Demographic compensation occurs in populations of Quercus oleoides Schltdl & Cham in fragments across an altitudinal gradient

A description of Quercus oleoides

Commonly known as tropical or white oak, Q. oleoides is a semi-deciduous tree reaching up to 15 m in height. Its outer bark is pale to dark grey and presents deep fissures 20 to 30 mm thick. Its seed (acorn) is recalcitrant, equipped to keep the necessary humidity to be viable and it doesn’t exhibit dormancy (Klemens, Deacon & Cavender-Bares, 2010). The tree blooms between the months of April and June and the production of seeds takes place between October and November. It is a monoecious species whose flowers are pollinated by the wind, though the movement of its seeds is known to be limited to very short distances due to the poor dispersion behaviour of their main dispersers (Boucher, 1983). It inhabits seasonally dry tropical forests in Mesoamerica, where it is the dominant species. It grows in poor, rocky soils (Boucher, 1983). In general, oaks do not have a persistent seed bank (Olson, 1974).

Study area

The study was conducted in the Priority Terrestrial Region (RTP) 104 “Tropical Oak Woods of the Coastal Plains of Veracruz”, which extends over an area of 905 km² at the centre of the state between latitudes 19°20.0 to 19°45.0 N, and longitudes 96°30.0 to 97°00.0 W (Table 1) (Arriaga et al., 2000). The climate is warm subhumid with a mean annual temperature above 22 °C and a coldest-month temperature above 18 °C, with an annual rainfall of between 500 and 2,500 mm, ranging from 0 to 60 mm in the driest month. Summer rainfalls represent from 5% to 10.2% of the annual total (Arriaga et al., 2000).

Different disturbance histories correspond with different evolutionary and adaptational pressures. The forest has been fragmented, giving way to isolated populations along the environmental gradient (Pennington & Sarukhán, 2005). Our study site includes these isolated populations. Extensive cattle raising, a common activity in forests dominated by Q. oleoides (Carlos Flores-Romero, 2019, personal observation), has been considered an intervening factor in the selection and transformation of plant populations and communities (Milchunas & Laurenroth, 1993).

Fieldwork data on the survival, transition, and reproduction of Quercus oleoides

In order to analyse the altitudinal range in which Q. oleoides forest occurs (0 to 840 m a.s.l.), we selected three populations resulting from forest fragmentation at different altitudes and with different disturbance histories (Table 1). The first one is located at 60 m a.s.l. in the locality of Miramar in the municipality of Actopan, Ver., with moderate cattle grazing during the rainy season. The second one at 400 m a.s.l, in the locality of Mesa de Veinticuatro in the municipality of Alto Lucero, Ver., without cattle grazing in the last 15 years, and the third population at 800 m a.s.l. in the locality of Otates in the municipality of Actopan, Ver., with more intense cattle grazing combined with some lime plantations (Table 1). The intensity of cattle grazing did not change during the study.

At each one of these altitudinal levels, we established five random square plots of 400 m² (20 × 20 m) (at 100–200 m from each other, total 15 plots) and within each one of them, all Q. oleoides individuals were registered each year. For those being 1.3 m in stature or shorter, we registered their total height with a measuring tape flexible (Trupper), while for the rest of individuals (i.e., those higher than 1.3 m) the diameter at breast height (dbh) was measured and registered each year with a diameter tape (Forestry Suppliers). We determined the geographical location of each individual with a Garmin GPS receiver (GpSmap 60CSx) and to facilitate their annual location and further registration each one was identified with an aluminium tag bearing a reference number.

Based on the annual post-breeding censuses, we calculated each year the survival and transition and reproduction for the size classes >1.3 m height, whereas for smaller individuals the seed-to-plant transition was estimated by dividing the number of new individuals <1.30 m height into the number of seeds from the previous period. We counted in each reproductive tree (November) the seeds on a randomly selected in the bottom, middle and top tree crown sections using a set of binoculars and a tally counter clicker. Also, we counted the number of branches in each section to calculate the total number of acorns per tree. We conducted the registers during four years to obtain three annual transition matrices per population (2016–2017, 2017–2018, and 2018–2019).

Data analysis

Annual transition matrices and asymptotic population growth rates

In order to determine the population vital rates per altitude (combining the five plots from each), we divided each of the three populations into six size classes: seed stage or acorn, <1.3 m height, >0 ≤ 10 cm dbh, >10 ≤ 20 cm dbh, >20 to ≤ 30 cm dbh, and >30 cm dbh (Fig. 1). We used the transition probabilities among size classes (P_ij, number of individuals in size i at time t + 1 divided per number of individuals in size j at time t), survival probability (G_ij, number of individuals that remained in size i at time t + 1 divided per number of individuals in size i at time t) and the average seed production by size class (F_ij is the average number of seeds produced by individuals in size i from time steps t to t + 1) to estimate the annual transition matrix and λ (the asymptotic population growth rate) (Caswell, 2001) (Fig. 1, Table 2). Therefore, we calculated the three transition matrices, and three average transition matrices for each population (Lewontin & Cohen, 1969; Caswell, 2001). We calculated λ from each of the three annual asymptotic transition matrices by an iterative matrix multiplication process (Caswell, 2001).

