Population Viability Analysis of the Federally Endangered Endemic Jacquemontia reclinata (Convolvulaceae): A Comparative Analysis of Average vs. Individual Matrix Dynamics

Abstract

Due to small population size, Population Viability Analysis (PVA) of endangered species often pools all individuals into a single matrix to decrease variation in estimation of transition rates. These pooled populations may mask significant environmental variation among populations, affecting estimates. Using 10 years of population data (2000–2010) on the endangered plant Jacquemontia reclinata in Southeastern Florida, USA, I parameterized a stage-structured matrix model and calculated annual growth rates (lambdas)and elasticity for each year using stochastic matrix models. The metapopulation model incorporating actual dynamics of the two largest populations showed a lower occupancy rate and higher risk of extinction at an earlier time compared to a model that used the average of all natural populations. Analyses were consistent that incorporating population variation versus average dynamics in modeling J. reclinata demography results in more variation and greater extinction risk. Local variation may be due to both weather (including minimum winter temperature and total annual precipitation) and local disturbance dynamics in these urban preserves.

1. Introduction

Plants face a variety of threats that are putting many at risk of extinction [1,2]. Major threats include climate change [3], habitat loss and fragmentation [4], and dispersal limitations [5]. A major tool in assessing population dynamics and extinction risk is Population Viability Analysis (PVA), which typically uses stochastic matrix models to study individual populations and metapopulation dynamics [6,7,8,9,10,11]. Population viability analysis (PVA) is a widely used tool for assessing extinction risk and informing conservation decisions [12,13]. PVAs integrate demographic data into predictive models that evaluate the effects of different management scenarios on population persistence. Long-term studies are particularly needed but are rarely performed due to cost and short-term funding constraints [14].

In studying population dynamics of endangered plants, a major challenge is the trade-off between small population sizes and the ability to build accurate and robust population models [15,16]. When populations are small, pooling all observed demographic transitions into a single matrix may yield more stable estimates, but it comes at the cost of masking variation across populations. This is especially critical in fragmented urban landscapes, where populations are isolated and subjected to different environmental pressures. In fragmented landscapes, metapopulation theory provides an important framework for understanding the dynamics of spatially separated populations connected by occasional dispersal [11]. Metapopulation persistence depends on the balance between local extinctions and colonization, and it is especially relevant for urban preserves where habitat patches are isolated by roads and development. The concepts of source–sink dynamics [17] and landscape connectivity [18] are essential for assessing the viability of such species. In such contexts, metapopulation theory—which addresses population dynamics across a network of spatially separated but interacting populations—offers a more realistic framework [19,20,21,22].

The federally endangered Jacquemontia reclinata, endemic to coastal southeast Florida, is an ideal candidate for PVA given its restricted range, fragmented habitat, and long-term monitoring data. This study uses a 10-year demographic dataset (2000–2010) of the endangered Jacquemontia reclinata to (1) test whether pooling data across four populations biases long-term population growth estimates and (2) assess whether using average matrix values instead of actual population-specific matrices affects metapopulation projections across the species’ range. Environmental stochasticity, including year-to-year variation in precipitation and temperature, can have strong effects on population growth rates and extinction risk [23,24]. Incorporating such stochasticity into models increases the realism and relevance of PVA outputs. The collapse of one of the largest studied populations, the South Beach population in Palm Beach County between 2010 and 2020 [25], further underscores the urgency of adopting accurate models for conservation forecasting.

2. Materials and Methods

The study species, Jacquemontia reclinata (Convolvulaceae), is a perennial vine endemic (Figure 1) to coastal dunes in SE Florida, ranging historically from Martin to Miami-Dade Counties [26].

The plant grows as long runners from a central rooted axis and is not a climber (Figure 1). Flowering occurs during the rainy season at the tips of growing shoots and fruits are dry capsules that split open in the fall. Seeds are passively released and form a transient seed bank. The primary habitat is open dunes beyond the intertidal zone. Due to coastal development, habitat loss, and an increase in shrubby and woody vegetation on coastal dunes, the species was extirpated in multiple sites. It was listed as endangered in 1993. By 2011, less than 700 wild plants remained in a few protected populations [26].

Intensive study, propagation, and conservation efforts were led by Fairchild Tropical Botanical Garden in Coral Gables, Florida. In 2000, I initiated a long-term demographic study across four populations (two large and two small). A meter square grid was overlaid over all plants remaining at Crandon Park in Miami-Dade County, and South Beach (Figure 2), South Beach Inlet and Loggerhead Park in Palm Beach County.

