Electronic supplement 1– Fertility factor

The acacia trees in the Negev desert of Israel are the starting point of our study. A lack of recruitment leads to concern about the long-term survival of these trees (Ashkenazi 1995; Ward and Rohner 1997; Rohner and Ward 1999). Within this framework, Wiegand et al. (1999, 2000a, 2000b) developed a spatially explicit, individual-based simulation model, SAM, to better understand the population dynamics of acacia trees. With a pattern-oriented modelling approach, these authors showed that there has been episodic recruitment for many decades (Wiegand et al. 2000b). This was done by comparing tree size-frequency distributions observed in the Negev to those produced under different SAM model scenarios. There, Wiegand et al. (2000b) determined thatcombinations of continuous and episodic recruitment and found that purely episodic recruitment leads to unstable dynamics of extreme mass recruitment and dieback.

In order to detect the relative importance of the different processes and how they affect the survival of A. raddiana trees,Wiegand et al. (1999) conducted a sensitivity analysis of model parameters and assumptions. These authors found that mortality rates at different life stages, the production of uninfested seeds, and the weather regime were the most influential in plant population dynamics of this species. Whereas the infection of trees by semi-parasitic mistletoes proved to be of minor importance, the most important result was that an increase in the germination rate of acacia seeds (such as resulted from passage through the digestive tract of large mammalian herbivores; Bodmer and Ward 2006), was capable of counteracting the detrimental effect of unfavourable climatic conditions.

Later, Wiegand et al. (2004) developed a simplification of the SAM modelthat focused on the question of how often recruitment events are needed to ensure the long-term survival of plants with a given longevity and seed production and no seed bank. These authors developed three alternative models which served to investigate the role of the temporal distribution of recruitment events. As a baseline model, they use a deterministic approximation (i.e. deterministic model) to determine the minimum frequency of episodic recruitment events yielding stable (in the sense of not declining) population size. Then, they conducted stochastic simulations (i.e. stochastic model) under the extreme assumption that all recruitment occurs during rare, yet large recruitment events. Finally, acknowledging Watson et al.’s (1997) results (i.e. in arid environments, recruitment of long-lived plants occur inepisodic pulses – see Chesson et al. 2004), they conduct simulations under the assumption of partly continuous and partly episodic recruitments (i.e. a semi-stochastic model).

The main motivation of the present work was to test the importance of seed removal by ungulates (as a proxy of ungulate abundance; Electronic supplement 2)foracacia regeneration, which affect key stages in its plant life cycle. The present simulation study was, in fact, motivated by the need for future research on this topic (Wiegand et al. 1999). Our model was based on the semi-stochastic population model presented by Wiegand et al. (2004), because this was considered to be the most realistic scenario for seedling recruitment for A. raddiana in the Negev desert. In the previous model, Wiegand et al. (2004) studied the number of minimum recruitment events of acacias necessary for long-term population survival in the Negev desert.Thus, the SAM model (Wiegand et al. 1999; Wiegand et al. 2000a; Wiegand et al. 2000b) serves as a strong basis for the present study as it is the best summary of the demography of the Negev’s acacias to date.

Here, we considered ‘fertility factor’ (FF, hereafter) as the number of seedlings an acacia tree of a given age-class produces after considering the multiple factors affectingthose seeds and seedlings until they survive for 5 years. The stages summarizing those factors affecting acacia seed production were summarized in Fig. A1.

Fig A1 - Diagram of the multiple factors affecting the number of seedlings that anacacia tree produces (i.e. ‘fertility factor’).

Plant age class

Following Kiyiapi (1994), we assumed that trees grow 1.5 cm in trunk circumference per year. We classified plants intoTage-class units of 5 years, as 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) in terms of age class T (5 years) is:

log S= 4.8 + 1.1 log T

Furthermore, individual plants do not produce seed every year,that is, 35% of the subadult and 84% of the adult trees produce seed in a given year(Wiegand et al. 1999).

Mistletoe infestation, moisture status and vitality of trees

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).

