# Modelling climate-change-induced nonlinear thresholds in cephalopod population dynamics

Version of Record online: 19 AUG 2010

DOI: 10.1111/j.1365-2486.2010.02223.x

© 2010 Blackwell Publishing Ltd

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#### How to Cite

ANDRÉ, J., HADDON, M. and PECL, G. T. (2010), Modelling climate-change-induced nonlinear thresholds in cephalopod population dynamics. Global Change Biology, 16: 2866–2875. doi: 10.1111/j.1365-2486.2010.02223.x

#### Publication History

- Issue online: 1 SEP 2010
- Version of Record online: 19 AUG 2010
- Received 25 September 2009; revised version received 15 March 2010 and accepted 16 March 2010

- Abstract
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**Figure S1.** Representation of the life cycle of *Octopus pallidus*. The diagram illustrates the various life stages and the corresponding size classes, with arrows representing the possible transitions between stages observed in our simulations. Probabilities *a _{j,i}* correspond to the probabilities of an octopus moving from stage

*i*to stage

*j*during the projection interval (i.e. 3 months) and

*F*represent the fecundity of each mature stage. Note that stage 11 and its corresponding fecundity

*F4*are not represented in the diagram as this stage was never populated in our simulations.

**Figure S2.** Population projection matrix *P* for *Octopus pallidus*. The projection matrix is based on the life cycle diagram in Fig. S1. All post-hatch transition probabilities *a _{j,i}* (in light grey) were determined using the bioenergetics model, while egg to hatchling transition probabilities (in dark grey) were calculated using the projected incubation times. Fecundities

*F*(in black) were determined using reproductive data from wild octopus in Bass Strait. A zero in the matrix indicates a transition that was not possible or not observed in our simulations. Note that stage 11 (i.e. females M4) was never populated in our simulations.

**Figure S3.** Temperature functions used in the bioenergetic model. (a) Temperature function for the climate-change scenario and (b) temperature function for the no-climate-change scenario. The blue line represents the mean temperature during the no-climate-change scenario, the red line the mean temperature during the climate-change scenario.

**Figure S4.** Predicted seasonal hatchling size distributions in 2005, 2030, 2050 and 2070. (a) Predicted summer distributions, (b) predicted autumn distributions, (c) predicted winter distributions and (d) predicted spring distributions. Hatchling size was described by a lognormal distribution *A*~L(μ,σ) where μ=In(*m*) and *m* is the median of the distribution.

**Figure S5.** Method for estimating yearly seasonal transition probabilities matrices. This diagram represents the method for estimating yearly seasonal transition probabilities matrices from the 2005, 2030, 2050 and 2070 seasonal transition probabilities matrices. The interpolation is a simple linear change between the estimated proportions.

**Figure S6.** Estimated relationship between body mass in mature females and number of eggs. The relationship was estimated using a type II regression. Circles represent data on 155 wild mature females from the Bass Strait region, taken between 2004 and 2006. White triangles represent the mean body weight for the mature stage. Data courtesy of Stephen Leporati.

**Figure S7.** Relationship between mean incubation temperature (*T*) and egg survival (*S*) for *Octopus pallidus*. This relationship was adapted from the egg survival curve of *Loligo gahi* by Cinti *et al*. (2004).

**Figure S8.** Survivorship logistic curves with 3% minimum survivorship and a range of maximum survivorships. The maximum survivorships used ranged from 50% to 85% in 5% increments. Survival in the post-spawning class PS was set to zero. The same method was applied to calculate survivorship curves with 1.5% minimum survivorship and 4.5% minimum survivorship.

**Figure S9.** Seasonal population abundance under the no-climate-change scenario for the 4.5% minimum/75% maximum survival curve. Summer; Autumn; Winter; Spring.

**Figure S10.** Seasonal population structure for selected years under the no-climate-change scenario: (a) summer, (b) autumn, (c) winter and (d) spring. Colours represent the proportion of each stage in the population ( J1; J2; J3; J4; J5; J6; J7; □ M1; M2; M3; PS) and plain lines represent the total population size in the selected year. Survivorship was set as a 4.5% minimum/75% maximum survival curve.

**Table S1.** Equations and parameter values for the bioenergetic model. *A* is the hatchling size, *t* is the age (in days) and *t _{hatch}* the hatching day in a 360-day year.

**Table S2.** Sequence of modelling under the climate-change scenario. *P* corresponds to one of 264 projection matrices, *S* the survival matrix and *N*(*t*) the population at time *t*.

**Table S3.** Sequence of modelling under the no-climate-change scenario. *P* corresponds to one of four projection matrices, *S* the survival matrix and *N*(population at time *t*.

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Filename | Format | Size | Description |
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GCB_2223_sm_supplinfo.pdf | 724K | Supporting info item |

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.