The corners of each m² were marked using PCV pipes embedded into the sand. Within each grid, a sub grid of 16 25 by 25 cm using stringed meter squares was used to: (1) locate plant roots (which received a metal tag staked into the sand), (2) estimate occupancy (presence or absence in each subgrid), (3) estimate cover (Braun-Blanquet categories of 25%) and (4) record numbers of fruit. Based on previous studies, the number of seeds per fruit was estimated to be 3.47. This census was repeated annually until 2010.

A stage-size matrix model was constructed using five stages: (1) seeds in seed bank; (2) seedlings resulting from germinated seeds that are not yet reproductive, (3) reproductive stage of various sizes (small, medium, and large) based on area of ground covered (number of subgrids with a vegetative shoot) [26] (Figure 3).

Matrices resulting from the pooled data from all four populations (Average) were compared to matrix results from the two largest populations (Crandon and South Beach) analyzed individually [27]. Transition elements for all three matrices are in Appendix A. I used MATLAB code from Morris and Doak [12] to calculate growth rates (Lambda, λ) for each year. For each set of matrices, the individual growth rates per matrix per year were bootstrapped (300 iterations) to calculate 95% confidence intervals (CI) for the 10-year period. Elasticity of stage-transitions was calculated for the average matrix and the individual matrices over the 10-year period. The stochastic growth rate was calculated assuming an IID (independently and identically distributed) model and probability of quasi-extinction where N = 10 adult plants as the extinction threshold. The extinction threshold was set to 10 adult individuals per population, consistent with previous PVAs of clonal or rare plants. The quasi-extinction model ignores seeds in seed bank and seedlings as these are difficult for land managers to accurately census. The stochastic growth rate used a starting population of 29,308 seeds, 6 seedlings, 57 small adults, 73 medium adults, and 21 large adults.

I used RAMAS (Risk Analysis and Management Alternatives Software Version 5) Metapop [28] to simulate metapopulation dynamics across 10 populations. One model used the average matrix for all populations; the other used the actual transition matrices for Crandon and South Beach with the average matrix used for the remaining eight. The metapopulation was based on 10 natural populations remaining in 2000 (Crandon, High Taylor, Hillsboro Beach, South Inlet, South Beach, Red Reef, Atlantic Dunes, Lake Worth, Loggerhead, and Carlin Park, Appendix B). The model started with 763 adults among the 10 populations, assumed no catastrophes, the extinction threshold was 50 adults, density dependence was exponential on adult fertility and survival, seeds had dispersal, and there was no correlation among populations (Appendix B). Environmental stochasticity followed a lognormal distribution, a commonly used assumption in plant PVAs reflecting multiplicative demographic processes. Zero dispersal was assumed between populations, justified by the urbanized matrix and limited seed movement observed in field studies. Although some environmental synchrony may exist, there was no strong evidence for correlated dynamics, thus independence was assumed. The extinction threshold was set to 10 adult individuals per population, consistent with previous PVAs of clonal or rare plants. The model calculated average population size, metapopulation occupancy, local population occupancy, interval extinction risk, terminal extinction risk, and time to quasi-extinction.

To examine the relationship of λ to local weather, the weather data (minimum temperature, mean temperature, and annual precipitation) from the local airports in Palm Beach County and Miami-Dade county [29] were correlated with annual λ in the individual matrix models and with each other.

3. Results

3.1. Annual Population Dynamics and Growth Rates

Annual growth rates (λ) calculated from the average matrix ranged from 0.86 to 1.25, with a mean of 1.03 (±0.0415 SE; 95% Confidence Interval (CI): 0.989–1.071) (

Table 1. Annual growth rates (λ) for the average matrix and for Crandon and South Beach ¹.

Variable	Average Matrix	Crandon	South Beach
2000–2001	1.04	0.95	0.95
2001–2002	0.94	1.00	1.03
2002–2003	0.86	0.58	1.0
2003–2004	1.02	1.00	0.91
2004–2005	1.02	0.93	0.76
2005–2006	0.86	1.31	1.05
2006–2007	1.25	1.28	0.96
2007–2008	1.11	0.86	0.92
2008–2009	0.99	1.26	1.0
2009–2010	1.21	0.99	0.86
Mean ± 95% CI	1.030 (0.949–1.111)	1.016 (0.878–1.154)	0.944 (0.890–0.998)

¹ Growth rates > than 1 indicate increasing populations, 1 = stable population, <1 decreasing populations.

