A concise guide to developing and using quantitative models in conservation management

Why More Biologists Must Embrace Quantitative Modeling

Biology as a field has transformed since the time of its foundation from an organized enterprise cataloging the diversity of the natural world to a quantitatively rigorous science seeking to answer complex questions about the functions of organisms and their interactions with each other and their environments. As the mathematical rigor of biological analyses has improved, quantitative models have been developed to describe multi-mechanistic systems and to test complex hypotheses. However, applications of quantitative models have been uneven across fields, and many biologists lack the foundational training necessary to apply them in their research or to interpret their results to inform biological problem-solving efforts. This gap in scientific training has created a false dichotomy of "biologists" and "modelers" that only exacerbates the barriers to working biologists seeking additional training in quantitative modeling. Here, we make the argument that all biologists are modelers and are capable of using sophisticated quantitative modeling in their work. We highlight four benefits of conducting biological research within the framework of quantitative models, identify the potential producers and consumers of information produced by such models, and make recommendations for strategies to overcome barriers to their widespread implementation. Improved understanding of quantitative modeling could guide the producers of biological information to better apply biological measurements through analyses that evaluate mechanisms, and allow consumers of biological information to better judge the quality and applications of the information they receive. As our explanations of biological phenomena increase in complexity, so too must we embrace modeling as a foundational skill.

Capturing the dynamics of small populations: A retrospective assessment using long-term data for an island reintroduction

The art of population modelling is to incorporate factors essential for capturing a population's dynamics while otherwise keeping the model as simple as possible. However, it is unclear how optimal model complexity should be assessed, and whether this optimal complexity has been affected by recent advances in modelling methodology. This issue is particularly relevant to small populations because they are subject to complex dynamics but inferences about those dynamics are often constrained by small sample sizes. We fitted Bayesian hierarchical models to long-term data on vital rates (survival and reproduction) for the toutouwai Petroica longipes population reintroduced to Tiritiri Matangi, a 220-ha New Zealand island, and quantified the performance of those models in terms of their likelihood of replicating the observed population dynamics. These dynamics consisted of overall growth from 33 (±0.3) to 160 (±6) birds from 1992-2018, including recoveries following five harvest events for further reintroductions to other sites. We initially included all factors found to affect vital rates, which included inbreeding, post-release effects (PRE), density-dependence, sex, age and random annual variation, then progressively removed these factors. We also compared performance of models where data analysis and simulations were done simultaneously to those produced with the traditional two-step approach, where vital rates are estimated first then fed into a separate simulation model. Parametric uncertainty and demographic stochasticity were incorporated in all projections. The essential factors for replicating the population's dynamics were density-dependence in juvenile survival and PRE, i.e. initial depression of survival and reproduction in translocated birds. Inclusion of other factors reduced the precision of projections, and therefore the likelihood of matching observed dynamics. However, this reduction was modest when the modelling was done in an integrated framework. In contrast, projections were much less precise when done with a two-step modelling approach, and the cost of additional parameters was much higher under the two-step approach. These results suggest that minimization of complexity may be less important than accounting for covariances in parameter estimates, which is facilitated by integrating data analysis and population projections using Bayesian methods.

Harnessing paleo-environmental modeling and genetic data to predict intraspecific genetic structure

Spatially explicit simulations of gene flow within complex landscapes could help forecast the responses of populations to global and anthropological changes. Simulating how past climate change shaped intraspecific genetic variation can provide a validation of models in anticipation of their use to predict future changes. We review simulation models that provide inferences on population genetic structure. Existing simulation models generally integrate complex demographic and genetic processes but are less focused on the landscape dynamics. In contrast to previous approaches integrating detailed demographic and genetic processes and only secondarily landscape dynamics, we present a model based on parsimonious biological mechanisms combining habitat suitability and cellular processes, applicable to complex landscapes. The simulation model takes as input (a) the species dispersal capacities as the main biological parameter, (b) the species habitat suitability, and (c) the landscape structure, modulating dispersal. Our model emphasizes the role of landscape features and their temporal dynamics in generating genetic differentiation among populations within species. We illustrate our model on caribou/reindeer populations sampled across the entire species distribution range in the Northern Hemisphere. We show that simulations over the past 21 kyr predict a population genetic structure that matches empirical data. This approach looking at the impact of historical landscape dynamics on intraspecific structure can be used to forecast population structure under climate change scenarios and evaluate how species range shifts might induce erosion of genetic variation within species.