulations experience different fire regimes.

Key to these predictions is knowledge on reproductive ecology of Tecate cypress. For instance, our results highlight the need to properly assess whether obligate seeders are able to recruit in the absence of fire. In our model, the probability (0·001) of seedling recruitment between fire events – while very low – was enough to maintain the population when fire return intervals were long (Fig. 1). While many models assume that obligate seeders cannot recruit in the absence of fire, our estimate of some recruitment is consistent with our census and other studies that have found that cones can open in the absence of fire (Armstrong 1966; Garcillan 2010; de Gouvenain & Delgadillo 2012); we recorded seedlings inside patches that had escaped fire for at least 28 years. Fecundity functions are also essential for building accurate models for obligate seeders. Based on a size-dependent reproductive function, we estimated a FRI (around 17 years) under which populations of Tecate cypress would not be viable. This estimate is lower than previously reported estimates (c. 44 years: De Gouvenain & Ansary 2006; Markovchick-Nicholls 2007) based on an age-dependent parabolic function that peaks between 30 and 40 years of age (Markovchick-Nicholls 2007). However, size is a much better descriptor of individual development for plants in general (Franco & Silvertown 2004) and for Tecate cypress in particular (De Gouvenain & Ansary 2006).

Conclusions

Temporal and spatial characteristics of fire regimes can interact to strongly affect fire-dependent plant populations of conservation concern, increasing their risk of local extinction under future climate change scenarios of more frequent and larger fires. We found strong interactions between temporal and spatial characteristics of the fire regime and nonlinear interactions between the influence of dispersal and fire frequency. Specifically, our results highlight the negative effect of spatially homogenous fire regimes for obligate seeders, especially when populations occur in isolated patches. Thus, spatial heterogeneity in fire regimes in relation to population extent might be a crucial criterion for conserving fire-dependent species.

Acknowledgements

This study was funded by the Nature Reserve of Orange County in partnership with the Irvine Ranch Conservancy, the US Forest Service (Cleveland District) and California Division of Fish and Game. We thank T. Valentovich, E.Nilsson and Q. Sorenson for field assistance and R. de Gouvenain, J. Gremer, members of the Suding Lab and two anonymous reviewers for comments on prior versions of the manuscript.

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