Matrix population models (MPMs) applied to ecology: a gentle guide from theory to practice / Modelos populacionais matriciais (MPMs) aplicados à ecologia: um guia gentil à teoria e prática

The use of matrix population models (MPMs) to portray the life cycles of organisms is a powerful tool for ecological and evolutionary approaches. However, MPMs have been underutilized, despite their importance in demographic studies. One explanation is that students and young researchers are not encouraged to explore the MPMs' potential. MPMs are often absent in elementary textbooks, and specialized literature can be mathematically challenging, especially if it lacks basic concepts of matrix algebra. Consequently, MPMs' bibliography is limited to a few books, their application is concentrated in the United States and Europe, and errors are not rare in the literature. Here, we advocate broadening the use of structured populations, where individuals contribute to the population growth rate according to their age, sex, or other variables. We present the theoretical development of the MPMs, relevant examples of ecological studies, and their mathematical proprieties. Finally, we offer mathematical formulation and practical exercises in R in the appendices. We conceived this manuscript to be the first stop for those students and researchers interested in entering the literature about MPMs.

Representar matematicamente os ciclos de vidas dos organismos a partir de modelos matriciais (MPMs) tem sido uma ferramenta poderosa para as mais diversas questões ecológicas e evolutivas. Apesar de ser uma ferramenta essencial nos estudos demográficos, os MPMs continuam sendo subutilizados. Uma explicação potencial para a subutilização dos modelos matriciais pode ser o pouco encorajamento de estudantes ou jovens pesquisadores para explorar suas potencialidades. MPMs geralmente não estão presentes nos livros textos básicos em ecologia e a literatura especializada pode ser bastante desafiadora, principalmente quando conceitos básicos de álgebra de matrizes não foram previamente ensinados durante a formação desses pesquisadores. O resultado disso é uma bibliografia restrita, aplicações dos MPMs concentradas nos Estados Unidos e Europa, além de uma literatura com muitos erros conceituais. Apresentar uma introdução gentil aos MPMs parte de uma tentativa de popularizar suas aplicações desde os anos iniciais da formação do pesquisador não familiarizado, seja com a língua inglesa ou com os conceitos matemáticos relativos à essa literatura. Dessa forma, o objetivo aqui é apresentar o ganho em considerar uma população estruturada (aquela em que cada indivíduo contribui para a população de acordo com seu peso, idade, sexo ou outra variável), o desenvolvimento teórico dos MPMs, algumas aplicações relevantes para estudos ecológicos, além das propriedades matemáticas essenciais dos MPMs ­ muitas das vezes difíceis de serem entendidas. Por fim, oferecemos nos apêndices formulações matemáticas e exercícios práticos no software R. Esperamos que esse manuscrito seja a primeira parada daqueles estudantes e pesquisadores interessados a adentrar na literatura dos modelos populacionais matriciais.

Large-Scale Climate Effects Meet an Amazonian Butterfly: Which Population Parameters Respond to El Niño?

One of the most tangible outcomes of climate change is change in the frequency of El Niño/La Niña events. They have a large impact on rainfall in the Western hemisphere, but their impact on tropical fauna is largely unknown. A decade long capture-mark-recapture study of the widespread Ecuadorian butterfly Nessaea hewitsoni (Felder & Felder) from an intact forest allowed us to analyze patterns of monthly and seasonal population dynamics before, during, and after an El Niño event. El Niño events did not affect long-term population size, but a 5-month delayed El Niño led to temporary emigration of females, with their subsequent return. Increased rainfall correlated with reduced survival in both sexes, but this effect was twice as strong in females. This investigation is the longest, continuous population study on any Neotropical insect species. Though we sampled on a modest scale, the magnitude of El Niño events suggests that our findings likely reflect insect population responses across a much larger portion of Amazonian forests. This study underscores the importance of analyzing multiple, interacting population parameters beyond local abundance in order to understand the biotic responses to El Niño and climate change in tropical systems. Had our analyses not included temporary emigration, no effect would have been detected because El Niño did not affect local population abundance.

Abundance of small mammals in the Atlantic Forest (ASMAF): a data set for analyzing tropical community patterns.

Local abundance results from the interaction between populational and environmental processes. The abundance of the species in a community is also one of the most basic descriptors of its structure. Despite its importance, information about species abundances is fragmentary, creating a knowledge gap about species abundances known as the Prestonian Shortfall. Here we present a comprehensive data set of small mammal abundance in the Atlantic Forest. Data were extracted from 114 published sources and from unpublished data collected by our research groups spanning from 1943 to 2017. The data set includes 1,902 records of at least 111 species in 155 localities, totaling 42,617 individuals represented. We selected studies that (1) were conducted in forested habitats of the Atlantic Forest, (2) had a minimum sampling effort of at least 500 trap-nights, and (3) contained species abundance data in detail. For each study, we recorded (1) latitude and longitude, (2) name of the locality, (3) employed sampling effort, (4) type of traps used, (5) study year, (6) country, and (7) species name with (8) its respective abundances. For every locality, we also obtained information regarding its (9) ecoregion, (10) predominant vegetation type, and (11) biogeographic subdivision. Whenever necessary, we also (12) updated the species names as new species were described and some genera suffered taxonomic revision since the publication. The localities are spread across the Atlantic Forest and most of the small mammal species known to occur in Atlantic Forest are present in the data set, making it representative of communities of the entire biome. This data set can be used to address various patterns in community ecology and geographical ecology, as the relation between local abundance and environmental suitability, hypothesis regarding local and regional factors on community structuring, species abundance distributions (SAD), functional and phylogenetic mechanisms on community assembling.