Flower browsing

Within a situation with ungulate herbivory (see Model with herbivory in Material and methods), we incorporated an additional term describing the intensity of browsing and its effects on reproduction (i.e. reduction of seed production based on flower browsing).

The proportion of flower browsing depended on three factors: a)ungulate preference, b) browsing intensity, and c) the proportion of plant age-class herbivory(i.e. which depended on the height of each acacia age-class and the maximum height at which each ungulate was able to feed).

a)The ungulate preferencemay depend on the ungulate preferences for a given plant species. Because there are no data available on A. raddianathat relate ungulate abundance to browsing intensity, we used information from a close relative, A. tortilis. A. raddiana is considered a subspecies of A. tortilis in East Africa although it is genetically distinct in the Middle East (Zohary 1972; Shrestha et al. 2002; Danin 2010). For our model, we considered it to bereasonable that up to 25% of the acacia canopy may be browsed in conditions of maximum ungulate abundance (Fornara and Du Toit 2008). However, this value may be an overestimate, because chemical defences (which directly affect herbivore preferences) are higher in A. raddiana than in A. tortilis(Rohner and Ward 1997).

b)The browsing intensity would depend on the ungulate abundance. In our case, we assumed that browsing intensity was directly related to seed removal, which, in turn, was defined as a proxy of ungulate abundance (Electronic supplement 2). The browsing intensity and ungulate preference (see above) were thus multiplied in order to get a browsing intensity weighted by ungulate preferencesforA. raddiana.

c)The proportion of plant age-class herbivory concurrently depended on two factors: i) the maximum height at which each ungulate was able to feed and ii) the age-dependent height of acacias.

i)We calculated the relationship between body mass (BM) and maximum height (MHU) of ungulates currently inhabiting the Negev desert. MHU was estimated as 1.3 times shoulder height (i.e. not including neck and head). Data on BM and MHU came from averaged information from reliable internet sources reviewed by mammal experts (i.e. In the present case, the relationship between MHU and BMwas:

MHU = 0.725 + 4.186×10-3BM (r2=0.928)

We know that trees grow 7.5 cm in trunk circumference per year and larger trees can growup to 6 m in height (Kiyiapi 1994) and, thus,we considered it to bereasonable that the maximum tree height increased 0.5 min each time step (i.e. 5 years). For a given plant age-class, we assumed that foliage can grow between its maximum canopy height (MCH) and one-half of MCT (i.e. minimum canopy height). Thus, we fitted a linear relationship of the proportion of foliage browsed by ungulates (FBU) as follows:

FBUij = ((MHUi – 0.5 MCHj)/ MCHj)

where i and j are the values for each ungulate body mass and plant age-class, respectively.The former equation is based on the assumptions that all the foliage was not available for ungulates (i.e. larger ungulates, such as camels, could reach up to 3 m height,which is half the height of the largest trees; Kiyiapi 1994) and that the probability of ungulate browsing decreased with plant age-class.

Furthermore, we also consider it reasonable that some part of the foliage may even escape from browsing and, so, we assumed a maximum FBU of 0.95. Likewise, we also assume that some part of the foliage may always be accessible, considering FBU=0.05 as the minimum probability that foliage may be browsed. We generated FBU values for each combination of plant size and ungulate body mass as follows:

Fig A2 –Probability of the foliage browsed by ungulates (FBU) as a combination of ungulate body mass and acacias’ age-classes. Plant age class was considered in T age class units of 5 years (see Plant-age class section).

We fitted polynomial distributions between plant age-class and FBU using the software Table Curve 2D (Jandel Scientific 1994). In our case, FBU and plant age-class best fitted to Laurent (i.e. for T=0: y= a+b/x+c/x2, adjusted r2= 0.925) and ordinary polynomial curves (i.e. for T>0: ln y = a+bx+cx2+dx3+ex4, average of the adjusted r2= 0.998). For plants older than T=10 age-class (i.e. larger than 6 m height), proportion of FBU was considered constant (i.e. 5%) and independent of ungulate body mass.Finally, the probability of flower browsing was calculated by multiplying the ‘intensity of browsing’ and FBU.

