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Relationships between demography and gene flow and their importance for the conservation of tree populations in tropical forests under selective felling regimes

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Abstract

Determining how tropical tree populations subject to selective felling (logging) pressure may be conserved is a crucial issue for forest management and studying this issue requires a comprehensive understanding of the relationships between population demography and gene flow. We used a simulation model, SELVA, to study (1) the relative impact of demographic factors (juvenile mortality, felling regime) and genetic factors (selfing, number and location of fathers, mating success) on long-term genetic diversity; and (2) the impact of different felling regimes on population size versus genetic diversity. Impact was measured by means of model sensitivity analyses. Juvenile mortality had the highest impact on the number of alleles and genotypes, and on the genetic distance between the original and final populations. Selfing had the greatest impact on observed heterozygote frequency and fixation index. Other factors and interactions had only minor effects. Overall, felling had a greater impact on population size than on genetic diversity. Interestingly, populations under relatively low felling pressure even had a somewhat lower fixation index than undisturbed populations (no felling). We conclude that demographic processes such as juvenile mortality should be modelled thoroughly to obtain reliable long-term predictions of genetic diversity. Mortality in selfed and outcrossed progenies should be modelled explicitly by taking inbreeding depression into account. The modelling of selfing based on population rate appeared to be oversimplifying and should account for inter-tree variation. Forest management should pay particular attention to the regeneration capacities of felled species.

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Acknowledgements

We are grateful to Sylvie Oddou-Muratorio of INRA (French National Institute for Agricultural Research) Avignon and to Ivan Scotti of INRA Kourou (French Guiana) for valuable discussions on the demography and gene flow of forest tree species. Moreover, we thank two anonymous reviewers for constructive and helpful comments on an earlier version of the manuscript. The work was funded by a joint post-doctoral fellowship from CIRAD (French Agricultural Research Centre for International Development) and INRA.

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Correspondence to Holger Wernsdörfer.

Appendices

Appendix 1: Gene flow sub-model

The description of the D. guianensis gene flow sub-model refers to the grey boxes in the flow chart (Fig. 1).

Number and clustering of seeds

The number of seeds, N seed, produced by a given mother tree at a given point in time was governed by forest dynamics. All seeds possessed the maternal genotype of the mother tree. To attribute the genotypes of several fathers, the seeds were subdivided into clusters with the number of clusters corresponding to the number of fathers, N father (=15 by default). The number of seeds per cluster, N cluster, was equal between clusters: N cluster = N seed/N father.

Search for fathers

One father was determined for each seed cluster by subsequently checking the occurrence of selfing and, if applicable, the location of the father.

Selfing

Selfing was a random event occurring with the probability P selfing (Table 1). In the event of selfing, the paternal genotype was the same as the maternal genotype. In the event of outcrossing (i.e. no selfing), the next step was to determine the location of the father.

Location of fathers

Fathers could be located both outside and inside the study area. The random event of a father being located outside the area occurred with the probability P outside (Table 1). If this event occurred, a paternal genotype was drawn at random from an allele frequency distribution, called a pollen cloud. The pollen cloud included allele frequencies for six loci, where the number of alleles per locus ranged between 5 and 15. Allele frequencies were based on 246 seeds collected inside the study area (Latouche-Hallé et al. 2004; samples from outside the area were not available), hypothesising that the observed seed genotypes represented the male allele frequencies occurring outside the area. In the event of the father being located inside the area, which occurred with the probability 1 − P outside, a father tree was drawn at random from among the population of potential father trees inside the area. This population included all trees ≥25 cm dbh apart from the mother tree, as selfing had already been checked in the previous step.

Mating success

For the random drawing of a father tree inside the area, the default setting accounted for an effect of dbh on mating success (Latouche-Hallé et al. 2004; Table 1). Potential father trees were classified by dbh and a weight was attributed to each tree according to its dbh class. Larger trees had higher mating success. As an alternative setting, a father was drawn independently of its traits. For both settings, father trees were drawn with replacement.