Table 2:

Average of transition matrices across three years of observations and its population growth rate (λ) of Quercus oleoide population from Miramar, Mesa de Veinticuatro and Otates localities, Veracruz, Mexico.

Size	Seeds	<1.3 h	>0–10 d	>10–20 d	>20–30 d	>30 d
Miramar $\overline{\lambda }$ = 1.076 (cl = [1.0759–1.0761])
Seeds	0	0	295.3 ± 138	3,000 ± 1,156	8,000 ± 1,156	7,833.3 ± 727
<1.3	3.82E−05 ± 2.1E−05	0.158 ± 0.0514	0	0	0	0
>0–10	0	0.444 ± 0.0241	0.759 ± 0.0110	0	0	0
>10–20	0	0	0.165 ± 0.0307	0.940 ± 0.1013	0	0
>20–30	0	0	0	0.022 ± 0.0973	0.307 ± 0.0882	0
>30	0	0	0	0	0.068 ± 0.0804	0.986 ± 0.0003
Mesa de Veinticuatro $\overline{\lambda }$ = 1.017 (cl = [1.0059–1.0061])
Seeds	0	0	931.2 ± 808	1,966 ± 607	5,000 ± 1,529	5,333 ± 1,858
<1.3	1.07E−05 ± 4.3E−06	0.069 ± 0.0231	0	0	0	0
>0–10	0	0.734 ± 0.0551	0.587 ± 0.1789	0	0	0
>10–20	0	0	0.281 ± 0.2033	0.648 ± 0.0934	0	0
>20–30	0	0	0	0.333 ± 0.0946	0.816 ± 0.0727	0
>30	0	0	0	0	0.174 ± 0.0735	0.988 ± 0
Otates $\overline{\lambda }$ = 1.042 (cl = [1.0223–1.0242])
Seeds	0	0	745 ± 343	4,500 ± 2,023	4,667 ± 2,188	2,500 ± 1,260
<1.3	4.33E−05 ± 1.5E−05	0.333 ± 0.1882	0	0	0	0
>0–10	0	0.541 ± 0.1943	0.761 ± 0.0399	0	0	0
<10–20	0	0	0.165 ± 0.0093	0.939 ± 0.0107	0	0
<20–30	0	0	0	0.029 ± 0.0139	0.600 ± 0.2840	0
>30	0	0	0	0	0.069 ± 0.0108	0.986 ± 3.3E−05

DOI: 10.7717/peerj.18980/table-2

Note:

d, diameter at breast height (cm); h, height (m); cl, confidence limits (95%); ±, mean standard deviation.

We used the model n_{(t + 1)} = A *n_(t), where matrix A ( $a_{ij}$) describes how individuals in each class in the vector n_(t) (structure of size) contributes to the size class n_{(t + 1)}, and specifically contains the values P_ij, G_ij and F_ij (Table 2, Fig. 1). The data obtained from the post-breeding census allowed for an estimate of the fecundity of class >0 ≤10 cm dbh with the equation P_3* F₄ (where P₃ is the probability of the size-class transition >0–10 cm dbh to >10–20 cm dbh, and F₄ is the fecundity of size class >10–20 cm dbh; Kendall et al., 2019) (see Fig. 1). This model provides information to obtain the population stable size distribution, λ and vital rates. We estimated a confidence interval for λ for each population with Program SIM_VAR.BAS, temporal stochasticity (Ebert, 1999). The confidence limits include the three matrices by each population and the Bootstrap process was used to choose any of the three transition matrices to estimate λ with 1,000 iterations. The average of the 25 lowest and 25 highest values of λ defined 95% of the confidence limits (Ebert, 1999).

To test the demographic compensation hypothesis in relation to the asymptotic population growth rates, we proceeded by the following method: (a) taking into account the three calculated λ from each population, one thousand λs we randomly selected within each population by way of the Bootstrap process. We used thousand times the value of 1, a population in equilibrium, as population control to compare the lambdas among populations (total n = 4,000); (b) we used SAS General Lineal Model procedure (SAS, 2016), to conducted a ANOVA and multiple comparisons through Bonferroni correction; (c) as indicated in the hypothesis, no significant differences or differences greater than 1 we expected with the population control.