, Figure 4). Crandon’s annual λ ranged from 0.58 to 1.31, with a mean of 1.016 (±0.0702 SE; 95% CI: 0.870–1.162). South Beach ranged from 0.76 to 1.05, with a mean of 0.944 (±0.028 SE; 95% CI: 0.889–0.999). These values demonstrate greater interannual variability in individual populations compared to the pooled average model.

3.2. Stochastic Growth Rates and Quasi-Extinction

The average matrix produced a stochastic growth rate of 1.018 (95% CI: 1.0155–1.0206). Crandon had a stochastic λ of 1.033 (95% CI: 1.0264–1.0395), while South Beach was 0.933 (95% CI: 0.9292–0.9365). Quasi-extinction risk (defined as <10 adults in 50 years) was <1% for the average matrix, 14% for Crandon, and 87% for South Beach (Figure 5 and Figure 6). These differences reflect the masking of risk in pooled estimates.

3.3. Elasticity Analysis

Elasticity analysis identified that the most influential transitions were adult survival (Lg→Lg and Md→Md) and transitions from seeds to seedlings (

Table 2. Elasticity values of transition elements for the average matrix, Crandon and South Beach populations.

Stage Transition	Average Matrix	Crandon	South Beach
Seed → Seedling	0.10	0.08	0.14
Seedling → Small	0.12	0.10	0.16
Small → Medium	0.18	0.17	0.19
Medium → Large	0.22	0.23	0.18
Large → Large	0.38	0.42	0.33

). In the average matrix, the largest elasticities were Lg→Lg = 0.38 and Md→Md = 0.27. In Crandon, these values were 0.42 and 0.23, respectively. South Beach showed lower elasticity in adult survival but higher values in seed transitions. These patterns suggest management should prioritize maintaining adult individuals and seedling recruitment.

3.4. Metapopulation Dynamics

Using the RAMAS Metapop model parameters (Appendix B), the model was run (A) for the Average matrix elements for all populations and (B) using the actual matrices of Crandon/South Beach with the other populations using the Average matrix elements.

Table 3. Model variables in RAMAS Metapop comparing 10 populations using the average matrix versus a model with actual dynamics of the two largest populations and average matrix transitions for the other 8 populations.

Variable	Average Matrix	Actual Crandon/South Beach Matrix
Average Population Size at 50 yrs	1363	1420
Metapopulation Occupancy (95% CI)	3.5 (0.9–6.2)	2.8 (0.3–5.3)
Local Occupancy (% Crandon)	38.6	32.7
Local Occupancy (% South Beach)	42.1	36.1
Local Extinction (% Crandon)	11.1	17
Local Extinction (% South Beach)	7.3	13
Interval Extinction Risk (95% CI)	14.6 (11.8–17.4)	22.4 (19.6–25.2)
Terminal Extinction Risk (95% CI)	13.2 (10.4–16.0)	20.7 (17.9–23.5)
Time to Quasi-Extinction	41.9 years	34.2 years

provides parameters of average population size at 50 yrs, metapopulation occupancy (Figure 6), local occupancy of Crandon and South Beach (Figure 7A), local extinction of Crandon and South Beach (Figure 7B), interval and terminal extinction risk (Figure 7C), and probability of quasi-extinction (Figure 7D). Using RAMAS, the average-matrix model predicted greater metapopulation persistence, with occupancy of 3.5/10 populations (95% CI: 0.9–6.2) and quasi-extinction in 41.9 years. The individual-matrix model showed lower occupancy (2.8/10, 95% CI: 0.3–5.3) and earlier quasi-extinction (34.2 years).

Annual population growth varied much more in the Crandon and South Beach models compared to the Average matrix (Crandon had 5 years where λ > 1 and 5 years where λ < 1, South Beach had 2 years with λ > 1, 1 year where λ = 1, and 7 years where λ < 1. In contrast, the Average matrix had 6 years with λ > 1 and 4 years where (λ) < 1). All three estimates are significantly different based on the Confidence Interval. While Crandon had a higher stochastic growth rate than the Average matrix, it has a higher risk of extinction due to greater variation among years (the Average matrix shows less variation).

The two weather stations (Palm Beach Airport, Miami-Dade Airport) had significantly positive (p < 0.01) correlations in both mean temperature (r = 0.99) and precipitation (r = 0.68). I found a weak but consistent positive correlation between λ and annual precipitation (r = 0.32, p = 0.04), and a negative correlation with minimum winter temperatures (r = –0.36, p = 0.03).