Seed loss

A further 90% reduction of acacia seeds was due to the transport of seeds out of wadis, either by floods and/or by ungulates (Miller 1994; Wiegand et al. 1999).

Survivaland removal of seeds

Seed infestation of A. raddiana in the Negev desert, mostly by Bruchidius arabicus(Bruchidae)and Caryedon palaestinicus(Bruchidae), is as high as 95%–98% (Rohner and Ward 1999; Ward et al 2010). These values represented a scenarioof absence of seed removal by ungulates (see Electronic supplement 2). In the present model, seed infestation by bruchids depended on bruchid abundance (i.e. which directly depended on seed removal). Seed destruction by ungulates is correlated withungulate body mass(Miller 1995): we used a linear relationship between the proportion of seeds surviving gut passage and ungulate body mass in A. tortilis(see Electronic supplement 3).We did not consider that ingested seeds may later be infested because seed infestation of acacia seeds is considerably lower in ingested than non-ingested seeds (Miller 1994).

Furthermore, camels and Nubian ibex can reach pods high on acacia trees (the goat-like Nubian ibex climb into some trees), but the majority of ungulates wait until the pods have dropped (Ward, pers. obs.). In the present model, we considered that fruit removal was independent of MHU (see above).

Seed germination

In the present model, we differentiated three groups of acaciaseeds as a function of ungulate abundance:a) seeds infested by bruchids, b) seeds ingested by ungulates (and not infested), and c) intact seeds or neither ingested, infested or both (Electronic supplement2).In the SAM model, Wiegand et al. (1999) assumed that infested seeds do not germinate. In the present model, however, infestedseed germinatedwith a probability of 0.001 (Or and Ward 2003). The germination probability of intact seeds was 0.025 (Rohner and Ward 1999). For ungulate-ingested seeds, we used the positive relationship between seed germination and ungulate body mass for A. raddiana and A. tortilis(Rohner and Ward 1999). We did not consider non-ruminant ungulates (i.e. mostly equids such as Asiatic wild asses, which may also consume acacia pods), owing to the difficulty of generalizing ruminant gut-passage effects to herbivores with different digestive systems (Clauss et al. 2007). Ostriches (Struthio camelus) are also known to consume acacia pods, but all seeds consumed by these birds did not germinate (Rohner and Ward 1997).

Summing up, the average seed germination increased both with seed removal and the body mass of ungulates(Fig A3).

Fig. A3 –Probability of seed germination between seed removal and body mass of ungulates. Probabilities were corrected according to the different abundance of seed groups (see Electronic supplement 3).

Seedling recruitment

Seed germination in arid environments primarily depends on local water availability (Wilson and Witkowski 1998). Under optimal conditions, about 16% of the non-infested seeds in safe sites germinate (Rohner and Ward 1999). Thus, two conditions need to be fulfilled for the successful germination of non-infested seeds: sufficient rainfall and location of the seed at a safe site (Miller 1994). In the SAM model of Wiegand et al. (1999), recruitment is modelled in several steps, in which each time step of the model is one year. Based on rainfall data, the model included three classes of years: good (23% occurrence probability), intermediate (61%), and bad (16%) years, as recorded in the Negev desert(Wiegand et al. 1999). Germination takes place in good years only and, within the first 2.5 years, seedling survival in the first 30 months is 40% in good, 20% in medium, and 0% in bad years(Wiegand et al. 1999; Rohner and Ward 1999). Thereafter, survival is assumed to be independent of the classification of the year.

Here, we modelled recruitment in basic time-stepsof 5 years (T) and only those seeds are considered that germinate and thereafter survive for each time-step. The proportion of potential recruits was based on the semi-stochastic simulation model ofWiegand et al. (2004), which departed from a combination of properties of both a deterministic and a stochastic model (see above). Under the deterministic model, the frequency of recruitment events (rec, hereafter) has a fixed value for each time-step and simulation run and describes the probability that such a recruitment event takes place.Forthe stochastic model, by contrast, recruitment takes place during rare events of high probability of recruitment, followed by stages of no potential recruitment.Thus, the stochastic model uses random numbers to decide if recruitment occurs in the current time step with respect to the probability that a recruitment event takes place (rec).