Miscellaneous

If the setting was such that fathers could be located both outside and inside the study area (i.e. P outside ≠ 0 and P outside ≠ 1), then P outside was adjusted to account for changes in the population of potential father trees occurring inside the area. Such changes could occur in the course of a simulation run due to mortality or felling, for instance. We assumed that P outside increased if the potential amount of pollen arriving from inside the area decreased, and vice versa. We also assumed an ideal D. guianensis population outside the area, which was undisturbed or managed in a manner such that pollen production was unaffected; the pollen cloud was constant at all times in a simulation run. We used two methods to calculate the change in P outside, depending on the mating success setting.

If mating success was independent of tree traits, P outside was adjusted to the number of potential father trees occurring inside the area at a given point in time during a simulation run, N pot. Let N pot_mean be the mean number of potential father trees occurring inside the area during a simulation run. Then, a fictitious number of potential father trees occurring outside the area can be calculated as N fict = N pot_mean × P outside/(1 − P outside). We assumed N fict to be constant at all time points during a simulation run. Based on this, at a given point in time, the probability of a father being located outside the area was calculated as Poutside = N fict/(N fict + N pot). To illustrate this, we plotted Poutside in relation to N pot for P outside = 0.62 and N pot_mean = 117 (Fig. 4). Note that Poutside clearly increased as values of N pot decreased. In contrast, a considerable pollen flow from outside the area was maintained even if N pot reached very high (unrealistic) values, e.g. Poutside > 0.3 for N pot = 400.

Fig. 4
figure 4

Probability of fathers being located outside the study area (Poutside), and inside the area (1 − Poutside), as a function of the number of potential father trees occurring inside the area at a given point in time during a simulation run (N pot). The mean number of potential father trees occurring inside the area during a simulation run was N pot_mean = 117. By default, P outside = 0.62

If mating success was weighted by dbh class, a similar method was applied. But instead of adjusting P outside to N pot, P outside was adjusted to the sum of the weights of the potential father trees occurring inside the area at a given point in time during a simulation run, pot. Let pot_mean be the sum of the weights of the average population of potential father trees occurring inside the area during a simulation run, and let fict =  pot_mean × P outside/(1 − P outside) be the fictitious sum of the weights of potential fathers occurring outside the area, then Poutside =  fict/( fict +  pot).

In the case of P outside = 0, father trees were always drawn from inside the area. Thus, for numerical reasons, we had to consider the special case where only one mother tree but no potential father tree was left inside the area (e.g. due to high mortality). In this special case, the father tree corresponded to the mother tree (selfing).

Appendix 2: Sensitivity measures

The sensitivity of an output variable Y to one input factor X i (first order effect) is measured as the ratio between the output variance V i, due to X i, and the total output variance V(Y) (Saltelli et al. 2004; Wernsdörfer et al. 2008):

$$ S_{\text{i}} = {\frac{{V_{i} }}{V(Y)}}. $$
(1)

Similarly, the sensitivity of Y to two input factors X i, X j (second order effect) and three input factors X i, X j, X m (third order effect) is measured as

$$ S_{\text{ij}} = {\frac{{V_{\text{ij}} }}{V(Y)}} $$
(2)

and

$$ S_{\text{ijm}} = {\frac{{V_{\text{ijm}} }}{V(Y)}}, $$
(3)

where V ij and V ijm are the output variances due to X i, X j and X i, X j, X m, respectively. The variances V i, V ij and V ijm are calculated as

$$ V_{\text{i}} = V[E(\left. Y \right|X_{\text{i}} )], $$
(4)
$$ V_{\text{ij}} = V[E(\left. Y \right|X_{\text{i}} ,X_{\text{j}} )] - V_{\text{i}} - V_{\text{j}} $$
(5)

and

$$ V_{\text{ijm}} = V[E(\left. Y \right|X_{\text{i}} ,X_{\text{j}} ,X_{\text{m}} )] - V_{\text{ij}} - V_{\text{im}} - V_{\text{jm}} - V_{\text{i}} - V_{\text{j}} - V_{\text{m}} , $$
(6)

where the expectation E is approximated as a mean.

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Wernsdörfer, H., Caron, H., Gerber, S. et al. Relationships between demography and gene flow and their importance for the conservation of tree populations in tropical forests under selective felling regimes. Conserv Genet 12, 15–29 (2011). https://doi.org/10.1007/s10592-009-9983-0

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