Using density surface models to estimate spatio‐temporal changes in population densities and trend

Richard J Camp,David L Miller,Stephen T Buckland,Len Thomas,Steve J Kendall

doi:10.1111/ecog.04859

Richard J Camp, David L Miller + Show 3 more

Open Access

https://doi.org/10.1111/ecog.04859

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Abstract

Precise measures of population abundance and trend are needed for species conservation; these are most difficult to obtain for rare and rapidly changing populations. We compare uncertainty in densities estimated from spatio–temporal models with that from standard design‐based methods. Spatio–temporal models allow us to target priority areas where, and at times when, a population may most benefit. Generalised additive models were fitted to a 31‐year time series of point‐transect surveys of an endangered Hawaiian forest bird, the Hawai‘i ‘ākepa Loxops coccineus. This allowed us to estimate bird densities over space and time. We used two methods to quantify uncertainty in density estimates from the spatio–temporal model: the delta method (which assumes independence between detection and distribution parameters) and a variance propagation method. With the delta method we observed a 52% decrease in the width of the design‐based 95% confidence interval (CI), while we observed a 37% decrease in CI width when propagating the variance. We mapped bird densities as they changed across space and time, allowing managers to evaluate management actions. Integrating detection function modelling with spatio–temporal modelling exploits survey data more efficiently by producing finer‐grained abundance estimates than are possible with design‐based methods as well as producing more precise abundance estimates. Model‐based approaches require switching from making assumptions about the survey design to assumptions about bird distribution. Such a switch warrants consideration. In this case the model‐based approach benefits conservation planning through improved management efficiency and reduced costs by taking into account both spatial shifts and temporal changes in population abundance and distribution.

Highlights

Species management, the conservation of rare species, is costly requiring increasingly limited funding, personnel and time
Our analysis shows that precision in animal abundance estimates can be improved through the application of spatio–temporal modelling using generalized additive model (GAM) and underscores the need to account for estimator uncertainty through variance propagation
Estimates produced through standard distance sampling analyses changed substantially between years, while annual density estimates from the spatio–temporal model are more biologically plausible (Fig. 2)

Summary

Introduction

The conservation of rare species, is costly requiring increasingly limited funding, personnel and time. Conservation planning focuses on Ecography published by John Wiley & Sons Ltd on behalf of Nordic Society Oikos Identifying the location and timing of greatest population change, such as fluctuations in a population as it expands into an area or contracts reversing species recovery and threatening species persistence, could deliver greater benefits through maximising the type and cost-effectiveness of management actions (Cattarino et al 2016, Tulloch et al 2016). We propose using spatio–temporal modelling to identify priority areas and times where a species may most benefit from management actions as it responds spatially and temporally to changing demographic parameters and environmental conditions. ‘Ākepa are restricted to five spatially distinct populations with an estimated global abundance in 2016 of 16 248 (95% confidence interval (CI) 10 074–25 198) birds (Judge et al 2018). The largest population, estimated to contain more than 11 000 birds in 2012 (Camp et al 2016), is on the eastern side of Mauna Kea volcano in Hakalau Forest National Wildlife Refuge (Judge et al 2018)

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