Un resorte de constante elástica 100 N/m se com prime 0,2 m al contacto con un bloque de masa

At a holistic level, the capacity of the model to demonstrate shifts (in either direction) between seaweed- and sea urchin dominated reefs represents a validation of the observed dynamics. First, parameters of influence on model dynamics can provide the most effective means to calibrate model behaviour accordingly to observations: sensitivity analysis with the first set of Monte-Carlo simulations, initialised in the seaweed bed state and run under

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historical fishing levels for the east coast of Tasmania, reveal that urchin and lobster recruitment rates are the most influential parameters on the model’s ability to shift to sea urchin barrens (Fig. 3.2a). Moreover, the relationship between the two variables in affecting the risk of barren habitat formation is non-linear (Fig. 3.2b); for a given level of sea urchin recruitment, with declining annual lobster recruitment (from 800 g.200 m−2.year−1) there is initially little affect on the likelihood of barrens formation until a threshold of 600 g.200 m−2.year−1 is reached, at which point risk of barrens increases linearly with declining lobster recruitment to 400 g.200 m−2.year−1, below which there is little further affect on the likelihood of barrens forming. The smallest value of mean sea urchin recruitment rate that can achieve levels of barrens formation (∼50% of reef area) observed in NSW (Andrew and O’Neill, 2000) and Tasmania (Johnson et al., 2005, 2011) in areas whereC. rodgersii is long established (i.e. the point at which the chance of barrens formation is 0.5; Fig. 3.2b) is 5000 g.200 m−2.year−1.). Consequently, sea urchin recruitment rates are varied between 5000 and 10000 g.200 m−2.year−1 in sensitivity tests presented in the rest of this paper.

Demonstrating the minor influence of the formulation of density dependence in lobsters’ predation on urchins also contributes to model validation. The second set of sensitivity tests investigated the effects of alternative formulations of lobster predation on sea urchins, i.e. of implementing Holling’s type I, II or III functional response. FAST sensitivity indices were computed for all parameters in TRITON under each formulation of the functional response, i.e. including the two parameters that define the shape of the functional response (Fig. 3.3). For each of the three formulations (i.e. Holling’s type I, II or III), the two parameters defining the shape of the functional response had no more influence on model behaviour than did most of the other 14 input factors. Indeed, the influence of the two parameters of the functional response was marginal compared to those parameters with greatest influence on model behaviour (i.e. lobster fishing mortality, initial urchin population, lobster recruitment, initial seaweed cover, sea urchin recruitment). The projection of simulation outcomes on the first two PCs also suggests that the type of functional response adopted has marginal influence on model behaviour (Fig. 3.4). The patterns of the scores on the first two PCs, which capture 91% of the total variability, are visually very similar for all three functional responses. While scores on the first two PCs with the Holling Type I response (Fig. 3.3b) show a slightly different distribution compared to the Type II and III, the overall patterns are virtually similar. Note, however,

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a

b

Figure 3.5: Frequency (logarithmic scale) of community states as a function of sea urchin versus seaweed bed biomass densities from (a) the 8000 Monte-Carlo simulations with TRITON and from (b) large-scale surveys on the east coast of Tasmania (Johnson et al., 2005, 2011). Arrows in (a) represent the mean simulation trajectory in terms of fortnightly change in sea urchin and seaweed bed biomass densities.

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that results from the MANOVA suggest significantly different mean scores on the first two PCs for each Holling Type functional response, but this is likely to occur due to the very large number of replication (8000 simulations) bringing the multivariate standard errors to marginal values. Given that the model wasn’t sensitive to the particular choice of functional response or to the parameterisation of this response, we chose to use Holling’s type III functional response in all of the following simulations given that it is the most commonly used response to describe predation behaviour in decapods (see Table A.8; Appendix A).

We aggregated monthly outputs from the 8000 Monte-Carlo simulations of the FAST global sensitivity analysis with random initial conditions to compare patterns emerging from simulations with TRITON to patterns observed in large-scale surveys (Johnson et al., 2005, 2011) of Tasmanian temperate reef communities (Fig. 3.5). Fig. 3.5a describes the frequency of the different community states in terms of seaweed bed versus sea urchin biomass densities with overlayed arrows representing the model mean trajectory (i.e. fortnightly change in biomass through simulations) at different points of reef state. In Fig. 3.5b, data from a large-scale survey (Johnson et al., 2005, 2011) describes the frequency of reef communities on the east coast of Tasmania in 2000-2002 being in any given state. Importantly, both the modelled and observed reef communities identify two dominant states representing (i) the seaweed bed state with a high cover of seaweed and a low density of sea urchin and (ii) the sea urchin barren state with virtually no algal cover and a high density of sea urchins. This indicates broad agreement of the behaviour of the model with observations of the occurrence of the two states in the field.