Population structures, transition matrices and λ of Quercus oleoides

In the three populations, productive individuals were those with a dbh of >10 cm, and no seed survival was there from 1 year to another (Fig. 1). In the three populations, the production of seeds occurred in each year, and an increase in the number of adults through time was observed (Fig. 2). The number of individuals (>0 cm dbh) per ha varied from 1,321 to 2,605 (Table 1), and the average number of seed produced per size class ranged were 156–571, 1,000–5,000, 8,000–10,000 and 6,500–8,000, for the size classes (dbh) >0.10, >10–20, >20–30, and >30, respectively (Appendix A, Table 1). The asymptotic population growth rates of the average matrices are higher than 1 indicates that the populations tend to increase (Table 2). The confidence intervals of λ were greater than 1 (Table 2). And among the annual transition matrix, Mesa de Veinticuatro had an exceptional λ of less than 1 (0.996) in 2017–2018 (Table 2, Appendix A). Significant differences were found in the average values of λ (from total n = 1,000 in each population versus control λ = 1) (F = 1,971.42, P < 0.0001), all populations were significantly higher than the control (λ = 1) (in all cases P < 0.0001, Miramar $\overline{\lambda }$ = 1.076 ± 0.0006, average ± mean standard deviation; Mesa de Veinticuatro $\overline{\lambda }$ = 1.017 ± 0.0006; and Otates $\overline{\lambda }$ = 1.042 ± 0.0004).

Elasticity analysis

The size classes that contributed the most to asymptotic population growth rates (λ) were the survival of individuals from >0–10 to >30 cm of dbh in Miramar (71% in their λ) (Table 3A), >30 dbh in Mesa de Veinticuatro (90.6% in their λ) (Table 3B), and >0–10, >10–20 and >30 cm dbh in Otates (84.2% in their λ) (Table 3C). Significant differences were found among the respective $e_{ij}$ average values of each element of the elasticity matrix from populations (values being from F = 791.1 to F = 12,953.2, and for all cases P < 0.0001) (all averages and each value’s ± mean standard deviation to [n = 39] are shown in Table 3).

LTRE analysis

Transition and survival variations in LTRE matrices also differed across populations. In Miramar, the highest variations occurred in transitions and survival to >10–20 and >20–30 cm dbh (Table 4A). In Mesa de Veinticuatro, the highest variation was in the survival and transition of >10–20 cm dbh (Table 4B). On the other hand, the maximum variation in Otates occurred in seed production among individuals of the class >10–20 cm dbh, as well as in the transitions and survival from <1.3 m high (Table 4C). Significant differences were found among the values from LTRE matrices of the populations (F = 204.64, P < 0.0001). LTRE average and mean standard deviation are 0.0062 ± 0.002, 0.0038 ± 0.0012 and 0.0055 ± 0.0019, to Miramar, Mesa de Veinticuatro, and Otales, respectively.

Population structure

Population size varies greatly among altitudes and years (Fig. 2). Due to the presence of livestock in two of the populations (moderate livestock farming in Miramar and intense livestock farming in Mesa de Veinticuatro), a lower regeneration of oaks would be expected. However, there is evidence that oak regeneration can be favored by the presence of livestock and ungulates in general, not only because some oaks are not palatable to livestock due to their toxicity (tannic acid) and unpleasant taste (e.g., Q. intricata Trel., Q. pringlei Seemen, Bacarrillo Rangel, 2015), but also because livestock can eliminate grass and herbs, which favors the regeneration of oaks (Hernández-Vargas et al., 2000; Bobiec et al., 2011; Leal, Bugalho & Palmeirim, 2022). There is little consensus as to whether ungulates in general have a positive or negative effect on oak regeneration. Intervening factors are the number of livestock individuals, the presence and amount of forage grasses and herbs, and the grazing season for livestock and other wild ungulates (Leal, Bugalho & Palmeirim, 2022). In any case, maintaining a steady population growth rate is more important than having a high regeneration potential (Tyler, Khun & Davis, 2006).