4. Discussion and Conclusions

The results demonstrate that metapopulation models based on individual-year matrices produce substantially higher extinction risk estimates than models based on the averaged matrix, corroborating findings from earlier simulation studies [12]. The average matrix overestimates population growth and masks the influence of unfavorable years. This result emphasizes the importance of incorporating interannual variability when assessing viability for rare species subject to climatic extremes. The individual matrices for Crandon and South Beach exhibited more temporal variability, and the latter’s collapse from 2010 to 2020 highlights the danger of relying on average trends. This underscores the need for population-specific models in conservation planning.

The metapopulation model incorporating actual dynamics of CR and SB showed a lower occupancy rate and higher risk of extinction at an earlier time compared to a model that used the average of all natural populations (2000–2010, Average matrix). This is consistent with theoretical models of plant population dynamics where interpopulation variation within years is greater than temporal variation across populations. Thus, modeling of future dynamics of this species should use individual matrices calculated from each population, including both natural populations and new outplanting in both the natural range and outside the natural range in suitable habitats. Both MATLAB (r2024a) and RAMAS Metapopulation (Version 5) analyses were consistent that incorporating population variation versus average dynamics in modeling J. reclinata demography results in more variation and greater extinction risk.

The population at Crandon Park consistently exhibited the highest λ values and contributed most to metapopulation persistence, suggesting it functions as a demographic source [17]. In contrast, South Beach demonstrated consistently low λ and a high risk of local extinction, marking it as a potential sink. This aligns with metapopulation theory predictions [11] and is consistent with the observed local extinction of South Beach post-2010. South Beach’s high extinction risk was linked to lower adult survival elasticity and greater demographic variability, supporting its classification as a demographic sink. Conversely, Crandon exhibited characteristics of a source population, with higher adult survival rates and lower extinction risk. This source-sink framework offers a valuable lens for prioritizing management actions and targeting conservation investment. Source-sink dynamics may be compromised by the current habitat fragmentation into small populations embedded in an urban landscape that limits seed dispersal and plant density [25].

Elasticity analyses showed that large adult survival and medium-to-large adult transitions had the greatest influence on λ, mirroring findings in other rare plant studies [30,31,32,33]. Conservation actions should prioritize enhancing adult survival, promoting recruitment into large size classes, and managing threats that disproportionately affect reproductive adults [34,35]. Protecting adult plants from trampling and limiting dense dune vegetation through physical removal or controlled burns are some of the main management techniques used in managing populations of J. reclinata [25].

Local variation may be influenced by specific weather factors such as minimum winter temperatures and annual precipitation. The modest positive correlation between annual λ and both precipitation and minimum winter temperature, suggests that climate variability influences population growth, likely through effects on recruitment and survival. Incorporating environmental stochasticity using a lognormal distribution, as supported by Lande [23] and Menges [24], provided a more realistic extinction risk estimate under projected future climate variability [36]. Including such predictors in future models could improve forecasting accuracy and inform adaptive management under climate change as well as by local disturbance dynamics, including both natural events and human activities within these urban preserves.

This finding is important in the actual dynamics of the species from 2010 to 2020, where one of the largest natural populations (SB in this study) collapsed [25], declining from over 200 plants to just six remaining plants. This was not predicted from the metapopulation model that used the average of all natural populations but was shown as possible when using the actual dynamics from that subpopulation. The higher rate of extinction is warranted due to the highly fragmented populations that face both natural (hurricanes, storm surge, natural succession, climate change) [36] and anthropogenic impacts (trampling, arson fires, landscaping [37,38]. This approach, however, will entail higher costs as it will require more sampling across individual populations in this highly urbanized landscape. An approach that incorporated greater spatial sampling to account for the variation observed could be modified to be performed on a non-annual basis, thus mitigating some of the costs of annual monitoring. Based on observed stochasticity, I recommend a triannual (every 3 years) monitoring strategy that balances cost with ecological sensitivity. This can be complemented by citizen science, using volunteers trained in standardized protocols to monitor survival, flowering, and recruitment [25].

These findings underscore the value of using long-term demographic data and multiple matrix models in PVAs. They also highlight the urgency of management interventions that buffer small populations from stochastic threats and habitat degradation. This study provides critical insights for the conservation management of Jacquemontia reclinata, a federally endangered and endemic species. Future research should aim to refine estimates of the minimum viable population size, which will inform targeted mitigation strategies to restore natural populations and identify suitable outplanting sites for long-term survival. Although our findings indicate ongoing population declines in South Florida, the modeling techniques employed—along with increased public and scientific awareness—have contributed to reducing the species’ overall extinction risk [25]. Importantly, this work underscores the value of demographic modeling in guiding conservation decisions, not only for J. reclinata but also as a framework for managing other endangered plant species facing similar threats.