The semi-stochastic model is a mixture of bothmodels in which, for each time-step, the semi-stochastic model has a 50% chance that the model will behave like the deterministic model.In the present model, we did not consider that the main cause for the differences in the size of recruitment during T time-steps were based on the between-year differences in weather conditions (i.e., good, medium and bad years) but the recruitment events depended on temporal variations in the number of recruits at a simplified phenomenological level mimicking the frequency of potential recruitment events (Wiegand et al. 2004). The modelmimicked the outcome of infrequent years which are optimal (or unfavourable) for recruitment via application of the rules of the stochastic (or the deterministic) model. In the model presented here, the average probability of seed recruitment for each time step (rec) was set to 0.1 (Wiegand et al. 2004). To avoid unrealistically high densities, we also restricted the number of recruits per recruitment event to 5,000. Seedling density considered here is an exceptionally large density of recruits; this judgement was also based on the dynamics of the previous detailed spatially-explicit model (Wiegand et al. 1999).The precise value of this upper limit does not influence the qualitative results of our study.

Plant survival

We assumed survival to be age-sizeindependent, because of the wide spacing among adult trees, which prevents suppression of small individuals by larger ones (Wiegand et al. 2000a). The number of survivors in an age-class category is drawn from a binomial distribution or, in the case of few individuals (<30), the survival of each individual is determined separately by random numbers (bernouilli distribution). Growth of surviving trees is modelled by shifting them into the next age class.

We also assumed that there is no increase in plant mortality with browsing intensity (Rohner and Ward 1999). This assumption was based on empirical knowledge. For instance, A. tortilis (a close relative of A. raddiana) was not affected by giraffe (Giraffa camelopardis) abundance, whereas the giraffe affected the mortality of adult trees of four of five acacia species (Bond and Loffell 2001). This is probably due to higher physical (Smit 1999) and/or chemical defences (Van Hoven and Furstenburg 1992; Rohner and Ward 1997) compared to other acacia species. In fact, A. raddiana have higher chemical defences than A. tortilis (Rohner and Ward 1997), and thus, we might not expect any relationship between ungulate abundance and tree survival.

Average fertility factor

To summarize, given a germination event under optimal weather conditions, a certain seed had a chance of 1.8×10-6 to evolve into a 5-year-old seedlingifthere is no seed removal by ungulates(i.e. in this case 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 of each tree (O) versus tree age-size (T) was calculated based on the following linear relationship measured in time-steps of 5 years(Wiegand et al. 2004):

O ≈ FF× T

For each combination of seed removal and body mass of ungulates, we calculated FF and Ofor the model with and without herbivory (Electronic supplement 3). We constructed 100 scenarios representing a combination of seed removal and body mass of ungulates: a) 10 scenarios representing an increase of 10% in seed removal and b) 10 scenarios representing the range of body masses of those ungulates which disperse A. raddiana seeds in the Negev desert: that is, from dorcas gazelle (c. 25 kg) to camel (c. 800 kg).Body masses were divided into 10 logarithmic mass-spans. We also created one scenario of no seed removal by ungulates (i.e. only seed predation by bruchids). In the model with herbivory, furthermore, O was reduced according to each combination of (weighted) flower browsing intensity and plant age size.

References

Ashkenazi S (1995) Acacia trees in the Negev and the Arava, Israel. Israel Land Development Authority, Jerusalem

Bond WJ, Loffell D (2001) Introduction of giraffe changes Acacia distribution in a South African savanna. Afr J Ecol 39:286-294

Chesson P, Gebauer RLE, Schwinning S, Huntly N, Wiegand K, Ernest MSK, Sher A, Novoplansky A, Weltzin JF (2004) Resource pulses, species interactions, and diversity maintenance in arid and semi-arid environments. Oecologia 141:236-253.

Clauss M, Schwarm A, Ortmann S, Streich WJ, Hummel J (2007) A case of non-scaling in mammalian physiology? Body size, digestive capacity, food intake, and ingesta passage in mammalian herbivores. Comp Biochem Phys A 148:249-265

Danin A . Flora of israel online. 2010.