Also, given the ability of Q. oleoides to regenerate under its own canopy (tolerant to shade) (Vanclay, 1994), we expected to obtain an inverted J-shape size distribution as other Quercus populations (Duan et al., 2024; Lian et al., 2024), mostly in Mesa de Veinticuatro (with no cattle ranging), that is, a larger number of individuals in each preceding size class. However, the distribution of the number of individuals within size classes at the three different altitudinal levels (Fig. 2) suggests regeneration pulses (Martínez-Ramos & Álvarez-Buylla, 1995), that similarity occur in others Quercus (Jazib, 2023; Šimková et al., 2023; Duan et al., 2024). This rather common phenomenon among tree species can be attributed either to seed synchronicity or to disturbances that detonate massive germination processes (Janzen, 1971). In 2019, a decrease in regeneration was observed in all three populations (individuals <1.30 m high) (Fig. 2). Comparatively, in the Himalayas, Q. semecarpifolia was found to have very scarce regeneration at intermediate altitudes and null at lower altitudes (Fartyal et al., 2022). A similar pattern was evident towards the end of our study, with a drastic decrease of regeneration at an intermediate altitude (Fig. 2). A scarce regeneration has also been reported in multiple studies on the California oak woods, which has nevertheless been enough to ensure the survival of populations (Tyler, Khun & Davis, 2006). In elucidating the stability of populations in general, population growth rates are more reliable indicators than simple regeneration observation (Tyler, Khun & Davis, 2006).

Demographic compensation

Demographic compensation can be observed in the asymptotic population growth rates. Located at different altitudes and having a different disturbance history, the three populations under study show significant differences in terms of control (λ = 1). In all cases, λ > 1.0 could change in response to density-dependence effects until reaching a λ ≈ 1 in the not-so-distant future. Moreover, there is evidence that compensation can follow different paths depending on the adjustments made to the different vital rates. In our case, this is evidenced in the elasticity and the variation (LTRE) matrices. This suggests the presence of different selection pressures among Q. oleoides populations (Van Groenendael, De Kroon & Tuljapurkar, 1994; De Kroon, Van Groenendael & Ehrlén, 2000) and a clear demographic compensation.

Population growth rate and management decision

Asymptotic population growth rates summarize population dynamics, and their confidence intervals indicate its variations. In our study, λs were slightly superior to 1, this coincides with the population growth rates of other oak species (Tlapa-Almonte, 2005; Alfonso-Corrado, Clark-Tapia & Mendoza, 2007; Trigueros Bañuelos, Villavicencio García & Santiago Pérez, 2014).

In the Miramar and Mesa de Veinticuatro populations, with moderate disturbance and without disturbance respectively, the size classes that contributed the most to λ were survival classes (specifically >20–30 and >30 cm dbh). However, in the Otates population the contribution was concentrated in the survival of size classes from >10–20 and >30 cm, the latter one presenting the highest disturbance (Table 3). The highest contribution to regeneration was observed in Miramar (intermediate disturbance) and the lowest in Mesa de Veinticuatro (without disturbance). This suggests that disturbances could have caused changes in the asymptotic population growth rate, and these are the most important ones for the conservation of this population. Conversely, conservation in the Miramar and Mesa de Veinticuatro populations relied on the proportionality of size classes >20–30 up to >30 cm dbh. Disturbances as natural selection processes may change the loops within the annual transition of populations (e.g., Sánchez-Velásquez et al., 2002; Elogne et al., 2023). Differences in size structure, size-class contributions (survival and transition) and elasticity values among populations of Q. oleoides with similar asymptotic population growth rates along an altitudinal gradient and different disturbance conditions suggests demographic compensation (Villellas et al., 2015; Yang et al., 2022).

Another important aspect of population dynamics and its interpretation when making management and conservation decisions is vital rate variation (e.g., Baldauf et al., 2015). As mentioned earlier, LTRE analysis provides information on transition and survival variations in a matrix. In this sense, our results also indicate a clear significant difference among the three populations in terms of variation (Table 4). When comparing the LTRE and elasticity matrices (Table 3), we concluded that the highest transition and permanence values in the LTRE matrices would merit more attention in terms of management decisions, for they are important stages in the contribution to λ and at the same time they have a wide variation (Table 4).

Other studies have obtained λ < 1, that is, population decline, notably in four oak species, two of them deciduous and the other two evergreen (Tyler, Khun & Davis, 2006; Alfonso-Corrado, Clark-Tapia & Mendoza, 2007; Conlisk et al., 2012; Trigueros Bañuelos, Villavicencio García & Santiago Pérez, 2014). This suggests the presence of effects that could surpass the demographic compensation threshold of a population, but which could also attain a balance during a long period until reaching λ ≈ 1. More detailed studies and simulations could help elucidate, on the one hand, the stages that allow demographic compensation and, on the other, identify the variations of the asymptotic population growth rates and the vital rates. It would also be beneficial to include other aspects such as environmental drivers (Römer et al., 2021) and the ability to produce sprouts after disturbances (Oldfield & Eastwood, 2007; Oldfield, Evans & Oldfield, 2021).

Finally, we have to acknowledge that the average vital rates and the asymptotic growth rates obtained were dependent on the environmental conditions prevalent during the years 2016–2019, and that they are likely to change under different conditions.