# An integrated integral projection model (IPM2 ) to disentangle size‐structured harvest and natural mortality

## TL;DR

A new model called IPM2 helps track how body size affects population changes in invasive green crabs, showing how removal efforts impact their numbers and size distribution.

## Contribution

The IPM2 framework integrates two modeling approaches to estimate complex, size-structured demographic rates from imperfect data.

## Key findings

- IPM2 enables distinct estimation of size-structured harvest and natural mortality rates in green crabs.
- High removal efforts reduce equilibrium population size but increase abundance of smaller crabs.
- The model provides first estimates of size-structured abundance for European green crabs.

## Abstract

Body size is one of the most important traits governing individual‐level demographic rates and modulating population‐level processes. Multiple size‐dependent demographic rates can simultaneously change population structure, so distinguishing their individual contributions to overall population dynamics remains a challenge.Disentangling size‐dependent harvest rates from other demographic rates is critical for assessing the impact of removal on populations of invasive species. Inference about invasive populations can be difficult, however, as observations are often collected opportunistically as part of removal programs, rather than experimentally designed. Yet accurate inference is essential for understanding the feasibility of population suppression and optimising management decisions.We develop an integrated integral projection model (IPM2) that leverages the strengths of the integrated population model and integral projection model to enable inference about complex, size‐structured demographic rates from imperfect observations. We apply the IPM2 in the context of invasive European green crab (Carcinus maenas), a species for which individual body size strongly regulates both the observation‐generating process and latent, population dynamics.The IPM2 facilitates the distinct estimation of green crab size‐structured harvest and natural mortality rates, parameters for which no explicit data is collected and that are unidentifiable in component datasets of the integrated population model. The model represents how the green crab population changes over time, providing the first estimates of size‐structured abundance of this high‐priority species.By forecasting the stable size distribution and equilibrium population size under varying removal efforts, we demonstrate that extremely high levels of removal effort can reduce the equilibrium green crab population size. Yet these high mortality rates also shift the stable size distribution and increase the equilibrium abundance of smaller crabs, since size‐selective removal alters intraspecific interactions. The ecological outcome of this shift in size structure will be variable, as green crab size modulates only some of its interactions with other species. These results highlight the value of the IPM2 framework for inferring complex population dynamics with information needs that outpace information in individual observational datasets, providing a path forward for accurate assessment of conservation programs.

Body size is one of the most important traits governing individual‐level demographic rates and modulating population‐level processes. Multiple size‐dependent demographic rates can simultaneously change population structure, so distinguishing their individual contributions to overall population dynamics remains a challenge.

Disentangling size‐dependent harvest rates from other demographic rates is critical for assessing the impact of removal on populations of invasive species. Inference about invasive populations can be difficult, however, as observations are often collected opportunistically as part of removal programs, rather than experimentally designed. Yet accurate inference is essential for understanding the feasibility of population suppression and optimising management decisions.

We develop an integrated integral projection model (IPM2) that leverages the strengths of the integrated population model and integral projection model to enable inference about complex, size‐structured demographic rates from imperfect observations. We apply the IPM2 in the context of invasive European green crab (Carcinus maenas), a species for which individual body size strongly regulates both the observation‐generating process and latent, population dynamics.

The IPM2 facilitates the distinct estimation of green crab size‐structured harvest and natural mortality rates, parameters for which no explicit data is collected and that are unidentifiable in component datasets of the integrated population model. The model represents how the green crab population changes over time, providing the first estimates of size‐structured abundance of this high‐priority species.

By forecasting the stable size distribution and equilibrium population size under varying removal efforts, we demonstrate that extremely high levels of removal effort can reduce the equilibrium green crab population size. Yet these high mortality rates also shift the stable size distribution and increase the equilibrium abundance of smaller crabs, since size‐selective removal alters intraspecific interactions. The ecological outcome of this shift in size structure will be variable, as green crab size modulates only some of its interactions with other species. These results highlight the value of the IPM2 framework for inferring complex population dynamics with information needs that outpace information in individual observational datasets, providing a path forward for accurate assessment of conservation programs.

An IPM2—a combination of an integrated population model and integral projection model—creates a synergistic modelling framework useful for disentangling multiple size‐structured demographic rates and understanding the effectiveness of invasive European green crab removal efforts.