Appendix C. Figures showing further examples of model spatiotemporal dynamics.

Figures showing further examples of model spatiotemporal dynamics

Supplement 1. MATLAB simulation code for the OBE model.

<h2>File List</h2><div> <p><a href="phode_obe.m">phode_obe.m</a> (MD5: 07325e3df93297cc4d12ee3705bf576b)</p> <p><a href="phfn_obe.m">phfn_obe.m</a> (MD5: 4cf8576c1ea77401f747467c4c05a013)</p> </div><h2>Description</h2><div> <p>phode_obe.m – This is the “main” file that is run at the Matlab prompt. Parameter values and numerical integration options are specified here. This file calls the “phfn_obe.m” file.</p> <p>phfn_obe.m – This file specifies the model structure and is called by “phode_obe.m”. The OBEM and LBEM models can be run using minor, straightforward alterations of code provided. </p> </div

Projection matrix for the hypothetical life history.

<p>Values in the first row represent fecundities (<i>f</i>). Fecundities were back calculated so that the dominant eigenvalue of the resulting matrix was equal to the <i>a priori</i> specified growth rate (λ). Therefore, fecundities vary per growth rate (λ). A given fecundity value was assumed to be the same across ages. Fecundity when λ = 0.9 was 0.4, fecundity when λ = 0.95 was 0.45, fecundity when λ = 1.0 was 0.5 and fecundity when, λ = 1.0250 was 0.5250. The off-diagonal values represent the survival rates.</p><p>Projection matrix for the hypothetical life history.</p

Combined Influences of Model Choice, Data Quality, and Data Quantity When Estimating Population Trends

<div><p>Estimating and projecting population trends using population viability analysis (PVA) are central to identifying species at risk of extinction and for informing conservation management strategies. Models for PVA generally fall within two categories, scalar (count-based) or matrix (demographic). Model structure, process error, measurement error, and time series length all have known impacts in population risk assessments, but their combined impact has not been thoroughly investigated. We tested the ability of scalar and matrix PVA models to predict percent decline over a ten-year interval, selected to coincide with the IUCN Red List criterion A.3, using data simulated for a hypothetical, short-lived organism with a simple life-history and for a threatened snail, <i>Tasmaphena lamproides</i>. PVA performance was assessed across different time series lengths, population growth rates, and levels of process and measurement error. We found that the magnitude of effects of measurement error, process error, and time series length, and interactions between these, depended on context. We found that high process and measurement error reduced the reliability of both models in predicted percent decline. Both sources of error contributed strongly to biased predictions, with process error tending to contribute to the spread of predictions more than measurement error. Increasing time series length improved precision and reduced bias of predicted population trends, but gains substantially diminished for time series lengths greater than 10–15 years. The simple parameterization scheme we employed contributed strongly to bias in matrix model predictions when both process and measurement error were high, causing scalar models to exhibit similar or greater precision and lower bias than matrix models. Our study provides evidence that, for short-lived species with structured but simple life histories, short time series and simple models can be sufficient for reasonably reliable conservation decision-making, and may be preferable for population projections when unbiased estimates of vital rates cannot be obtained.</p></div

Box and whisker plots showing the difference in percent decline between the “true” and median “estimated” model projections for <i>T</i>. <i>lamproides</i>.

<p>Boxes are centered about the median difference while the box extension covers the interquartile range. a-c) Matrix model, <i>λ</i> = 0.9. d-f) Scalar model, <i>λ</i> = 0.9. g-i) Matrix model, <i>λ</i> = 1.025. j-l) Scalar model, <i>λ</i> = 1.025.</p

Projection matrix for <i>T. lamproides</i>.

<p>Values in the first row represent fecundities (<i>f</i>). Fecundities were back calculated so that the dominant eigenvalue of the resulting matrix was equal to the <i>a priori</i> specified growth rate (λ). Therefore, fecundities vary per growth rate (λ). A given fecundity value was assumed to be the same across ages. Fecundity when λ = 0.9 was 0.3292, fecundity when λ = 0.95 was 0.3976, fecundity when λ = 1.0 was 0.4630 and fecundity when, λ = 1.0250 was 0.4947. The off-diagonal values represent the survival rates.</p><p>Projection matrix for <i>T. lamproides</i>.</p

Parameter values used in simulations.

<p>A total of 336 parameter combinations (referred to as scenarios) were considered.</p><p>^aA coefficient of variation of 0.45 instead of 0.5 was used to generate “true” sets of data for <i>T</i>. <i>lamproides</i>.</p><p>Parameter values used in simulations.</p

An illustration of the methodology used in this study.

<p>a) “True” time series (gray) are generated with underlying process error. b) Measurement error is then added, yielding the “observed” time series (dashed). The “observed” series is then sampled over a specific time period, and these data are used to parameterize matrix and scalar population models, called “estimated” models. c) The “true” series and “estimated” models (black) are projected into the future. The dashed vertical line divides between “past” and projection time frames. d) This process was repeated such that each parameter combination yielded 1000 “true” time series, and each “true” time series led to 1000 replicate projections from both “estimated” matrix and scalar models.</p

Box and whisker plots showing the difference in percent decline between the “true” and median “estimated” model projections for the hypothetical life history.

<p>Boxes are centered about the median difference while the box extension covers the interquartile range. a-c) Matrix model, <i>λ</i> = 0.9. d-f) Scalar model, <i>λ</i> = 0.9. g-i) Matrix model, <i>λ</i> = 1.025. j-l) Scalar model, <i>λ</i> = 1.025.</p