Minimum recruitment frequency in plants with episodic recruitment

Abstract

There is concern about the lack of recruitment of Acacia trees in the Negev desert of Israel. We have developed three models to estimate the frequency of recruitment necessary for long-term population survival (i.e. positive average population growth for 1,000 years and <10% probability of extinction). Two models assume purely episodic recruitment based on the general notion that recruitment in arid environments is highly episodic. They differ in that the deterministic model investigates average dynamics while the stochastic model does not. Studies indicating that recruitment episodes in arid environments have been overemphasized motivated the development of the third model. This semi-stochastic model simulates a mixture of continuous and episodic recruitment. Model analysis was done analytically for the deterministic model and via running model simulations for the stochastic and semi-stochastic models. The deterministic and stochastic models predict that, on average, 2.2 and 3.7 recruitment events per century, respectively, are necessary to sustain the population. According to the semi-stochastic model, 1.6 large recruitment events per century and an annual probability of 50% that a small recruitment event occurs are needed. A consequence of purely episodic recruitment is that all recruitment episodes produce extremely large numbers of recruits (i.e. at odds with field observations), an evaluation that holds even when considering that rare events must be large. Thus, the semi-stochastic model appears to be the most realistic model. Comparing the prediction of the semi-stochastic model to field observations in the Negev desert shows that the absence of observations of extremely large recruitment events is no reason for concern. However, the almost complete absence of small recruitment events is a serious reason for concern. The lack of recruitment may be due to decreased densities of large mammalian herbivores and might be further exacerbated by possible changes in climate, both in terms of average precipitation and the temporal distribution of rain.

Appendix

Assuming that trees grow 1.5 cm in trunk circumference per year (cf. Kiyiapi 1994) and using age T in units of 5 years, trees can be classified into non-reproducing seedlings (<15 cm, T /5 years=0, 1), subadults with low seed production(15 cm–45 cm, T /5 years=2, 3, 4, 5), and adults (≥45 m, T /5 years ≥6) with full seed production (Wiegand et al. 1999). The number of seeds produced by a tree (S) of trunk circumference (tc; cm) is:

$$ \log S = 3.8 + 1.1\;\log tc $$

(Wiegand et al. 1999) or, in terms of age T (5 years):

$$ \log S = 4.8 + 1.1\;\log T $$

Thirty-five percent of the subadult and 84% of the adult trees reproduce in a given year. On average, the number of seeds produced is reduced by 84% (subadults) and 75% (adults) due to mistletoe infestation and unfavourable moisture status (Wiegand et al. 1999).

Given a germination event under optimal weather conditions, a certain seed has a chance of 1.8×10^-6 to evolve into a 5-year-old seedling. This is because 96.5% of the seeds are infested by seed beetles, 93% of the seeds get lost, 50% land at a safe site, 15.6% of the seeds at safe sites germinate, and semi-annual seedling mortality is 60% within the first 2.5 years and 1.74% over the following 2 years (Wiegand et al. 1999).

Thus, the number of offspring (O) produced by a subadult tree for a potential recruitment event is:

$$ \log O = - 1.5 + 1.1\;\log T $$

and the number of offspring produced by adults is:

$$ \log O = - 1.1 + 1.1\;\log T $$

Plotting number of offspring versus age reveals a linear relationship, which is approximately: O ≈0.12 T /Δt.